From 93021161c2a273df8447b17e09de6b3f2fc9c23f Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Fri, 19 Jun 2020 16:07:44 +0000
Subject: [PATCH] Documentation for aaa08b0150acc987a47f87b26d64dbbdf96945ac

---
 annotated.html                                |  150 +
 annotated_dup.js                              |   37 +
 bc_s.png                                      |  Bin 0 -> 676 bytes
 bdwn.png                                      |  Bin 0 -> 147 bytes
 classes.html                                  |  192 ++
 closed.png                                    |  Bin 0 -> 132 bytes
 d0/d01/smallest__circle_8cpp.html             |  572 ++++
 d0/d01/smallest__circle_8cpp.js               |   12 +
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 d0/d04/qr__decompose_8h__incl.svg             |  128 +
 d0/d08/realtime__stats_8cpp.html              |  313 ++
 d0/d08/realtime__stats_8cpp.js                |    7 +
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 d0/d1f/structnode__coll__graph.md5            |    1 +
 d0/d1f/structnode__coll__graph.svg            |   33 +
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 d0/d77/linear__search_8cpp__incl.svg          |   37 +
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 d0/d80/classgraph__coll__graph.md5            |    1 +
 d0/d80/classgraph__coll__graph.svg            |   78 +
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 d0/da1/string__fibonacci_8cpp__incl.md5       |    1 +
 d0/da1/string__fibonacci_8cpp__incl.svg       |   52 +
 .../number__of__positive__divisors_8cpp.html  |  241 ++
 d0/da2/number__of__positive__divisors_8cpp.js |    5 +
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 d0/db6/non__recursive__merge__sort_8cpp.js    |    8 +
 d0/db7/smallest__circle_8cpp__incl.map        |    6 +
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 d0/dd1/binaryheap_8cpp__incl.md5              |    1 +
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 d0/dd2/class_queue___array.html               |  148 +
 d0/dd2/class_queue___array.js                 |   11 +
 d0/dd5/ode__midpoint__euler_8cpp__incl.map    |    8 +
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 d0/dd5/ode__midpoint__euler_8cpp__incl.svg    |   98 +
 d0/de2/gaussian__elimination_8cpp.html        |  226 ++
 d0/de2/gaussian__elimination_8cpp.js          |    4 +
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 d0/dfc/sqrt__double_8cpp__incl.map            |    5 +
 d0/dfc/sqrt__double_8cpp__incl.md5            |    1 +
 d0/dfc/sqrt__double_8cpp__incl.svg            |   52 +
 d0/dff/structlinkedlist.html                  |  131 +
 d0/dff/structlinkedlist.js                    |    5 +
 d1/d06/ternary__search_8cpp__incl.map         |    4 +
 d1/d06/ternary__search_8cpp__incl.md5         |    1 +
 d1/d06/ternary__search_8cpp__incl.svg         |   37 +
 d1/d07/class_solution-members.html            |  119 +
 d1/d11/gcd__of__n__numbers_8cpp.html          |  223 ++
 d1/d11/gcd__of__n__numbers_8cpp.js            |    5 +
 ...66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map |    5 +
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 d1/d1d/class_graph-members.html               |  153 +
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 d1/d1d/pascal__triangle_8cpp__incl.md5        |    1 +
 d1/d1d/pascal__triangle_8cpp__incl.svg        |   67 +
 d1/d21/quick__sort_8cpp.html                  |  202 ++
 d1/d21/quick__sort_8cpp.js                    |    7 +
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 d1/d57/classcll__coll__graph.md5              |    1 +
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 d1/d77/structmst.html                         |  128 +
 d1/d77/structmst.js                           |    6 +
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 d1/db3/structcompare.html                     |  122 +
 d1/db3/structcompare.js                       |    4 +
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 d1/dc2/class_graph__coll__graph.md5           |    1 +
 d1/dc2/class_graph__coll__graph.svg           |  123 +
 d1/dc2/classstack.html                        |  520 ++++
 d1/dc2/classstack.js                          |   14 +
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 d1/df9/qr__decomposition_8cpp__incl.md5       |    1 +
 d1/df9/qr__decomposition_8cpp__incl.svg       |  191 ++
 d2/d05/class_min_heap.html                    |  478 +++
 d2/d05/class_min_heap.js                      |   16 +
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 d2/d07/class_bit__coll__graph.md5             |    1 +
 d2/d07/class_bit__coll__graph.svg             |   38 +
 d2/d0b/fast__power_8cpp.html                  |  301 ++
 d2/d0b/fast__power_8cpp.js                    |    6 +
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 d2/d22/jump__search_8cpp.html                 |  209 ++
 d2/d22/jump__search_8cpp.js                   |    5 +
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 d2/d2c/structtower.js                         |    5 +
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 d2/dc4/classstack__linked_list.js             |    9 +
 d2/dcf/namespacestatistics.html               |  124 +
 d2/dcf/namespacestatistics.js                 |    5 +
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 d3/d19/sparse__matrix_8cpp.html               |  188 ++
 d3/d19/sparse__matrix_8cpp.js                 |    4 +
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 ...se__fermat__little__theorem_8cpp__incl.md5 |    1 +
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 d3/d24/qr__decomposition_8cpp.html            |  203 ++
 d3/d24/qr__decomposition_8cpp.js              |    4 +
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 d3/d26/binary__search__tree_8cpp.html         |  174 ++
 d3/d26/binary__search__tree_8cpp.js           |   16 +
 d3/d30/hash__search_8cpp__incl.map            |    5 +
 d3/d30/hash__search_8cpp__incl.md5            |    1 +
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 d3/d56/binomial__dist_8cpp__incl.svg          |   53 +
 d3/d61/vector__important__functions_8cpp.html |  197 ++
 d3/d61/vector__important__functions_8cpp.js   |    4 +
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 d3/d66/structlinkedlist__coll__graph.svg      |   29 +
 .../brute__force__string__searching_8cpp.html |  206 ++
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 de/d69/knuth__morris__pratt_8cpp__incl.svg    |   68 +
 de/d6a/knuth__morris__pratt_8cpp.html         |  195 ++
 de/d6a/knuth__morris__pratt_8cpp.js           |    6 +
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 de/d85/decimal__to__roman__numeral_8cpp.html  |  322 ++
 de/d85/decimal__to__roman__numeral_8cpp.js    |    7 +
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 de/d91/class_queue___array-members.html       |  119 +
 de/d91/structlist-members.html                |  123 +
 de/d9b/prime__numbers_8cpp.html               |  211 ++
 de/d9b/prime__numbers_8cpp.js                 |    5 +
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 de/db2/quick__sort_8cpp__incl.md5             |    1 +
 de/db2/quick__sort_8cpp__incl.svg             |   52 +
 de/db5/class_edge-members.html                |  123 +
 de/dc3/binaryheap_8cpp.html                   |  138 +
 de/dc3/binaryheap_8cpp.js                     |    5 +
 de/dc8/classlarge__number-members.html        |  134 +
 de/dcf/binary__exponent_8cpp.html             |  265 ++
 de/dcf/binary__exponent_8cpp.js               |    6 +
 de/dd3/newton__raphson__method_8cpp.html      |  281 ++
 de/dd3/newton__raphson__method_8cpp.js        |    8 +
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 de/de4/fibonacci__large_8cpp.html             |  175 ++
 de/de4/fibonacci__large_8cpp.js               |    5 +
 df/d06/decimal__to__binary_8cpp.html          |  217 ++
 df/d06/decimal__to__binary_8cpp.js            |    6 +
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 df/d0f/fibonacci_8cpp__incl.map               |    5 +
 df/d0f/fibonacci_8cpp__incl.md5               |    1 +
 df/d0f/fibonacci_8cpp__incl.svg               |   52 +
 df/d27/class_bit.html                         |  157 +
 df/d27/class_bit.js                           |   11 +
 df/d39/interpolation__search2_8cpp.html       |  231 ++
 df/d39/interpolation__search2_8cpp.js         |    5 +
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 df/d3c/exponential__search_8cpp__incl.map     |    7 +
 df/d3c/exponential__search_8cpp__incl.md5     |    1 +
 df/d3c/exponential__search_8cpp__incl.svg     |   83 +
 df/d86/rabin__karp_8cpp__incl.map             |    7 +
 df/d86/rabin__karp_8cpp__incl.md5             |    1 +
 df/d86/rabin__karp_8cpp__incl.svg             |   82 +
 df/dc8/successive__approximation_8cpp.html    |  246 ++
 df/dc8/successive__approximation_8cpp.js      |    6 +
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 df/dd4/stairs__pattern_8cpp__incl.map         |    4 +
 df/dd4/stairs__pattern_8cpp__incl.md5         |    1 +
 df/dd4/stairs__pattern_8cpp__incl.svg         |   37 +
 df/dd5/binary__search_8cpp.html               |  257 ++
 df/dd5/binary__search_8cpp.js                 |    5 +
 ...f9e6b7e6f15df4b525a2e7705ba3089_cgraph.map |    5 +
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 df/dd7/structlinkedlist-members.html          |  113 +
 df/ddc/struct_node__coll__graph.map           |    3 +
 df/ddc/struct_node__coll__graph.md5           |    1 +
 df/ddc/struct_node__coll__graph.svg           |   29 +
 df/def/power__for__huge__numbers_8cpp.html    |  327 ++
 df/def/power__for__huge__numbers_8cpp.js      |    7 +
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 dir_19b2bf9199a15c634a08b1ede1dd896a.html     |  143 +
 dir_19b2bf9199a15c634a08b1ede1dd896a.js       |   13 +
 dir_296d53ceaeaa7e099814a6def439fe8a.html     |  190 ++
 dir_296d53ceaeaa7e099814a6def439fe8a.js       |   31 +
 dir_2e746e9d06bf2d8ff842208bcc6ebcfc.html     |  131 +
 dir_2e746e9d06bf2d8ff842208bcc6ebcfc.js       |   11 +
 dir_3343723ae086de42ee4ca9774da3a13f.html     |  122 +
 dir_3343723ae086de42ee4ca9774da3a13f.js       |    6 +
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 dir_82e494173a87936756866de2fa774307.html     |  125 +
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 dir_8a20dd5bfd5341a725342bf72b6b686f.html     |  109 +
 dir_9510827d0b234b3cc54b29892f217477.html     |  163 +
 dir_9510827d0b234b3cc54b29892f217477.js       |   20 +
 dir_9c6faab82c22511b50177aa2e38e2780.html     |  155 +
 dir_9c6faab82c22511b50177aa2e38e2780.js       |   17 +
 dir_bb1b521853a9c46347182a9d10420771.html     |  124 +
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 dir_e3380d2178455503f266746fb14246a5.html     |  116 +
 dir_e3380d2178455503f266746fb14246a5.js       |    4 +
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 dir_f1797d0c2a0a12033e7d74efffeb14e1.html     |  109 +
 dir_f1797d0c2a0a12033e7d74efffeb14e1.js       |    4 +
 doc.png                                       |  Bin 0 -> 746 bytes
 doxygen.css                                   | 1730 +++++++++++
 doxygen.png                                   |  Bin 0 -> 3779 bytes
 dynsections.js                                |  121 +
 files.html                                    |  213 ++
 files_dup.js                                  |   13 +
 folderclosed.png                              |  Bin 0 -> 616 bytes
 folderopen.png                                |  Bin 0 -> 597 bytes
 functions.html                                |  447 +++
 functions_func.html                           |  364 +++
 functions_rela.html                           |  123 +
 functions_vars.html                           |  154 +
 globals.html                                  |  114 +
 globals_a.html                                |  135 +
 globals_b.html                                |  142 +
 globals_c.html                                |  132 +
 globals_d.html                                |  123 +
 globals_defs.html                             |  151 +
 globals_dup.js                                |   24 +
 globals_e.html                                |  134 +
 globals_f.html                                |  154 +
 globals_func.html                             |  111 +
 globals_func.js                               |   23 +
 globals_func_a.html                           |  123 +
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 globals_func_c.html                           |  132 +
 globals_func_d.html                           |  120 +
 globals_func_e.html                           |  131 +
 globals_func_f.html                           |  148 +
 globals_func_g.html                           |  139 +
 globals_func_h.html                           |  117 +
 globals_func_i.html                           |  141 +
 globals_func_j.html                           |  111 +
 globals_func_l.html                           |  126 +
 globals_func_m.html                           |  211 ++
 globals_func_n.html                           |  114 +
 globals_func_o.html                           |  127 +
 globals_func_p.html                           |  159 +
 globals_func_r.html                           |  114 +
 globals_func_s.html                           |  156 +
 globals_func_t.html                           |  179 ++
 globals_func_u.html                           |  111 +
 globals_g.html                                |  139 +
 globals_h.html                                |  123 +
 globals_i.html                                |  147 +
 globals_j.html                                |  111 +
 globals_k.html                                |  111 +
 globals_l.html                                |  135 +
 globals_m.html                                |  230 ++
 globals_n.html                                |  117 +
 globals_o.html                                |  127 +
 globals_p.html                                |  171 ++
 globals_r.html                                |  114 +
 globals_s.html                                |  159 +
 globals_t.html                                |  185 ++
 globals_type.html                             |  112 +
 globals_u.html                                |  111 +
 globals_vars.html                             |  149 +
 graph_legend.html                             |  168 +
 graph_legend.md5                              |    1 +
 graph_legend.svg                              |  117 +
 index.html                                    |  118 +
 jquery.js                                     |   35 +
 menu.js                                       |   51 +
 menudata.js                                   |  133 +
 modules.html                                  |  114 +
 modules.js                                    |    5 +
 namespacemembers.html                         |  172 ++
 namespacemembers_func.html                    |  172 ++
 namespaces.html                               |  118 +
 namespaces_dup.js                             |    9 +
 nav_f.png                                     |  Bin 0 -> 153 bytes
 nav_g.png                                     |  Bin 0 -> 95 bytes
 nav_h.png                                     |  Bin 0 -> 98 bytes
 navtree.css                                   |  146 +
 navtree.js                                    |  546 ++++
 navtreedata.js                                |  109 +
 navtreeindex0.js                              |  253 ++
 navtreeindex1.js                              |  253 ++
 navtreeindex2.js                              |  253 ++
 navtreeindex3.js                              |  174 ++
 open.png                                      |  Bin 0 -> 123 bytes
 pages.html                                    |  116 +
 resize.js                                     |  140 +
 search/all_0.html                             |   36 +
 search/all_0.js                               |    7 +
 search/all_1.html                             |   36 +
 search/all_1.js                               |   96 +
 search/all_10.html                            |   36 +
 search/all_10.js                              |   96 +
 search/all_11.html                            |   36 +
 search/all_11.js                              |   18 +
 search/all_12.html                            |   36 +
 search/all_12.js                              |   97 +
 search/all_13.html                            |   36 +
 search/all_13.js                              |  201 ++
 search/all_14.html                            |   36 +
 search/all_14.js                              |   96 +
 search/all_15.html                            |   36 +
 search/all_15.js                              |   62 +
 search/all_16.html                            |   36 +
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 search/all_17.html                            |   36 +
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 search/all_18.html                            |   36 +
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 search/all_1a.js                              |    5 +
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 search/all_2.html                             |   36 +
 search/all_2.js                               |   82 +
 search/all_3.html                             |   36 +
 search/all_3.js                               |   91 +
 search/all_4.html                             |   36 +
 search/all_4.js                               |   90 +
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 search/all_6.html                             |   36 +
 search/all_6.js                               |  118 +
 search/all_7.html                             |   36 +
 search/all_7.js                               |   60 +
 search/all_8.html                             |   36 +
 search/all_8.js                               |   25 +
 search/all_9.html                             |   36 +
 search/all_9.js                               |  176 ++
 search/all_a.html                             |   36 +
 search/all_a.js                               |    8 +
 search/all_b.html                             |   36 +
 search/all_b.js                               |   16 +
 search/all_c.html                             |   36 +
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 search/classes_7.js                           |    8 +
 search/classes_8.html                         |   36 +
 search/classes_8.js                           |  101 +
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+<a href="#nested-classes">Classes</a> &#124;
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">smallest_circle.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Get centre and radius of the <a href="https://en.wikipedia.org/wiki/Smallest-circle_problem">smallest circle</a> that circumscribes given set of points.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;vector&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for smallest_circle.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/db7/smallest__circle_8cpp__incl.svg" width="248" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
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+Classes</h2></td></tr>
+<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/dc8/struct_point.html">Point</a></td></tr>
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+</table><table class="memberdecls">
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+<tr class="memitem:a3cbebd6f4d2cdf227663c67fe41ba12a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a> (const <a class="el" href="../../d8/dc8/struct_point.html">Point</a> &amp;A, const <a class="el" href="../../d8/dc8/struct_point.html">Point</a> &amp;B)</td></tr>
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+<tr class="memitem:ae1a3968e7947464bee7714f6d43b7002"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a> ()</td></tr>
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+<tr class="memitem:a6d0455dd5c30adda100e95f0423c786e"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a> ()</td></tr>
+<tr class="separator:a6d0455dd5c30adda100e95f0423c786e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d01/smallest__circle_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Get centre and radius of the <a href="https://en.wikipedia.org/wiki/Smallest-circle_problem">smallest circle</a> that circumscribes given set of points. </p>
+<dl class="section see"><dt>See also</dt><dd><a href="https://www.nayuki.io/page/smallest-enclosing-circle">other implementation</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a0b0676df8e4da7a08c7ccaecea344903"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0b0676df8e4da7a08c7ccaecea344903">&#9670;&nbsp;</a></span>circle()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double circle </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="el" href="../../d8/dc8/struct_point.html">Point</a> &gt; &amp;&#160;</td>
+          <td class="paramname"><em>P</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Find the centre and radius of a circle enclosing a set of points.<br  />
+The function returns the radius of the circle and prints the coordinated of the centre of the circle. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">P</td><td>vector of points </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>radius of the circle </dd></dl>
+<div class="fragment"><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;                                         {</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <span class="keywordtype">double</span> minR = INFINITY;</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    <span class="keywordtype">double</span> R;</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <a class="code" href="../../d8/dc8/struct_point.html">Point</a> C;</div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <a class="code" href="../../d8/dc8/struct_point.html">Point</a> minC;</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160; </div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="comment">/* This code is invalid and does not give correct result for TEST 3 */</span></div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    <span class="comment">// for each point in the list</span></div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; P.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 2; i++)</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;        <span class="comment">// for every subsequent point in the list</span></div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = i + 1; j &lt; P.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++)</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;            <span class="comment">// for every subsequent point in the list</span></div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = j + 1; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; P.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;                <span class="comment">// here, we now have picked three points from the given set of</span></div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;                <span class="comment">// points that we can use</span></div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;                <span class="comment">// viz., P[i], P[j] and P[k]</span></div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;                C.x = -0.5 * ((P[i].y * (P[j].x * P[j].x + P[j].y * P[j].y -</div>
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+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                               P[j].y * (P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].x * P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].x + P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].y * P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].y -</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;                                         P[i].x * P[i].x - P[i].y * P[i].y) +</div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;                               P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].y * (P[i].x * P[i].x + P[i].y * P[i].y -</div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                                         P[j].x * P[j].x - P[j].y * P[j].y)) /</div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;                              (P[i].x * (P[j].y - P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].y) +</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                               P[j].x * (P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].y - P[i].y) +</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;                               P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].x * (P[i].y - P[j].y)));</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;                C.<a class="code" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = 0.5 * ((P[i].x * (P[j].x * P[j].x + P[j].y * P[j].y -</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;                                        P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].x * P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].x - P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].y * P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].y) +</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;                              P[j].x * (P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].x * P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].x + P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].y * P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].y -</div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;                                        P[i].x * P[i].x - P[i].y * P[i].y) +</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;                              P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].x * (P[i].x * P[i].x + P[i].y * P[i].y -</div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;                                        P[j].x * P[j].x - P[j].y * P[j].y)) /</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;                             (P[i].x * (P[j].y - P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].y) +</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;                              P[j].x * (P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].y - P[i].y) +</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;                              P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>].x * (P[i].y - P[j].y)));</div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;                R = (<a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(P[i], P[j]) * <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(P[j], P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>]) *</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;                     <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>], P[i])) /</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;                    (4 * <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a94682a4a70d5906857ca09de5b9fb2cc">TriangleArea</a>(P[i], P[j], P[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>]));</div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;                <span class="keywordflow">if</span> (!<a class="code" href="../../d0/d01/smallest__circle_8cpp.html#aee6d48762c1dfb9f14627927f0c16fad">PointInCircle</a>(P, C, R)) {</div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;                    <span class="keywordflow">continue</span>;</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;                }</div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;                <span class="keywordflow">if</span> (R &lt;= minR) {</div>
+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;                    minR = R;</div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;                    minC = C;</div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                }</div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;            }</div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160; </div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    <span class="comment">// for each point in the list</span></div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; P.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 1; i++)</div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;        <span class="comment">// for every subsequent point in the list</span></div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = i + 1; j &lt; P.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {</div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;            <span class="comment">// check for diameterically opposite points</span></div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;            C.x = (P[i].x + P[j].x) / 2;</div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;            C.<a class="code" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = (P[i].y + P[j].y) / 2;</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;            R = <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(C, P[i]);</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;            <span class="keywordflow">if</span> (!<a class="code" href="../../d0/d01/smallest__circle_8cpp.html#aee6d48762c1dfb9f14627927f0c16fad">PointInCircle</a>(P, C, R)) {</div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;                <span class="keywordflow">continue</span>;</div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;            }</div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;            <span class="keywordflow">if</span> (R &lt;= minR) {</div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;                minR = R;</div>
+<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;                minC = C;</div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;            }</div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;        }</div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minC.x &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; minC.<a class="code" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="keywordflow">return</span> minR;</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/d01/smallest__circle_8cpp_a0b0676df8e4da7a08c7ccaecea344903_cgraph.svg" width="492" height="218"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a3cbebd6f4d2cdf227663c67fe41ba12a"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a3cbebd6f4d2cdf227663c67fe41ba12a">&#9670;&nbsp;</a></span>LenghtLine()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double LenghtLine </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="el" href="../../d8/dc8/struct_point.html">Point</a> &amp;&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="el" href="../../d8/dc8/struct_point.html">Point</a> &amp;&#160;</td>
+          <td class="paramname"><em>B</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Compute the Euclidian distance between two points \(A\equiv(x_1,y_1)\) and \(B\equiv(x_2,y_2)\) using the formula: </p><p class="formulaDsp">
+\[d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}\]
+</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>point A </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">B</td><td>point B </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>ditance </dd></dl>
+<div class="fragment"><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;                                                  {</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    <span class="keywordtype">double</span> dx = B.x - A.x;</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keywordtype">double</span> dy = B.<a class="code" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> - A.<a class="code" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a>;</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>((dx * dx) + (dy * dy));</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/d01/smallest__circle_8cpp_a3cbebd6f4d2cdf227663c67fe41ba12a_cgraph.svg" width="215" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main program </p>
+<div class="fragment"><div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;           {</div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d0/d01/smallest__circle_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="100%" height="532"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="aee6d48762c1dfb9f14627927f0c16fad"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aee6d48762c1dfb9f14627927f0c16fad">&#9670;&nbsp;</a></span>PointInCircle()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool PointInCircle </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="el" href="../../d8/dc8/struct_point.html">Point</a> &gt; &amp;&#160;</td>
+          <td class="paramname"><em>P</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="el" href="../../d8/dc8/struct_point.html">Point</a> &amp;&#160;</td>
+          <td class="paramname"><em>Center</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>R</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Check if a set of points lie within given circle. This is true if the distance of all the points from the centre of the circle is less than the radius of the circle </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">P</td><td>set of points to check </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">Center</td><td>coordinates to centre of the circle </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">R</td><td>radius of the circle </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>True if P lies on or within the circle </dd>
+<dd>
+False if P lies outside the circle </dd></dl>
+<div class="fragment"><div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;                                                                             {</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; P.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(P[i], Center) &gt; R)</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    }</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/d01/smallest__circle_8cpp_aee6d48762c1dfb9f14627927f0c16fad_cgraph.svg" width="391" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ae1a3968e7947464bee7714f6d43b7002"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae1a3968e7947464bee7714f6d43b7002">&#9670;&nbsp;</a></span>test()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test case: result should be: <br  />
+ Circle with <br  />
+ radius 3.318493136080724 <br  />
+ centre at (3.0454545454545454, 1.3181818181818181) </p>
+<div class="fragment"><div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;            {</div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Point&gt;</a> Pv;</div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(0, 0));</div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(5, 4));</div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(1, 3));</div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(4, 1));</div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(3, -2));</div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a0b0676df8e4da7a08c7ccaecea344903">circle</a>(Pv) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d0/d01/smallest__circle_8cpp_ae1a3968e7947464bee7714f6d43b7002_cgraph.svg" width="100%" height="466"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a0283886819c7c140a023582b7269e2d0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0283886819c7c140a023582b7269e2d0">&#9670;&nbsp;</a></span>test2()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test2 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test case: result should be: <br  />
+ Circle with <br  />
+ radius 1.4142135623730951 <br  />
+ centre at (1.0, 1.0) </p>
+<div class="fragment"><div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;             {</div>
+<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Point&gt;</a> Pv;</div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(0, 0));</div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(0, 2));</div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(2, 2));</div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(2, 0));</div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a0b0676df8e4da7a08c7ccaecea344903">circle</a>(Pv) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d0/d01/smallest__circle_8cpp_a0283886819c7c140a023582b7269e2d0_cgraph.svg" width="100%" height="466"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a6d0455dd5c30adda100e95f0423c786e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a6d0455dd5c30adda100e95f0423c786e">&#9670;&nbsp;</a></span>test3()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test3 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test case: result should be: <br  />
+ Circle with <br  />
+ radius 1.821078397711709 <br  />
+ centre at (2.142857142857143, 1.7857142857142856) </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000006">Todo:</a></b></dt><dd>This test fails </dd></dl>
+<div class="fragment"><div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;             {</div>
+<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Point&gt;</a> Pv;</div>
+<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(0.5, 1));</div>
+<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(3.5, 3));</div>
+<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(2.5, 0));</div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;    Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(2, 1.5));</div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a0b0676df8e4da7a08c7ccaecea344903">circle</a>(Pv) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d0/d01/smallest__circle_8cpp_a6d0455dd5c30adda100e95f0423c786e_cgraph.svg" width="100%" height="466"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a94682a4a70d5906857ca09de5b9fb2cc"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a94682a4a70d5906857ca09de5b9fb2cc">&#9670;&nbsp;</a></span>TriangleArea()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double TriangleArea </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="el" href="../../d8/dc8/struct_point.html">Point</a> &amp;&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="el" href="../../d8/dc8/struct_point.html">Point</a> &amp;&#160;</td>
+          <td class="paramname"><em>B</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="el" href="../../d8/dc8/struct_point.html">Point</a> &amp;&#160;</td>
+          <td class="paramname"><em>C</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Compute the area of triangle formed by three points using <a href="https://en.wikipedia.org/wiki/Heron%27s_formula">Heron's formula</a>. If the lengths of the sides of the triangle are \(a,\,b,\,c\) and \(s=\displaystyle\frac{a+b+c}{2}\) is the semi-perimeter then the area is given by </p><p class="formulaDsp">
+\[A=\sqrt{s(s-a)(s-b)(s-c)}\]
+</p>
+ <dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>vertex A </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">B</td><td>vertex B </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">C</td><td>vertex C </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>area of triangle </dd></dl>
+<div class="fragment"><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;                                                                    {</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keywordtype">double</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(A, B);</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keywordtype">double</span> b = <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(B, C);</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keywordtype">double</span> c = <a class="code" href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a>(C, A);</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="keywordtype">double</span> p = (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> + b + c) / 2;</div>
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+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/d01/smallest__circle_8cpp_a94682a4a70d5906857ca09de5b9fb2cc_cgraph.svg" width="358" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="asmallest__circle_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="../../d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdef"><b>Definition:</b> smallest_circle.cpp:188</div></div>
+<div class="ttc" id="asmallest__circle_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../d0/d01/smallest__circle_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition:</b> smallest_circle.cpp:173</div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
+<div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
+<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
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+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
+<div class="ttc" id="amatrix__exponentiation_8cpp_html_afcf0d19607cd0edd8ae333d2b9c220c0"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a></div><div class="ttdeci">ll k</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:48</div></div>
+<div class="ttc" id="asmallest__circle_8cpp_html_a3cbebd6f4d2cdf227663c67fe41ba12a"><div class="ttname"><a href="../../d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a">LenghtLine</a></div><div class="ttdeci">double LenghtLine(const Point &amp;A, const Point &amp;B)</div><div class="ttdef"><b>Definition:</b> smallest_circle.cpp:37</div></div>
+<div class="ttc" id="asmallest__circle_8cpp_html_a94682a4a70d5906857ca09de5b9fb2cc"><div class="ttname"><a href="../../d0/d01/smallest__circle_8cpp.html#a94682a4a70d5906857ca09de5b9fb2cc">TriangleArea</a></div><div class="ttdeci">double TriangleArea(const Point &amp;A, const Point &amp;B, const Point &amp;C)</div><div class="ttdef"><b>Definition:</b> smallest_circle.cpp:54</div></div>
+<div class="ttc" id="asmallest__circle_8cpp_html_a0b0676df8e4da7a08c7ccaecea344903"><div class="ttname"><a href="../../d0/d01/smallest__circle_8cpp.html#a0b0676df8e4da7a08c7ccaecea344903">circle</a></div><div class="ttdeci">double circle(const std::vector&lt; Point &gt; &amp;P)</div><div class="ttdef"><b>Definition:</b> smallest_circle.cpp:87</div></div>
+<div class="ttc" id="amatrix__exponentiation_8cpp_html_a9ecd98ce0064e2f7f97bb6a92f58ee72"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a></div><div class="ttdeci">vector&lt; ll &gt; a</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:53</div></div>
+<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
+<div class="ttc" id="asmallest__circle_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition:</b> smallest_circle.cpp:158</div></div>
+<div class="ttc" id="astruct_point_html"><div class="ttname"><a href="../../d8/dc8/struct_point.html">Point</a></div><div class="ttdef"><b>Definition:</b> line_segment_intersection.cpp:12</div></div>
+<div class="ttc" id="asmallest__circle_8cpp_html_aee6d48762c1dfb9f14627927f0c16fad"><div class="ttname"><a href="../../d0/d01/smallest__circle_8cpp.html#aee6d48762c1dfb9f14627927f0c16fad">PointInCircle</a></div><div class="ttdeci">bool PointInCircle(const std::vector&lt; Point &gt; &amp;P, const Point &amp;Center, double R)</div><div class="ttdef"><b>Definition:</b> smallest_circle.cpp:72</div></div>
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="navelem"><a class="el" href="../../dir_9510827d0b234b3cc54b29892f217477.html">others</a></li><li class="navelem"><a class="el" href="../../d0/d01/smallest__circle_8cpp.html">smallest_circle.cpp</a></li>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:44 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
diff --git a/d0/d01/smallest__circle_8cpp.js b/d0/d01/smallest__circle_8cpp.js
new file mode 100644
index 000000000..c9dcaab89
--- /dev/null
+++ b/d0/d01/smallest__circle_8cpp.js
@@ -0,0 +1,12 @@
+var smallest__circle_8cpp =
+[
+    [ "Point", "d8/dc8/struct_point.html", "d8/dc8/struct_point" ],
+    [ "circle", "d0/d01/smallest__circle_8cpp.html#a0b0676df8e4da7a08c7ccaecea344903", null ],
+    [ "LenghtLine", "d0/d01/smallest__circle_8cpp.html#a3cbebd6f4d2cdf227663c67fe41ba12a", null ],
+    [ "main", "d0/d01/smallest__circle_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4", null ],
+    [ "PointInCircle", "d0/d01/smallest__circle_8cpp.html#aee6d48762c1dfb9f14627927f0c16fad", null ],
+    [ "test", "d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002", null ],
+    [ "test2", "d0/d01/smallest__circle_8cpp.html#a0283886819c7c140a023582b7269e2d0", null ],
+    [ "test3", "d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e", null ],
+    [ "TriangleArea", "d0/d01/smallest__circle_8cpp.html#a94682a4a70d5906857ca09de5b9fb2cc", null ]
+];
\ No newline at end of file
diff --git a/d0/d01/smallest__circle_8cpp_a0283886819c7c140a023582b7269e2d0_cgraph.map b/d0/d01/smallest__circle_8cpp_a0283886819c7c140a023582b7269e2d0_cgraph.map
new file mode 100644
index 000000000..a346886ba
--- /dev/null
+++ b/d0/d01/smallest__circle_8cpp_a0283886819c7c140a023582b7269e2d0_cgraph.map
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+<tr class="memdesc:d2/dcf/namespacestatistics"><td class="mdescLeft">&#160;</td><td class="mdescRight">Statistical algorithms. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:aa54c915581fcc495489175a4386d59fd"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d08/realtime__stats_8cpp.html#aa54c915581fcc495489175a4386d59fd">test_function</a> (const float *test_data, const int number_of_samples)</td></tr>
+<tr class="separator:aa54c915581fcc495489175a4386d59fd"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d08/realtime__stats_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
+<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Compute statistics for data entered in rreal-time. </p>
+<p>This algorithm is really beneficial to compute statistics on data read in realtime. For example, devices reading biometrics data. The algorithm is simple enough to be easily implemented in an embedded system. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>argc</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char **&#160;</td>
+          <td class="paramname"><em>argv</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;                                {</div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> test_data1[] = {3, 4, 5, -1.4, -3.6, 1.9, 1.};</div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    <a class="code" href="../../d0/d08/realtime__stats_8cpp.html#aa54c915581fcc495489175a4386d59fd">test_function</a>(test_data1, <span class="keyword">sizeof</span>(test_data1) / <span class="keyword">sizeof</span>(test_data1[0]));</div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160; </div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;        &lt;&lt; <span class="stringliteral">&quot;Enter data. Any non-numeric data will terminate the data input.&quot;</span></div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;        &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160; </div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    <a class="code" href="../../d7/d7c/classstatistics_1_1stats__computer1.html">stats_computer1&lt;float&gt;</a> stats1;</div>
+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    <a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html">stats_computer2&lt;float&gt;</a> stats2;</div>
+<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160; </div>
+<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;    <span class="keywordflow">while</span> (1) {</div>
+<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;        <span class="keywordtype">double</span> val;</div>
+<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number: &quot;</span>;</div>
+<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; val;</div>
+<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160; </div>
+<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;        <span class="comment">// check for failure to read input. Happens for</span></div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;        <span class="comment">// non-numeric data</span></div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;        <span class="keywordflow">if</span> (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.fail())</div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;            <span class="keywordflow">break</span>;</div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160; </div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;        stats1.<a class="code" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#aa13bf7c38de112f71921a5525d71a2f2">new_val</a>(val);</div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;        stats2.<a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html#ade6de704deea24fdc88077b3d9a0d534">new_val</a>(val);</div>
+<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160; </div>
+<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tMethod 1:&quot;</span></div>
+<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;\tMean: &quot;</span> &lt;&lt; stats1.<a class="code" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a390697dcee210b91823ceff04b25081b">mean</a>()</div>
+<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; stats1.<a class="code" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a27f0a03e2fd2254f1c81fe668226bd92">variance</a>()</div>
+<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;\t Std: &quot;</span> &lt;&lt; stats1.<a class="code" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#af57e942d49f4fd70f059f224b4ac07e1">std</a>() &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tMethod 2:&quot;</span></div>
+<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;\tMean: &quot;</span> &lt;&lt; stats2.<a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html#a8290966ad468f2a8c266d008bc60720e">mean</a>()</div>
+<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; stats2.<a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">variance</a>()</div>
+<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;\t Std: &quot;</span> &lt;&lt; stats2.<a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html#acf2e84df4fc386bb3295016ef8fd156e">std</a>() &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    }</div>
+<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160; </div>
+<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d0/d08/realtime__stats_8cpp_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="100%" height="600"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="aa54c915581fcc495489175a4386d59fd"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa54c915581fcc495489175a4386d59fd">&#9670;&nbsp;</a></span>test_function()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test_function </td>
+          <td>(</td>
+          <td class="paramtype">const float *&#160;</td>
+          <td class="paramname"><em>test_data</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const int&#160;</td>
+          <td class="paramname"><em>number_of_samples</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test the algorithm implementation </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">test_data</td><td>array of data to test the algorithms </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;                                                                        {</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    <span class="keywordtype">float</span> mean = 0.f, variance = 0.f;</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160; </div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <a class="code" href="../../d7/d7c/classstatistics_1_1stats__computer1.html">stats_computer1&lt;float&gt;</a> stats01;</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    <a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html">stats_computer2&lt;float&gt;</a> stats02;</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160; </div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; number_of_samples; i++) {</div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;        stats01.<a class="code" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#aa13bf7c38de112f71921a5525d71a2f2">new_val</a>(test_data[i]);</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;        stats02.<a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html#ade6de704deea24fdc88077b3d9a0d534">new_val</a>(test_data[i]);</div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;        mean += test_data[i];</div>
+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;    }</div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160; </div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    mean /= number_of_samples;</div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160; </div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; number_of_samples; i++) {</div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;        <span class="keywordtype">float</span> temp = test_data[i] - mean;</div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;        variance += temp * temp;</div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    }</div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    variance /= number_of_samples;</div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160; </div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt; Test Function &gt;&gt;&gt;&gt;&gt;&gt;&gt;&gt;&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;Expected: Mean: &quot;</span> &lt;&lt; mean &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; variance</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;              &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tMethod 1:&quot;</span></div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;\tMean: &quot;</span> &lt;&lt; stats01.<a class="code" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a390697dcee210b91823ceff04b25081b">mean</a>()</div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; stats01.<a class="code" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a27f0a03e2fd2254f1c81fe668226bd92">variance</a>()</div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;\t Std: &quot;</span> &lt;&lt; stats01.<a class="code" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#af57e942d49f4fd70f059f224b4ac07e1">std</a>() &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tMethod 2:&quot;</span></div>
+<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;\tMean: &quot;</span> &lt;&lt; stats02.<a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html#a8290966ad468f2a8c266d008bc60720e">mean</a>()</div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;\t Variance: &quot;</span> &lt;&lt; stats02.<a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">variance</a>()</div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;\t Std: &quot;</span> &lt;&lt; stats02.<a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html#acf2e84df4fc386bb3295016ef8fd156e">std</a>() &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160; </div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    assert(std::abs(stats01.<a class="code" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a390697dcee210b91823ceff04b25081b">mean</a>() - mean) &lt; 0.01);</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;    assert(std::abs(stats02.<a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html#a8290966ad468f2a8c266d008bc60720e">mean</a>() - mean) &lt; 0.01);</div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    assert(std::abs(stats02.<a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">variance</a>() - variance) &lt; 0.01);</div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160; </div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(Tests passed)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/d08/realtime__stats_8cpp_aa54c915581fcc495489175a4386d59fd_cgraph.svg" width="591" height="503"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="aclassstatistics_1_1stats__computer1_html_af57e942d49f4fd70f059f224b4ac07e1"><div class="ttname"><a href="../../d7/d7c/classstatistics_1_1stats__computer1.html#af57e942d49f4fd70f059f224b4ac07e1">statistics::stats_computer1::std</a></div><div class="ttdeci">double std() const</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:48</div></div>
+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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+<div class="title">number_of_positive_divisors.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>C++ Program to calculate number of divisors.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;vector&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for number_of_positive_divisors.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/da4/number__of__positive__divisors_8cpp__incl.svg" width="179" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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+</div><table class="memberdecls">
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+Functions</h2></td></tr>
+<tr class="memitem:ad89ccced8504b5116046cfa03066ffeb"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a> (int n)</td></tr>
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>C++ Program to calculate number of divisors. </p>
+<p>This algorithm use the prime factorization approach. Any number can be written in multiplication of its prime factors. <br  />
+Let N = P1^E1 * P2^E2 ... Pk^Ek <br  />
+Therefore. number-of-divisors(N) = (E1+1) * (E2+1) ... (Ek+1). <br  />
+Where P1, P2 ... Pk are prime factors and E1, E2 ... Ek are exponents respectively.</p>
+<p>Example:- <br  />
+N = 36 <br  />
+36 = (3^2 * 2^2) <br  />
+number_of_positive_divisors(36) = (2+1) * (2+1) = 9. <br  />
+list of positive divisors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.</p>
+<p>Similarly if N is -36 at that time number of positive divisors remain same.</p>
+<p>Example:- <br  />
+N = -36 <br  />
+-36 = -1 * (3^2 * 2^2) <br  />
+number_of_positive_divisors(-36) = (2+1) * (2+1) = 9. <br  />
+list of positive divisors of -36 = 1, 2, 3, 4, 6, 9, 12, 18, 36. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
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+
+<div class="memitem">
+<div class="memproto">
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+        <tr>
+          <td class="memname">int number_of_positive_divisors </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
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+      </table>
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+<p>Algorithm </p>
+<div class="fragment"><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;                                       {</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> prime_exponent_count;</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i * i &lt;= n; i++) {</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;        <span class="keywordtype">int</span> prime_count = 0;</div>
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+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;            n /= i;</div>
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+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160; </div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; prime_exponent_count.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        divisors_count = divisors_count * (prime_exponent_count[i] + 1);</div>
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+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">gaussian_elimination.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a href="https://en.wikipedia.org/wiki/Gaussian_elimination">Gaussian elimination method</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for gaussian_elimination.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/ddd/gaussian__elimination_8cpp__incl.svg" width="202" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
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+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/de2/gaussian__elimination_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Gaussian_elimination">Gaussian elimination method</a> </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;           {</div>
+<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;    <span class="keywordtype">int</span> mat_size, i, j, step;</div>
+<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160; </div>
+<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Matrix size: &quot;</span>;</div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; mat_size;</div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;    <span class="comment">// create a 2D matrix by dynamic memory allocation</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;    <span class="keywordtype">double</span> **mat = <span class="keyword">new</span> <span class="keywordtype">double</span> *[mat_size + 1], **x = <span class="keyword">new</span> <span class="keywordtype">double</span> *[mat_size];</div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt;= mat_size; i++) {</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;        mat[i] = <span class="keyword">new</span> <span class="keywordtype">double</span>[mat_size + 1];</div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;        <span class="keywordflow">if</span> (i &lt; mat_size)</div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;            x[i] = <span class="keyword">new</span> <span class="keywordtype">double</span>[mat_size + 1];</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    }</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160; </div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    <span class="comment">// get the matrix elements from user</span></div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <span class="stringliteral">&quot;Enter value of the matrix: &quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; mat_size; i++) {</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;        <span class="keywordflow">for</span> (j = 0; j &lt;= mat_size; j++) {</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt;</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;                mat[i][j];  <span class="comment">// Enter (mat_size*mat_size) value of the matrix.</span></div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;        }</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    }</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160; </div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="comment">// perform Gaussian elimination</span></div>
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+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        <span class="keywordflow">for</span> (i = step; i &lt; mat_size - 1; i++) {</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;            <span class="keywordtype">double</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = (mat[i + 1][step] / mat[step][step]);</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160; </div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;            <span class="keywordflow">for</span> (j = step; j &lt;= mat_size; j++)</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;                mat[i + 1][j] = mat[i + 1][j] - (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> * mat[step][j]);</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;        }</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    }</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160; </div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;Matrix using Gaussian Elimination method: &quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; mat_size; i++) {</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;        <span class="keywordflow">for</span> (j = 0; j &lt;= mat_size; j++) {</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;            x[i][j] = mat[i][j];</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; mat[i][j] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;        }</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    }</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;Value of the Gaussian Elimination method: &quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <span class="keywordflow">for</span> (i = mat_size - 1; i &gt;= 0; i--) {</div>
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+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        <span class="keywordflow">if</span> (x[i][i] == 0)</div>
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+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;            x[i][i] = (x[i][mat_size] - sum) / (x[i][i]);</div>
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+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;x&quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;= &quot;</span> &lt;&lt; x[i][i] &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
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+<div class="title">gcd_of_n_numbers.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>This program aims at calculating the GCD of n numbers by division method.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for gcd_of_n_numbers.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/d7d/gcd__of__n__numbers_8cpp__incl.svg" width="202" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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+Functions</h2></td></tr>
+<tr class="memitem:a25034543c20f271da04fb24ad2b2747a"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a25034543c20f271da04fb24ad2b2747a">gcd</a> (int *<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, int n)</td></tr>
+<tr class="separator:a25034543c20f271da04fb24ad2b2747a"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>This program aims at calculating the GCD of n numbers by division method. </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html" title="Compute the greatest common denominator of two integers using iterative form of Euclidean algorithm">gcd_iterative_euclidean.cpp</a>, <a class="el" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html" title="Compute the greatest common denominator of two integers using recursive form of Euclidean algorithm">gcd_recursive_euclidean.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a25034543c20f271da04fb24ad2b2747a"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a25034543c20f271da04fb24ad2b2747a">&#9670;&nbsp;</a></span>gcd()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int gcd </td>
+          <td>(</td>
+          <td class="paramtype">int *&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Compute GCD using division algorithm</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">a</td><td>array of integers to compute GCD for </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>number of integers in array <code>a</code> </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;                       {</div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;    <span class="keywordtype">int</span> j = 1;  <span class="comment">// to access all elements of the array starting from 1</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;    <span class="keywordtype">int</span> <a class="code" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a25034543c20f271da04fb24ad2b2747a">gcd</a> = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>[0];</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;    <span class="keywordflow">while</span> (j &lt; n) {</div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>[j] % <a class="code" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a25034543c20f271da04fb24ad2b2747a">gcd</a> == 0)  <span class="comment">// value of gcd is as needed so far</span></div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;            j++;              <span class="comment">// so we check for next element</span></div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;        <span class="keywordflow">else</span></div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;            <a class="code" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a25034543c20f271da04fb24ad2b2747a">gcd</a> = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>[j] % <a class="code" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a25034543c20f271da04fb24ad2b2747a">gcd</a>;  <span class="comment">// calculating GCD by division method</span></div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    }</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    <span class="keywordflow">return</span> <a class="code" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a25034543c20f271da04fb24ad2b2747a">gcd</a>;</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;           {</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <span class="keywordtype">int</span> n;</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter value of n:&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="keywordtype">int</span> *<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = <span class="keyword">new</span> <span class="keywordtype">int</span>[n];</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="keywordtype">int</span> i;</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the n numbers:&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; n; i++) std::cin &gt;&gt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>[i];</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160; </div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;GCD of entered n numbers:&quot;</span> &lt;&lt; <a class="code" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a25034543c20f271da04fb24ad2b2747a">gcd</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, n) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160; </div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keyword">delete</span>[] <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
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+<p>This is the complete list of members for <a class="el" href="../../da/d9a/class_graph.html">Graph</a>, including all inherited members.</p>
+<table class="directory">
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>addEdge</b>(int src, int dst, int weight) (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>addEdge</b>(int src, int dst, int weight) (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="../../da/d9a/class_graph.html#af765dda8f21280e1cecea19e129f1bc5">addEdge</a>(Edge const &amp;edge)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr><td class="entry"><a class="el" href="../../da/d9a/class_graph.html#ac85c63bcca4764a621f9f8609a8e5910">addEdge</a>(unsigned int source, unsigned int destination)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>addEdge</b>(int src, int dst, int weight) (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr><td class="entry"><a class="el" href="../../da/d9a/class_graph.html#ac5a4d9a4f894a179198936042c778413">addVertices</a>(unsigned int num=1)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>bfs</b>(int source, int sink) (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">inline</span><span class="mlabel">private</span></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>capacity</b> (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>edge_participated</b> (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>edgeNum</b> (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>edges</b> (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>edges</b> (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>ford_fulkerson</b>(void) (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
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+  <tr bgcolor="#f0f0f0"><td class="entry"><b>Graph</b>(int V, int E) (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>Graph</b>(int V) (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>Graph</b>() (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>Graph</b>(Graph &amp;&amp;)=default (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"></td></tr>
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+  <tr bgcolor="#f0f0f0"><td class="entry"><b>m_adjList</b> (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>m_vertices</b> (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>max_flow</b> (defined in <a class="el" href="../../da/d9a/class_graph.html">Graph</a>)</td><td class="entry"><a class="el" href="../../da/d9a/class_graph.html">Graph</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
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+  <div class="summary">
+<a href="#namespaces">Namespaces</a> &#124;
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">quick_sort.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Quick sort algorithm.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cstdlib&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for quick_sort.cpp:</div>
+<div class="dyncontent">
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+</div>
+</div>
+</div><table class="memberdecls">
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+<tr class="memdesc:d5/d91/namespacesorting"><td class="mdescLeft">&#160;</td><td class="mdescRight">Sorting algorithms. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a7e7f25f31c50523990437abf2ac3907e"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#a7e7f25f31c50523990437abf2ac3907e">sorting::partition</a> (int arr[], int low, int high)</td></tr>
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+<tr class="memitem:a50b66a1c652291b9a346ec7342967178"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#a50b66a1c652291b9a346ec7342967178">sorting::quickSort</a> (int arr[], int low, int high)</td></tr>
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+void&#160;</td><td class="memItemRight" valign="bottom"><b>show</b> (int arr[], int size)</td></tr>
+<tr class="separator:ad34859945724cc7de3cc71936715aec6"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/d21/quick__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Quick sort algorithm. </p>
+<p>Implementation Details - Quick Sort is a divide and conquer algorithm. It picks and element as pivot and partition the given array around the picked pivot. There are many different versions of quickSort that pick pivot in different ways.</p>
+<ol type="1">
+<li>Always pick the first element as pivot</li>
+<li>Always pick the last element as pivot (implemented below)</li>
+<li>Pick a random element as pivot</li>
+<li>Pick median as pivot</li>
+</ol>
+<p>The key process in quickSort is <a class="el" href="../../d5/d91/namespacesorting.html#a7e7f25f31c50523990437abf2ac3907e">partition()</a>. Target of partition is, given an array and an element x(say) of array as pivot, put x at it's correct position in sorted array and put all smaller elements (samller than x) before x, and put all greater elements (greater than x) after x. All this should be done in linear time </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
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+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
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+<p>Driver program to test above functions </p>
+<div class="fragment"><div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;           {</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <span class="keywordtype">int</span> size;</div>
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+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160; </div>
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+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
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+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <a class="code" href="../../d5/d91/namespacesorting.html#a50b66a1c652291b9a346ec7342967178">quickSort</a>(arr, 0, size);</div>
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+<p>A buzz number is a number that is either divisible by 7 or has last digit as 7.  
+<a href="#details">More...</a></p>
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+</div><div class="textblock"><div class="dynheader">
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+<div class="header">
+  <div class="summary">
+<a href="#pub-methods">Public Member Functions</a> &#124;
+<a href="#pri-attribs">Private Attributes</a> &#124;
+<a href="../../dd/d51/classstack-members.html">List of all members</a>  </div>
+  <div class="headertitle">
+<div class="title">stack&lt; Type &gt; Class Template Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+<div class="dynheader">
+Collaboration diagram for stack&lt; Type &gt;:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/dcb/classstack__coll__graph.svg" width="170" height="322"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+<center><span class="legend">[<a target="top" href="../../graph_legend.html">legend</a>]</span></center></div>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
+Public Member Functions</h2></td></tr>
+<tr class="memitem:a67f65710c376f67d1ba3bde45a9cb628"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/dc2/classstack.html#a67f65710c376f67d1ba3bde45a9cb628">display</a> ()</td></tr>
+<tr class="separator:a67f65710c376f67d1ba3bde45a9cb628"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a5b64337ec34b12e98458bb9b9d5f8f83"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/dc2/classstack.html#a5b64337ec34b12e98458bb9b9d5f8f83">stack</a> ()</td></tr>
+<tr class="separator:a5b64337ec34b12e98458bb9b9d5f8f83"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a0ac1dba9c7019acdc825b31d06eb0b71"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/dc2/classstack.html#a0ac1dba9c7019acdc825b31d06eb0b71">~stack</a> ()</td></tr>
+<tr class="separator:a0ac1dba9c7019acdc825b31d06eb0b71"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a066e4505155b009913c47b2648b1067a"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/dc2/classstack.html#a066e4505155b009913c47b2648b1067a">isEmptyStack</a> ()</td></tr>
+<tr class="separator:a066e4505155b009913c47b2648b1067a"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a5705c3926dcf5fd3f9c964467a50b81d"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/dc2/classstack.html#a5705c3926dcf5fd3f9c964467a50b81d">push</a> (Type item)</td></tr>
+<tr class="separator:a5705c3926dcf5fd3f9c964467a50b81d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a21c0bb6ce7dcfe445cc12031977ea344"><td class="memItemLeft" align="right" valign="top">Type&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/dc2/classstack.html#a21c0bb6ce7dcfe445cc12031977ea344">top</a> ()</td></tr>
+<tr class="separator:a21c0bb6ce7dcfe445cc12031977ea344"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a6cd4b95d5de00d41b2491392338384dc"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/dc2/classstack.html#a6cd4b95d5de00d41b2491392338384dc">pop</a> ()</td></tr>
+<tr class="separator:a6cd4b95d5de00d41b2491392338384dc"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a5cc5efbbd4ea14b3e378580f1388423b"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/dc2/classstack.html#a5cc5efbbd4ea14b3e378580f1388423b">clear</a> ()</td></tr>
+<tr class="separator:a5cc5efbbd4ea14b3e378580f1388423b"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a61370d5fbaf9ec6bca4a8c114c1058e1"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/dc2/classstack.html#a61370d5fbaf9ec6bca4a8c114c1058e1">operator=</a> (const <a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt; &amp;otherStack)</td></tr>
+<tr class="separator:a61370d5fbaf9ec6bca4a8c114c1058e1"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-attribs"></a>
+Private Attributes</h2></td></tr>
+<tr class="memitem:a7289037c059aaad492b4d68e6bd54453"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d5/da1/structnode.html">node</a>&lt; Type &gt; *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a></td></tr>
+<tr class="separator:a7289037c059aaad492b4d68e6bd54453"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ac512a3efdc84a5f5c9f53905c8e219b0"><td class="memItemLeft" align="right" valign="top"><a id="ac512a3efdc84a5f5c9f53905c8e219b0"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>size</b></td></tr>
+<tr class="separator:ac512a3efdc84a5f5c9f53905c8e219b0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
+<a id="a5b64337ec34b12e98458bb9b9d5f8f83"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a5b64337ec34b12e98458bb9b9d5f8f83">&#9670;&nbsp;</a></span>stack()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Type &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt;::<a class="el" href="../../d1/dc2/classstack.html">stack</a> </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Default constructor </p>
+<div class="fragment"><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;            {</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;        <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = NULL;</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        size = 0;</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a0ac1dba9c7019acdc825b31d06eb0b71"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0ac1dba9c7019acdc825b31d06eb0b71">&#9670;&nbsp;</a></span>~stack()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Type &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt;::~<a class="el" href="../../d1/dc2/classstack.html">stack</a> </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Destructor </p>
+<div class="fragment"><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;{}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<h2 class="groupheader">Member Function Documentation</h2>
+<a id="a5cc5efbbd4ea14b3e378580f1388423b"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a5cc5efbbd4ea14b3e378580f1388423b">&#9670;&nbsp;</a></span>clear()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Type &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void <a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt;::clear </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Clear stack </p>
+<div class="fragment"><div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;{ <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = NULL; }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a67f65710c376f67d1ba3bde45a9cb628"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a67f65710c376f67d1ba3bde45a9cb628">&#9670;&nbsp;</a></span>display()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Type &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void <a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt;::display </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Show stack </p>
+<div class="fragment"><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;                   {</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;        <a class="code" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a> *current = <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>;</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Top --&gt; &quot;</span>;</div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;        <span class="keywordflow">while</span> (current != NULL) {</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; current-&gt;data &lt;&lt; <span class="stringliteral">&quot;  &quot;</span>;</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;            current = current-&gt;next;</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;        }</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Size of stack: &quot;</span> &lt;&lt; size &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/dc2/classstack_a67f65710c376f67d1ba3bde45a9cb628_cgraph.svg" width="234" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a066e4505155b009913c47b2648b1067a"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a066e4505155b009913c47b2648b1067a">&#9670;&nbsp;</a></span>isEmptyStack()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Type &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool <a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt;::isEmptyStack </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Determine whether the stack is empty </p>
+<div class="fragment"><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;{ <span class="keywordflow">return</span> (<a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> == NULL); }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a61370d5fbaf9ec6bca4a8c114c1058e1"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a61370d5fbaf9ec6bca4a8c114c1058e1">&#9670;&nbsp;</a></span>operator=()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Type &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt;Type&gt;&amp; <a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt;::operator= </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt; &amp;&#160;</td>
+          <td class="paramname"><em>otherStack</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Overload "=" the assignment operator </p>
+<div class="fragment"><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;                                                          {</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        <a class="code" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a> *newNode, *current, *last;</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160; </div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        <span class="comment">/* If stack is no empty, make it empty */</span></div>
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+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;            <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = NULL;</div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        }</div>
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+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;            <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = NULL;</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;        } <span class="keywordflow">else</span> {</div>
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+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;            <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = <span class="keyword">new</span> <a class="code" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a>;</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;            <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>-&gt;data = current-&gt;data;</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;            <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>-&gt;next = NULL;</div>
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+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;            <span class="keywordflow">while</span> (current != NULL) {</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;                newNode = <span class="keyword">new</span> <a class="code" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a>;</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;                newNode-&gt;data = current-&gt;data;</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;                newNode-&gt;next = NULL;</div>
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+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a6cd4b95d5de00d41b2491392338384dc"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a6cd4b95d5de00d41b2491392338384dc">&#9670;&nbsp;</a></span>pop()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Type &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void <a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt;::pop </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Remove the top element of the stack </p>
+<div class="fragment"><div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;               {</div>
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+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        <span class="keywordflow">if</span> (!<a class="code" href="../../d1/dc2/classstack.html#a066e4505155b009913c47b2648b1067a">isEmptyStack</a>()) {</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;            temp = <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>;</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;            <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>-&gt;next;</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;            <span class="keyword">delete</span> temp;</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;            size--;</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;        } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Stack is empty !&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        }</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/dc2/classstack_a6cd4b95d5de00d41b2491392338384dc_cgraph.svg" width="286" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a5705c3926dcf5fd3f9c964467a50b81d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a5705c3926dcf5fd3f9c964467a50b81d">&#9670;&nbsp;</a></span>push()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Type &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void <a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt;::push </td>
+          <td>(</td>
+          <td class="paramtype">Type&#160;</td>
+          <td class="paramname"><em>item</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Add new item to the stack </p>
+<div class="fragment"><div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;                         {</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;        <a class="code" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a> *newNode;</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        newNode = <span class="keyword">new</span> <a class="code" href="../../d5/da1/structnode.html">node&lt;Type&gt;</a>;</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;        newNode-&gt;data = item;</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;        newNode-&gt;next = <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>;</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> = newNode;</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        size++;</div>
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+</div><!-- fragment -->
+</div>
+</div>
+<a id="a21c0bb6ce7dcfe445cc12031977ea344"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a21c0bb6ce7dcfe445cc12031977ea344">&#9670;&nbsp;</a></span>top()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Type &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">Type <a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt;::top </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Return the top element of the stack </p>
+<div class="fragment"><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;               {</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;        assert(<a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a> != NULL);</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stackTop</a>-&gt;data;</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<h2 class="groupheader">Member Data Documentation</h2>
+<a id="a7289037c059aaad492b4d68e6bd54453"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a7289037c059aaad492b4d68e6bd54453">&#9670;&nbsp;</a></span>stackTop</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Type &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d5/da1/structnode.html">node</a>&lt;Type&gt;* <a class="el" href="../../d1/dc2/classstack.html">stack</a>&lt; Type &gt;::stackTop</td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">private</span></span>  </td>
+  </tr>
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+</div><div class="memdoc">
+<p>Pointer to the stack </p>
+
+</div>
+</div>
+<hr/>The documentation for this class was generated from the following file:<ul>
+<li>data_structures/<a class="el" href="../../d7/de0/stack_8h_source.html">stack.h</a></li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node&lt; Type &gt;</a></div></div>
+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
+<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
+<div class="ttc" id="aclassstack_html_a066e4505155b009913c47b2648b1067a"><div class="ttname"><a href="../../d1/dc2/classstack.html#a066e4505155b009913c47b2648b1067a">stack::isEmptyStack</a></div><div class="ttdeci">bool isEmptyStack()</div><div class="ttdef"><b>Definition:</b> stack.h:41</div></div>
+<div class="ttc" id="aclassstack_html_a7289037c059aaad492b4d68e6bd54453"><div class="ttname"><a href="../../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stack::stackTop</a></div><div class="ttdeci">node&lt; Type &gt; * stackTop</div><div class="ttdef"><b>Definition:</b> stack.h:107</div></div>
+<!-- start footer part -->
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+  <ul>
+    <li class="navelem"><a class="el" href="../../d1/dc2/classstack.html">stack</a></li>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+<a href="#var-members">Variables</a>  </div>
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+<div class="title">hash_search.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Hash Search Algorithm - Best Time Complexity Ω(1)  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cstdlib&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for hash_search.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/d30/hash__search_8cpp__incl.svg" width="175" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="nested-classes"></a>
+Classes</h2></td></tr>
+<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d10/structlist.html">list</a></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="define-members"></a>
+Macros</h2></td></tr>
+<tr class="memitem:a392fb874e547e582e9c66a08a1f23326"><td class="memItemLeft" align="right" valign="top"><a id="a392fb874e547e582e9c66a08a1f23326"></a>
+#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/df3/hash__search_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a>&#160;&#160;&#160;6</td></tr>
+<tr class="memdesc:a392fb874e547e582e9c66a08a1f23326"><td class="mdescLeft">&#160;</td><td class="mdescRight">Determines how much data. <br /></td></tr>
+<tr class="separator:a392fb874e547e582e9c66a08a1f23326"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a77c722016053a1d484aa177ce205b367"><td class="memItemLeft" align="right" valign="top"><a id="a77c722016053a1d484aa177ce205b367"></a>
+#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/df3/hash__search_8cpp.html#a77c722016053a1d484aa177ce205b367">HASHMAX</a>&#160;&#160;&#160;5</td></tr>
+<tr class="memdesc:a77c722016053a1d484aa177ce205b367"><td class="mdescLeft">&#160;</td><td class="mdescRight">Determines the length of the hash table. <br /></td></tr>
+<tr class="separator:a77c722016053a1d484aa177ce205b367"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="typedef-members"></a>
+Typedefs</h2></td></tr>
+<tr class="memitem:a8ca8dcb494104d273679e219e53d0555"><td class="memItemLeft" align="right" valign="top">typedef struct <a class="el" href="../../d8/d10/structlist.html">list</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a></td></tr>
+<tr class="separator:a8ca8dcb494104d273679e219e53d0555"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ad6fcd983304f85afa199d97a9b0ca9f6"><td class="memItemLeft" align="right" valign="top"><a id="ad6fcd983304f85afa199d97a9b0ca9f6"></a>
+typedef struct <a class="el" href="../../d8/d10/structlist.html">list</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/df3/hash__search_8cpp.html#ad6fcd983304f85afa199d97a9b0ca9f6">link</a></td></tr>
+<tr class="memdesc:ad6fcd983304f85afa199d97a9b0ca9f6"><td class="mdescLeft">&#160;</td><td class="mdescRight">pointer to nodes <br /></td></tr>
+<tr class="separator:ad6fcd983304f85afa199d97a9b0ca9f6"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a566eaf0ffafd50bc61e644561fd27001"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> (int key)</td></tr>
+<tr class="separator:a566eaf0ffafd50bc61e644561fd27001"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ad0831425f1389166a9518f422d0c6ec5"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/df3/hash__search_8cpp.html#ad0831425f1389166a9518f422d0c6ec5">create_list</a> (int key)</td></tr>
+<tr class="separator:ad0831425f1389166a9518f422d0c6ec5"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a36ea13c16028f18ef2d5ff47f3fda7a2"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/df3/hash__search_8cpp.html#a36ea13c16028f18ef2d5ff47f3fda7a2">hash_search</a> (int key, int *counter)</td></tr>
+<tr class="separator:a36ea13c16028f18ef2d5ff47f3fda7a2"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/df3/hash__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="var-members"></a>
+Variables</h2></td></tr>
+<tr class="memitem:a6e1a77282bc65ad359d753d25df23243"><td class="memItemLeft" align="right" valign="top"><a id="a6e1a77282bc65ad359d753d25df23243"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> [<a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a692ac7187ee88621a9f78fca78ec498d">MAX</a>] = {1, 10, 15, 5, 8, 7}</td></tr>
+<tr class="memdesc:a6e1a77282bc65ad359d753d25df23243"><td class="mdescLeft">&#160;</td><td class="mdescRight">test data <br /></td></tr>
+<tr class="separator:a6e1a77282bc65ad359d753d25df23243"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:af413b1740073db54796642b0ab814d6d"><td class="memItemLeft" align="right" valign="top"><a id="af413b1740073db54796642b0ab814d6d"></a>
+<a class="el" href="../../d5/da1/structnode.html">node</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a> [<a class="el" href="../../d1/df3/hash__search_8cpp.html#a77c722016053a1d484aa177ce205b367">HASHMAX</a>]</td></tr>
+<tr class="memdesc:af413b1740073db54796642b0ab814d6d"><td class="mdescLeft">&#160;</td><td class="mdescRight">array of nodes <br /></td></tr>
+<tr class="separator:af413b1740073db54796642b0ab814d6d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Hash Search Algorithm - Best Time Complexity Ω(1) </p>
+<dl class="section copyright"><dt>Copyright</dt><dd>2020 Arctic2333</dd></dl>
+<p>In this algorithm, we use the method of division and reservation remainder to construct the hash function, and use the method of chain address to solve the conflict, that is, we link a chain list after the data, and store all the records whose keywords are synonyms in the same linear chain list.</p>
+<dl class="section warning"><dt>Warning</dt><dd>This program is only for educational purposes. It has serious flaws in implementation with regards to memory management resulting in large amounts of memory leaks. </dd></dl>
+<dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000007">Todo:</a></b></dt><dd>fix the program for memory leaks and better structure in C++ and not C fashion </dd></dl>
+</div><h2 class="groupheader">Typedef Documentation</h2>
+<a id="a8ca8dcb494104d273679e219e53d0555"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a8ca8dcb494104d273679e219e53d0555">&#9670;&nbsp;</a></span>node</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">typedef struct <a class="el" href="../../d8/d10/structlist.html">list</a> <a class="el" href="../../d5/da1/structnode.html">node</a></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>a one-way linked list define node as one item list </p>
+
+</div>
+</div>
+<h2 class="groupheader">Function Documentation</h2>
+<a id="ad0831425f1389166a9518f422d0c6ec5"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ad0831425f1389166a9518f422d0c6ec5">&#9670;&nbsp;</a></span>create_list()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void create_list </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>key</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>The same after the remainder will be added after the same hash header To avoid conflict, zipper method is used Insert elements into the linked list in the header </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">key</td><td>key to add to list </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section warning"><dt>Warning</dt><dd>dynamic memory allocated to <code>n</code> never gets freed. </dd></dl>
+<dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000008">Todo:</a></b></dt><dd>fix memory leak </dd></dl>
+<div class="fragment"><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;                          {  <span class="comment">// Construct hash table</span></div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">link</a> p, n;</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keywordtype">int</span> index;</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    n = (<a class="code" href="../../d1/df3/hash__search_8cpp.html#ad6fcd983304f85afa199d97a9b0ca9f6">link</a>)<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/c/malloc.html">malloc</a>(<span class="keyword">sizeof</span>(<a class="code" href="../../d5/da1/structnode.html">node</a>));</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    n-&gt;key = key;</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    n-&gt;next = NULL;</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    index = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>(key);</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    p = <a class="code" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a>[index].next;</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="keywordflow">if</span> (p != NULL) {</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        n-&gt;next = p;</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a>[index].next = n;</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a>[index].next = n;</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    }</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/df3/hash__search_8cpp_ad0831425f1389166a9518f422d0c6ec5_cgraph.svg" width="180" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a566eaf0ffafd50bc61e644561fd27001"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a566eaf0ffafd50bc61e644561fd27001">&#9670;&nbsp;</a></span>h()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int h </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>key</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Mode of hash detection : Division method </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">key</td><td>to hash </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>hash value for <code>key</code> </dd></dl>
+<div class="fragment"><div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;{ <span class="keywordflow">return</span> key % <a class="code" href="../../d1/df3/hash__search_8cpp.html#a77c722016053a1d484aa177ce205b367">HASHMAX</a>; }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a36ea13c16028f18ef2d5ff47f3fda7a2"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a36ea13c16028f18ef2d5ff47f3fda7a2">&#9670;&nbsp;</a></span>hash_search()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int hash_search </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>key</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int *&#160;</td>
+          <td class="paramname"><em>counter</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Input the key to be searched, and get the hash header position through the H (int key) function, then one-dimensional linear search. If found </p><dl class="section return"><dt>Returns</dt><dd>element depth and number of searches If not found </dd>
+<dd>
+-1 </dd></dl>
+<div class="fragment"><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;                                       {  <span class="comment">// Hash lookup function</span></div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">link</a> pointer;</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <span class="keywordtype">int</span> index;</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160; </div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    *counter = 0;</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    index = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>(key);</div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    pointer = <a class="code" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a>[index].next;</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160; </div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;data[&quot;</span> &lt;&lt; index &lt;&lt; <span class="stringliteral">&quot;]:&quot;</span>;</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160; </div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    <span class="keywordflow">while</span> (pointer != NULL) {</div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;        counter[0]++;</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;data[&quot;</span> &lt;&lt; pointer-&gt;key &lt;&lt; <span class="stringliteral">&quot;]:&quot;</span>;</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        <span class="keywordflow">if</span> (pointer-&gt;key == key)</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;            <span class="keywordflow">return</span> 1;</div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        <span class="keywordflow">else</span></div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;            pointer = pointer-&gt;next;</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    }</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160; </div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/df3/hash__search_8cpp_a36ea13c16028f18ef2d5ff47f3fda7a2_cgraph.svg" width="194" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;           {</div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">link</a> p;</div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    <span class="keywordtype">int</span> key, index, i, counter;  <span class="comment">// Key is the value to be found</span></div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    index = 0;</div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160; </div>
+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    <span class="comment">// You can write the input mode here</span></div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    <span class="keywordflow">while</span> (index &lt; <a class="code" href="../../d1/df3/hash__search_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a>) {  <span class="comment">// Construct hash table</span></div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#ad0831425f1389166a9518f422d0c6ec5">create_list</a>(<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[index]);</div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        index++;</div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    }</div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160; </div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code" href="../../d1/df3/hash__search_8cpp.html#a77c722016053a1d484aa177ce205b367">HASHMAX</a>; i++) {  <span class="comment">// Output hash table</span></div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;hashtab [&quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;]\n&quot;</span>;</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160; </div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        p = <a class="code" href="../../d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hashtab</a>[i].next;</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;        <span class="keywordflow">while</span> (p != NULL) {</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;please int key:&quot;</span>;</div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;            <span class="keywordflow">if</span> (p-&gt;key &gt; 0)</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;                <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;[&quot;</span> &lt;&lt; p-&gt;key &lt;&lt; <span class="stringliteral">&quot;]&quot;</span>;</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;            p = p-&gt;next;</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;        }</div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    }</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160; </div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    <span class="keywordflow">while</span> (key != -1) {</div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;        <span class="comment">// You can write the input mode here</span></div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;        <span class="comment">// test key = 10</span></div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;        key = 10;</div>
+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d1/df3/hash__search_8cpp.html#a36ea13c16028f18ef2d5ff47f3fda7a2">hash_search</a>(key, &amp;counter))</div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;search time = &quot;</span> &lt;&lt; counter &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;        <span class="keywordflow">else</span></div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;no found!\n&quot;</span>;</div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        key = -1;  <span class="comment">// Exit test</span></div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;        <span class="comment">/* The test sample is returned as:</span></div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="comment">         * data[0]:data[5]:data[15]:data[10]:search time = 3 The search is</span></div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="comment">         * successful. There are 10 in this set of data */</span></div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    }</div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160; </div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/df3/hash__search_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="292" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="ahash__search_8cpp_html_a36ea13c16028f18ef2d5ff47f3fda7a2"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a36ea13c16028f18ef2d5ff47f3fda7a2">hash_search</a></div><div class="ttdeci">int hash_search(int key, int *counter)</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:76</div></div>
+<div class="ttc" id="alist_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list.html">std::list</a></div><div class="ttdoc">STL class.</div></div>
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+<div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
+<div class="ttc" id="ahash__search_8cpp_html_a392fb874e547e582e9c66a08a1f23326"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a></div><div class="ttdeci">#define MAX</div><div class="ttdoc">Determines how much data.</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:21</div></div>
+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
+<div class="ttc" id="ahash__search_8cpp_html_a566eaf0ffafd50bc61e644561fd27001"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a></div><div class="ttdeci">int h(int key)</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:45</div></div>
+<div class="ttc" id="ahash__search_8cpp_html_ad6fcd983304f85afa199d97a9b0ca9f6"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#ad6fcd983304f85afa199d97a9b0ca9f6">link</a></div><div class="ttdeci">struct list * link</div><div class="ttdoc">pointer to nodes</div></div>
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+<div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
+<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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+<div class="ttc" id="amalloc_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/c/malloc.html">std::malloc</a></div><div class="ttdeci">T malloc(T... args)</div></div>
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+  <ul>
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+    <li class="footer">Generated on Fri Jun 19 2020 16:06:44 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+    [ "MAX", "d1/df3/hash__search_8cpp.html#a392fb874e547e582e9c66a08a1f23326", null ],
+    [ "link", "d1/df3/hash__search_8cpp.html#ad6fcd983304f85afa199d97a9b0ca9f6", null ],
+    [ "node", "d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555", null ],
+    [ "create_list", "d1/df3/hash__search_8cpp.html#ad0831425f1389166a9518f422d0c6ec5", null ],
+    [ "h", "d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001", null ],
+    [ "hash_search", "d1/df3/hash__search_8cpp.html#a36ea13c16028f18ef2d5ff47f3fda7a2", null ],
+    [ "main", "d1/df3/hash__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4", null ],
+    [ "data", "d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243", null ],
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+];
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+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
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+ -->
+<!-- Title: hash_search Pages: 1 -->
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+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 24)">
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+ -->
+<!-- Title: create_list Pages: 1 -->
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+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 24)">
+<title>create_list</title>
+<polygon fill="white" stroke="transparent" points="-4,4 -4,-24 131,-24 131,4 -4,4"/>
+<!-- Node1 -->
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+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+<div class="header">
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+<a href="#pub-methods">Public Member Functions</a> &#124;
+<a href="#pri-attribs">Private Attributes</a> &#124;
+<a href="../../d4/d1f/class_min_heap-members.html">List of all members</a>  </div>
+  <div class="headertitle">
+<div class="title">MinHeap Class Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
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+<tr class="memitem:ad89ca80a217655a735d266618197965e"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d05/class_min_heap.html#ad89ca80a217655a735d266618197965e">MinHeap</a> (int <a class="el" href="../../d2/d05/class_min_heap.html#a88b4aa3e66392a3eabbf2517a9a79a02">capacity</a>)</td></tr>
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+<tr class="memitem:aaef438c1056492cb62c4a4d9035b5cad"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d05/class_min_heap.html#aaef438c1056492cb62c4a4d9035b5cad">MinHeapify</a> (int)</td></tr>
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+<tr class="memitem:a0e893f9deb4be4cf4f9990e736483e81"><td class="memItemLeft" align="right" valign="top"><a id="a0e893f9deb4be4cf4f9990e736483e81"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>parent</b> (int i)</td></tr>
+<tr class="separator:a0e893f9deb4be4cf4f9990e736483e81"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aa8c6c141e3de664819686aa637e1afca"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d05/class_min_heap.html#aa8c6c141e3de664819686aa637e1afca">left</a> (int i)</td></tr>
+<tr class="separator:aa8c6c141e3de664819686aa637e1afca"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ac760b85cf90265b8d674b942a43fb70e"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d05/class_min_heap.html#ac760b85cf90265b8d674b942a43fb70e">right</a> (int i)</td></tr>
+<tr class="separator:ac760b85cf90265b8d674b942a43fb70e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a4014f1edaed0bd7db0c0d2ca53228980"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d05/class_min_heap.html#a4014f1edaed0bd7db0c0d2ca53228980">extractMin</a> ()</td></tr>
+<tr class="separator:a4014f1edaed0bd7db0c0d2ca53228980"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aa7f726cc6327955d22871592227432f5"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d05/class_min_heap.html#aa7f726cc6327955d22871592227432f5">decreaseKey</a> (int i, int new_val)</td></tr>
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+<tr class="memitem:a37ac126eabb0c3ce04047172abccca29"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d05/class_min_heap.html#a37ac126eabb0c3ce04047172abccca29">deleteKey</a> (int i)</td></tr>
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+<tr class="memitem:aef78f3384f5a0ae880ad0883d2d44b82"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d05/class_min_heap.html#aef78f3384f5a0ae880ad0883d2d44b82">insertKey</a> (int <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>)</td></tr>
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+Private Attributes</h2></td></tr>
+<tr class="memitem:a34a93a87967308eb516328c0aca3c48e"><td class="memItemLeft" align="right" valign="top"><a id="a34a93a87967308eb516328c0aca3c48e"></a>
+int *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a></td></tr>
+<tr class="memdesc:a34a93a87967308eb516328c0aca3c48e"><td class="mdescLeft">&#160;</td><td class="mdescRight">pointer to array of elements in heap <br /></td></tr>
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+<tr class="memitem:a88b4aa3e66392a3eabbf2517a9a79a02"><td class="memItemLeft" align="right" valign="top"><a id="a88b4aa3e66392a3eabbf2517a9a79a02"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d05/class_min_heap.html#a88b4aa3e66392a3eabbf2517a9a79a02">capacity</a></td></tr>
+<tr class="memdesc:a88b4aa3e66392a3eabbf2517a9a79a02"><td class="mdescLeft">&#160;</td><td class="mdescRight">maximum possible size of min heap <br /></td></tr>
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+int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a></td></tr>
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+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>A class for Min Heap </p>
+</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
+<a id="ad89ca80a217655a735d266618197965e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ad89ca80a217655a735d266618197965e">&#9670;&nbsp;</a></span>MinHeap()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">MinHeap::MinHeap </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>cap</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Constructor </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">capacity</td><td>initial heap capacity</td></tr>
+  </table>
+  </dd>
+</dl>
+<p>Constructor: Builds a heap from a given array a[] of given size </p>
+<div class="fragment"><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;                        {</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    <a class="code" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> = 0;</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    <a class="code" href="../../d2/d05/class_min_heap.html#a88b4aa3e66392a3eabbf2517a9a79a02">capacity</a> = cap;</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a> = <span class="keyword">new</span> <span class="keywordtype">int</span>[cap];</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<h2 class="groupheader">Member Function Documentation</h2>
+<a id="aa7f726cc6327955d22871592227432f5"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa7f726cc6327955d22871592227432f5">&#9670;&nbsp;</a></span>decreaseKey()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void MinHeap::decreaseKey </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>i</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>new_val</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Decreases key value of key at index i to new_val</p>
+<p>Decreases value of key at index 'i' to new_val. It is assumed that new_val is smaller than harr[i]. </p>
+<div class="fragment"><div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;                                            {</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i] = new_val;</div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <span class="keywordflow">while</span> (i != 0 &amp;&amp; <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[parent(i)] &gt; <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i]) {</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(<a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i], <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[parent(i)]);</div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        i = parent(i);</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    }</div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d05/class_min_heap_aa7f726cc6327955d22871592227432f5_cgraph.svg" width="296" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a37ac126eabb0c3ce04047172abccca29"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a37ac126eabb0c3ce04047172abccca29">&#9670;&nbsp;</a></span>deleteKey()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void MinHeap::deleteKey </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>i</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Deletes a key stored at index i</p>
+<p>This function deletes key at index i. It first reduced value to minus infinite, then calls <a class="el" href="../../d2/d05/class_min_heap.html#a4014f1edaed0bd7db0c0d2ca53228980">extractMin()</a> </p>
+<div class="fragment"><div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;                             {</div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    <a class="code" href="../../d2/d05/class_min_heap.html#aa7f726cc6327955d22871592227432f5">decreaseKey</a>(i, INT_MIN);</div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <a class="code" href="../../d2/d05/class_min_heap.html#a4014f1edaed0bd7db0c0d2ca53228980">extractMin</a>();</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d2/d05/class_min_heap_a37ac126eabb0c3ce04047172abccca29_cgraph.svg" width="100%" height="404"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a4014f1edaed0bd7db0c0d2ca53228980"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a4014f1edaed0bd7db0c0d2ca53228980">&#9670;&nbsp;</a></span>extractMin()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int MinHeap::extractMin </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>to extract the root which is the minimum element </p>
+<div class="fragment"><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;                        {</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <span class="keywordflow">if</span> (<a class="code" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> &lt;= 0)</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        <span class="keywordflow">return</span> INT_MAX;</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <span class="keywordflow">if</span> (<a class="code" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> == 1) {</div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        <a class="code" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a>--;</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[0];</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    }</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160; </div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <span class="comment">// Store the minimum value, and remove it from heap</span></div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <span class="keywordtype">int</span> root = <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[0];</div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[0] = <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[<a class="code" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> - 1];</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    <a class="code" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a>--;</div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <a class="code" href="../../d2/d05/class_min_heap.html#aaef438c1056492cb62c4a4d9035b5cad">MinHeapify</a>(0);</div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160; </div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    <span class="keywordflow">return</span> root;</div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d05/class_min_heap_a4014f1edaed0bd7db0c0d2ca53228980_cgraph.svg" width="504" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a336ac71f0d857269fe9a98058a3cd130"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a336ac71f0d857269fe9a98058a3cd130">&#9670;&nbsp;</a></span>getMin()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">int MinHeap::getMin </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Returns the minimum key (key at root) from min heap </p>
+<div class="fragment"><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;{ <span class="keywordflow">return</span> <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[0]; }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="aef78f3384f5a0ae880ad0883d2d44b82"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aef78f3384f5a0ae880ad0883d2d44b82">&#9670;&nbsp;</a></span>insertKey()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void MinHeap::insertKey </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>k</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Inserts a new key 'k' </p>
+<div class="fragment"><div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;                             {</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="keywordflow">if</span> (<a class="code" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> == <a class="code" href="../../d2/d05/class_min_heap.html#a88b4aa3e66392a3eabbf2517a9a79a02">capacity</a>) {</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nOverflow: Could not insertKey\n&quot;</span>;</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        <span class="keywordflow">return</span>;</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    }</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160; </div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="comment">// First insert the new key at the end</span></div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    <a class="code" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a>++;</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <span class="keywordtype">int</span> i = <a class="code" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> - 1;</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i] = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>;</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160; </div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="comment">// Fix the min heap property if it is violated</span></div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <span class="keywordflow">while</span> (i != 0 &amp;&amp; <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[parent(i)] &gt; <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i]) {</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(<a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i], <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[parent(i)]);</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;        i = parent(i);</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    }</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d05/class_min_heap_aef78f3384f5a0ae880ad0883d2d44b82_cgraph.svg" width="275" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="aa8c6c141e3de664819686aa637e1afca"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa8c6c141e3de664819686aa637e1afca">&#9670;&nbsp;</a></span>left()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">int MinHeap::left </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>i</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>to get index of left child of node at index i </p>
+<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;{ <span class="keywordflow">return</span> (2 * i + 1); }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="aaef438c1056492cb62c4a4d9035b5cad"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aaef438c1056492cb62c4a4d9035b5cad">&#9670;&nbsp;</a></span>MinHeapify()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void MinHeap::MinHeapify </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>i</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>to heapify a subtree with the root at given index</p>
+<p>A recursive method to heapify a subtree with the root at given index This method assumes that the subtrees are already heapified </p>
+<div class="fragment"><div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;                              {</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    <span class="keywordtype">int</span> l = <a class="code" href="../../d2/d05/class_min_heap.html#aa8c6c141e3de664819686aa637e1afca">left</a>(i);</div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <span class="keywordtype">int</span> r = <a class="code" href="../../d2/d05/class_min_heap.html#ac760b85cf90265b8d674b942a43fb70e">right</a>(i);</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    <span class="keywordtype">int</span> smallest = i;</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    <span class="keywordflow">if</span> (l &lt; <a class="code" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> &amp;&amp; <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[l] &lt; <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i])</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;        smallest = l;</div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <span class="keywordflow">if</span> (r &lt; <a class="code" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a> &amp;&amp; <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[r] &lt; <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[smallest])</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        smallest = r;</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    <span class="keywordflow">if</span> (smallest != i) {</div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(<a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[i], <a class="code" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a>[smallest]);</div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;        <a class="code" href="../../d2/d05/class_min_heap.html#aaef438c1056492cb62c4a4d9035b5cad">MinHeapify</a>(smallest);</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    }</div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d05/class_min_heap_aaef438c1056492cb62c4a4d9035b5cad_cgraph.svg" width="314" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ac760b85cf90265b8d674b942a43fb70e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac760b85cf90265b8d674b942a43fb70e">&#9670;&nbsp;</a></span>right()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">int MinHeap::right </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>i</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>to get index of right child of node at index i </p>
+<div class="fragment"><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;{ <span class="keywordflow">return</span> (2 * i + 2); }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<hr/>The documentation for this class was generated from the following file:<ul>
+<li>data_structures/<a class="el" href="../../de/dc3/binaryheap_8cpp.html">binaryheap.cpp</a></li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="aclass_min_heap_html_ae4d358bf063bb196a1945b3fb99b4913"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">MinHeap::heap_size</a></div><div class="ttdeci">int heap_size</div><div class="ttdoc">Current number of elements in min heap.</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:13</div></div>
+<div class="ttc" id="aclass_min_heap_html_aa7f726cc6327955d22871592227432f5"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#aa7f726cc6327955d22871592227432f5">MinHeap::decreaseKey</a></div><div class="ttdeci">void decreaseKey(int i, int new_val)</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:78</div></div>
+<div class="ttc" id="aclass_min_heap_html_a88b4aa3e66392a3eabbf2517a9a79a02"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#a88b4aa3e66392a3eabbf2517a9a79a02">MinHeap::capacity</a></div><div class="ttdeci">int capacity</div><div class="ttdoc">maximum possible size of min heap</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:12</div></div>
+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
+<div class="ttc" id="amatrix__exponentiation_8cpp_html_afcf0d19607cd0edd8ae333d2b9c220c0"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a></div><div class="ttdeci">ll k</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:48</div></div>
+<div class="ttc" id="aclass_min_heap_html_a34a93a87967308eb516328c0aca3c48e"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">MinHeap::harr</a></div><div class="ttdeci">int * harr</div><div class="ttdoc">pointer to array of elements in heap</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:11</div></div>
+<div class="ttc" id="aclass_min_heap_html_aaef438c1056492cb62c4a4d9035b5cad"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#aaef438c1056492cb62c4a4d9035b5cad">MinHeap::MinHeapify</a></div><div class="ttdeci">void MinHeapify(int)</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:115</div></div>
+<div class="ttc" id="aclass_min_heap_html_aa8c6c141e3de664819686aa637e1afca"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#aa8c6c141e3de664819686aa637e1afca">MinHeap::left</a></div><div class="ttdeci">int left(int i)</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:28</div></div>
+<div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
+<div class="ttc" id="aclass_min_heap_html_a4014f1edaed0bd7db0c0d2ca53228980"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#a4014f1edaed0bd7db0c0d2ca53228980">MinHeap::extractMin</a></div><div class="ttdeci">int extractMin()</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:87</div></div>
+<div class="ttc" id="aclass_min_heap_html_ac760b85cf90265b8d674b942a43fb70e"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#ac760b85cf90265b8d674b942a43fb70e">MinHeap::right</a></div><div class="ttdeci">int right(int i)</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:31</div></div>
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="navelem"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></li>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
diff --git a/d2/d05/class_min_heap.js b/d2/d05/class_min_heap.js
new file mode 100644
index 000000000..464af9847
--- /dev/null
+++ b/d2/d05/class_min_heap.js
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+var class_min_heap =
+[
+    [ "MinHeap", "d2/d05/class_min_heap.html#ad89ca80a217655a735d266618197965e", null ],
+    [ "decreaseKey", "d2/d05/class_min_heap.html#aa7f726cc6327955d22871592227432f5", null ],
+    [ "deleteKey", "d2/d05/class_min_heap.html#a37ac126eabb0c3ce04047172abccca29", null ],
+    [ "extractMin", "d2/d05/class_min_heap.html#a4014f1edaed0bd7db0c0d2ca53228980", null ],
+    [ "getMin", "d2/d05/class_min_heap.html#a336ac71f0d857269fe9a98058a3cd130", null ],
+    [ "insertKey", "d2/d05/class_min_heap.html#aef78f3384f5a0ae880ad0883d2d44b82", null ],
+    [ "left", "d2/d05/class_min_heap.html#aa8c6c141e3de664819686aa637e1afca", null ],
+    [ "MinHeapify", "d2/d05/class_min_heap.html#aaef438c1056492cb62c4a4d9035b5cad", null ],
+    [ "parent", "d2/d05/class_min_heap.html#a0e893f9deb4be4cf4f9990e736483e81", null ],
+    [ "right", "d2/d05/class_min_heap.html#ac760b85cf90265b8d674b942a43fb70e", null ],
+    [ "capacity", "d2/d05/class_min_heap.html#a88b4aa3e66392a3eabbf2517a9a79a02", null ],
+    [ "harr", "d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e", null ],
+    [ "heap_size", "d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913", null ]
+];
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+   &#160;<span id="projectnumber">1.0.0</span>
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+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+
+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">fast_power.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Faster computation for \(a^b\).  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
+<code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;cstdint&gt;</code><br />
+<code>#include &lt;cstdlib&gt;</code><br />
+<code>#include &lt;ctime&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for fast_power.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d30/fast__power_8cpp__incl.svg" width="506" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a8399b847626e5bba983cab7c7918b445"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:a8399b847626e5bba983cab7c7918b445"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a> (T <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, T b)</td></tr>
+<tr class="separator:a8399b847626e5bba983cab7c7918b445"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a0d4e3f0099a6975b74a314a35bd0f94d"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:a0d4e3f0099a6975b74a314a35bd0f94d"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a> (T <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, T b)</td></tr>
+<tr class="separator:a0d4e3f0099a6975b74a314a35bd0f94d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d0b/fast__power_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Faster computation for \(a^b\). </p>
+<p>Program that computes \(a^b\) in \(O(logN)\) time. It is based on formula that:</p><ol type="1">
+<li>if \(b\) is even: \(a^b = a^\frac{b}{2} \cdot a^\frac{b}{2} = {a^\frac{b}{2}}^2\)</li>
+<li>if \(b\) is odd: \(a^b = a^\frac{b-1}{2} \cdot a^\frac{b-1}{2} \cdot a = {a^\frac{b-1}{2}}^2 \cdot a\)</li>
+</ol>
+<p>We can compute \(a^b\) recursively using above algorithm. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a0d4e3f0099a6975b74a314a35bd0f94d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0d4e3f0099a6975b74a314a35bd0f94d">&#9670;&nbsp;</a></span>fast_power_linear()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">double fast_power_linear </td>
+          <td>(</td>
+          <td class="paramtype">T&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">T&#160;</td>
+          <td class="paramname"><em>b</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Same algorithm with little different formula. It still calculates in \(O(\log N)\) </p>
+<div class="fragment"><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;                                   {</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    <span class="comment">// negative power. a^b = 1 / (a^-b)</span></div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    <span class="keywordflow">if</span> (b &lt; 0)</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        <span class="keywordflow">return</span> 1.0 / <a class="code" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, -b);</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160; </div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keywordtype">double</span> result = 1;</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keywordflow">while</span> (b) {</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        <span class="keywordflow">if</span> (b &amp; 1)</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;            result = result * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        b = b &gt;&gt; 1;</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    }</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <span class="keywordflow">return</span> result;</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a8399b847626e5bba983cab7c7918b445"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a8399b847626e5bba983cab7c7918b445">&#9670;&nbsp;</a></span>fast_power_recursive()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">double fast_power_recursive </td>
+          <td>(</td>
+          <td class="paramtype">T&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">T&#160;</td>
+          <td class="paramname"><em>b</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>algorithm implementation for \(a^b\) </p>
+<div class="fragment"><div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;                                      {</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="comment">// negative power. a^b = 1 / (a^-b)</span></div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    <span class="keywordflow">if</span> (b &lt; 0)</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;        <span class="keywordflow">return</span> 1.0 / <a class="code" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, -b);</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160; </div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="keywordflow">if</span> (b == 0)</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;        <span class="keywordflow">return</span> 1;</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    T bottom = <a class="code" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b &gt;&gt; 1);</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <span class="comment">// Since it is integer division b/2 = (b-1)/2 where b is odd.</span></div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="comment">// Therefore, case2 is easily solved by integer division.</span></div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160; </div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="keywordtype">double</span> result;</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    <span class="keywordflow">if</span> ((b &amp; 1) == 0)  <span class="comment">// case1</span></div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;        result = bottom * bottom;</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <span class="keywordflow">else</span>  <span class="comment">// case2</span></div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;        result = bottom * bottom * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    <span class="keywordflow">return</span> result;</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;           {</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/sync_with_stdio.html">std::ios_base::sync_with_stdio</a>(<span class="keyword">false</span>);</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160; </div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Testing...&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 20; i++) {</div>
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+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">jump_search.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>C++ program to implement <a href="https://en.wikipedia.org/wiki/Jump_search">Jump Search</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
+<code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for jump_search.cpp:</div>
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+Functions</h2></td></tr>
+<tr class="memitem:ab49fd8f401bfc71f63b74711390cccf0"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d22/jump__search_8cpp.html#ab49fd8f401bfc71f63b74711390cccf0">jumpSearch</a> (int arr[], int x, int n)</td></tr>
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+int&#160;</td><td class="memItemRight" valign="bottom"><b>main</b> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>C++ program to implement <a href="https://en.wikipedia.org/wiki/Jump_search">Jump Search</a> </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ab49fd8f401bfc71f63b74711390cccf0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ab49fd8f401bfc71f63b74711390cccf0">&#9670;&nbsp;</a></span>jumpSearch()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int jumpSearch </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>arr</em>[], </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>jump search implementation </p>
+<div class="fragment"><div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;                                        {</div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;    <span class="comment">// Finding block size to be jumped</span></div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;    <span class="keywordtype">int</span> step = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(n);</div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;    <span class="comment">// Finding the block where element is</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;    <span class="comment">// present (if it is present)</span></div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;    <span class="keywordtype">int</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a> = 0;</div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;    <span class="keywordflow">while</span> (arr[<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(step, n) - 1] &lt; x) {</div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a> = step;</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;        step += <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(n);</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;        <span class="keywordflow">if</span> (prev &gt;= n)</div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;            <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    }</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160; </div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <span class="comment">// Doing a linear search for x in block</span></div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="comment">// beginning with prev.</span></div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    <span class="keywordflow">while</span> (arr[prev] &lt; x) {</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a>++;</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160; </div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;        <span class="comment">// If we reached next block or end of</span></div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;        <span class="comment">// array, element is not present.</span></div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;        <span class="keywordflow">if</span> (prev == <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(step, n))</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;            <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    }</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <span class="comment">// If element is found</span></div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="keywordflow">if</span> (arr[prev] == x)</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;        <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/prev.html">prev</a>;</div>
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+<div class="textblock"><p>Define the state of tower </p>
+</div><hr/>The documentation for this struct was generated from the following file:<ul>
+<li>others/<a class="el" href="../../db/d3c/tower__of__hanoi_8cpp.html">tower_of_hanoi.cpp</a></li>
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+class queue&lt; Kind &gt;</h3>
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+<p>Definition of the queue class </p>
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+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
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+<p>Default constructor </p>
+<div class="fragment"><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;            {</div>
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+  </td>
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+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Destructor </p>
+<div class="fragment"><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;{}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<h2 class="groupheader">Member Function Documentation</h2>
+<a id="ab2019d91e28c06de325fb3076b93a930"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ab2019d91e28c06de325fb3076b93a930">&#9670;&nbsp;</a></span>clear()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Kind &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void <a class="el" href="../../d2/d36/structqueue.html">queue</a>&lt; Kind &gt;::clear </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Clear queue </p>
+<div class="fragment"><div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;{ <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> = NULL; }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a089d4af5532e0a801f560070da6e1f86"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a089d4af5532e0a801f560070da6e1f86">&#9670;&nbsp;</a></span>deQueue()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Kind &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void <a class="el" href="../../d2/d36/structqueue.html">queue</a>&lt; Kind &gt;::deQueue </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Remove the top element of the queue </p>
+<div class="fragment"><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;                   {</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;        <a class="code" href="../../d5/da1/structnode.html">node&lt;Kind&gt;</a> *temp;</div>
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+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;            temp = <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a>;</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;            <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> = <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a>-&gt;next;</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;            <span class="keyword">delete</span> temp;</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;            size--;</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Queue is empty !&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        }</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d36/structqueue_a089d4af5532e0a801f560070da6e1f86_cgraph.svg" width="327" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a26f48801df462ade003b50739196fa4c"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a26f48801df462ade003b50739196fa4c">&#9670;&nbsp;</a></span>display()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Kind &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void <a class="el" href="../../d2/d36/structqueue.html">queue</a>&lt; Kind &gt;::display </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Show queue </p>
+<div class="fragment"><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;                   {</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;        <a class="code" href="../../d5/da1/structnode.html">node&lt;Kind&gt;</a> *current = <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a>;</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Front --&gt; &quot;</span>;</div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;        <span class="keywordflow">while</span> (current != NULL) {</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; current-&gt;data &lt;&lt; <span class="stringliteral">&quot;    &quot;</span>;</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;            current = current-&gt;next;</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;        }</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Size of queue: &quot;</span> &lt;&lt; size &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d36/structqueue_a26f48801df462ade003b50739196fa4c_cgraph.svg" width="238" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a592c0580551ec0d3b4d43e8198d8a377"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a592c0580551ec0d3b4d43e8198d8a377">&#9670;&nbsp;</a></span>enQueue()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Kind &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void <a class="el" href="../../d2/d36/structqueue.html">queue</a>&lt; Kind &gt;::enQueue </td>
+          <td>(</td>
+          <td class="paramtype">Kind&#160;</td>
+          <td class="paramname"><em>item</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Add new item to the queue </p>
+<div class="fragment"><div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;                            {</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        <a class="code" href="../../d5/da1/structnode.html">node&lt;Kind&gt;</a> *newNode;</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;        newNode = <span class="keyword">new</span> <a class="code" href="../../d5/da1/structnode.html">node&lt;Kind&gt;</a>;</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;        newNode-&gt;data = item;</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        newNode-&gt;next = NULL;</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> == NULL) {</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;            <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> = newNode;</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;            <a class="code" href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queueRear</a> = newNode;</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;            <a class="code" href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queueRear</a>-&gt;next = newNode;</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;            <a class="code" href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queueRear</a> = <a class="code" href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queueRear</a>-&gt;next;</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;        }</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        size++;</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a36d47fdbedc199609818385110d9f922"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a36d47fdbedc199609818385110d9f922">&#9670;&nbsp;</a></span>front()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Kind &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">Kind <a class="el" href="../../d2/d36/structqueue.html">queue</a>&lt; Kind &gt;::front </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Return the first element of the queue </p>
+<div class="fragment"><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;                 {</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        assert(<a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> != NULL);</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a>-&gt;data;</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ac2fff88dce4d7d2eb7134af382bd1b31"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac2fff88dce4d7d2eb7134af382bd1b31">&#9670;&nbsp;</a></span>isEmptyQueue()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Kind &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool <a class="el" href="../../d2/d36/structqueue.html">queue</a>&lt; Kind &gt;::isEmptyQueue </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Determine whether the queue is empty </p>
+<div class="fragment"><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;{ <span class="keywordflow">return</span> (<a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> == NULL); }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<h2 class="groupheader">Member Data Documentation</h2>
+<a id="ac16ccadebb765e1ddbe415cdce1a17a5"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac16ccadebb765e1ddbe415cdce1a17a5">&#9670;&nbsp;</a></span>queueFront</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Kind &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d5/da1/structnode.html">node</a>&lt;Kind&gt;* <a class="el" href="../../d2/d36/structqueue.html">queue</a>&lt; Kind &gt;::queueFront</td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">private</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Pointer to the front of the queue </p>
+
+</div>
+</div>
+<a id="ae2a7a36270f5d15218a180fa59e5b3a5"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae2a7a36270f5d15218a180fa59e5b3a5">&#9670;&nbsp;</a></span>queueRear</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Kind &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d5/da1/structnode.html">node</a>&lt;Kind&gt;* <a class="el" href="../../d2/d36/structqueue.html">queue</a>&lt; Kind &gt;::queueRear</td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">private</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Pointer to the rear of the queue <br  />
+ </p>
+
+</div>
+</div>
+<hr/>The documentation for this class was generated from the following files:<ul>
+<li>data_structures/<a class="el" href="../../d3/d26/binary__search__tree_8cpp.html">binary_search_tree.cpp</a></li>
+<li>data_structures/<a class="el" href="../../d8/d38/queue_8h_source.html">queue.h</a></li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
+<div class="ttc" id="astructqueue_html_ae2a7a36270f5d15218a180fa59e5b3a5"><div class="ttname"><a href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queue::queueRear</a></div><div class="ttdeci">node&lt; Kind &gt; * queueRear</div><div class="ttdef"><b>Definition:</b> queue.h:84</div></div>
+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
+<div class="ttc" id="astructqueue_html_ac2fff88dce4d7d2eb7134af382bd1b31"><div class="ttname"><a href="../../d2/d36/structqueue.html#ac2fff88dce4d7d2eb7134af382bd1b31">queue::isEmptyQueue</a></div><div class="ttdeci">bool isEmptyQueue()</div><div class="ttdef"><b>Definition:</b> queue.h:42</div></div>
+<div class="ttc" id="astructqueue_html_ac16ccadebb765e1ddbe415cdce1a17a5"><div class="ttname"><a href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queue::queueFront</a></div><div class="ttdeci">node&lt; Kind &gt; * queueFront</div><div class="ttdef"><b>Definition:</b> queue.h:83</div></div>
+<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="navelem"><a class="el" href="../../d2/d36/structqueue.html">queue</a></li>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
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diff --git a/d2/d36/structqueue.js b/d2/d36/structqueue.js
new file mode 100644
index 000000000..38858d353
--- /dev/null
+++ b/d2/d36/structqueue.js
@@ -0,0 +1,17 @@
+var structqueue =
+[
+    [ "queue", "d2/d36/structqueue.html#a21381ee7f95daae0332665914780e970", null ],
+    [ "~queue", "d2/d36/structqueue.html#ad215eee654953d25150bb25d5ac12b7c", null ],
+    [ "clear", "d2/d36/structqueue.html#ab2019d91e28c06de325fb3076b93a930", null ],
+    [ "deQueue", "d2/d36/structqueue.html#a089d4af5532e0a801f560070da6e1f86", null ],
+    [ "display", "d2/d36/structqueue.html#a26f48801df462ade003b50739196fa4c", null ],
+    [ "enQueue", "d2/d36/structqueue.html#a592c0580551ec0d3b4d43e8198d8a377", null ],
+    [ "front", "d2/d36/structqueue.html#a36d47fdbedc199609818385110d9f922", null ],
+    [ "isEmptyQueue", "d2/d36/structqueue.html#ac2fff88dce4d7d2eb7134af382bd1b31", null ],
+    [ "front", "d2/d36/structqueue.html#a5e48e536f1fce666f59e78c16183d586", null ],
+    [ "queueFront", "d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5", null ],
+    [ "queueRear", "d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5", null ],
+    [ "rear", "d2/d36/structqueue.html#ad3f87c5be45a8c56252ecc96847871a8", null ],
+    [ "size", "d2/d36/structqueue.html#ab45a4bfef7eba256a9c027bae86fc196", null ],
+    [ "t", "d2/d36/structqueue.html#ac330f181d25faba50a95d181ca12f42d", null ]
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+<p>Functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</a> of any rectangular matrix.  
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+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;double&gt; qr_algorithm::eigen_values </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">bool&#160;</td>
+          <td class="paramname"><em>print_intermediates</em> = <code>false</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Compute eigen values using iterative shifted QR decomposition algorithm as follows:</p><ol type="1">
+<li>Use last diagonal element of A as eigen value approximation \(c\)</li>
+<li>Shift diagonals of matrix \(A&#39; = A - cI\)</li>
+<li>Decompose matrix \(A&#39;=QR\)</li>
+<li>Compute next approximation \(A&#39;_1 = RQ \)</li>
+<li>Shift diagonals back \(A_1 = A&#39;_1 + cI\)</li>
+<li>Termination condition check: last element below diagonal is almost 0<ol type="a">
+<li>If not 0, go back to step 1 with the new approximation \(A_1\)</li>
+<li>If 0, continue to step 7</li>
+</ol>
+</li>
+<li>Save last known \(c\) as the eigen value.</li>
+<li>Are all eigen values found?<ol type="a">
+<li>If not, remove last row and column of \(A_1\) and go back to step 1.</li>
+<li>If yes, stop.</li>
+</ol>
+</li>
+</ol>
+<dl class="section note"><dt>Note</dt><dd>The matrix \(A\) gets modified</dd></dl>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">A</td><td>matrix to compute eigen values for </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">print_intermediates</td><td>(optional) whether to print intermediate A, Q and R matrices (default = <code>false</code>) </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;                                                                     {</div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;    <span class="keywordtype">int</span> rows = A-&gt;size();</div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    <span class="keywordtype">int</span> columns = rows;</div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    <span class="keywordtype">int</span> counter = 0, num_eigs = rows - 1;</div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    <span class="keywordtype">double</span> last_eig = 0;</div>
+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160; </div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; Q(rows);</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; R(columns);</div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160; </div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    <span class="comment">/* number of eigen values = matrix size */</span></div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eigen_vals(rows);</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; rows; i++) {</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        Q[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(columns);</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        R[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(columns);</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    }</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    <span class="comment">/* continue till all eigen values are found */</span></div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    <span class="keywordflow">while</span> (num_eigs &gt; 0) {</div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;        <span class="comment">/* iterate with QR decomposition */</span></div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;        <span class="keywordflow">while</span> (std::abs(A[0][num_eigs][num_eigs - 1]) &gt;</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;               <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits&lt;double&gt;::epsilon</a>()) {</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;            <span class="comment">// initial approximation = last diagonal element</span></div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;            last_eig = A[0][num_eigs][num_eigs];</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; rows; i++) {</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;                A[0][i][i] -= last_eig; <span class="comment">/* A - cI */</span></div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;            }</div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160; </div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;            <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#ab1ac74497ffb2101040cc1efe3546de8">qr_decompose</a>(*A, &amp;Q, &amp;R);</div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160; </div>
+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;            <span class="keywordflow">if</span> (print_intermediates) {</div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;                <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; *A &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; Q &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;                <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; R &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;                <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">printf</a>(<span class="stringliteral">&quot;-------------------- %d ---------------------\n&quot;</span>,</div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;                       ++counter);</div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;            }</div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160; </div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;            <span class="comment">// new approximation A&#39; = R * Q</span></div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;            <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a7558fd7779bf207157ced66f275951a0">mat_mul</a>(R, Q, A);</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160; </div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; rows; i++) {</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;                A[0][i][i] += last_eig; <span class="comment">/* A + cI */</span></div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;            }</div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;        }</div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160; </div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;        <span class="comment">/* store the converged eigen value */</span></div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;        eigen_vals[num_eigs] = last_eig;</div>
+<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;        <span class="comment">// A[0][num_eigs][num_eigs];</span></div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        <span class="keywordflow">if</span> (print_intermediates) {</div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;========================\n&quot;</span>;</div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Eigen value: &quot;</span> &lt;&lt; last_eig &lt;&lt; <span class="stringliteral">&quot;,\n&quot;</span>;</div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;========================\n&quot;</span>;</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;        }</div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160; </div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        num_eigs--;</div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;        rows--;</div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        columns--;</div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;    }</div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    eigen_vals[0] = A[0][0][0];</div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160; </div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <span class="keywordflow">if</span> (print_intermediates) {</div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; Q &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; R &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    }</div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160; </div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;    <span class="keywordflow">return</span> eigen_vals;</div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d2/d3b/namespaceqr__algorithm_a763896dbb4a7e95c4a1e614ac0819d66_cgraph.svg" width="100%" height="385"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a7c63c78d6839b8ad73b77c161210b514"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a7c63c78d6839b8ad73b77c161210b514">&#9670;&nbsp;</a></span>operator&lt;&lt;() <span class="overload">[1/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a>&amp; qr_algorithm::operator&lt;&lt; </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;&#160;</td>
+          <td class="paramname"><em>out</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt;&gt; const &amp;&#160;</td>
+          <td class="paramname"><em>v</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>operator to print a matrix </p>
+<div class="fragment"><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;                                                               {</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> width = 12;</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160; </div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    out.precision(4);</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++) {</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; v[row].size(); col++)</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;            out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::right</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;                &lt;&lt; v[row][col];</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    }</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160; </div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    <span class="keywordflow">return</span> out;</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d3b/namespaceqr__algorithm_a7c63c78d6839b8ad73b77c161210b514_cgraph.svg" width="302" height="190"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a240edf2b6b5942c0e5f2c9d3e326797f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a240edf2b6b5942c0e5f2c9d3e326797f">&#9670;&nbsp;</a></span>operator&lt;&lt;() <span class="overload">[2/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a>&amp; qr_algorithm::operator&lt;&lt; </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;&#160;</td>
+          <td class="paramname"><em>out</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; const &amp;&#160;</td>
+          <td class="paramname"><em>v</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>operator to print a vector </p>
+<div class="fragment"><div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;                                                                 {</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160; </div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    out.precision(4);</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++) {</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::right</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;            &lt;&lt; v[row];</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    }</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160; </div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="keywordflow">return</span> out;</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d3b/namespaceqr__algorithm_a240edf2b6b5942c0e5f2c9d3e326797f_cgraph.svg" width="302" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ab1ac74497ffb2101040cc1efe3546de8"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ab1ac74497ffb2101040cc1efe3546de8">&#9670;&nbsp;</a></span>qr_decompose()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">void qr_algorithm::qr_decompose </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt;&gt; &amp;&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>Q</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>R</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Decompose matrix \(A\) using <a href="https://en.wikipedia.org/wiki/QR_decomposition">Gram-Schmidt process</a>.</p>
+<p class="formulaDsp">
+\begin{eqnarray*} \text{given that}\quad A &amp;=&amp; *\left[\mathbf{a}_1,\mathbf{a}_2,\ldots,\mathbf{a}_{N-1},\right]\\ \text{where}\quad\mathbf{a}_i &amp;=&amp; \left[a_{0i},a_{1i},a_{2i},\ldots,a_{(M-1)i}\right]^T\quad\ldots\mbox{(column vectors)}\\ \text{then}\quad\mathbf{u}_i &amp;=&amp; \mathbf{a}_i *-\sum_{j=0}^{i-1}\text{proj}_{\mathbf{u}_j}\mathbf{a}_i\\ \mathbf{e}_i &amp;=&amp;\frac{\mathbf{u}_i}{\left|\mathbf{u}_i\right|}\\ Q &amp;=&amp; \begin{bmatrix}\mathbf{e}_0 &amp; \mathbf{e}_1 &amp; \mathbf{e}_2 &amp; \dots &amp; \mathbf{e}_{N-1}\end{bmatrix}\\ R &amp;=&amp; \begin{bmatrix}\langle\mathbf{e}_0\,,\mathbf{a}_0\rangle &amp; \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &amp; \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp; \dots \\ 0 &amp; \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &amp; \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp; \dots\\ 0 &amp; 0 &amp; \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp; \dots\\ \vdots &amp; \vdots &amp; \vdots &amp; \ddots \end{bmatrix}\\ \end{eqnarray*}
+</p>
+ <dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">A</td><td>input matrix to decompose </td></tr>
+    <tr><td class="paramname">Q</td><td>output decomposed matrix </td></tr>
+    <tr><td class="paramname">R</td><td>output decomposed matrix </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;  {</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> ROWS = A.size();        <span class="comment">// number of rows of A</span></div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> COLUMNS = A[0].size();  <span class="comment">// number of columns of A</span></div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> col_vector(ROWS);</div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> col_vector2(ROWS);</div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> tmp_vector(ROWS);</div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160; </div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; COLUMNS; i++) {</div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;        <span class="comment">/* for each column =&gt; R is a square matrix of NxN */</span></div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;        <span class="keywordtype">int</span> j;</div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;        R[0][i] = 0.; <span class="comment">/* make R upper triangular */</span></div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160; </div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;        <span class="comment">/* get corresponding Q vector */</span></div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;<span class="comment">// parallelize on threads</span></div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;        <span class="keywordflow">for</span> (j = 0; j &lt; ROWS; j++) {</div>
+<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;            tmp_vector[j] = A[j][i]; <span class="comment">/* accumulator for uk */</span></div>
+<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;            col_vector[j] = A[j][i];</div>
+<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;        }</div>
+<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;        <span class="keywordflow">for</span> (j = 0; j &lt; i; j++) {</div>
+<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = 0; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; ROWS; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
+<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;                col_vector2[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] = Q[0][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>][j];</div>
+<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;            }</div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;            col_vector2 = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">vector_proj</a>(col_vector, col_vector2);</div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;            tmp_vector -= col_vector2;</div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;        }</div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160; </div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;        <span class="keywordtype">double</span> mag = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">vector_mag</a>(tmp_vector);</div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160; </div>
+<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="comment">// parallelize on threads</span></div>
+<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;        <span class="keywordflow">for</span> (j = 0; j &lt; ROWS; j++) Q[0][j][i] = tmp_vector[j] / mag;</div>
+<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160; </div>
+<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;            <span class="comment">/* compute upper triangular values of R */</span></div>
+<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;<span class="comment">// parallelize on threads</span></div>
+<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk &lt; ROWS; kk++) {</div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;            col_vector[kk] = Q[0][kk][i];</div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;        }</div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160; </div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;<span class="comment">// parallelize on threads</span></div>
+<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = i; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; COLUMNS; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk &lt; ROWS; kk++) {</div>
+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;                col_vector2[kk] = A[kk][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>];</div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;            }</div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;            R[0][i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] = (col_vector * col_vector2).sum();</div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;        }</div>
+<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    }</div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d3b/namespaceqr__algorithm_ab1ac74497ffb2101040cc1efe3546de8_cgraph.svg" width="626" height="114"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a8ea313a1a1b5f9d0e3e332c29c6446ec"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a8ea313a1a1b5f9d0e3e332c29c6446ec">&#9670;&nbsp;</a></span>vector_dot()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">double qr_algorithm::vector_dot </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;&#160;</td>
+          <td class="paramname"><em>b</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Compute dot product of two vectors of equal lengths</p>
+<p>If \(\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\) and \(\vec{b}=\left[b_0,b_1,b_1,...,b_L\right]\) then \(\vec{a}\cdot\vec{b}=\displaystyle\sum_{i=0}^L a_i\times b_i\)</p>
+<dl class="section return"><dt>Returns</dt><dd>\(\vec{a}\cdot\vec{b}\) </dd></dl>
+<div class="fragment"><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;                                                                           {</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="keywordflow">return</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> * b).sum();</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <span class="comment">// could also use following</span></div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    <span class="comment">// return std::inner_product(std::begin(a), std::end(a), std::begin(b),</span></div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <span class="comment">// 0.f);</span></div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ad16da2183db22378435042f26af43d5f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ad16da2183db22378435042f26af43d5f">&#9670;&nbsp;</a></span>vector_mag()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">double qr_algorithm::vector_mag </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;&#160;</td>
+          <td class="paramname"><em>a</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Compute magnitude of vector.</p>
+<p>If \(\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\) then \(\left|\vec{a}\right|=\sqrt{\displaystyle\sum_{i=0}^L a_i^2}\)</p>
+<dl class="section return"><dt>Returns</dt><dd>\(\left|\vec{a}\right|\) </dd></dl>
+<div class="fragment"><div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;                                                  {</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="keywordtype">double</span> dot = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>);</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(dot);</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d3b/namespaceqr__algorithm_ad16da2183db22378435042f26af43d5f_cgraph.svg" width="391" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a5422c76bfa322620de611083bd518d71"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a5422c76bfa322620de611083bd518d71">&#9670;&nbsp;</a></span>vector_proj()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;T&gt; qr_algorithm::vector_proj </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;&#160;</td>
+          <td class="paramname"><em>b</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Compute projection of vector \(\vec{a}\) on \(\vec{b}\) defined as </p><p class="formulaDsp">
+\[\text{proj}_\vec{b}\vec{a}=\frac{\vec{a}\cdot\vec{b}}{\left|\vec{b}\right|^2}\vec{b}\]
+</p>
+<dl class="section return"><dt>Returns</dt><dd>NULL if error, otherwise pointer to output </dd></dl>
+<p>check for division by zero using machine epsilon</p>
+<div class="fragment"><div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                                                      {</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <span class="keywordtype">double</span> num = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b);</div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    <span class="keywordtype">double</span> deno = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(b, b);</div>
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+<a href="#func-members">Functions</a>  </div>
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+<div class="title">ode_semi_implicit_euler.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Solve a multivariable first order <a href="https://en.wikipedia.org/wiki/Ordinary_differential_equation">ordinary differential equation (ODEs)</a> using <a href="https://en.wikipedia.org/wiki/Semi-implicit_Euler_method">semi implicit Euler method</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;ctime&gt;</code><br />
+<code>#include &lt;fstream&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;valarray&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for ode_semi_implicit_euler.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/db4/ode__semi__implicit__euler_8cpp__incl.svg" width="430" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:abaeae8f62a018d197f0187a1c80a90fe"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a> (const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</td></tr>
+<tr class="memdesc:abaeae8f62a018d197f0187a1c80a90fe"><td class="mdescLeft">&#160;</td><td class="mdescRight">Problem statement for a system with first-order differential equations. Updates the system differential variables.  <a href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">More...</a><br /></td></tr>
+<tr class="separator:abaeae8f62a018d197f0187a1c80a90fe"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:af3adf7b092a87868917ee5fb4255192b"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a> (const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y)</td></tr>
+<tr class="memdesc:af3adf7b092a87868917ee5fb4255192b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Exact solution of the problem. Used for solution comparison.  <a href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">More...</a><br /></td></tr>
+<tr class="separator:af3adf7b092a87868917ee5fb4255192b"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga827bf009831ddc477c5fa8891d5cb35f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a> (const double dx, const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</td></tr>
+<tr class="memdesc:ga827bf009831ddc477c5fa8891d5cb35f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute next step approximation using the semi-implicit-Euler method.  <a href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">More...</a><br /></td></tr>
+<tr class="separator:ga827bf009831ddc477c5fa8891d5cb35f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga3874d294ab00fe9ce8731c5b7991a089"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga3874d294ab00fe9ce8731c5b7991a089">semi_implicit_euler</a> (double dx, double x0, double x_max, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, bool save_to_file=false)</td></tr>
+<tr class="memdesc:ga3874d294ab00fe9ce8731c5b7991a089"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute approximation using the semi-implicit-Euler method in the given limits.  <a href="../../d6/d60/group__ode.html#ga3874d294ab00fe9ce8731c5b7991a089">More...</a><br /></td></tr>
+<tr class="separator:ga3874d294ab00fe9ce8731c5b7991a089"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aa13517b8e5de1b75592052db7f7e237f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a> (const double &amp;X0, const double &amp;X_MAX, const double &amp;step_size, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &amp;Y0)</td></tr>
+<tr class="separator:aa13517b8e5de1b75592052db7f7e237f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
+<tr class="separator:a0ddf1224851353fc92bfbff6f499fa97"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Solve a multivariable first order <a href="https://en.wikipedia.org/wiki/Ordinary_differential_equation">ordinary differential equation (ODEs)</a> using <a href="https://en.wikipedia.org/wiki/Semi-implicit_Euler_method">semi implicit Euler method</a> </p>
+<dl class="section author"><dt>Authors</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
+<p>The ODE being solved is: </p><p class="formulaDsp">
+\begin{eqnarray*} \dot{u} &amp;=&amp; v\\ \dot{v} &amp;=&amp; -\omega^2 u\\ \omega &amp;=&amp; 1\\ [x_0, u_0, v_0] &amp;=&amp; [0,1,0]\qquad\ldots\text{(initial values)} \end{eqnarray*}
+</p>
+<p> The exact solution for the above problem is: </p><p class="formulaDsp">
+\begin{eqnarray*} u(x) &amp;=&amp; \cos(x)\\ v(x) &amp;=&amp; -\sin(x)\\ \end{eqnarray*}
+</p>
+<p> The computation results are stored to a text file <code>semi_implicit_euler.csv</code> and the exact soltuion results in <code>exact.csv</code> for comparison. <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/numerical_methods/ode_semi_implicit_euler.svg" alt="Implementation solution" style="pointer-events: none;" class="inline"/></p>
+<p>To implement <a href="https://en.wikipedia.org/wiki/Van_der_Pol_oscillator">Van der Pol oscillator</a>, change the <a class="el" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe" title="Problem statement for a system with first-order differential equations. Updates the system differenti...">problem</a> function to: </p><div class="fragment"><div class="line"><span class="keyword">const</span> <span class="keywordtype">double</span> mu = 2.0;</div>
+<div class="line">dy[0] = y[1];</div>
+<div class="line">dy[1] = mu * (1.f - y[0] * y[0]) * y[1] - y[0];</div>
+</div><!-- fragment --><dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d6/dd3/ode__midpoint__euler_8cpp.html" title="Solve a multivariable first order ordinary differential equation (ODEs) using midpoint Euler method">ode_midpoint_euler.cpp</a>, <a class="el" href="../../db/dd3/ode__forward__euler_8cpp.html" title="Solve a multivariable first order ordinary differential equation (ODEs) using forward Euler method">ode_forward_euler.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="af3adf7b092a87868917ee5fb4255192b"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af3adf7b092a87868917ee5fb4255192b">&#9670;&nbsp;</a></span>exact_solution()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void exact_solution </td>
+          <td>(</td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>y</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Exact solution of the problem. Used for solution comparison. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>independent variable </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>dependent variable </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;                                                             {</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    y[0][0] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(x);</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    y[0][1] = -<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(x);</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/d06/ode__semi__implicit__euler_8cpp_af3adf7b092a87868917ee5fb4255192b_cgraph.svg" width="235" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a0ddf1224851353fc92bfbff6f499fa97"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>argc</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char *&#160;</td>
+          <td class="paramname"><em>argv</em>[]&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main Function </p>
+<div class="fragment"><div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;                                 {</div>
+<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    <span class="keywordtype">double</span> X0 = 0.f;                       <span class="comment">/* initial value of x0 */</span></div>
+<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    <span class="keywordtype">double</span> X_MAX = 10.F;                   <span class="comment">/* upper limit of integration */</span></div>
+<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> Y0 = {1.f, 0.f}; <span class="comment">/* initial value Y = y(x = x_0) */</span></div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;    <span class="keywordtype">double</span> step_size;</div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160; </div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    <span class="keywordflow">if</span> (argc == 1) {</div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter the step size: &quot;</span>;</div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; step_size;</div>
+<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;        <span class="comment">// use commandline argument as independent variable step size</span></div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;        step_size = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[1]);</div>
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+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160; </div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    <span class="comment">// get approximate solution</span></div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    <span class="keywordtype">double</span> total_time = <a class="code" href="../../d6/d60/group__ode.html#ga3874d294ab00fe9ce8731c5b7991a089">semi_implicit_euler</a>(step_size, X0, X_MAX, &amp;Y0, <span class="keyword">true</span>);</div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tTime = &quot;</span> &lt;&lt; total_time &lt;&lt; <span class="stringliteral">&quot; ms\n&quot;</span>;</div>
+<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160; </div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    <span class="comment">/* compute exact solution for comparion */</span></div>
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+<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/d06/ode__semi__implicit__euler_8cpp_a0ddf1224851353fc92bfbff6f499fa97_cgraph.svg" width="582" height="367"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="abaeae8f62a018d197f0187a1c80a90fe"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#abaeae8f62a018d197f0187a1c80a90fe">&#9670;&nbsp;</a></span>problem()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void problem </td>
+          <td>(</td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>y</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>dy</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Problem statement for a system with first-order differential equations. Updates the system differential variables. </p>
+<dl class="section note"><dt>Note</dt><dd>This function can be updated to and ode of any order.</dd></dl>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>independent variable(s) </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>dependent variable(s) </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">dy</td><td>first-derivative of dependent variable(s) </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;                                      {</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> omega = 1.F;             <span class="comment">// some const for the problem</span></div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    dy[0][0] = y[0][1];                   <span class="comment">// x dot</span></div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    dy[0][1] = -omega * omega * y[0][0];  <span class="comment">// y dot</span></div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="aa13517b8e5de1b75592052db7f7e237f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa13517b8e5de1b75592052db7f7e237f">&#9670;&nbsp;</a></span>save_exact_solution()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void save_exact_solution </td>
+          <td>(</td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>X0</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>X_MAX</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>step_size</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &amp;&#160;</td>
+          <td class="paramname"><em>Y0</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Function to compute and save exact solution for comparison</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">X0</td><td>initial value of independent variable </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">X_MAX</td><td>final value of independent variable </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">step_size</td><td>independent variable step size </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">Y0</td><td>initial values of dependent variables </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;                                                        {</div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;    <span class="keywordtype">double</span> x = X0;</div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> y = Y0;</div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160; </div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(<span class="stringliteral">&quot;exact.csv&quot;</span>, std::ostream::out);</div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    <span class="keywordflow">if</span> (!fp.is_open()) {</div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">&quot;Error! &quot;</span>);</div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;        <span class="keywordflow">return</span>;</div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    }</div>
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+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160; </div>
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+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    <span class="keywordflow">do</span> {</div>
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+    <a href="http://www.doxygen.org/index.html">
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+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">qr_decomposition.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Program to compute the <a href="https://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</a> of a given matrix.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;array&gt;</code><br />
+<code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;cstdlib&gt;</code><br />
+<code>#include &lt;ctime&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &quot;<a class="el" href="../../d4/d68/qr__decompose_8h_source.html">./qr_decompose.h</a>&quot;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for qr_decomposition.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/df9/qr__decomposition_8cpp__incl.svg" width="616" height="202"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a840291bc02cba5474a4cb46a9b9566fe"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/d24/qr__decomposition_8cpp.html#a840291bc02cba5474a4cb46a9b9566fe">main</a> (void)</td></tr>
+<tr class="separator:a840291bc02cba5474a4cb46a9b9566fe"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Program to compute the <a href="https://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</a> of a given matrix. </p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a840291bc02cba5474a4cb46a9b9566fe"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a840291bc02cba5474a4cb46a9b9566fe">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">void&#160;</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
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+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> ROWS, COLUMNS;</div>
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+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of rows and columns: &quot;</span>;</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; ROWS &gt;&gt; COLUMNS;</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160; </div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter matrix elements row-wise:\n&quot;</span>;</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160; </div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; A(ROWS);</div>
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+<p>A simple tree implementation using structured nodes.  
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+<dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000002">Todo:</a></b></dt><dd>update code to use C++ STL library features and OO structure </dd></dl>
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+<p>A C++ program to demonstrate working of <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort()</a>, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/reverse.html">std::reverse()</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;numeric&gt;</code><br />
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+<a href="#namespaces">Namespaces</a> &#124;
+<a href="#func-members">Functions</a> &#124;
+<a href="#var-members">Variables</a>  </div>
+  <div class="headertitle">
+<div class="title">brute_force_string_searching.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>String pattern search - brute force.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;cstring&gt;</code><br />
+<code>#include &lt;vector&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for brute_force_string_searching.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/dbf/brute__force__string__searching_8cpp__incl.svg" width="251" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="namespaces"></a>
+Namespaces</h2></td></tr>
+<tr class="memitem:d9/d03/namespacestring__search"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d03/namespacestring__search.html">string_search</a></td></tr>
+<tr class="memdesc:d9/d03/namespacestring__search"><td class="mdescLeft">&#160;</td><td class="mdescRight">String search algorithms. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:aeb2cd81064717aedd62bfb096b1a73d8"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d03/namespacestring__search.html#aeb2cd81064717aedd62bfb096b1a73d8">string_search::brute_force</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;text, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;pattern)</td></tr>
+<tr class="separator:aeb2cd81064717aedd62bfb096b1a73d8"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/d7d/brute__force__string__searching_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
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+Variables</h2></td></tr>
+<tr class="memitem:ae2abaa9caa13fff35e45edca00bee123"><td class="memItemLeft" align="right" valign="top">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/d7d/brute__force__string__searching_8cpp.html#ae2abaa9caa13fff35e45edca00bee123">test_set</a></td></tr>
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+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>String pattern search - brute force. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
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+      <table class="memname">
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+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
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+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
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+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160; </div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;        <span class="keywordflow">if</span> (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(output) == <a class="code" href="../../d3/d7d/brute__force__string__searching_8cpp.html#ae2abaa9caa13fff35e45edca00bee123">test_set</a>[i][2])</div>
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+
+<div class="memitem">
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+        <tr>
+          <td class="memname">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&gt; &gt; test_set</td>
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+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+ </tbody>
+</table>
+</div>
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+<div class="title">statistics::stats_computer2&lt; T &gt; Member List</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>This is the complete list of members for <a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a>, including all inherited members.</p>
+<table class="directory">
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>M</b> (defined in <a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a>)</td><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html#a8290966ad468f2a8c266d008bc60720e">mean</a>() const</td><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>mu</b> (defined in <a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a>)</td><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>n</b> (defined in <a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a>)</td><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html#ade6de704deea24fdc88077b3d9a0d534">new_val</a>(T x)</td><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html#a7e7a1a2b0a03df0a70cac40d193421d2">operator&gt;&gt;</a>(std::istream &amp;input, stats_computer2 &amp;stat)</td><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a></td><td class="entry"><span class="mlabel">friend</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html#acf2e84df4fc386bb3295016ef8fd156e">std</a>() const</td><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>var</b> (defined in <a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a>)</td><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">variance</a>() const</td><td class="entry"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2&lt; T &gt;</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
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+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+<title>Algorithms_in_C++: CycleCheck Class Reference</title>
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+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+        name="MSearchResults" id="MSearchResults">
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+<div class="header">
+  <div class="summary">
+<a href="#pub-static-methods">Static Public Member Functions</a> &#124;
+<a href="#pri-types">Private Types</a> &#124;
+<a href="#pri-static-methods">Static Private Member Functions</a> &#124;
+<a href="../../d8/d55/class_cycle_check-members.html">List of all members</a>  </div>
+  <div class="headertitle">
+<div class="title">CycleCheck Class Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-methods"></a>
+Static Public Member Functions</h2></td></tr>
+<tr class="memitem:ad9a270ffba3a68539b92272c702e3474"><td class="memItemLeft" align="right" valign="top">static bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/dbb/class_cycle_check.html#ad9a270ffba3a68539b92272c702e3474">isCyclicDFS</a> (<a class="el" href="../../da/d9a/class_graph.html">Graph</a> const &amp;<a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td></tr>
+<tr class="separator:ad9a270ffba3a68539b92272c702e3474"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a399292a33edf87499daa52b51315aca5"><td class="memItemLeft" align="right" valign="top">static bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/dbb/class_cycle_check.html#a399292a33edf87499daa52b51315aca5">isCyclicBFS</a> (<a class="el" href="../../da/d9a/class_graph.html">Graph</a> const &amp;<a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td></tr>
+<tr class="separator:a399292a33edf87499daa52b51315aca5"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-types"></a>
+Private Types</h2></td></tr>
+<tr class="memitem:ae68a1f08ee8c0b6323ab0f281862eadf"><td class="memItemLeft" align="right" valign="top"><a id="ae68a1f08ee8c0b6323ab0f281862eadf"></a>enum &#160;</td><td class="memItemRight" valign="bottom"><b>nodeStates</b> : uint8_t { <b>not_visited</b> = 0, 
+<b>in_stack</b>, 
+<b>visited</b>
+ }</td></tr>
+<tr class="separator:ae68a1f08ee8c0b6323ab0f281862eadf"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-static-methods"></a>
+Static Private Member Functions</h2></td></tr>
+<tr class="memitem:a2f4485c08b45e7a21a2e86f9c3f01d8b"><td class="memItemLeft" align="right" valign="top">static bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">isCyclicDFSHelper</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map.html">AdjList</a> const &amp;adjList, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; nodeStates &gt; *state, unsigned int <a class="el" href="../../d5/da1/structnode.html">node</a>)</td></tr>
+<tr class="separator:a2f4485c08b45e7a21a2e86f9c3f01d8b"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<h2 class="groupheader">Member Function Documentation</h2>
+<a id="a399292a33edf87499daa52b51315aca5"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a399292a33edf87499daa52b51315aca5">&#9670;&nbsp;</a></span>isCyclicBFS()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">static bool CycleCheck::isCyclicBFS </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../da/d9a/class_graph.html">Graph</a> const &amp;&#160;</td>
+          <td class="paramname"><em>graph</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">static</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Check if a graph has cycle or not.</p>
+<p>This function uses BFS to check if a graph is cyclic or not.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">graph</td><td>which needs to be evaluated for the presence of cycle. </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>true if a cycle is detected, else false. </dd></dl>
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+<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;            <span class="comment">// definately not result in a cycle and can be visited safely.</span></div>
+<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;            <span class="keywordflow">if</span> (!indegree[<a class="code" href="../../d5/da1/structnode.html">node</a>]) {</div>
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+<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160; </div>
+<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;        <span class="comment">// Vertices that need to be traversed.</span></div>
+<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;        <span class="keyword">auto</span> remain = <a class="code" href="../../dd/d9b/classgraph.html">graph</a>.getVertices();</div>
+<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;        <span class="comment">// While there are safe nodes that we can visit.</span></div>
+<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;        <span class="keywordflow">while</span> (!can_be_solved.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/empty.html">empty</a>()) {</div>
+<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;            <span class="keyword">auto</span> front = can_be_solved.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/front.html">front</a>();</div>
+<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;            <span class="comment">// Visit the node.</span></div>
+<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;            can_be_solved.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/pop.html">pop</a>();</div>
+<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;            <span class="comment">// Decrease number of nodes that need to be traversed.</span></div>
+<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;            remain--;</div>
+<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160; </div>
+<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;            <span class="comment">// Visit all the children of the visited node.</span></div>
+<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;            <span class="keywordflow">if</span> (<span class="keyword">auto</span> it = graphAjdList.find(front); it != graphAjdList.end()) {</div>
+<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;                <span class="keywordflow">for</span> (<span class="keyword">auto</span> child : it-&gt;second) {</div>
+<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;                    <span class="comment">// Check if we can visited the node safely.</span></div>
+<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;                    <span class="keywordflow">if</span> (--indegree[child] == 0) {</div>
+<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;                        <span class="comment">// if node can be visited safely, then add that node to</span></div>
+<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;                        <span class="comment">// the visit queue.</span></div>
+<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;                        can_be_solved.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/emplace.html">emplace</a>(child);</div>
+<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;                    }</div>
+<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;                }</div>
+<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;            }</div>
+<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;        }</div>
+<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160; </div>
+<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;        <span class="comment">// If there are still nodes that we can&#39;t visit, then it means that</span></div>
+<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;        <span class="comment">// there is a cycle and return true, else return false.</span></div>
+<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;        <span class="keywordflow">return</span> !(remain == 0);</div>
+<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/dbb/class_cycle_check_a399292a33edf87499daa52b51315aca5_cgraph.svg" width="374" height="190"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ad9a270ffba3a68539b92272c702e3474"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ad9a270ffba3a68539b92272c702e3474">&#9670;&nbsp;</a></span>isCyclicDFS()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">static bool CycleCheck::isCyclicDFS </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../da/d9a/class_graph.html">Graph</a> const &amp;&#160;</td>
+          <td class="paramname"><em>graph</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">static</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Driver function to check if a graph has a cycle.</p>
+<p>This function uses DFS to check for cycle in the graph.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">graph</td><td>which needs to be evaluated for the presence of cycle. </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>true if a cycle is detected, else false. </dd></dl>
+<p>State of the node.</p>
+<p>It is a vector of "nodeStates" which represents the state node is in. It can take only 3 values: "not_visited", "in_stack", and "visited".</p>
+<p>Initially, all nodes are in "not_visited" state.</p>
+<div class="fragment"><div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;                                                {<span class="comment"></span></div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;<span class="comment">        /** State of the node.</span></div>
+<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;<span class="comment">         *</span></div>
+<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;<span class="comment">         * It is a vector of &quot;nodeStates&quot; which represents the state node is in.</span></div>
+<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;<span class="comment">         * It can take only 3 values: &quot;not_visited&quot;, &quot;in_stack&quot;, and &quot;visited&quot;.</span></div>
+<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;<span class="comment">         *</span></div>
+<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;<span class="comment">         * Initially, all nodes are in &quot;not_visited&quot; state.</span></div>
+<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;<span class="comment">         */</span></div>
+<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;nodeStates&gt;</a> state(<a class="code" href="../../dd/d9b/classgraph.html">graph</a>.getVertices(), not_visited);</div>
+<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160; </div>
+<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;        <span class="comment">// Start visiting each node.</span></div>
+<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;        <span class="keywordflow">for</span> (<span class="keyword">auto</span> <a class="code" href="../../d5/da1/structnode.html">node</a> = 0; <a class="code" href="../../d5/da1/structnode.html">node</a> &lt; <a class="code" href="../../dd/d9b/classgraph.html">graph</a>.getVertices(); <a class="code" href="../../d5/da1/structnode.html">node</a>++) {</div>
+<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;            <span class="comment">// If a node is not visited, only then check for presence of cycle.</span></div>
+<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;            <span class="comment">// There is no need to check for presence of cycle for a visited</span></div>
+<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;            <span class="comment">// node as it has already been checked for presence of cycle.</span></div>
+<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;            <span class="keywordflow">if</span> (state[<a class="code" href="../../d5/da1/structnode.html">node</a>] == not_visited) {</div>
+<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;                <span class="comment">// Check for cycle.</span></div>
+<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;                <span class="keywordflow">if</span> (<a class="code" href="../../d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">isCyclicDFSHelper</a>(<a class="code" href="../../dd/d9b/classgraph.html">graph</a>.getAdjList(), &amp;state, <a class="code" href="../../d5/da1/structnode.html">node</a>)) {</div>
+<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;                    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;                }</div>
+<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;            }</div>
+<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;        }</div>
+<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160; </div>
+<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;        <span class="comment">// All nodes have been safely traversed, that means there is no cycle in</span></div>
+<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;        <span class="comment">// the graph. Return false.</span></div>
+<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/dbb/class_cycle_check_ad9a270ffba3a68539b92272c702e3474_cgraph.svg" width="664" height="104"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a2f4485c08b45e7a21a2e86f9c3f01d8b"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a2f4485c08b45e7a21a2e86f9c3f01d8b">&#9670;&nbsp;</a></span>isCyclicDFSHelper()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">static bool CycleCheck::isCyclicDFSHelper </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map.html">AdjList</a> const &amp;&#160;</td>
+          <td class="paramname"><em>adjList</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; nodeStates &gt; *&#160;</td>
+          <td class="paramname"><em>state</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>node</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">static</span><span class="mlabel">private</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Helper function of "isCyclicDFS".</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">adjList</td><td>is the adjacency list representation of some graph. </td></tr>
+    <tr><td class="paramname">state</td><td>is the state of the nodes of the graph. </td></tr>
+    <tr><td class="paramname">node</td><td>is the node being evaluated.</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>true if graph has a cycle, else false. </dd></dl>
+<div class="fragment"><div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;                                                     {</div>
+<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;        <span class="comment">// Add node &quot;in_stack&quot; state.</span></div>
+<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;        (*state)[<a class="code" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>] = in_stack;</div>
+<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160; </div>
+<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;        <span class="comment">// If the node has children, then recursively visit all children of the</span></div>
+<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;        <span class="comment">// node.</span></div>
+<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;        <span class="keywordflow">if</span> (<span class="keyword">auto</span> <span class="keyword">const</span>&amp; it = adjList.find(<a class="code" href="../../d5/da1/structnode.html">node</a>); it != adjList.end()) {</div>
+<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;            <span class="keywordflow">for</span> (<span class="keyword">auto</span> child : it-&gt;second) {</div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;                <span class="comment">// If state of child node is &quot;not_visited&quot;, evaluate that child</span></div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;                <span class="comment">// for presence of cycle.</span></div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;                <span class="keywordflow">if</span> (<span class="keyword">auto</span> state_of_child = (*state)[child];</div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;                    state_of_child == not_visited) {</div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;                    <span class="keywordflow">if</span> (<a class="code" href="../../d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">isCyclicDFSHelper</a>(adjList, state, child)) {</div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;                        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;                    }</div>
+<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;                } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (state_of_child == in_stack) {</div>
+<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;                    <span class="comment">// If child node was &quot;in_stack&quot;, then that means that there</span></div>
+<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;                    <span class="comment">// is a cycle in the graph. Return true for presence of the</span></div>
+<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;                    <span class="comment">// cycle.</span></div>
+<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;                    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;                }</div>
+<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;            }</div>
+<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;        }</div>
+<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160; </div>
+<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;        <span class="comment">// Current node has been evaluated for the presence of cycle and had no</span></div>
+<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;        <span class="comment">// cycle. Mark current node as &quot;visited&quot;.</span></div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;        (*state)[<a class="code" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>] = visited;</div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;        <span class="comment">// Return that current node didn&#39;t result in any cycles.</span></div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/dbb/class_cycle_check_a2f4485c08b45e7a21a2e86f9c3f01d8b_cgraph.svg" width="440" height="104"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<hr/>The documentation for this class was generated from the following file:<ul>
+<li>graph/cycle_check_directed_graph.cpp</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="aclassgraph_html"><div class="ttname"><a href="../../dd/d9b/classgraph.html">graph</a></div><div class="ttdef"><b>Definition:</b> bfs.cpp:3</div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; unsigned int &gt;</a></div></div>
+<div class="ttc" id="aemplace_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/emplace.html">std::queue::emplace</a></div><div class="ttdeci">T emplace(T... args)</div></div>
+<div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
+<div class="ttc" id="ahash__search_8cpp_html_a8ca8dcb494104d273679e219e53d0555"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a></div><div class="ttdeci">struct list node</div></div>
+<div class="ttc" id="aqueue_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="afront_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/front.html">std::queue::front</a></div><div class="ttdeci">T front(T... args)</div></div>
+<div class="ttc" id="aclass_cycle_check_html_a2f4485c08b45e7a21a2e86f9c3f01d8b"><div class="ttname"><a href="../../d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">CycleCheck::isCyclicDFSHelper</a></div><div class="ttdeci">static bool isCyclicDFSHelper(AdjList const &amp;adjList, std::vector&lt; nodeStates &gt; *state, unsigned int node)</div><div class="ttdef"><b>Definition:</b> cycle_check_directed_graph.cpp:165</div></div>
+<div class="ttc" id="apop_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/pop.html">std::queue::pop</a></div><div class="ttdeci">T pop(T... args)</div></div>
+<div class="ttc" id="aempty_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/empty.html">std::queue::empty</a></div><div class="ttdeci">T empty(T... args)</div></div>
+<div class="ttc" id="aunordered_map_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/unordered_map.html">std::unordered_map&lt; unsigned int, std::vector&lt; unsigned int &gt; &gt;</a></div></div>
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="navelem"><a class="el" href="../../d3/dbb/class_cycle_check.html">CycleCheck</a></li>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
diff --git a/d3/dbb/class_cycle_check.js b/d3/dbb/class_cycle_check.js
new file mode 100644
index 000000000..032218c69
--- /dev/null
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+  <div class="headertitle">
+<div class="title">linkedlist_implentation_usingarray.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Linked list implementation using Arrays.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for linkedlist_implentation_usingarray.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d7/d3e/linkedlist__implentation__usingarray_8cpp__incl.svg" width="200" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
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+Classes</h2></td></tr>
+<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d8b/struct_node.html">Node</a></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ac2fa82ac5ae366cc3aca53a40bb7cd70"><td class="memItemLeft" align="right" valign="top"><a id="ac2fa82ac5ae366cc3aca53a40bb7cd70"></a>
+void&#160;</td><td class="memItemRight" valign="bottom"><b>initialise_list</b> ()</td></tr>
+<tr class="separator:ac2fa82ac5ae366cc3aca53a40bb7cd70"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a73e11e0871f56342a30da93b6c93e8be"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#a73e11e0871f56342a30da93b6c93e8be">getnode</a> ()</td></tr>
+<tr class="separator:a73e11e0871f56342a30da93b6c93e8be"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a08ba214242a900e7251cec556b592f02"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#a08ba214242a900e7251cec556b592f02">freeNode</a> (int nodeToBeDeleted)</td></tr>
+<tr class="separator:a08ba214242a900e7251cec556b592f02"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:afcb07da7984e20b3207934696791f5df"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#afcb07da7984e20b3207934696791f5df">insertAtTheBeginning</a> (int <a class="el" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</td></tr>
+<tr class="separator:afcb07da7984e20b3207934696791f5df"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a92e0c1bb3b270143881e36b5fea8a60d"><td class="memItemLeft" align="right" valign="top"><a id="a92e0c1bb3b270143881e36b5fea8a60d"></a>
+void&#160;</td><td class="memItemRight" valign="bottom"><b>insertAtTheEnd</b> (int <a class="el" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</td></tr>
+<tr class="separator:a92e0c1bb3b270143881e36b5fea8a60d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a1e5b20fed15743656bb6d2e6a6ea6269"><td class="memItemLeft" align="right" valign="top"><a id="a1e5b20fed15743656bb6d2e6a6ea6269"></a>
+void&#160;</td><td class="memItemRight" valign="bottom"><b>display</b> ()</td></tr>
+<tr class="separator:a1e5b20fed15743656bb6d2e6a6ea6269"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="var-members"></a>
+Variables</h2></td></tr>
+<tr class="memitem:aed19b403f559fc5d5a4bce724f9e263c"><td class="memItemLeft" align="right" valign="top"><a id="aed19b403f559fc5d5a4bce724f9e263c"></a>
+<a class="el" href="../../db/d8b/struct_node.html">Node</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a> [100]</td></tr>
+<tr class="memdesc:aed19b403f559fc5d5a4bce724f9e263c"><td class="mdescLeft">&#160;</td><td class="mdescRight">array that will act as nodes of a linked list. <br /></td></tr>
+<tr class="separator:aed19b403f559fc5d5a4bce724f9e263c"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a20358970b1abaf992eb85e071e454653"><td class="memItemLeft" align="right" valign="top"><a id="a20358970b1abaf992eb85e071e454653"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>head</b> = -1</td></tr>
+<tr class="separator:a20358970b1abaf992eb85e071e454653"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ab84c7d9bed2aa1ade1fd61fbf5c2e07e"><td class="memItemLeft" align="right" valign="top"><a id="ab84c7d9bed2aa1ade1fd61fbf5c2e07e"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>avail</b> = 0</td></tr>
+<tr class="separator:ab84c7d9bed2aa1ade1fd61fbf5c2e07e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Linked list implementation using Arrays. </p>
+<p>The difference between the pointer implementation of linked list and array implementation of linked list:</p><ol type="1">
+<li>The NULL is represented by -1;</li>
+<li>Limited size. (in the following case it is 100 nodes at max). But we can reuse the nodes that are to be deleted by again linking it bacj to the list. </li>
+</ol>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a08ba214242a900e7251cec556b592f02"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a08ba214242a900e7251cec556b592f02">&#9670;&nbsp;</a></span>freeNode()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void freeNode </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>nodeToBeDeleted</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>This function when called will delete the node with the index presented as an argument, and will put back that node into the array. </p>
+<div class="fragment"><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;                                   {</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <a class="code" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[nodeToBeDeleted].next = avail;</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    avail = nodeToBeDeleted;</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a73e11e0871f56342a30da93b6c93e8be"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a73e11e0871f56342a30da93b6c93e8be">&#9670;&nbsp;</a></span>getnode()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int getnode </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>This will return the index of the first free node present in the avail list </p>
+<div class="fragment"><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;              {</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="keywordtype">int</span> NodeIndexToBeReturned = avail;</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    avail = <a class="code" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[avail].next;</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keywordflow">return</span> NodeIndexToBeReturned;</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="afcb07da7984e20b3207934696791f5df"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#afcb07da7984e20b3207934696791f5df">&#9670;&nbsp;</a></span>insertAtTheBeginning()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void insertAtTheBeginning </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>data</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>The function will insert the given data into the front of the linked list. </p>
+<div class="fragment"><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;                                    {</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    <span class="keywordtype">int</span> newNode = <a class="code" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#a73e11e0871f56342a30da93b6c93e8be">getnode</a>();</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    <a class="code" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[newNode].data = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <a class="code" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">AvailArray</a>[newNode].next = head;</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    head = newNode;</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/dce/linkedlist__implentation__usingarray_8cpp_afcb07da7984e20b3207934696791f5df_cgraph.svg" width="274" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;           {</div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    initialise_list();</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    <span class="keywordtype">int</span> x, y, z;</div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    <span class="keywordflow">for</span> (;;) {</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1. Insert At The Beginning&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2. Insert At The End&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3. Display&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4.Exit&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter Your choice&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; z;</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        <span class="keywordflow">switch</span> (z) {</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        <span class="keywordflow">case</span> 1:</div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number you want to enter&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; x;</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;            <a class="code" href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#afcb07da7984e20b3207934696791f5df">insertAtTheBeginning</a>(x);</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;            <span class="keywordflow">break</span>;</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;        <span class="keywordflow">case</span> 2:</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number you want to enter&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; y;</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;            insertAtTheEnd(y);</div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;            <span class="keywordflow">break</span>;</div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;        <span class="keywordflow">case</span> 3:</div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;                &lt;&lt; <span class="stringliteral">&quot;The linked list contains the following element in order&quot;</span></div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;                &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;            display();</div>
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+<table class="directory">
+  <tr class="even"><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html#a88b4aa3e66392a3eabbf2517a9a79a02">capacity</a></td><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
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+  <tr class="even"><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html#a37ac126eabb0c3ce04047172abccca29">deleteKey</a>(int i)</td><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></td><td class="entry"></td></tr>
+  <tr><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html#a4014f1edaed0bd7db0c0d2ca53228980">extractMin</a>()</td><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></td><td class="entry"></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html#a336ac71f0d857269fe9a98058a3cd130">getMin</a>()</td><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">harr</a></td><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">heap_size</a></td><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html#aef78f3384f5a0ae880ad0883d2d44b82">insertKey</a>(int k)</td><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></td><td class="entry"></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html#aa8c6c141e3de664819686aa637e1afca">left</a>(int i)</td><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html#ad89ca80a217655a735d266618197965e">MinHeap</a>(int capacity)</td><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></td><td class="entry"></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html#aaef438c1056492cb62c4a4d9035b5cad">MinHeapify</a>(int)</td><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>parent</b>(int i) (defined in <a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a>)</td><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html#ac760b85cf90265b8d674b942a43fb70e">right</a>(int i)</td><td class="entry"><a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+</table></div><!-- contents -->
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+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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diff --git a/d4/d21/least__common__multiple_8cpp.html b/d4/d21/least__common__multiple_8cpp.html
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+   &#160;<span id="projectnumber">1.0.0</span>
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+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">least_common_multiple.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for least_common_multiple.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d5/d8b/least__common__multiple_8cpp__incl.svg" width="228" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a8ba1fc66e4134ab25b2602b323150563"><td class="memItemLeft" align="right" valign="top">unsigned int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a> (unsigned int x, unsigned int y)</td></tr>
+<tr class="separator:a8ba1fc66e4134ab25b2602b323150563"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aa8d0e241db517813725e721a152e3a25"><td class="memItemLeft" align="right" valign="top">unsigned int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a> (unsigned int x, unsigned int y)</td></tr>
+<tr class="separator:aa8d0e241db517813725e721a152e3a25"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a88ec9ad42717780d6caaff9d3d6977f9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a> ()</td></tr>
+<tr class="separator:a88ec9ad42717780d6caaff9d3d6977f9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Copyright 2020 </p><dl class="section author"><dt>Author</dt><dd>tjgurwara99</dd></dl>
+<p>A basic implementation of LCM function </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a8ba1fc66e4134ab25b2602b323150563"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a8ba1fc66e4134ab25b2602b323150563">&#9670;&nbsp;</a></span>gcd()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">unsigned int gcd </td>
+          <td>(</td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>y</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Function for finding greatest common divisor of two numbers. @params two integers x and y whose gcd we want to find. </p><dl class="section return"><dt>Returns</dt><dd>greatest common divisor of x and y. </dd></dl>
+<div class="fragment"><div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;                                                 {</div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;    <span class="keywordflow">if</span> (x == 0) {</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;        <span class="keywordflow">return</span> y;</div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;    }</div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;    <span class="keywordflow">if</span> (y == 0) {</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;        <span class="keywordflow">return</span> x;</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;    }</div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    <span class="keywordflow">if</span> (x == y) {</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;        <span class="keywordflow">return</span> x;</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    }</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <span class="keywordflow">if</span> (x &gt; y) {</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;        <span class="comment">// The following is valid because we have checked whether y == 0</span></div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160; </div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;        <span class="keywordtype">int</span> temp = x / y;</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(y, x - temp * y);</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    }</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="comment">// Again the following is valid because we have checked whether x == 0</span></div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160; </div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <span class="keywordtype">int</span> temp = y / x;</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keywordflow">return</span> <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y - temp * x);</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="aa8d0e241db517813725e721a152e3a25"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa8d0e241db517813725e721a152e3a25">&#9670;&nbsp;</a></span>lcm()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">unsigned int lcm </td>
+          <td>(</td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>y</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Function for finding the least common multiple of two numbers. @params integer x and y whose lcm we want to find. </p><dl class="section return"><dt>Returns</dt><dd>lcm of x and y using the relation x * y = gcd(x, y) * lcm(x, y) </dd></dl>
+<div class="fragment"><div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;{ <span class="keywordflow">return</span> x * y / <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y); }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/d21/least__common__multiple_8cpp_aa8d0e241db517813725e721a152e3a25_cgraph.svg" width="144" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
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+          <td class="memname">int main </td>
+          <td>(</td>
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+          <td></td>
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+<p>Main function </p>
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+<p>Function for testing the <a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm()</a> functions with some assert statements. </p>
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+<a href="#func-members">Functions</a> &#124;
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+<div class="title">fibonacci_fast.cpp File Reference</div>  </div>
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+<div class="contents">
+
+<p>Faster computation of Fibonacci series.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cinttypes&gt;</code><br />
+<code>#include &lt;cstdio&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for fibonacci_fast.cpp:</div>
+<div class="dyncontent">
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+</div>
+</div>
+</div><table class="memberdecls">
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+Functions</h2></td></tr>
+<tr class="memitem:a5712edca101204eca8accdb1e096707f"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a> (uint64_t n)</td></tr>
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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+<tr class="memitem:a3ba232425d45f9e9c0b87a8cf7ab69d9"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a> [<a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a692ac7187ee88621a9f78fca78ec498d">MAX</a>] = {0}</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Faster computation of Fibonacci series. </p>
+<p>An efficient way to calculate nth fibonacci number faster and simpler than \(O(n\log n)\) method of matrix exponentiation This works by using both recursion and dynamic programming. as 93rd fibonacci exceeds 19 digits, which cannot be stored in a single long long variable, we can only use it till 92nd fibonacci we can use it for 10000th fibonacci etc, if we implement bigintegers. This algorithm works with the fact that nth fibonacci can easily found if we have already found n/2th or (n+1)/2th fibonacci It is a property of fibonacci similar to matrix exponentiation.</p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/de4/fibonacci__large_8cpp.html" title="Computes N^th Fibonacci number given as input argument. Uses custom build arbitrary integers library ...">fibonacci_large.cpp</a>, <a class="el" href="../../d9/d89/fibonacci_8cpp.html" title="Generate fibonacci sequence.">fibonacci.cpp</a>, <a class="el" href="../../de/d47/string__fibonacci_8cpp.html" title="This Programme returns the Nth fibonacci as a string.">string_fibonacci.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a5712edca101204eca8accdb1e096707f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a5712edca101204eca8accdb1e096707f">&#9670;&nbsp;</a></span>fib()</h2>
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+          <td class="memname">uint64_t fib </td>
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+</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#a3ba232425d45f9e9c0b87a8cf7ab69d9">&#9670;&nbsp;</a></span>f</h2>
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+<p>Array of computed fibonacci numbers </p>
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+<div class="title">gcd_recursive_euclidean.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Compute the greatest common denominator of two integers using <em>recursive form</em> of <a href="https://en.wikipedia.org/wiki/Euclidean_algorithm">Euclidean algorithm</a>  
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+Functions</h2></td></tr>
+<tr class="memitem:ae48807fa2b7000afae599e67f327545e"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> (int num1, int num2)</td></tr>
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Compute the greatest common denominator of two integers using <em>recursive form</em> of <a href="https://en.wikipedia.org/wiki/Euclidean_algorithm">Euclidean algorithm</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html" title="Compute the greatest common denominator of two integers using iterative form of Euclidean algorithm">gcd_iterative_euclidean.cpp</a>, <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp.html" title="This program aims at calculating the GCD of n numbers by division method.">gcd_of_n_numbers.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae48807fa2b7000afae599e67f327545e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae48807fa2b7000afae599e67f327545e">&#9670;&nbsp;</a></span>gcd()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int gcd </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>num1</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>num2</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>algorithm </p>
+<div class="fragment"><div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;                            {</div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;    <span class="keywordflow">if</span> (num1 &lt;= 0 | num2 &lt;= 0) {</div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;        <span class="keywordflow">throw</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/domain_error.html">std::domain_error</a>(<span class="stringliteral">&quot;Euclidean algorithm domain is for ints &gt; 0&quot;</span>);</div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;    }</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;    <span class="keywordflow">if</span> (num1 == num2) {</div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;        <span class="keywordflow">return</span> num1;</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    }</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160; </div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    <span class="comment">// Everything divides 0</span></div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    <span class="keywordflow">if</span> (num1 == 0)</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;        <span class="keywordflow">return</span> num2;</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <span class="keywordflow">if</span> (num2 == 0)</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;        <span class="keywordflow">return</span> num1;</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160; </div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <span class="comment">// base case</span></div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="keywordflow">if</span> (num1 == num2)</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;        <span class="keywordflow">return</span> num1;</div>
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+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="comment">// a is greater</span></div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <span class="keywordflow">if</span> (num1 &gt; num2)</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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+<div class="ttc" id="adomain_error_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/domain_error.html">std::domain_error</a></div><div class="ttdoc">STL class.</div></div>
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+<p>Library functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</a> of a given matrix.  
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+<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;cstdlib&gt;</code><br />
+<code>#include &lt;iomanip&gt;</code><br />
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+<tr class="memitem:a5422c76bfa322620de611083bd518d71"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">qr_algorithm::vector_proj</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;b)</td></tr>
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+<tr class="memitem:ab1ac74497ffb2101040cc1efe3546de8"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:ab1ac74497ffb2101040cc1efe3546de8"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#ab1ac74497ffb2101040cc1efe3546de8">qr_algorithm::qr_decompose</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt;&gt; &amp;A, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt;&gt; *Q, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt;&gt; *R)</td></tr>
+<tr class="separator:ab1ac74497ffb2101040cc1efe3546de8"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Library functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</a> of a given matrix. </p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
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+    <li class="footer">Generated on Fri Jun 19 2020 16:06:44 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+    [ "qr_decompose", "d4/d68/qr__decompose_8h.html#ab1ac74497ffb2101040cc1efe3546de8", null ],
+    [ "vector_dot", "d4/d68/qr__decompose_8h.html#a8ea313a1a1b5f9d0e3e332c29c6446ec", null ],
+    [ "vector_mag", "d4/d68/qr__decompose_8h.html#ad16da2183db22378435042f26af43d5f", null ],
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+<div class="header">
+  <div class="headertitle">
+<div class="title">qr_decompose.h</div>  </div>
+</div><!--header-->
+<div class="contents">
+<a href="../../d4/d68/qr__decompose_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/**</span></div>
+<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment"> * @file</span></div>
+<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment"> * \brief Library functions to compute [QR</span></div>
+<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment"> * decomposition](https://en.wikipedia.org/wiki/QR_decomposition) of a given</span></div>
+<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment"> * matrix.</span></div>
+<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment"> * \author [Krishna Vedala](https://github.com/kvedala)</span></div>
+<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment"> */</span></div>
+<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160; </div>
+<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="preprocessor">#ifndef NUMERICAL_METHODS_QR_DECOMPOSE_H_</span></div>
+<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#define NUMERICAL_METHODS_QR_DECOMPOSE_H_</span></div>
+<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160; </div>
+<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#include &lt;cmath&gt;</span></div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &lt;cstdlib&gt;</span></div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &lt;iomanip&gt;</span></div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &lt;limits&gt;</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#include &lt;numeric&gt;</span></div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="preprocessor">#include &lt;valarray&gt;</span></div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#include &lt;omp.h&gt;</span></div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00023"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html">   23</a></span>&#160;<span class="comment">/** \namespace qr_algorithm</span></div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment"> * \brief Functions to compute [QR</span></div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment"> * decomposition](https://en.wikipedia.org/wiki/QR_decomposition) of any</span></div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment"> * rectangular matrix</span></div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment"> */</span></div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="keyword">namespace </span><a class="code" href="../../d2/d3b/namespaceqr__algorithm.html">qr_algorithm</a> {<span class="comment"></span></div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="comment">/**</span></div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="comment"> * operator to print a matrix</span></div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="comment"> */</span></div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
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+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;                         <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a>&gt; <span class="keyword">const</span> &amp;v) {</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> width = 12;</div>
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+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;                &lt;&lt; v[row][col];</div>
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+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="comment"> * operator to print a vector</span></div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;<span class="comment"> */</span></div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
+<div class="line"><a name="l00053"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a240edf2b6b5942c0e5f2c9d3e326797f">   53</a></span>&#160;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;<a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a7c63c78d6839b8ad73b77c161210b514">operator&lt;&lt;</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;out, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> <span class="keyword">const</span> &amp;v) {</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
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+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++) {</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::right</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;            &lt;&lt; v[row];</div>
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+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;<span class="comment">/**</span></div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="comment"> * Compute dot product of two vectors of equal lengths</span></div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;<span class="comment"> *</span></div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;<span class="comment"> * If \f$\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\f$ and</span></div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="comment"> * \f$\vec{b}=\left[b_0,b_1,b_1,...,b_L\right]\f$ then</span></div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="comment"> * \f$\vec{a}\cdot\vec{b}=\displaystyle\sum_{i=0}^L a_i\times b_i\f$</span></div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;<span class="comment"> *</span></div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="comment"> * \returns \f$\vec{a}\cdot\vec{b}\f$</span></div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="comment"> */</span></div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
+<div class="line"><a name="l00076"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">   76</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(<span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, <span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;b) {</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="keywordflow">return</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> * b).sum();</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <span class="comment">// could also use following</span></div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    <span class="comment">// return std::inner_product(std::begin(a), std::end(a), std::begin(b),</span></div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <span class="comment">// 0.f);</span></div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;}</div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;<span class="comment">/**</span></div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;<span class="comment"> * Compute magnitude of vector.</span></div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="comment"> *</span></div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;<span class="comment"> * If \f$\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\f$ then</span></div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="comment"> * \f$\left|\vec{a}\right|=\sqrt{\displaystyle\sum_{i=0}^L a_i^2}\f$</span></div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="comment"> *</span></div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;<span class="comment"> * \returns \f$\left|\vec{a}\right|\f$</span></div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;<span class="comment"> */</span></div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
+<div class="line"><a name="l00092"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">   92</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">vector_mag</a>(<span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>) {</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="keywordtype">double</span> dot = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>);</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(dot);</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;}</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;<span class="comment">/**</span></div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;<span class="comment"> * Compute projection of vector \f$\vec{a}\f$ on \f$\vec{b}\f$ defined as</span></div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;<span class="comment"> * \f[\text{proj}_\vec{b}\vec{a}=\frac{\vec{a}\cdot\vec{b}}{\left|\vec{b}\right|^2}\vec{b}\f]</span></div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;<span class="comment"> *</span></div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;<span class="comment"> * \returns NULL if error, otherwise pointer to output</span></div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;<span class="comment"> */</span></div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
+<div class="line"><a name="l00104"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">  104</a></span>&#160;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">vector_proj</a>(<span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>,</div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                             <span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;b) {</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <span class="keywordtype">double</span> num = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b);</div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    <span class="keywordtype">double</span> deno = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(b, b);</div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;<span class="comment">    /*! check for division by zero using machine epsilon */</span></div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="keywordflow">if</span> (deno &lt;= <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits&lt;double&gt;::epsilon</a>()) {</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;[&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;] Possible division by zero\n&quot;</span>;</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;  <span class="comment">// return vector a back</span></div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    }</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    <span class="keywordtype">double</span> scalar = num / deno;</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160; </div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <span class="keywordflow">return</span> b * scalar;</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;}</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;<span class="comment">/**</span></div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;<span class="comment"> * Decompose matrix \f$A\f$ using [Gram-Schmidt</span></div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;<span class="comment"> *process](https://en.wikipedia.org/wiki/QR_decomposition).</span></div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="comment"> *</span></div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;<span class="comment"> * \f{eqnarray*}{</span></div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="comment"> * \text{given that}\quad A &amp;=&amp;</span></div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;<span class="comment"> *\left[\mathbf{a}_1,\mathbf{a}_2,\ldots,\mathbf{a}_{N-1},\right]\\</span></div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;<span class="comment"> * \text{where}\quad\mathbf{a}_i &amp;=&amp;</span></div>
+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;<span class="comment"> * \left[a_{0i},a_{1i},a_{2i},\ldots,a_{(M-1)i}\right]^T\quad\ldots\mbox{(column</span></div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;<span class="comment"> * vectors)}\\</span></div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="comment"> * \text{then}\quad\mathbf{u}_i &amp;=&amp; \mathbf{a}_i</span></div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;<span class="comment"> *-\sum_{j=0}^{i-1}\text{proj}_{\mathbf{u}_j}\mathbf{a}_i\\</span></div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="comment"> * \mathbf{e}_i &amp;=&amp;\frac{\mathbf{u}_i}{\left|\mathbf{u}_i\right|}\\</span></div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;<span class="comment"> * Q &amp;=&amp; \begin{bmatrix}\mathbf{e}_0 &amp; \mathbf{e}_1 &amp; \mathbf{e}_2 &amp; \dots &amp;</span></div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="comment"> * \mathbf{e}_{N-1}\end{bmatrix}\\</span></div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="comment"> * R &amp;=&amp; \begin{bmatrix}\langle\mathbf{e}_0\,,\mathbf{a}_0\rangle &amp;</span></div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="comment"> * \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &amp;</span></div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="comment"> * \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp; \dots \\</span></div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;<span class="comment"> *                  0 &amp; \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &amp;</span></div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;<span class="comment"> * \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp; \dots\\</span></div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;<span class="comment"> *                  0 &amp; 0 &amp; \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp;</span></div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;<span class="comment"> * \dots\\ \vdots &amp; \vdots &amp; \vdots &amp; \ddots</span></div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="comment"> *      \end{bmatrix}\\</span></div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="comment"> * \f}</span></div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="comment"> */</span></div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
+<div class="line"><a name="l00146"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#ab1ac74497ffb2101040cc1efe3546de8">  146</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#ab1ac74497ffb2101040cc1efe3546de8">qr_decompose</a>(</div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;    <span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a>&gt; &amp;A, <span class="comment">/**&lt; input matrix to decompose */</span></div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a>&gt; *Q,       <span class="comment">/**&lt; output decomposed matrix */</span></div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a>&gt; *R        <span class="comment">/**&lt; output decomposed matrix */</span></div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;) {</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> ROWS = A.size();        <span class="comment">// number of rows of A</span></div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> COLUMNS = A[0].size();  <span class="comment">// number of columns of A</span></div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> col_vector(ROWS);</div>
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+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> tmp_vector(ROWS);</div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160; </div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; COLUMNS; i++) {</div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;        <span class="comment">/* for each column =&gt; R is a square matrix of NxN */</span></div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;        <span class="keywordtype">int</span> j;</div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;        R[0][i] = 0.; <span class="comment">/* make R upper triangular */</span></div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160; </div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;        <span class="comment">/* get corresponding Q vector */</span></div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;<span class="comment">// parallelize on threads</span></div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;        <span class="keywordflow">for</span> (j = 0; j &lt; ROWS; j++) {</div>
+<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;            tmp_vector[j] = A[j][i]; <span class="comment">/* accumulator for uk */</span></div>
+<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;            col_vector[j] = A[j][i];</div>
+<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;        }</div>
+<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;        <span class="keywordflow">for</span> (j = 0; j &lt; i; j++) {</div>
+<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = 0; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; ROWS; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
+<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;                col_vector2[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] = Q[0][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>][j];</div>
+<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;            }</div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;            col_vector2 = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">vector_proj</a>(col_vector, col_vector2);</div>
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+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;        }</div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160; </div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;        <span class="keywordtype">double</span> mag = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">vector_mag</a>(tmp_vector);</div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160; </div>
+<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="comment">// parallelize on threads</span></div>
+<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;<span class="preprocessor">#endif</span></div>
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+<p><a href="https://en.wikipedia.org/wiki/Shell_sort">Shell sort</a> algorithm  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
+<code>#include &lt;cstdlib&gt;</code><br />
+<code>#include &lt;ctime&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;utility&gt;</code><br />
+<code>#include &lt;vector&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for shell_sort2.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d86/shell__sort2_8cpp__incl.svg" width="496" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="namespaces"></a>
+Namespaces</h2></td></tr>
+<tr class="memitem:d5/d91/namespacesorting"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html">sorting</a></td></tr>
+<tr class="memdesc:d5/d91/namespacesorting"><td class="mdescLeft">&#160;</td><td class="mdescRight">Sorting algorithms. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a951127aea9d7e1e53ea9ae0868633246"><td class="memTemplParams" colspan="2">template&lt;class T &gt; </td></tr>
+<tr class="memitem:a951127aea9d7e1e53ea9ae0868633246"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a> (T *arr, size_t LEN)</td></tr>
+<tr class="separator:a951127aea9d7e1e53ea9ae0868633246"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a63aaff7cabfa3da2da8b9477b5fad9d6"><td class="memTemplParams" colspan="2">template&lt;typename T , size_t N&gt; </td></tr>
+<tr class="memitem:a63aaff7cabfa3da2da8b9477b5fad9d6"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d7a/shell__sort2_8cpp.html#a63aaff7cabfa3da2da8b9477b5fad9d6">show_data</a> (T(&amp;arr)[N])</td></tr>
+<tr class="separator:a63aaff7cabfa3da2da8b9477b5fad9d6"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a5669396c6a6b1e14b97589b6e37980aa"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:a5669396c6a6b1e14b97589b6e37980aa"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#a5669396c6a6b1e14b97589b6e37980aa">sorting::shell_sort</a> (T *arr, size_t LEN)</td></tr>
+<tr class="separator:a5669396c6a6b1e14b97589b6e37980aa"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a4d76603c54d3dc56146e92d10a043924"><td class="memTemplParams" colspan="2">template&lt;typename T , size_t N&gt; </td></tr>
+<tr class="memitem:a4d76603c54d3dc56146e92d10a043924"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#a4d76603c54d3dc56146e92d10a043924">sorting::shell_sort</a> (T(&amp;arr)[N])</td></tr>
+<tr class="separator:a4d76603c54d3dc56146e92d10a043924"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:af2c5b92cbfe73f63f6074c61b0a45331"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:af2c5b92cbfe73f63f6074c61b0a45331"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">sorting::shell_sort</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; *arr)</td></tr>
+<tr class="separator:af2c5b92cbfe73f63f6074c61b0a45331"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a7eb77daed2cf1513f6d68c47a1c2db1c"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:a7eb77daed2cf1513f6d68c47a1c2db1c"><td class="memTemplItemLeft" align="right" valign="top">int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d7a/shell__sort2_8cpp.html#a7eb77daed2cf1513f6d68c47a1c2db1c">compare</a> (const void *<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, const void *b)</td></tr>
+<tr class="separator:a7eb77daed2cf1513f6d68c47a1c2db1c"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a895b313cb2671e8f712040460325573e"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">test_int</a> (const int NUM_DATA)</td></tr>
+<tr class="separator:a895b313cb2671e8f712040460325573e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a22ea0d1f7943ebb4371d31e44b465b6d"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">test_f</a> (const int NUM_DATA)</td></tr>
+<tr class="separator:a22ea0d1f7943ebb4371d31e44b465b6d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d7a/shell__sort2_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
+<tr class="separator:a0ddf1224851353fc92bfbff6f499fa97"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Shell_sort">Shell sort</a> algorithm </p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a7eb77daed2cf1513f6d68c47a1c2db1c"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a7eb77daed2cf1513f6d68c47a1c2db1c">&#9670;&nbsp;</a></span>compare()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">int <a class="el" href="../../d1/db3/structcompare.html">compare</a> </td>
+          <td>(</td>
+          <td class="paramtype">const void *&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const void *&#160;</td>
+          <td class="paramname"><em>b</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>function to compare sorting using cstdlib's qsort </p>
+<div class="fragment"><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;                                          {</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    T arg1 = *<span class="keyword">static_cast&lt;</span><span class="keyword">const </span>T *<span class="keyword">&gt;</span>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>);</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    T arg2 = *<span class="keyword">static_cast&lt;</span><span class="keyword">const </span>T *<span class="keyword">&gt;</span>(b);</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160; </div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <span class="keywordflow">if</span> (arg1 &lt; arg2)</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="keywordflow">if</span> (arg1 &gt; arg2)</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;        <span class="keywordflow">return</span> 1;</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160; </div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    <span class="comment">//  return (arg1 &gt; arg2) - (arg1 &lt; arg2); // possible shortcut</span></div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    <span class="comment">//  return arg1 - arg2; // erroneous shortcut (fails if INT_MIN is present)</span></div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a0ddf1224851353fc92bfbff6f499fa97"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>argc</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char *&#160;</td>
+          <td class="paramname"><em>argv</em>[]&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;                                 {</div>
+<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    <span class="comment">// initialize random number generator - once per program</span></div>
+<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(NULL));</div>
+<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160; </div>
+<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    <a class="code" href="../../d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">test_int</a>(100);  <span class="comment">// test with sorting random array of 100 values</span></div>
+<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 - 100 int values - passed. \n&quot;</span>;</div>
+<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <a class="code" href="../../d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">test_int</a>(1000);  <span class="comment">// test with sorting random array of 1000 values</span></div>
+<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 - 1000 int values - passed.\n&quot;</span>;</div>
+<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    <a class="code" href="../../d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">test_int</a>(10000);  <span class="comment">// test with sorting random array of 10000 values</span></div>
+<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 - 10000 int values - passed.\n&quot;</span>;</div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160; </div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;    <a class="code" href="../../d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">test_f</a>(100);  <span class="comment">// test with sorting random array of 100 values</span></div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 - 100 float values - passed. \n&quot;</span>;</div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    <a class="code" href="../../d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">test_f</a>(1000);  <span class="comment">// test with sorting random array of 1000 values</span></div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 - 1000 float values - passed.\n&quot;</span>;</div>
+<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    <a class="code" href="../../d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">test_f</a>(10000);  <span class="comment">// test with sorting random array of 10000 values</span></div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 - 10000 float values - passed.\n&quot;</span>;</div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160; </div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    <span class="keywordtype">int</span> i, NUM_DATA;</div>
+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160; </div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    <span class="keywordflow">if</span> (argc == 2)</div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;        NUM_DATA = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    <span class="keywordflow">else</span></div>
+<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;        NUM_DATA = 200;</div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160; </div>
+<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;    <span class="comment">// int array = new int[NUM_DATA];</span></div>
+<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    <span class="keywordtype">int</span> *<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> = <span class="keyword">new</span> <span class="keywordtype">int</span>[NUM_DATA];</div>
+<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <span class="comment">// int array2 = new int[NUM_DATA];</span></div>
+<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;    <span class="keywordtype">int</span> range = 1800;</div>
+<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160; </div>
+<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a>(NULL));</div>
+<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; NUM_DATA; i++) {</div>
+<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;        <span class="comment">// allocate random numbers in the given range</span></div>
+<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - (range &gt;&gt; 1);</div>
+<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    }</div>
+<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160; </div>
+<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Unsorted original data: &quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    <a class="code" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a>(<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
+<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    <a class="code" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);  <span class="comment">// perform sorting</span></div>
+<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160; </div>
+<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
+<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;Data Sorted using custom implementation: &quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    <a class="code" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a>(<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
+<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160; </div>
+<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;    <span class="keywordtype">double</span> elapsed_time = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) * 1.<a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a> / CLOCKS_PER_SEC;</div>
+<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting: &quot;</span> &lt;&lt; elapsed_time &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160; </div>
+<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;    <span class="keyword">delete</span>[] <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
+<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/d7a/shell__sort2_8cpp_a0ddf1224851353fc92bfbff6f499fa97_cgraph.svg" width="542" height="398"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a951127aea9d7e1e53ea9ae0868633246"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a951127aea9d7e1e53ea9ae0868633246">&#9670;&nbsp;</a></span>show_data() <span class="overload">[1/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">void show_data </td>
+          <td>(</td>
+          <td class="paramtype">T *&#160;</td>
+          <td class="paramname"><em>arr</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">size_t&#160;</td>
+          <td class="paramname"><em>LEN</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>pretty print array </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">arr</td><td>array to print </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">LEN</td><td>length of array to print </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;                                   {</div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;    <span class="keywordtype">size_t</span> i;</div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160; </div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; LEN; i++) {</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; arr[i] &lt;&lt; <span class="stringliteral">&quot;, &quot;</span>;</div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    }</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/d7a/shell__sort2_8cpp_a951127aea9d7e1e53ea9ae0868633246_cgraph.svg" width="216" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a63aaff7cabfa3da2da8b9477b5fad9d6"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a63aaff7cabfa3da2da8b9477b5fad9d6">&#9670;&nbsp;</a></span>show_data() <span class="overload">[2/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T , size_t N&gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">void show_data </td>
+          <td>(</td>
+          <td class="paramtype">T(&amp;)&#160;</td>
+          <td class="paramname"><em>arr</em>[N]</td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>pretty print array </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">arr</td><td>array to print </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">N</td><td>length of array to print </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;                            {</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <a class="code" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a>(arr, N);</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/d7a/shell__sort2_8cpp_a63aaff7cabfa3da2da8b9477b5fad9d6_cgraph.svg" width="350" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a22ea0d1f7943ebb4371d31e44b465b6d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a22ea0d1f7943ebb4371d31e44b465b6d">&#9670;&nbsp;</a></span>test_f()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test_f </td>
+          <td>(</td>
+          <td class="paramtype">const int&#160;</td>
+          <td class="paramname"><em>NUM_DATA</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test implementation of shell_sort on float arrays by comparing results against <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/qsort.html">std::qsort</a>. </p>
+<div class="fragment"><div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;                                {</div>
+<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    <span class="comment">// int array = new int[NUM_DATA];</span></div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;    <span class="keywordtype">float</span> *<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> = <span class="keyword">new</span> <span class="keywordtype">float</span>[NUM_DATA];</div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    <span class="keywordtype">float</span> *data2 = <span class="keyword">new</span> <span class="keywordtype">float</span>[NUM_DATA];</div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    <span class="comment">// int array2 = new int[NUM_DATA];</span></div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="keywordtype">int</span> range = 1000;</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160; </div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++) {</div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = data2[i] = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - (range &gt;&gt; 1)) / 100.;</div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;    }</div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160; </div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;    <span class="comment">/* sort using our implementation */</span></div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;    <a class="code" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    <span class="keywordtype">double</span> elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting using shell_sort2: &quot;</span> &lt;&lt; elapsed_time</div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160; </div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;    <span class="comment">/* sort using std::qsort */</span></div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;    start = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/qsort.html">std::qsort</a>(data2, NUM_DATA, <span class="keyword">sizeof</span>(data2[0]), <a class="code" href="../../d1/db3/structcompare.html">compare&lt;float&gt;</a>);</div>
+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160; </div>
+<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;    elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
+<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting using std::qsort: &quot;</span> &lt;&lt; elapsed_time</div>
+<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
+<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160; </div>
+<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++) {</div>
+<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;        assert(<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] == data2[i]);  <span class="comment">// ensure that our sorting results match</span></div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;                                      <span class="comment">// the standard results</span></div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    }</div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160; </div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <span class="keyword">delete</span>[] <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    <span class="keyword">delete</span>[] data2;</div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/d7a/shell__sort2_8cpp_a22ea0d1f7943ebb4371d31e44b465b6d_cgraph.svg" width="412" height="190"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a895b313cb2671e8f712040460325573e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a895b313cb2671e8f712040460325573e">&#9670;&nbsp;</a></span>test_int()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test_int </td>
+          <td>(</td>
+          <td class="paramtype">const int&#160;</td>
+          <td class="paramname"><em>NUM_DATA</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test implementation of shell_sort on integer arrays by comparing results against <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/qsort.html">std::qsort</a>. </p>
+<div class="fragment"><div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                                  {</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <span class="comment">// int array = new int[NUM_DATA];</span></div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    <span class="keywordtype">int</span> *<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> = <span class="keyword">new</span> <span class="keywordtype">int</span>[NUM_DATA];</div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    <span class="keywordtype">int</span> *data2 = <span class="keyword">new</span> <span class="keywordtype">int</span>[NUM_DATA];</div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <span class="comment">// int array2 = new int[NUM_DATA];</span></div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="keywordtype">int</span> range = 1800;</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160; </div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++)</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = data2[i] = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - (range &gt;&gt; 1);</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    <span class="comment">/* sort using our implementation */</span></div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <a class="code" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    <span class="keywordtype">double</span> elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time spent sorting using shell_sort2: &quot;</span> &lt;&lt; elapsed_time</div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160; </div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    <span class="comment">/* sort using std::qsort */</span></div>
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+<p>Library to perform arithmatic operations on arbitrarily large numbers.  
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+<div class="header">
+  <div class="headertitle">
+<div class="title">large_number.h</div>  </div>
+</div><!--header-->
+<div class="contents">
+<a href="../../d4/d86/large__number_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/**</span></div>
+<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment"> * @file</span></div>
+<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment"> * @brief Library to perform arithmatic operations on arbitrarily large</span></div>
+<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment"> * numbers.</span></div>
+<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment"> * \author [Krishna Vedala](https://github.com/kvedala)</span></div>
+<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment"> */</span></div>
+<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160; </div>
+<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="preprocessor">#ifndef MATH_LARGE_NUMBER_H_</span></div>
+<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="preprocessor">#define MATH_LARGE_NUMBER_H_</span></div>
+<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#include &lt;algorithm&gt;</span></div>
+<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#include &lt;cassert&gt;</span></div>
+<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#include &lt;cinttypes&gt;</span></div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &lt;cstring&gt;</span></div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="preprocessor">#include &lt;type_traits&gt;</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">/**</span></div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment"> * Store large unsigned numbers as a C++ vector</span></div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment"> * The class provides convenience functions to add a</span></div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment"> * digit to the number, perform multiplication of</span></div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment"> * large number with long unsigned integers.</span></div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment"> **/</span></div>
+<div class="line"><a name="l00024"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html">   24</a></span>&#160;<span class="keyword">class </span><a class="code" href="../../db/d82/classlarge__number.html">large_number</a> {</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160; <span class="keyword">public</span>:<span class="comment"></span></div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment">    /**&lt; initializer with value = 1 */</span></div>
+<div class="line"><a name="l00027"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">   27</a></span>&#160;    <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>() { <a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(1); }</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160; </div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <span class="comment">// /**&lt; initializer from an integer */</span></div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="comment">// explicit large_number(uint64_t n) {</span></div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="comment">//     uint64_t carry = n;</span></div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="comment">//     do {</span></div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="comment">//         add_digit(carry % 10);</span></div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <span class="comment">//         carry /= 10;</span></div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="comment">//     } while (carry != 0);</span></div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <span class="comment">// }</span></div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="comment">    /**&lt; initializer from an integer */</span></div>
+<div class="line"><a name="l00039"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#af4598f1f2794b5e17e10c25e0501e41a">   39</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="../../db/d82/classlarge__number.html#af4598f1f2794b5e17e10c25e0501e41a">large_number</a>(<span class="keywordtype">int</span> n) {</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        <span class="keywordtype">int</span> carry = n;</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;        <span class="keywordflow">do</span> {</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;            <a class="code" href="../../db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">add_digit</a>(carry % 10);</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;            carry /= 10;</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        } <span class="keywordflow">while</span> (carry != 0);</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    }</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="comment">    /**&lt; initializer from another large_number */</span></div>
+<div class="line"><a name="l00048"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#a0b1efd203274e38a67b78937dfb9b872">   48</a></span>&#160;    <a class="code" href="../../db/d82/classlarge__number.html#a0b1efd203274e38a67b78937dfb9b872">large_number</a>(<span class="keyword">const</span> <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> &amp;<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>) : <a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>.<a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>) {}</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="comment">    /**&lt; initializer from a vector */</span></div>
+<div class="line"><a name="l00051"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#a76ddf1ed1b00fb8c107ea56f7f91e42f">   51</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="../../db/d82/classlarge__number.html#a76ddf1ed1b00fb8c107ea56f7f91e42f">large_number</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;unsigned char&gt;</a> &amp;vec) : <a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>(vec) {}</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;<span class="comment">    /**&lt; initializer from a string */</span></div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    <span class="keyword">explicit</span> <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(<span class="keywordtype">char</span> <span class="keyword">const</span> *number_str) {</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = strlen(number_str); i &gt; 0; i--) {</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;            <span class="keywordtype">unsigned</span> <span class="keywordtype">char</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = number_str[i - 1] - <span class="charliteral">&#39;0&#39;</span>;</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;            <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &gt;= 0 &amp;&amp; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;= 9)</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;                <a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>);</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        }</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    }</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;<span class="comment">     * Function to check implementation</span></div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00065"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#a959c5c1a982949bbf98e1ea0f9afe6a9">   65</a></span>&#160;    <span class="keyword">static</span> <span class="keywordtype">bool</span> <a class="code" href="../../db/d82/classlarge__number.html#a959c5c1a982949bbf98e1ea0f9afe6a9">test</a>() {</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------ Checking `large_number` class implementations\t&quot;</span></div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;                  &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;        <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>(40);</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        <span class="comment">// 1. test multiplication</span></div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> *= 10;</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> != <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(400)) {</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 1/6 (&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot;!=400)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        }</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 1/6...&quot;</span>;</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        <span class="comment">// 2. test compound addition with integer</span></div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> += 120;</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> != <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(520)) {</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 2/6 (&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot;!=520)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;        }</div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 2/6...&quot;</span>;</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        <span class="comment">// 3. test compound multiplication again</span></div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> *= 10;</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> != <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(5200)) {</div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 3/6 (&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot;!=5200)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;        }</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 3/6...&quot;</span>;</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        <span class="comment">// 4. test increment (prefix)</span></div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        ++<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> != <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(5201)) {</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 4/6 (&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot;!=5201)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;        }</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 4/6...&quot;</span>;</div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        <span class="comment">// 5. test increment (postfix)</span></div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>++;</div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> != <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(5202)) {</div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 5/6 (&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot;!=5202)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        }</div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 5/6...&quot;</span>;</div>
+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        <span class="comment">// 6. test addition with another large number</span></div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> + <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(<span class="stringliteral">&quot;7000000000000000000000000000000&quot;</span>);</div>
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+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 6/6 (&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a></div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                      &lt;&lt; <span class="stringliteral">&quot;!=7000000000000000000000000005202)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;        }</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 6/6...&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;<span class="comment">     * add a digit at MSB to the large number</span></div>
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+<div class="line"><a name="l00118"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">  118</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="../../db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">add_digit</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> value) {</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;        <span class="keywordflow">if</span> (value &gt; 9) {</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;digit &gt; 9!!\n&quot;</span>;</div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;            exit(EXIT_FAILURE);</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        }</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160; </div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;        <a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(value);</div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    }</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;<span class="comment">     * Get number of digits in the number</span></div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00130"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">  130</a></span>&#160;    <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); }</div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;<span class="comment">     * operator over load to access the</span></div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="comment">     * i^th digit conveniently and also</span></div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="comment">     * assign value to it</span></div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00137"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#ace19126cf343a09efc0010735f6e3a8d">  137</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">char</span> &amp;<a class="code" href="../../db/d82/classlarge__number.html#ace19126cf343a09efc0010735f6e3a8d">operator[]</a>(<span class="keywordtype">size_t</span> n) { <span class="keywordflow">return</span> this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>[n]; }</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160; </div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">char</span> &amp;<a class="code" href="../../db/d82/classlarge__number.html#ace19126cf343a09efc0010735f6e3a8d">operator[]</a>(<span class="keywordtype">size_t</span> n)<span class="keyword"> const </span>{</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;        <span class="keywordflow">return</span> this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>[n];</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    }</div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="comment">     * operator overload to compare two numbers</span></div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00146"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#a778428c4761b6ea5e7770743f0eab5ab">  146</a></span>&#160;    <span class="keyword">friend</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;<a class="code" href="../../db/d82/classlarge__number.html#a778428c4761b6ea5e7770743f0eab5ab">operator&lt;&lt;</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;out, <span class="keyword">const</span> <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> &amp;<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>) {</div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>.num_digits(); i &gt; 0; i--)</div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;            out &lt;&lt; static_cast&lt;int&gt;(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>[i - 1]);</div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        <span class="keywordflow">return</span> out;</div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    }</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;<span class="comment">     * operator overload to compare two numbers</span></div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00155"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#a7ba872b9a3ce1f3da6c06c5409663cca">  155</a></span>&#160;    <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="../../db/d82/classlarge__number.html#a7ba872b9a3ce1f3da6c06c5409663cca">operator==</a>(<a class="code" href="../../db/d82/classlarge__number.html">large_number</a> <span class="keyword">const</span> &amp;<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> <span class="keyword">const</span> &amp;b) {</div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;        <span class="keywordtype">size_t</span> N = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>.num_digits();</div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;        <span class="keywordflow">if</span> (N != b.num_digits())</div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;            <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>[i] != b[i])</div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;                <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;<span class="comment">     * operator overload to compare two numbers</span></div>
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+<div class="line"><a name="l00168"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#a72ae1ef050c4c28c50952ecab22d4b94">  168</a></span>&#160;    <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="../../db/d82/classlarge__number.html#a72ae1ef050c4c28c50952ecab22d4b94">operator!=</a>(<a class="code" href="../../db/d82/classlarge__number.html">large_number</a> <span class="keyword">const</span> &amp;<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> <span class="keyword">const</span> &amp;b) {</div>
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+<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="comment">     * operator overload to increment (prefix)</span></div>
+<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00175"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#a622d84883180ff42f04955909adea5a9">  175</a></span>&#160;    <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> &amp;<a class="code" href="../../db/d82/classlarge__number.html#a622d84883180ff42f04955909adea5a9">operator++</a>() {</div>
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+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
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+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="comment">     * operator overload to increment (postfix)</span></div>
+<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00183"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#ac4fafa6289295419d48d444f0ae4b706">  183</a></span>&#160;    <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> &amp;<a class="code" href="../../db/d82/classlarge__number.html#ac4fafa6289295419d48d444f0ae4b706">operator++</a>(<span class="keywordtype">int</span>) {</div>
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+<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;        ++(*this);</div>
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+<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;<span class="comment">     * operator overload to add</span></div>
+<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00192"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#ac27b399ed872731758ec33ebb102730e">  192</a></span>&#160;    <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> &amp;<a class="code" href="../../db/d82/classlarge__number.html#ac27b399ed872731758ec33ebb102730e">operator+=</a>(<a class="code" href="../../db/d82/classlarge__number.html">large_number</a> n) {</div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;        <span class="comment">// if adding with another large_number</span></div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;        <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> *b = <span class="keyword">reinterpret_cast&lt;</span><a class="code" href="../../db/d82/classlarge__number.html">large_number</a> *<span class="keyword">&gt;</span>(&amp;n);</div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">size_t</span> max_L = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>(), b-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>());</div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> carry = 0;</div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;        <span class="keywordtype">size_t</span> i;</div>
+<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;        <span class="keywordflow">for</span> (i = 0; i &lt; max_L || carry != 0; i++) {</div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;            <span class="keywordflow">if</span> (i &lt; b-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>())</div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;                carry += (*b)[i];</div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;            <span class="keywordflow">if</span> (i &lt; this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>())</div>
+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;                carry += (*this)[i];</div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;            <span class="keywordflow">if</span> (i &lt; this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>())</div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;                (*this)[i] = carry % 10;</div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;            <span class="keywordflow">else</span></div>
+<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;                this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">add_digit</a>(carry % 10);</div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;            carry /= 10;</div>
+<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;        }</div>
+<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    }</div>
+<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160; </div>
+<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;    <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> &amp;<a class="code" href="../../db/d82/classlarge__number.html#ac27b399ed872731758ec33ebb102730e">operator+=</a>(<span class="keywordtype">int</span> n) { <span class="keywordflow">return</span> (*<span class="keyword">this</span>) += <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(n); }</div>
+<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;    <span class="comment">// large_number &amp;operator+=(uint64_t n) { return (*this) += large_number(n);</span></div>
+<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;    <span class="comment">// }</span></div>
+<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;<span class="comment">     * operator overload to perform addition</span></div>
+<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;</div>
+<div class="line"><a name="l00220"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#a70d23d67535e67030db570e56c00e16d">  220</a></span>&#160;    <span class="keyword">friend</span> <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> &amp;<a class="code" href="../../db/d82/classlarge__number.html#a70d23d67535e67030db570e56c00e16d">operator+</a>(<span class="keyword">const</span> <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> &amp;<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, <span class="keyword">const</span> T &amp;b) {</div>
+<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;        <span class="keyword">static</span> <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> c = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;        c += b;</div>
+<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;        <span class="keywordflow">return</span> c;</div>
+<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    }</div>
+<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;<span class="comment">     * assignment operator</span></div>
+<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00229"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#aeb22d2aae39d1b1e0bd39c7f47b333eb">  229</a></span>&#160;    <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> &amp;<a class="code" href="../../db/d82/classlarge__number.html#aeb22d2aae39d1b1e0bd39c7f47b333eb">operator=</a>(<span class="keyword">const</span> <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> &amp;b) {</div>
+<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;        this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a> = b.<a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>;</div>
+<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;    }</div>
+<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;<span class="comment">     * operator overload to increment</span></div>
+<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;</div>
+<div class="line"><a name="l00238"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#ab1af3e0f425cdf7ea2039c9dcfe22f0b">  238</a></span>&#160;    <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> &amp;<a class="code" href="../../db/d82/classlarge__number.html#ab1af3e0f425cdf7ea2039c9dcfe22f0b">operator*=</a>(<span class="keyword">const</span> T n) {</div>
+<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;        static_assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/is_integral.html">std::is_integral&lt;T&gt;::value</a>,</div>
+<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;                      <span class="stringliteral">&quot;Must be integer addition unsigned integer types.&quot;</span>);</div>
+<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;        this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2f5571e66305cf68bb8283e4aeda58bc">multiply</a>(n);</div>
+<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;    }</div>
+<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;<span class="comment">     * returns i^th digit as an ASCII character</span></div>
+<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00248"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#af530d90830d385c76973658ff3214f98">  248</a></span>&#160;    <span class="keyword">const</span> <span class="keywordtype">char</span> <a class="code" href="../../db/d82/classlarge__number.html#af530d90830d385c76973658ff3214f98">digit_char</a>(<span class="keywordtype">size_t</span> i)<span class="keyword"> const </span>{</div>
+<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>[<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>() - i - 1] + <span class="charliteral">&#39;0&#39;</span>;</div>
+<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;    }</div>
+<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160; </div>
+<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160; <span class="keyword">private</span>:<span class="comment"></span></div>
+<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;<span class="comment">    /**</span></div>
+<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;<span class="comment">     * multiply large number with another integer and</span></div>
+<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;<span class="comment">     * store the result in the same large number</span></div>
+<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;<span class="comment">     **/</span></div>
+<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;</div>
+<div class="line"><a name="l00258"></a><span class="lineno"><a class="line" href="../../db/d82/classlarge__number.html#a2f5571e66305cf68bb8283e4aeda58bc">  258</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="../../db/d82/classlarge__number.html#a2f5571e66305cf68bb8283e4aeda58bc">multiply</a>(<span class="keyword">const</span> T n) {</div>
+<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;        static_assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/is_integral.html">std::is_integral&lt;T&gt;::value</a>,</div>
+<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;                      <span class="stringliteral">&quot;Can only have integer types.&quot;</span>);</div>
+<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;        <span class="comment">// assert(!(std::is_signed&lt;T&gt;::value)); //, &quot;Implemented only for</span></div>
+<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;        <span class="comment">// unsigned integer types.&quot;);</span></div>
+<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160; </div>
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+<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160; </div>
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+<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160; </div>
+<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;unsigned char&gt;</a></div>
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+<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;};</div>
+<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160; </div>
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+</div><!-- fragment --></div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="abinary__exponent_8cpp_html_aeb48dce0725e63d19147944f41843c73"><div class="ttname"><a href="../../de/dcf/binary__exponent_8cpp.html#aeb48dce0725e63d19147944f41843c73">binExpo</a></div><div class="ttdeci">int binExpo(int a, int b)</div><div class="ttdef"><b>Definition:</b> binary_exponent.cpp:28</div></div>
+<div class="ttc" id="aclasslarge__number_html_a60c436d1a1c5e3795d6177d3815ad615"><div class="ttname"><a href="../../db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">large_number::add_digit</a></div><div class="ttdeci">void add_digit(unsigned int value)</div><div class="ttdef"><b>Definition:</b> large_number.h:118</div></div>
+<div class="ttc" id="ashowpoint_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/showpoint.html">std::showpoint</a></div><div class="ttdeci">T showpoint(T... args)</div></div>
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+<div class="ttc" id="astructtrie_html"><div class="ttname"><a href="../../d4/dd9/structtrie.html">trie</a></div><div class="ttdef"><b>Definition:</b> trie_tree.cpp:8</div></div>
+<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
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+<div class="ttc" id="asetprecision_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/setprecision.html">std::setprecision</a></div><div class="ttdeci">T setprecision(T... args)</div></div>
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+<div class="ttc" id="abitset_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/bitset.html">std::bitset&lt; MAXN &gt;</a></div></div>
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+<div class="ttc" id="astrlen_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/strlen.html">std::strlen</a></div><div class="ttdeci">T strlen(T... args)</div></div>
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+<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a></div><div class="ttdoc">STL class.</div></div>
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+<div class="ttc" id="alist_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list.html">std::list</a></div><div class="ttdoc">STL class.</div></div>
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+<div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
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+<div class="ttc" id="amove_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a></div><div class="ttdeci">T move(T... args)</div></div>
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+<div class="ttc" id="apair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a></div></div>
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+<div class="ttc" id="aclass_trie_html"><div class="ttname"><a href="../../dd/d2f/class_trie.html">Trie</a></div><div class="ttdef"><b>Definition:</b> trie_modern.cpp:16</div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int &gt;</a></div></div>
+<div class="ttc" id="asystem_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/program/system.html">std::system</a></div><div class="ttdeci">T system(T... args)</div></div>
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+<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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+<div class="ttc" id="astack_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/stack.html">std::stack</a></div><div class="ttdoc">STL class.</div></div>
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+<div class="ttc" id="afibonacci__large_8cpp_html_adf3e906875ab257f7fab3bc1370aa2db"><div class="ttname"><a href="../../de/de4/fibonacci__large_8cpp.html#adf3e906875ab257f7fab3bc1370aa2db">fib</a></div><div class="ttdeci">large_number fib(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_large.cpp:24</div></div>
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+<div class="ttc" id="aiterator_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/iterator.html">std::iterator</a></div></div>
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+<div class="ttc" id="aclass_trie_html_a6d10eb1669453395d1900ebd401954fb"><div class="ttname"><a href="../../dd/d2f/class_trie.html#a6d10eb1669453395d1900ebd401954fb">Trie::hasChildren</a></div><div class="ttdeci">static bool hasChildren(std::shared_ptr&lt; TrieNode &gt; node)</div><div class="ttdef"><b>Definition:</b> trie_modern.cpp:41</div></div>
+<div class="ttc" id="aemplace_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/emplace.html">std::queue::emplace</a></div><div class="ttdeci">T emplace(T... args)</div></div>
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+<div class="ttc" id="astruct_trie_1_1_trie_node_html"><div class="ttname"><a href="../../de/d48/struct_trie_1_1_trie_node.html">Trie::TrieNode</a></div><div class="ttdef"><b>Definition:</b> trie_modern.cpp:26</div></div>
+<div class="ttc" id="adistance_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/distance.html">std::distance</a></div><div class="ttdeci">T distance(T... args)</div></div>
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+<div class="ttc" id="alarge__number_8h_html"><div class="ttname"><a href="../../d4/d86/large__number_8h.html">large_number.h</a></div><div class="ttdoc">Library to perform arithmatic operations on arbitrarily large numbers.</div></div>
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+<div class="ttc" id="abinary__exponent_8cpp_html_a31dbf5f7ceb9c9eec831ef9f7782291f"><div class="ttname"><a href="../../de/dcf/binary__exponent_8cpp.html#a31dbf5f7ceb9c9eec831ef9f7782291f">binExpo_alt</a></div><div class="ttdeci">int binExpo_alt(int a, int b)</div><div class="ttdef"><b>Definition:</b> binary_exponent.cpp:42</div></div>
+<div class="ttc" id="asearch_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/search.html">std::search</a></div><div class="ttdeci">T search(T... args)</div></div>
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+<div class="ttc" id="ahash__search_8cpp_html_a8ca8dcb494104d273679e219e53d0555"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a></div><div class="ttdeci">struct list node</div></div>
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+<div class="ttc" id="areverse_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/reverse.html">std::reverse</a></div><div class="ttdeci">T reverse(T... args)</div></div>
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+<div class="ttc" id="aback_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/back.html">std::vector::back</a></div><div class="ttdeci">T back(T... args)</div></div>
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+<div class="ttc" id="aclassmachine__learning_1_1adaline_html_ab11242d9ad5b03a75911e29b04f78fd3"><div class="ttname"><a href="../../d6/d30/classmachine__learning_1_1adaline.html#ab11242d9ad5b03a75911e29b04f78fd3">machine_learning::adaline::predict</a></div><div class="ttdeci">int predict(const std::vector&lt; double &gt; &amp;x, double *out=nullptr)</div><div class="ttdef"><b>Definition:</b> adaline_learning.cpp:90</div></div>
+<div class="ttc" id="anamespacemachine__learning_html"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html">machine_learning</a></div><div class="ttdoc">Machine learning algorithms.</div></div>
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+<div class="ttc" id="aqueue_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue</a></div><div class="ttdoc">STL class.</div></div>
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+<div class="ttc" id="aclass_solution_html"><div class="ttname"><a href="../../dd/d4f/class_solution.html">Solution</a></div><div class="ttdef"><b>Definition:</b> bridge_finding_with_tarjan_algorithm.cpp:13</div></div>
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+<div class="ttc" id="aclasslarge__number_html_a2305a82e7b372617419337b2d2119c7d"><div class="ttname"><a href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">large_number::num_digits</a></div><div class="ttdeci">const size_t num_digits() const</div><div class="ttdef"><b>Definition:</b> large_number.h:130</div></div>
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+<div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
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+<div class="ttc" id="aclass_cycle_check_html_a2f4485c08b45e7a21a2e86f9c3f01d8b"><div class="ttname"><a href="../../d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">CycleCheck::isCyclicDFSHelper</a></div><div class="ttdeci">static bool isCyclicDFSHelper(AdjList const &amp;adjList, std::vector&lt; nodeStates &gt; *state, unsigned int node)</div><div class="ttdef"><b>Definition:</b> cycle_check_directed_graph.cpp:165</div></div>
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+<div class="ttc" id="ais_integral_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/is_integral.html">std::is_integral</a></div></div>
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+<div class="title">primes_up_to_billion.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Compute prime numbers upto 1 billion.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cstring&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
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+</div>
+</div>
+</div><table class="memberdecls">
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+Functions</h2></td></tr>
+<tr class="memitem:a031cada84819ed6426f58e4f7e81261c"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d9c/primes__up__to__billion_8cpp.html#a031cada84819ed6426f58e4f7e81261c">Sieve</a> (int64_t n)</td></tr>
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d9c/primes__up__to__billion_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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+Variables</h2></td></tr>
+<tr class="memitem:ac0f4b77b901ddb15dab4c4dee1ac6e95"><td class="memItemLeft" align="right" valign="top">char&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d9c/primes__up__to__billion_8cpp.html#ac0f4b77b901ddb15dab4c4dee1ac6e95">prime</a> [100000000]</td></tr>
+<tr class="separator:ac0f4b77b901ddb15dab4c4dee1ac6e95"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Compute prime numbers upto 1 billion. </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/d9b/prime__numbers_8cpp.html" title="Get list of prime numbers.">prime_numbers.cpp</a> <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html" title="Get list of prime numbers using Sieve of Eratosthenes Sieve of Eratosthenes is an algorithm to find t...">sieve_of_eratosthenes.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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+<div class="memitem">
+<div class="memproto">
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+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;           {</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <a class="code" href="../../d4/d9c/primes__up__to__billion_8cpp.html#a031cada84819ed6426f58e4f7e81261c">Sieve</a>(100000000);</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    int64_t n;</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;  <span class="comment">// 10006187</span></div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="keywordflow">if</span> (<a class="code" href="../../d4/d9c/primes__up__to__billion_8cpp.html#ac0f4b77b901ddb15dab4c4dee1ac6e95">prime</a>[n] == <span class="charliteral">&#39;1&#39;</span>)</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;YES\n&quot;</span>;</div>
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+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
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+</div>
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+</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#a031cada84819ed6426f58e4f7e81261c">&#9670;&nbsp;</a></span>Sieve()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void Sieve </td>
+          <td>(</td>
+          <td class="paramtype">int64_t&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Perform Sieve algorithm </p>
+<div class="fragment"><div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;                      {</div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/memset.html">memset</a>(<a class="code" href="../../d4/d9c/primes__up__to__billion_8cpp.html#ac0f4b77b901ddb15dab4c4dee1ac6e95">prime</a>, <span class="charliteral">&#39;1&#39;</span>, <span class="keyword">sizeof</span>(<a class="code" href="../../d4/d9c/primes__up__to__billion_8cpp.html#ac0f4b77b901ddb15dab4c4dee1ac6e95">prime</a>));  <span class="comment">// intitize &#39;1&#39; to every index</span></div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;    <a class="code" href="../../d4/d9c/primes__up__to__billion_8cpp.html#ac0f4b77b901ddb15dab4c4dee1ac6e95">prime</a>[0] = <span class="charliteral">&#39;0&#39;</span>;                     <span class="comment">// 0 is not prime</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;    <a class="code" href="../../d4/d9c/primes__up__to__billion_8cpp.html#ac0f4b77b901ddb15dab4c4dee1ac6e95">prime</a>[1] = <span class="charliteral">&#39;0&#39;</span>;                     <span class="comment">// 1 is not prime</span></div>
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+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = p * p; i &lt;= n; i += p)</div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;                <a class="code" href="../../d4/d9c/primes__up__to__billion_8cpp.html#ac0f4b77b901ddb15dab4c4dee1ac6e95">prime</a>[i] = <span class="charliteral">&#39;0&#39;</span>;  <span class="comment">// set all multiples of p to false</span></div>
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+
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+</div><!-- doc-content -->
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+
+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">gcd_iterative_euclidean.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Compute the greatest common denominator of two integers using <em>iterative form</em> of <a href="https://en.wikipedia.org/wiki/Euclidean_algorithm">Euclidean algorithm</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;stdexcept&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for gcd_iterative_euclidean.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/deb/gcd__iterative__euclidean_8cpp__incl.svg" width="187" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ae48807fa2b7000afae599e67f327545e"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> (int num1, int num2)</td></tr>
+<tr class="separator:ae48807fa2b7000afae599e67f327545e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Compute the greatest common denominator of two integers using <em>iterative form</em> of <a href="https://en.wikipedia.org/wiki/Euclidean_algorithm">Euclidean algorithm</a> </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html" title="Compute the greatest common denominator of two integers using recursive form of Euclidean algorithm">gcd_recursive_euclidean.cpp</a>, <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp.html" title="This program aims at calculating the GCD of n numbers by division method.">gcd_of_n_numbers.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae48807fa2b7000afae599e67f327545e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae48807fa2b7000afae599e67f327545e">&#9670;&nbsp;</a></span>gcd()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int gcd </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>num1</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>num2</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
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+</div><div class="memdoc">
+<p>algorithm </p>
+<div class="fragment"><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;                            {</div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;    <span class="keywordflow">if</span> (num1 &lt;= 0 | num2 &lt;= 0) {</div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;        <span class="keywordflow">throw</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/domain_error.html">std::domain_error</a>(<span class="stringliteral">&quot;Euclidean algorithm domain is for ints &gt; 0&quot;</span>);</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;    }</div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; </div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;    <span class="keywordflow">if</span> (num1 == num2) {</div>
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+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keywordflow">if</span> (num1 &gt; num2) {</div>
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+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;        base_num = num2;</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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+<p>Main function </p>
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+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;gcd of 289,204 is &quot;</span> &lt;&lt; (<a class="code" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(289, 204)) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d8/dc8/struct_point.html">Point</a>&#160;</td>
+          <td class="paramname"><em>first_point</em>, </td>
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+          <td class="memname">bool SegmentIntersection::on_segment </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d8/dc8/struct_point.html">Point</a>&#160;</td>
+          <td class="paramname"><em>first_point</em>, </td>
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+<p>This method determines whether a point known to be colinear with a segment lies on that segment. </p>
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+<a href="#func-members">Functions</a>  </div>
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+<div class="title">fast_interger_input.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Read integers from stdin continuously as they are entered without waiting for the <code>\n</code> character.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for fast_interger_input.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/dda/fast__interger__input_8cpp__incl.svg" width="146" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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+Functions</h2></td></tr>
+<tr class="memitem:a4e097ac8509b717bdc8ab09ecd86ae82"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/de8/fast__interger__input_8cpp.html#a4e097ac8509b717bdc8ab09ecd86ae82">fastinput</a> (int *number)</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Read integers from stdin continuously as they are entered without waiting for the <code>\n</code> character. </p>
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+<h2 class="memtitle"><span class="permalink"><a href="#a4e097ac8509b717bdc8ab09ecd86ae82">&#9670;&nbsp;</a></span>fastinput()</h2>
+
+<div class="memitem">
+<div class="memproto">
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+        <tr>
+          <td class="memname">void fastinput </td>
+          <td>(</td>
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+<p>Function to read the number from stdin. The function reads input until a non numeric character is entered. </p>
+<div class="fragment"><div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;                            {</div>
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+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
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+<div class="title">kohonen_som_topology.cpp File Reference<div class="ingroups"><a class="el" href="../../d9/d66/group__machine__learning.html">Machine Learning Algorithms</a></div></div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a href="https://en.wikipedia.org/wiki/Self-organizing_map">Kohonen self organizing map</a> (topological map)  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
+<code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;cstdlib&gt;</code><br />
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+<code>#include &lt;fstream&gt;</code><br />
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+<code>#include &lt;valarray&gt;</code><br />
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+<tr class="separator:a2256c10b16edba377b64a44b6c656908"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Self-organizing_map">Kohonen self organizing map</a> (topological map) </p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> This example implements a powerful unsupervised learning algorithm called as a self organizing map. The algorithm creates a connected network of weights that closely follows the given data points. This thus creates a topological map of the given data i.e., it maintains the relationship between varipus data points in a much higher dimesional space by creating an equivalent in a 2-dimensional space. <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/machine_learning/2D_Kohonen_SOM.svg" alt="Trained topological maps for the test cases in the program" style="pointer-events: none;" class="inline"/> </dd></dl>
+<dl class="section note"><dt>Note</dt><dd>This C++ version of the program is considerable slower than its <a href="https://github.com/kvedala/C/blob/master/machine_learning/kohonen_som_trace.c">C counterpart</a> </dd>
+<dd>
+The compiled code is much slower when compiled with MS Visual C++ 2019 than with GCC on windows </dd></dl>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d9/d49/kohonen__som__trace_8cpp.html" title="Kohonen self organizing map (data tracing)">kohonen_som_trace.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a2256c10b16edba377b64a44b6c656908"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a2256c10b16edba377b64a44b6c656908">&#9670;&nbsp;</a></span>get_clock_diff()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double get_clock_diff </td>
+          <td>(</td>
+          <td class="paramtype">clock_t&#160;</td>
+          <td class="paramname"><em>start_t</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">clock_t&#160;</td>
+          <td class="paramname"><em>end_t</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Convert clock cycle difference to time in seconds</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">start_t</td><td>start clock </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">end_t</td><td>end clock </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>time difference in seconds </dd></dl>
+<div class="fragment"><div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;                                                      {</div>
+<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_t - start_t) / CLOCKS_PER_SEC;</div>
+<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>argc</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char **&#160;</td>
+          <td class="paramname"><em>argv</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;                                {</div>
+<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Using OpenMP based parallelization\n&quot;</span>;</div>
+<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;<span class="preprocessor">#else</span></div>
+<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;NOT using OpenMP based parallelization\n&quot;</span>;</div>
+<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160; </div>
+<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
+<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160; </div>
+<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;    <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
+<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;    <span class="keyword">auto</span> end_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 completed in &quot;</span> &lt;&lt; <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
+<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160; </div>
+<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;    start_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;    <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
+<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;    end_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 completed in &quot;</span> &lt;&lt; <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
+<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160; </div>
+<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;    start_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;    <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
+<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;    end_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 completed in &quot;</span> &lt;&lt; <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
+<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160; </div>
+<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
+<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;        &lt;&lt; <span class="stringliteral">&quot;(Note: Calculated times include: creating test sets, training &quot;</span></div>
+<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;           <span class="stringliteral">&quot;model and writing files to disk.)\n\n&quot;</span>;</div>
+<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d4/def/kohonen__som__topology_8cpp_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="100%" height="600"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a1440a7779ac56f47a3f355ce4a8c7da0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">&#9670;&nbsp;</a></span>test1()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test1 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test that creates a random set of points distributed in four clusters in circumference of a circle and trains an SOM that finds that circular pattern. The following <a href="https://en.wikipedia.org/wiki/Comma-separated_values">CSV</a> files are created to validate the execution:</p><ul>
+<li><code>test1.csv</code>: random test samples points with a circular pattern</li>
+<li><code>w11.csv</code>: initial random map</li>
+<li><code>w12.csv</code>: trained SOM map </li>
+</ul>
+<div class="fragment"><div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;             {</div>
+<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;    <span class="keywordtype">int</span> j, N = 300;</div>
+<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;    <span class="keywordtype">int</span> features = 2;</div>
+<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;    <span class="keywordtype">int</span> num_out = 30;</div>
+<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
+<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;        <span class="keywordflow">if</span> (i &lt; N)  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;            X[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;            W[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt;(num_out);</div>
+<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = 0; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; num_out; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
+<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;                W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++)</div>
+<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;                    <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;                    W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>][j] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
+<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;            }</div>
+<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;        }</div>
+<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;    }</div>
+<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160; </div>
+<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;    <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a6b5e744876fd980a3451cbb385d4e755">test_2d_classes</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
+<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336">save_2d_data</a>(<span class="stringliteral">&quot;test1.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
+<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w11.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
+<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#adc731720947b4bc2ab047c141e7d0299">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
+<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w12.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
+<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d4/def/kohonen__som__topology_8cpp_a1440a7779ac56f47a3f355ce4a8c7da0_cgraph.svg" width="100%" height="600"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a0283886819c7c140a023582b7269e2d0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0283886819c7c140a023582b7269e2d0">&#9670;&nbsp;</a></span>test2()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test2 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test that creates a random set of points distributed in 4 clusters in 3D space and trains an SOM that finds the topological pattern. The following <a href="https://en.wikipedia.org/wiki/Comma-separated_values">CSV</a> files are created to validate the execution:</p><ul>
+<li><code>test2.csv</code>: random test samples points with a lamniscate pattern</li>
+<li><code>w21.csv</code>: initial random map</li>
+<li><code>w22.csv</code>: trained SOM map </li>
+</ul>
+<div class="fragment"><div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;             {</div>
+<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;    <span class="keywordtype">int</span> j, N = 300;</div>
+<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;    <span class="keywordtype">int</span> features = 3;</div>
+<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    <span class="keywordtype">int</span> num_out = 30;</div>
+<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
+<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;        <span class="keywordflow">if</span> (i &lt; N)  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;            X[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;            W[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt;(num_out);</div>
+<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = 0; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; num_out; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
+<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;                W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++)</div>
+<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;                    <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;                    W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>][j] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
+<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;            }</div>
+<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;        }</div>
+<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;    }</div>
+<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160; </div>
+<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;    <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#ab3081e021270ba21a9fd88646f6a6e26">test_3d_classes1</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
+<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336">save_2d_data</a>(<span class="stringliteral">&quot;test2.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
+<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w21.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
+<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#adc731720947b4bc2ab047c141e7d0299">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
+<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w22.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
+<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d4/def/kohonen__som__topology_8cpp_a0283886819c7c140a023582b7269e2d0_cgraph.svg" width="100%" height="600"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a6d0455dd5c30adda100e95f0423c786e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a6d0455dd5c30adda100e95f0423c786e">&#9670;&nbsp;</a></span>test3()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test3 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test that creates a random set of points distributed in eight clusters in 3D space and trains an SOM that finds the topological pattern. The following <a href="https://en.wikipedia.org/wiki/Comma-separated_values">CSV</a> files are created to validate the execution:</p><ul>
+<li><code>test3.csv</code>: random test samples points with a circular pattern</li>
+<li><code>w31.csv</code>: initial random map</li>
+<li><code>w32.csv</code>: trained SOM map </li>
+</ul>
+<div class="fragment"><div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;             {</div>
+<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;    <span class="keywordtype">int</span> j, N = 500;</div>
+<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;    <span class="keywordtype">int</span> features = 3;</div>
+<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;    <span class="keywordtype">int</span> num_out = 30;</div>
+<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::valarray&lt;double&gt;</a>&gt;&gt; W(num_out);</div>
+<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;        <span class="keywordflow">if</span> (i &lt; N)  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;            X[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;            W[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt;(num_out);</div>
+<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = 0; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; num_out; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
+<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;                W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;                <span class="keywordflow">for</span> (j = 0; j &lt; features; j++)</div>
+<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;                    <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;                    W[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>][j] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-10, 10);</div>
+<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;            }</div>
+<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;        }</div>
+<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;    }</div>
+<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160; </div>
+<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;    <a class="code" href="../../d4/def/kohonen__som__topology_8cpp.html#a0e7435446ed7c763f7de79a468add2e0">test_3d_classes2</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
+<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336">save_2d_data</a>(<span class="stringliteral">&quot;test3.csv&quot;</span>, X);  <span class="comment">// save test data points</span></div>
+<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w31.csv&quot;</span>, W);   <span class="comment">// save initial random weights</span></div>
+<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#adc731720947b4bc2ab047c141e7d0299">kohonen_som</a>(X, &amp;W, 1e-4);      <span class="comment">// train the SOM</span></div>
+<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">save_u_matrix</a>(<span class="stringliteral">&quot;w32.csv&quot;</span>, W);   <span class="comment">// save the resultant weights</span></div>
+<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d4/def/kohonen__som__topology_8cpp_a6d0455dd5c30adda100e95f0423c786e_cgraph.svg" width="100%" height="600"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a6b5e744876fd980a3451cbb385d4e755"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a6b5e744876fd980a3451cbb385d4e755">&#9670;&nbsp;</a></span>test_2d_classes()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test_2d_classes </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>data</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Creates a random set of points distributed in four clusters in 3D space with centroids at the points</p><ul>
+<li>\((0,5, 0.5, 0.5)\)</li>
+<li>\((0,5,-0.5, -0.5)\)</li>
+<li>\((-0,5, 0.5, 0.5)\)</li>
+<li>\((-0,5,-0.5, -0.5)\)</li>
+</ul>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[out]</td><td class="paramname">data</td><td>matrix to store data in </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;                                                           {</div>
+<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
+<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.3;  <span class="comment">// radius of cluster</span></div>
+<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;    <span class="keywordtype">int</span> i;</div>
+<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 4;</div>
+<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> centres[][2] = {</div>
+<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;        <span class="comment">// centres of each class cluster</span></div>
+<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;        {.5, .5},   <span class="comment">// centre of class 1</span></div>
+<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;        {.5, -.5},  <span class="comment">// centre of class 2</span></div>
+<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;        {-.5, .5},  <span class="comment">// centre of class 3</span></div>
+<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;        {-.5, -.5}  <span class="comment">// centre of class 4</span></div>
+<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;    };</div>
+<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160; </div>
+<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; N; i++) {</div>
+<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;        <span class="comment">// select a random class for the point</span></div>
+<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;        <span class="keywordtype">int</span> cls = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;</div>
+<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160; </div>
+<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
+<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
+<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
+<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160; </div>
+<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;        <span class="comment">/* The follosing can also be used</span></div>
+<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;<span class="comment">        for (int j = 0; j &lt; 2; j++)</span></div>
+<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;<span class="comment">            data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);</span></div>
+<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;<span class="comment">        */</span></div>
+<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;    }</div>
+<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/def/kohonen__som__topology_8cpp_a6b5e744876fd980a3451cbb385d4e755_cgraph.svg" width="250" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ab3081e021270ba21a9fd88646f6a6e26"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ab3081e021270ba21a9fd88646f6a6e26">&#9670;&nbsp;</a></span>test_3d_classes1()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test_3d_classes1 </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>data</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Creates a random set of points distributed in four clusters in 3D space with centroids at the points</p><ul>
+<li>\((0,5, 0.5, 0.5)\)</li>
+<li>\((0,5,-0.5, -0.5)\)</li>
+<li>\((-0,5, 0.5, 0.5)\)</li>
+<li>\((-0,5,-0.5, -0.5)\)</li>
+</ul>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[out]</td><td class="paramname">data</td><td>matrix to store data in </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;                                                            {</div>
+<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
+<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.3;  <span class="comment">// radius of cluster</span></div>
+<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;    <span class="keywordtype">int</span> i;</div>
+<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 4;</div>
+<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> centres[][3] = {</div>
+<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;        <span class="comment">// centres of each class cluster</span></div>
+<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;        {.5, .5, .5},    <span class="comment">// centre of class 1</span></div>
+<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;        {.5, -.5, -.5},  <span class="comment">// centre of class 2</span></div>
+<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;        {-.5, .5, .5},   <span class="comment">// centre of class 3</span></div>
+<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;        {-.5, -.5 - .5}  <span class="comment">// centre of class 4</span></div>
+<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;    };</div>
+<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160; </div>
+<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; N; i++) {</div>
+<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;        <span class="comment">// select a random class for the point</span></div>
+<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;        <span class="keywordtype">int</span> cls = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;</div>
+<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160; </div>
+<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
+<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
+<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
+<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][2] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][2] - R, centres[cls][2] + R);</div>
+<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160; </div>
+<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;        <span class="comment">/* The follosing can also be used</span></div>
+<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;<span class="comment">        for (int j = 0; j &lt; 3; j++)</span></div>
+<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;<span class="comment">            data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);</span></div>
+<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;<span class="comment">        */</span></div>
+<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;    }</div>
+<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/def/kohonen__som__topology_8cpp_ab3081e021270ba21a9fd88646f6a6e26_cgraph.svg" width="256" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a0e7435446ed7c763f7de79a468add2e0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0e7435446ed7c763f7de79a468add2e0">&#9670;&nbsp;</a></span>test_3d_classes2()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test_3d_classes2 </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>data</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Creates a random set of points distributed in four clusters in 3D space with centroids at the points</p><ul>
+<li>\((0,5, 0.5, 0.5)\)</li>
+<li>\((0,5,-0.5, -0.5)\)</li>
+<li>\((-0,5, 0.5, 0.5)\)</li>
+<li>\((-0,5,-0.5, -0.5)\)</li>
+</ul>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[out]</td><td class="paramname">data</td><td>matrix to store data in </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;                                                            {</div>
+<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
+<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.2;  <span class="comment">// radius of cluster</span></div>
+<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;    <span class="keywordtype">int</span> i;</div>
+<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 8;</div>
+<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> centres[][3] = {</div>
+<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;        <span class="comment">// centres of each class cluster</span></div>
+<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;        {.5, .5, .5},    <span class="comment">// centre of class 1</span></div>
+<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;        {.5, .5, -.5},   <span class="comment">// centre of class 2</span></div>
+<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;        {.5, -.5, .5},   <span class="comment">// centre of class 3</span></div>
+<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;        {.5, -.5, -.5},  <span class="comment">// centre of class 4</span></div>
+<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;        {-.5, .5, .5},   <span class="comment">// centre of class 5</span></div>
+<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;        {-.5, .5, -.5},  <span class="comment">// centre of class 6</span></div>
+<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;        {-.5, -.5, .5},  <span class="comment">// centre of class 7</span></div>
+<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;        {-.5, -.5, -.5}  <span class="comment">// centre of class 8</span></div>
+<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;    };</div>
+<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160; </div>
+<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; N; i++) {</div>
+<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;        <span class="comment">// select a random class for the point</span></div>
+<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;        <span class="keywordtype">int</span> cls = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;</div>
+<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160; </div>
+<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
+<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
+<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
+<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][2] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][2] - R, centres[cls][2] + R);</div>
+<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160; </div>
+<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;        <span class="comment">/* The follosing can also be used</span></div>
+<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;<span class="comment">        for (int j = 0; j &lt; 3; j++)</span></div>
+<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;<span class="comment">            data[i][j] = _random(centres[class][j] - R, centres[class][j] + R);</span></div>
+<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;<span class="comment">        */</span></div>
+<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;    }</div>
+<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/def/kohonen__som__topology_8cpp_a0e7435446ed7c763f7de79a468add2e0_cgraph.svg" width="256" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
+<div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="akohonen__som__topology_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:357</div></div>
+<div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
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+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
+<div class="ttc" id="amatrix__exponentiation_8cpp_html_afcf0d19607cd0edd8ae333d2b9c220c0"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a></div><div class="ttdeci">ll k</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:48</div></div>
+<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="akohonen__som__topology_8cpp_html_ab3081e021270ba21a9fd88646f6a6e26"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#ab3081e021270ba21a9fd88646f6a6e26">test_3d_classes1</a></div><div class="ttdeci">void test_3d_classes1(std::vector&lt; std::valarray&lt; double &gt;&gt; *data)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:397</div></div>
+<div class="ttc" id="akohonen__som__topology_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:437</div></div>
+<div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
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+<div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
+<div class="ttc" id="anamespacemachine__learning_html_a1d577f5d95b774ae97eb6838852d0df5"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">machine_learning::save_u_matrix</a></div><div class="ttdeci">int save_u_matrix(const char *fname, const std::vector&lt; std::vector&lt; std::valarray&lt; double &gt;&gt;&gt; &amp;W)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:133</div></div>
+<div class="ttc" id="akohonen__som__topology_8cpp_html_a2256c10b16edba377b64a44b6c656908"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a></div><div class="ttdeci">double get_clock_diff(clock_t start_t, clock_t end_t)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:559</div></div>
+<div class="ttc" id="atime_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a></div><div class="ttdeci">T time(T... args)</div></div>
+<div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
+<div class="ttc" id="akohonen__som__topology_8cpp_html_a6b5e744876fd980a3451cbb385d4e755"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#a6b5e744876fd980a3451cbb385d4e755">test_2d_classes</a></div><div class="ttdeci">void test_2d_classes(std::vector&lt; std::valarray&lt; double &gt;&gt; *data)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:318</div></div>
+<div class="ttc" id="anamespacemachine__learning_html_adc731720947b4bc2ab047c141e7d0299"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#adc731720947b4bc2ab047c141e7d0299">machine_learning::kohonen_som</a></div><div class="ttdeci">void kohonen_som(const std::vector&lt; std::valarray&lt; double &gt;&gt; &amp;X, std::vector&lt; std::vector&lt; std::valarray&lt; double &gt;&gt;&gt; *W, double alpha_min)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:259</div></div>
+<div class="ttc" id="akohonen__som__topology_8cpp_html_a0e7435446ed7c763f7de79a468add2e0"><div class="ttname"><a href="../../d4/def/kohonen__som__topology_8cpp.html#a0e7435446ed7c763f7de79a468add2e0">test_3d_classes2</a></div><div class="ttdeci">void test_3d_classes2(std::vector&lt; std::valarray&lt; double &gt;&gt; *data)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:477</div></div>
+<div class="ttc" id="agroup__machine__learning_html_gaf5ce14f026d6d231bef29161bac2b485"><div class="ttname"><a href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a></div><div class="ttdeci">double _random(double a, double b)</div><div class="ttdef"><b>Definition:</b> kohonen_som_topology.cpp:48</div></div>
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="navelem"><a class="el" href="../../dir_3343723ae086de42ee4ca9774da3a13f.html">machine_learning</a></li><li class="navelem"><a class="el" href="../../d4/def/kohonen__som__topology_8cpp.html">kohonen_som_topology.cpp</a></li>
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diff --git a/d4/def/kohonen__som__topology_8cpp.js b/d4/def/kohonen__som__topology_8cpp.js
new file mode 100644
index 000000000..11d9f207e
--- /dev/null
+++ b/d4/def/kohonen__som__topology_8cpp.js
@@ -0,0 +1,19 @@
+var kohonen__som__topology_8cpp =
+[
+    [ "_USE_MATH_DEFINES", "d9/d66/group__machine__learning.html#ga525335710b53cb064ca56b936120431e", null ],
+    [ "MIN_DISTANCE", "d4/def/kohonen__som__topology_8cpp.html#a549d41dcf9444ed7d6df1da3c73e7d16", null ],
+    [ "_random", "d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485", null ],
+    [ "get_clock_diff", "d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908", null ],
+    [ "get_min_2d", "d9/d66/group__machine__learning.html#gab53c14440b2b2dd3172c66afc5c2f63f", null ],
+    [ "kohonen_som", "d4/def/kohonen__som__topology_8cpp.html#adc731720947b4bc2ab047c141e7d0299", null ],
+    [ "main", "d4/def/kohonen__som__topology_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627", null ],
+    [ "save_2d_data", "d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336", null ],
+    [ "save_u_matrix", "d4/def/kohonen__som__topology_8cpp.html#a1d577f5d95b774ae97eb6838852d0df5", null ],
+    [ "test1", "d4/def/kohonen__som__topology_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0", null ],
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+</div><!--header-->
+<div class="contents">
+
+<p><a href="https://en.wikipedia.org/wiki/Bayes%27_theorem">Bayes' theorem</a>  
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+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
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+<tr class="memitem:a655bfe51252468d232dc639a340656ba"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d67/bayes__theorem_8cpp.html#a655bfe51252468d232dc639a340656ba">bayes_AgivenB</a> (double BgivenA, double A, double B)</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Bayes%27_theorem">Bayes' theorem</a> </p>
+<p>Bayes' theorem allows one to find \(P(A|B)\) given \(P(B|A)\) or \(P(B|A)\) given \(P(A|B)\) and \(P(A)\) and \(P(B)\).<br  />
+Note that \(P(A|B)\) is read 'The probability of A given that the event B has occured'. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a655bfe51252468d232dc639a340656ba"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a655bfe51252468d232dc639a340656ba">&#9670;&nbsp;</a></span>bayes_AgivenB()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double bayes_AgivenB </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>BgivenA</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>B</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>returns P(A|B) </p>
+<div class="fragment"><div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;                                                         {</div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;    <span class="keywordflow">return</span> (BgivenA * A) / B;</div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;}</div>
+</div><!-- fragment -->
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+</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#abb4f22dc05887c2259fdfc55c687598f">&#9670;&nbsp;</a></span>bayes_BgivenA()</h2>
+
+<div class="memitem">
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+        <tr>
+          <td class="memname">double bayes_BgivenA </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>AgivenB</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>B</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
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+<p>returns P(B|A) </p>
+<div class="fragment"><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;                                                         {</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    <span class="keywordflow">return</span> (AgivenB * B) / A;</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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+        </tr>
+      </table>
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+<div class="title">List of all files </div>  </div>
+</div><!--header-->
+<div class="contents">
+<div class="textblock"><h1><a class="anchor" id="autotoc_md14"></a>
+Backtracking</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/graph_coloring.cpp">Graph Coloring</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/knight_tour.cpp">Knight Tour</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/minimax.cpp">Minimax</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/n_queens.cpp">N Queens</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/n_queens_all_solution_optimised.cpp">N Queens All Solution Optimised</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/nqueen_print_all_solutions.cpp">Nqueen Print All Solutions</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/rat_maze.cpp">Rat Maze</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/sudoku_solve.cpp">Sudoku Solve</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md15"></a>
+Data Structures</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/avltree.cpp">Avltree</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/binary_search_tree.cpp">Binary Search Tree</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/binaryheap.cpp">Binaryheap</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/circular_queue_using_linked_list.cpp">Circular Queue Using Linked List</a></li>
+<li>Cll<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/cll/cll.cpp">Cll</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/cll/cll.h">Cll</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/cll/main_cll.cpp">Main Cll</a></li>
+</ul>
+</li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/disjoint_set.cpp">Disjoint Set</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/doubly_linked_list.cpp">Doubly Linked List</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/linked_list.cpp">Linked List</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/linkedlist_implentation_usingarray.cpp">Linkedlist Implentation Usingarray</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/list_array.cpp">List Array</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/morrisinorder.cpp">Morrisinorder</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue.h">Queue</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_array.cpp">Queue Using Array</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_array2.cpp">Queue Using Array2</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_linked_list.cpp">Queue Using Linked List</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_linkedlist.cpp">Queue Using Linkedlist</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/stack.h">Stack</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/stack_using_array.cpp">Stack Using Array</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/stack_using_linked_list.cpp">Stack Using Linked List</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/test_queue.cpp">Test Queue</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/test_stack.cpp">Test Stack</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/test_stack_students.cpp">Test Stack Students</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/tree.cpp">Tree</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/trie_modern.cpp">Trie Modern</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/trie_tree.cpp">Trie Tree</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md16"></a>
+Dynamic Programming</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/0_1_knapsack.cpp">0 1 Knapsack</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/armstrong_number.cpp">Armstrong Number</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/bellman_ford.cpp">Bellman Ford</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/catalan_numbers.cpp">Catalan Numbers</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/coin_change.cpp">Coin Change</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/cut_rod.cpp">Cut Rod</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/edit_distance.cpp">Edit Distance</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/egg_dropping_puzzle.cpp">Egg Dropping Puzzle</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/fibonacci_bottom_up.cpp">Fibonacci Bottom Up</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/fibonacci_top_down.cpp">Fibonacci Top Down</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/floyd_warshall.cpp">Floyd Warshall</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/kadane.cpp">Kadane</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_common_string.cpp">Longest Common String</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_common_subsequence.cpp">Longest Common Subsequence</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_increasing_subsequence.cpp">Longest Increasing Subsequence</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_increasing_subsequence_(nlogn).cpp">Longest Increasing Subsequence (Nlogn)</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/matrix_chain_multiplication.cpp">Matrix Chain Multiplication</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/searching_of_element_in_dynamic_array.cpp">Searching Of Element In Dynamic Array</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/tree_height.cpp">Tree Height</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md17"></a>
+Geometry</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/geometry/line_segment_intersection.cpp">Line Segment Intersection</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md18"></a>
+Graph</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/bfs.cpp">Bfs</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/bridge_finding_with_tarjan_algorithm.cpp">Bridge Finding With Tarjan Algorithm</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/connected_components.cpp">Connected Components</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/connected_components_with_dsu.cpp">Connected Components With Dsu</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/cycle_check_directed_graph.cpp">Cycle Check Directed Graph</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/dfs.cpp">Dfs</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/dfs_with_stack.cpp">Dfs With Stack</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/dijkstra.cpp">Dijkstra</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/kosaraju.cpp">Kosaraju</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/kruskal.cpp">Kruskal</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/lca.cpp">Lca</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/max_flow_with_ford_fulkerson_and_edmond_karp_algo.cpp">Max Flow With Ford Fulkerson And Edmond Karp Algo</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/prim.cpp">Prim</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/topological_sort.cpp">Topological Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/topological_sort_by_kahns_algo.cpp">Topological Sort By Kahns Algo</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md19"></a>
+Greedy Algorithms</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/dijkstra.cpp">Dijkstra</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/huffman.cpp">Huffman</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/knapsack.cpp">Knapsack</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/kruskals_minimum_spanning_tree.cpp">Kruskals Minimum Spanning Tree</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/prims_minimum_spanning_tree.cpp">Prims Minimum Spanning Tree</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md20"></a>
+Hashing</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/chaining.cpp">Chaining</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/double_hash_hash_table.cpp">Double Hash Hash Table</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/linear_probing_hash_table.cpp">Linear Probing Hash Table</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/quadratic_probing_hash_table.cpp">Quadratic Probing Hash Table</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md21"></a>
+Machine Learning</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/adaline_learning.cpp">Adaline Learning</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/kohonen_som_topology.cpp">Kohonen Som Topology</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/kohonen_som_trace.cpp">Kohonen Som Trace</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md22"></a>
+Math</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/binary_exponent.cpp">Binary Exponent</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/check_prime.cpp">Check Prime</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/double_factorial.cpp">Double Factorial</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/eulers_totient_function.cpp">Eulers Totient Function</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/extended_euclid_algorithm.cpp">Extended Euclid Algorithm</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/factorial.cpp">Factorial</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fast_power.cpp">Fast Power</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci.cpp">Fibonacci</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci_fast.cpp">Fibonacci Fast</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci_large.cpp">Fibonacci Large</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_iterative_euclidean.cpp">Gcd Iterative Euclidean</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_of_n_numbers.cpp">Gcd Of N Numbers</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_recursive_euclidean.cpp">Gcd Recursive Euclidean</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/large_factorial.cpp">Large Factorial</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/large_number.h">Large Number</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/least_common_multiple.cpp">Least Common Multiple</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_inverse_fermat_little_theorem.cpp">Modular Inverse Fermat Little Theorem</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/number_of_positive_divisors.cpp">Number Of Positive Divisors</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/power_for_huge_numbers.cpp">Power For Huge Numbers</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/prime_factorization.cpp">Prime Factorization</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/prime_numbers.cpp">Prime Numbers</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/primes_up_to_billion.cpp">Primes Up To Billion</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/realtime_stats.cpp">Realtime Stats</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sieve_of_eratosthenes.cpp">Sieve Of Eratosthenes</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sqrt_double.cpp">Sqrt Double</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/string_fibonacci.cpp">String Fibonacci</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md23"></a>
+Numerical Methods</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/bisection_method.cpp">Bisection Method</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/durand_kerner_roots.cpp">Durand Kerner Roots</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/false_position.cpp">False Position</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/gaussian_elimination.cpp">Gaussian Elimination</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/lu_decompose.cpp">Lu Decompose</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/newton_raphson_method.cpp">Newton Raphson Method</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/ode_forward_euler.cpp">Ode Forward Euler</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/ode_midpoint_euler.cpp">Ode Midpoint Euler</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/ode_semi_implicit_euler.cpp">Ode Semi Implicit Euler</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/ordinary_least_squares_regressor.cpp">Ordinary Least Squares Regressor</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/qr_decompose.h">Qr Decompose</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/qr_decomposition.cpp">Qr Decomposition</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/qr_eigen_values.cpp">Qr Eigen Values</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/successive_approximation.cpp">Successive Approximation</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md24"></a>
+Operations On Datastructures</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/array_left_rotation.cpp">Array Left Rotation</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/array_right_rotation.cpp">Array Right Rotation</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/circular_linked_list.cpp">Circular Linked List</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/circular_queue_using_array.cpp">Circular Queue Using Array</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/get_size_of_linked_list.cpp">Get Size Of Linked List</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/intersection_of_2_arrays.cpp">Intersection Of 2 Arrays</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/reverse_a_linked_list_using_recusion.cpp">Reverse A Linked List Using Recusion</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/selectionsortlinkedlist.cpp">Selectionsortlinkedlist</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/union_of_2_arrays.cpp">Union Of 2 Arrays</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md25"></a>
+Others</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/buzz_number.cpp">Buzz Number</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/decimal_to_binary.cpp">Decimal To Binary</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/decimal_to_hexadecimal.cpp">Decimal To Hexadecimal</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/decimal_to_roman_numeral.cpp">Decimal To Roman Numeral</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/fast_interger_input.cpp">Fast Interger Input</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/happy_number.cpp">Happy Number</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/matrix_exponentiation.cpp">Matrix Exponentiation</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/palindrome_of_number.cpp">Palindrome Of Number</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/paranthesis_matching.cpp">Paranthesis Matching</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/pascal_triangle.cpp">Pascal Triangle</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/primality_test.cpp">Primality Test</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/smallest_circle.cpp">Smallest Circle</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/sparse_matrix.cpp">Sparse Matrix</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/spiral_print.cpp">Spiral Print</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/stairs_pattern.cpp">Stairs Pattern</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/tower_of_hanoi.cpp">Tower Of Hanoi</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/vector_important_functions.cpp">Vector Important Functions</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md26"></a>
+Probability</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/addition_rule.cpp">Addition Rule</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/bayes_theorem.cpp">Bayes Theorem</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/binomial_dist.cpp">Binomial Dist</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/poisson_dist.cpp">Poisson Dist</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md27"></a>
+Range Queries</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/bit.cpp">Bit</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/fenwicktree.cpp">Fenwicktree</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/mo.cpp">Mo</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/segtree.cpp">Segtree</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md28"></a>
+Search</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/binary_search.cpp">Binary Search</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/exponential_search.cpp">Exponential Search</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/hash_search.cpp">Hash Search</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/interpolation_search.cpp">Interpolation Search</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/interpolation_search2.cpp">Interpolation Search2</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/jump_search.cpp">Jump Search</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/linear_search.cpp">Linear Search</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/median_search.cpp">Median Search</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/ternary_search.cpp">Ternary Search</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/text_search.cpp">Text Search</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md29"></a>
+Sorting</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bead_sort.cpp">Bead Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bitonic_sort.cpp">Bitonic Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bubble_sort.cpp">Bubble Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bucket_sort.cpp">Bucket Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/cocktail_selection_sort.cpp">Cocktail Selection Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/comb_sort.cpp">Comb Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/counting_sort.cpp">Counting Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/counting_sort_string.cpp">Counting Sort String</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/heap_sort.cpp">Heap Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/insertion_sort.cpp">Insertion Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/library_sort.cpp">Library Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/merge_sort.cpp">Merge Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/non_recursive_merge_sort.cpp">Non Recursive Merge Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/numeric_string_sort.cpp">Numeric String Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/odd_even_sort.cpp">Odd Even Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/quick_sort.cpp">Quick Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/radix_sort.cpp">Radix Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/selection_sort.cpp">Selection Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/shell_sort.cpp">Shell Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/shell_sort2.cpp">Shell Sort2</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/slow_sort.cpp">Slow Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/swap_sort.cpp">Swap Sort</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/tim_sort.cpp">Tim Sort</a></li>
+</ul>
+<h1><a class="anchor" id="autotoc_md30"></a>
+Strings</h1>
+<ul>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/brute_force_string_searching.cpp">Brute Force String Searching</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/knuth_morris_pratt.cpp">Knuth Morris Pratt</a></li>
+<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/rabin_karp.cpp">Rabin Karp</a> </li>
+</ul>
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+<a href="#func-members">Functions</a>  </div>
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+<div class="title">sorting Namespace Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Sorting algorithms.  
+<a href="../../d5/d91/namespacesorting.html#details">More...</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:aa26de383227859210f14dcf12201a079"><td class="memTemplParams" colspan="2">template&lt;class Iterator &gt; </td></tr>
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+<tr class="memdesc:aa26de383227859210f14dcf12201a079"><td class="mdescLeft">&#160;</td><td class="mdescRight">merges 2 sorted adjacent segments into a larger sorted segment  <a href="../../d5/d91/namespacesorting.html#aa26de383227859210f14dcf12201a079">More...</a><br /></td></tr>
+<tr class="separator:aa26de383227859210f14dcf12201a079"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a140d913e42fb94176a0b2c8b29a80420"><td class="memTemplParams" colspan="2">template&lt;class Iterator &gt; </td></tr>
+<tr class="memitem:a140d913e42fb94176a0b2c8b29a80420"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#a140d913e42fb94176a0b2c8b29a80420">non_recursive_merge_sort</a> (const Iterator first, const Iterator last, const size_t n)</td></tr>
+<tr class="memdesc:a140d913e42fb94176a0b2c8b29a80420"><td class="mdescLeft">&#160;</td><td class="mdescRight">bottom-up merge sort which sorts elements in a non-decreasing order  <a href="../../d5/d91/namespacesorting.html#a140d913e42fb94176a0b2c8b29a80420">More...</a><br /></td></tr>
+<tr class="separator:a140d913e42fb94176a0b2c8b29a80420"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a27236b8d3df3832e1f1225576a122534"><td class="memTemplParams" colspan="2">template&lt;class Iterator &gt; </td></tr>
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+<tr class="memdesc:a27236b8d3df3832e1f1225576a122534"><td class="mdescLeft">&#160;</td><td class="mdescRight">bottom-up merge sort which sorts elements in a non-decreasing order  <a href="../../d5/d91/namespacesorting.html#a27236b8d3df3832e1f1225576a122534">More...</a><br /></td></tr>
+<tr class="separator:a27236b8d3df3832e1f1225576a122534"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae97f4dd815654c4682f564afd718e824"><td class="memTemplParams" colspan="2">template&lt;class Iterator &gt; </td></tr>
+<tr class="memitem:ae97f4dd815654c4682f564afd718e824"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#ae97f4dd815654c4682f564afd718e824">non_recursive_merge_sort</a> (const Iterator first, const Iterator last)</td></tr>
+<tr class="memdesc:ae97f4dd815654c4682f564afd718e824"><td class="mdescLeft">&#160;</td><td class="mdescRight">bottom-up merge sort which sorts elements in a non-decreasing order  <a href="../../d5/d91/namespacesorting.html#ae97f4dd815654c4682f564afd718e824">More...</a><br /></td></tr>
+<tr class="separator:ae97f4dd815654c4682f564afd718e824"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a7e7f25f31c50523990437abf2ac3907e"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#a7e7f25f31c50523990437abf2ac3907e">partition</a> (int arr[], int low, int high)</td></tr>
+<tr class="separator:a7e7f25f31c50523990437abf2ac3907e"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="memitem:a5669396c6a6b1e14b97589b6e37980aa"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
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+<tr class="separator:a5669396c6a6b1e14b97589b6e37980aa"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a4d76603c54d3dc56146e92d10a043924"><td class="memTemplParams" colspan="2">template&lt;typename T , size_t N&gt; </td></tr>
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+<tr class="memitem:af2c5b92cbfe73f63f6074c61b0a45331"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Sorting algorithms. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="aa26de383227859210f14dcf12201a079"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa26de383227859210f14dcf12201a079">&#9670;&nbsp;</a></span>merge()</h2>
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+      <table class="memname">
+        <tr>
+          <td class="memname">void sorting::merge </td>
+          <td>(</td>
+          <td class="paramtype">Iterator&#160;</td>
+          <td class="paramname"><em>l</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">Iterator&#160;</td>
+          <td class="paramname"><em>r</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const Iterator&#160;</td>
+          <td class="paramname"><em>e</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char&#160;</td>
+          <td class="paramname"><em>b</em>[]&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>merges 2 sorted adjacent segments into a larger sorted segment </p>
+<p>best-case = worst-case = O(n) </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">l</td><td>points to the left part </td></tr>
+    <tr><td class="paramname">r</td><td>points to the right part, end of left part </td></tr>
+    <tr><td class="paramname">e</td><td>points to end of right part </td></tr>
+    <tr><td class="paramname">b</td><td>points at the buffer </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;                                                               {</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="comment">// create 2 pointers to point at the buffer</span></div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    <span class="keyword">auto</span> p(<span class="keyword">reinterpret_cast&lt;</span>std::remove_reference_t&lt;decltype(*l)<span class="keyword">&gt;</span>*&gt;(b)), c(p);</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="comment">// move the left part of the segment</span></div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    <span class="keywordflow">for</span> (Iterator t(l); r != t; ++t) *p++ = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(*t);</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <span class="comment">// while neither the buffer nor the right part has been exhausted</span></div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="comment">// move the smallest element of the two back to the container</span></div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    <span class="keywordflow">while</span> (e != r &amp;&amp; c != p) *l++ = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(*r &lt; *c ? *r++ : *c++);</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <span class="comment">// notice only one of the two following loops will be executed</span></div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <span class="comment">// while the right part hasn&#39;t bee exhausted, move it back</span></div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    <span class="keywordflow">while</span> (e != r) *l++ = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(*r++);</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="comment">// while the buffer hasn&#39;t bee exhausted, move it back</span></div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <span class="keywordflow">while</span> (c != p) *l++ = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(*c++);</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae97f4dd815654c4682f564afd718e824"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae97f4dd815654c4682f564afd718e824">&#9670;&nbsp;</a></span>non_recursive_merge_sort() <span class="overload">[1/3]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Iterator &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">void sorting::non_recursive_merge_sort </td>
+          <td>(</td>
+          <td class="paramtype">const Iterator&#160;</td>
+          <td class="paramname"><em>first</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const Iterator&#160;</td>
+          <td class="paramname"><em>last</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>bottom-up merge sort which sorts elements in a non-decreasing order </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">first</td><td>points to the first element </td></tr>
+    <tr><td class="paramname">last</td><td>points to 1-step past the last element </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;                                                                         {</div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <a class="code" href="../../d5/d91/namespacesorting.html#ae97f4dd815654c4682f564afd718e824">non_recursive_merge_sort</a>(first, last, last - first);</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d5/d91/namespacesorting_ae97f4dd815654c4682f564afd718e824_cgraph.svg" width="514" height="52"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a140d913e42fb94176a0b2c8b29a80420"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a140d913e42fb94176a0b2c8b29a80420">&#9670;&nbsp;</a></span>non_recursive_merge_sort() <span class="overload">[2/3]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Iterator &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">void sorting::non_recursive_merge_sort </td>
+          <td>(</td>
+          <td class="paramtype">const Iterator&#160;</td>
+          <td class="paramname"><em>first</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const Iterator&#160;</td>
+          <td class="paramname"><em>last</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const size_t&#160;</td>
+          <td class="paramname"><em>n</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>bottom-up merge sort which sorts elements in a non-decreasing order </p>
+<p>sorts elements non-recursively by breaking them into small segments, merging adjacent segments into larger sorted segments, then increasing the sizes of segments by factors of 2 and repeating the same process. best-case = worst-case = O(n log(n)) </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">first</td><td>points to the first element </td></tr>
+    <tr><td class="paramname">last</td><td>points to 1-step past the last element </td></tr>
+    <tr><td class="paramname">n</td><td>the number of elements </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;                                              {</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="comment">// create a buffer large enough to store all elements</span></div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    <span class="comment">// dynamically allocated to comply with cpplint</span></div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <span class="keywordtype">char</span>* buffer = <span class="keyword">new</span> <span class="keywordtype">char</span>[n * <span class="keyword">sizeof</span>(*first)];</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="comment">// buffer size can be optimized to largest power of 2 less than n</span></div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="comment">// elements divide the container into equally-sized segments whose</span></div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="comment">// length start at 1 and keeps increasing by factors of 2</span></div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> length(1); length &lt; n; length &lt;&lt;= 1) {</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        <span class="comment">// merge adjacent segments whose number is n / (length * 2)</span></div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;        Iterator <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>(first);</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> counter(n / (length &lt;&lt; 1)); counter; --counter) {</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;            Iterator <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>(left + length), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>(right + length);</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;            <a class="code" href="../../d5/d91/namespacesorting.html#aa26de383227859210f14dcf12201a079">merge</a>(left, right, end, buffer);</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>;</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        }</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;        <span class="comment">// if the number of remaining elements (n * 2 % length) is longer</span></div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        <span class="comment">// than a segment, merge the remaining elements</span></div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        <span class="keywordflow">if</span> ((n &amp; ((length &lt;&lt; 1) - 1)) &gt; length)</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;            <a class="code" href="../../d5/d91/namespacesorting.html#aa26de383227859210f14dcf12201a079">merge</a>(left, left + length, last, buffer);</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    }</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    <span class="keyword">delete</span>[] buffer;</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d5/d91/namespacesorting_a140d913e42fb94176a0b2c8b29a80420_cgraph.svg" width="315" height="52"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a27236b8d3df3832e1f1225576a122534"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a27236b8d3df3832e1f1225576a122534">&#9670;&nbsp;</a></span>non_recursive_merge_sort() <span class="overload">[3/3]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Iterator &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">void sorting::non_recursive_merge_sort </td>
+          <td>(</td>
+          <td class="paramtype">const Iterator&#160;</td>
+          <td class="paramname"><em>first</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const size_t&#160;</td>
+          <td class="paramname"><em>n</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>bottom-up merge sort which sorts elements in a non-decreasing order </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">first</td><td>points to the first element </td></tr>
+    <tr><td class="paramname">n</td><td>the number of elements </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;                                                                    {</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <a class="code" href="../../d5/d91/namespacesorting.html#ae97f4dd815654c4682f564afd718e824">non_recursive_merge_sort</a>(first, first + n, n);</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d5/d91/namespacesorting_a27236b8d3df3832e1f1225576a122534_cgraph.svg" width="514" height="52"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a7e7f25f31c50523990437abf2ac3907e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a7e7f25f31c50523990437abf2ac3907e">&#9670;&nbsp;</a></span>partition()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int sorting::partition </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>arr</em>[], </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>low</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>high</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>This function takes last element as pivot, places the pivot element at its correct position in sorted array, and places all smaller (smaller than pivot) to left of pivot and all greater elements to right of pivot </p>
+<div class="fragment"><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;                                            {</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    <span class="keywordtype">int</span> pivot = arr[high];  <span class="comment">// taking the last element as pivot</span></div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keywordtype">int</span> i = (low - 1);      <span class="comment">// Index of smaller element</span></div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160; </div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = low; j &lt; high; j++) {</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        <span class="comment">// If current element is smaller than or</span></div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        <span class="comment">// equal to pivot</span></div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        <span class="keywordflow">if</span> (arr[j] &lt;= pivot) {</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;            i++;  <span class="comment">// increment index of smaller element</span></div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;            <span class="keywordtype">int</span> temp = arr[i];</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;            arr[i] = arr[j];</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;            arr[j] = temp;</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        }</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    }</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    <span class="keywordtype">int</span> temp = arr[i + 1];</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    arr[i + 1] = arr[high];</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    arr[high] = temp;</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    <span class="keywordflow">return</span> (i + 1);</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a50b66a1c652291b9a346ec7342967178"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a50b66a1c652291b9a346ec7342967178">&#9670;&nbsp;</a></span>quickSort()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void sorting::quickSort </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>arr</em>[], </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>low</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>high</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>The main function that implements QuickSort arr[] --&gt; Array to be sorted, low --&gt; Starting index, high --&gt; Ending index </p>
+<div class="fragment"><div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;                                             {</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    <span class="keywordflow">if</span> (low &lt; high) {</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        <span class="keywordtype">int</span> p = <a class="code" href="../../d5/d91/namespacesorting.html#a7e7f25f31c50523990437abf2ac3907e">partition</a>(arr, low, high);</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        <a class="code" href="../../d5/d91/namespacesorting.html#a50b66a1c652291b9a346ec7342967178">quickSort</a>(arr, low, p - 1);</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;        <a class="code" href="../../d5/d91/namespacesorting.html#a50b66a1c652291b9a346ec7342967178">quickSort</a>(arr, p + 1, high);</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    }</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d5/d91/namespacesorting_a50b66a1c652291b9a346ec7342967178_cgraph.svg" width="298" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="af2c5b92cbfe73f63f6074c61b0a45331"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af2c5b92cbfe73f63f6074c61b0a45331">&#9670;&nbsp;</a></span>shell_sort() <span class="overload">[1/3]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">void sorting::shell_sort </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; *&#160;</td>
+          <td class="paramname"><em>arr</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>function overload - when input array is of type <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html" title="STL class.">std::vector</a>, simply send the data content and the data length to the above function. </p>
+<div class="fragment"><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;                                   {</div>
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+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
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+</div>
+</div>
+
+</div>
+</div>
+<a id="a5669396c6a6b1e14b97589b6e37980aa"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a5669396c6a6b1e14b97589b6e37980aa">&#9670;&nbsp;</a></span>shell_sort() <span class="overload">[2/3]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">void sorting::shell_sort </td>
+          <td>(</td>
+          <td class="paramtype">T *&#160;</td>
+          <td class="paramname"><em>arr</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">size_t&#160;</td>
+          <td class="paramname"><em>LEN</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Optimized algorithm - takes half the time by utilizing Mar </p>
+<div class="fragment"><div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;                                    {</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> gaps[] = {701, 301, 132, 57, 23, 10, 4, 1};</div>
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+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160; </div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;            <span class="keywordflow">for</span> (j = i; j &gt;= gap &amp;&amp; (arr[j - gap] - tmp) &gt; 0; j -= gap) {</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;                arr[j] = arr[j - gap];</div>
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+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160; </div>
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+</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#a4d76603c54d3dc56146e92d10a043924">&#9670;&nbsp;</a></span>shell_sort() <span class="overload">[3/3]</span></h2>
+
+<div class="memitem">
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+          <td class="memname">void sorting::shell_sort </td>
+          <td>(</td>
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+          <td class="paramname"><em>arr</em>[N]</td><td>)</td>
+          <td></td>
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+</div><div class="memdoc">
+<p>function overload - when input array is of a known length array type </p>
+<div class="fragment"><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;                             {</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <a class="code" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(arr, N);</div>
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+</div><!-- doc-content -->
+<div class="ttc" id="amove_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a></div><div class="ttdeci">T move(T... args)</div></div>
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+<div class="ttc" id="anamespacesorting_html_aa26de383227859210f14dcf12201a079"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#aa26de383227859210f14dcf12201a079">sorting::merge</a></div><div class="ttdeci">void merge(Iterator, Iterator, const Iterator, char[])</div><div class="ttdoc">merges 2 sorted adjacent segments into a larger sorted segment</div><div class="ttdef"><b>Definition:</b> non_recursive_merge_sort.cpp:57</div></div>
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+<div class="ttc" id="aleft_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a></div><div class="ttdeci">T left(T... args)</div></div>
+<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a></div><div class="ttdeci">T end(T... args)</div></div>
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+<div class="ttc" id="anamespacesorting_html_af2c5b92cbfe73f63f6074c61b0a45331"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">sorting::shell_sort</a></div><div class="ttdeci">void shell_sort(std::vector&lt; T &gt; *arr)</div><div class="ttdef"><b>Definition:</b> shell_sort2.cpp:75</div></div>
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+    <li class="navelem"><a class="el" href="../../d5/d91/namespacesorting.html">sorting</a></li>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
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+<a href="#pub-attribs">Public Attributes</a> &#124;
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+  <div class="headertitle">
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+<a href="#nested-classes">Classes</a> &#124;
+<a href="#namespaces">Namespaces</a> &#124;
+<a href="#define-members">Macros</a> &#124;
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">adaline_learning.cpp File Reference<div class="ingroups"><a class="el" href="../../d9/d66/group__machine__learning.html">Machine Learning Algorithms</a></div></div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a href="https://en.wikipedia.org/wiki/ADALINE">Adaptive Linear Neuron (ADALINE)</a> implementation  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
+<code>#include &lt;climits&gt;</code><br />
+<code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;cstdlib&gt;</code><br />
+<code>#include &lt;ctime&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;numeric&gt;</code><br />
+<code>#include &lt;vector&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for adaline_learning.cpp:</div>
+<div class="dyncontent">
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+</div>
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+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="namespaces"></a>
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+<tr class="memdesc:d8/d77/namespacemachine__learning"><td class="mdescLeft">&#160;</td><td class="mdescRight">Machine learning algorithms. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="define-members"></a>
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+#define&#160;</td><td class="memItemRight" valign="bottom"><b>MAX_ITER</b>&#160;&#160;&#160;500</td></tr>
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+<tr class="memitem:a52053d88ea1bcbbed9aca67ab4eeb499"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/db0/adaline__learning_8cpp.html#a52053d88ea1bcbbed9aca67ab4eeb499">test1</a> (double eta=0.01)</td></tr>
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+<tr class="memitem:a379f7488a305f2571f2932b319931f82"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/db0/adaline__learning_8cpp.html#a379f7488a305f2571f2932b319931f82">test2</a> (double eta=0.01)</td></tr>
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+<tr class="memitem:a992bdf1fdb0b9d414bcf7981d2d87aa9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/db0/adaline__learning_8cpp.html#a992bdf1fdb0b9d414bcf7981d2d87aa9">test3</a> (double eta=0.01)</td></tr>
+<tr class="separator:a992bdf1fdb0b9d414bcf7981d2d87aa9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/db0/adaline__learning_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
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+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/ADALINE">Adaptive Linear Neuron (ADALINE)</a> implementation </p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
+<p><img src="https://upload.wikimedia.org/wikipedia/commons/b/be/Adaline_flow_chart.gif" alt="" width="200px" class="inline"/> <a href="https://commons.wikimedia.org/wiki/File:Adaline_flow_chart.gif">source</a> ADALINE is one of the first and simplest single layer artificial neural network. The algorithm essentially implements a linear function </p><p class="formulaDsp">
+\[ f\left(x_0,x_1,x_2,\ldots\right) = \sum_j x_jw_j+\theta \]
+</p>
+<p> where \(x_j\) are the input features of a sample, \(w_j\) are the coefficients of the linear function and \(\theta\) is a constant. If we know the \(w_j\), then for any given set of features, \(y\) can be computed. Computing the \(w_j\) is a supervised learning algorithm wherein a set of features and their corresponding outputs are given and weights are computed using stochastic gradient descent method. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&nbsp;</a></span>main()</h2>
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+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>argc</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char **&#160;</td>
+          <td class="paramname"><em>argv</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;                                {</div>
+<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));  <span class="comment">// initialize random number generator</span></div>
+<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160; </div>
+<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;    <span class="keywordtype">double</span> eta = 0.1;  <span class="comment">// default value of eta</span></div>
+<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;    <span class="keywordflow">if</span> (argc == 2)     <span class="comment">// read eta value from commandline argument if present</span></div>
+<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;        eta = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strtof.html">strtof</a>(argv[1], <span class="keyword">nullptr</span>);</div>
+<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160; </div>
+<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;    <a class="code" href="../../d5/db0/adaline__learning_8cpp.html#a52053d88ea1bcbbed9aca67ab4eeb499">test1</a>(eta);</div>
+<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160; </div>
+<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Press ENTER to continue...&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.get();</div>
+<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160; </div>
+<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;    <a class="code" href="../../d5/db0/adaline__learning_8cpp.html#a379f7488a305f2571f2932b319931f82">test2</a>(eta);</div>
+<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160; </div>
+<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Press ENTER to continue...&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>.get();</div>
+<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160; </div>
+<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;    <a class="code" href="../../d5/db0/adaline__learning_8cpp.html#a992bdf1fdb0b9d414bcf7981d2d87aa9">test3</a>(eta);</div>
+<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160; </div>
+<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d5/db0/adaline__learning_8cpp_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="100%" height="600"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a52053d88ea1bcbbed9aca67ab4eeb499"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a52053d88ea1bcbbed9aca67ab4eeb499">&#9670;&nbsp;</a></span>test1()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test1 </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>eta</em> = <code>0.01</code></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>test function to predict points in a 2D coordinate system above the line \(x=y\) as +1 and others as -1. Note that each point is defined by 2 values or 2 features. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">eta</td><td>learning rate (optional, default=0.01) </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;                              {</div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(2, eta);  <span class="comment">// 2 features</span></div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160; </div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = 10;  <span class="comment">// number of sample points</span></div>
+<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160; </div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> X[N] = {{0, 1},  {1, -2},   {2, 3},   {3, -1},</div>
+<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;                                {4, 1},  {6, -5},   {-7, -3}, {-8, 5},</div>
+<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;                                {-9, 2}, {-10, -15}};</div>
+<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <span class="keywordtype">int</span> y[] = {1, -1, 1, -1, -1, -1, 1, 1, 1, -1};  <span class="comment">// corresponding y-values</span></div>
+<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160; </div>
+<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 1 -------&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160; </div>
+<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    ada.fit(X, y);</div>
+<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model after fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160; </div>
+<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;    <span class="keywordtype">int</span> predict = ada.predict({5, -3});</div>
+<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(5,-3): &quot;</span> &lt;&lt; predict;</div>
+<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    assert(predict == -1);</div>
+<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160; </div>
+<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    predict = ada.predict({5, 8});</div>
+<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(5,8): &quot;</span> &lt;&lt; predict;</div>
+<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;    assert(predict == 1);</div>
+<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d5/db0/adaline__learning_8cpp_a52053d88ea1bcbbed9aca67ab4eeb499_cgraph.svg" width="100%" height="544"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a379f7488a305f2571f2932b319931f82"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a379f7488a305f2571f2932b319931f82">&#9670;&nbsp;</a></span>test2()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test2 </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>eta</em> = <code>0.01</code></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>test function to predict points in a 2D coordinate system above the line \(x+3y=-1\) as +1 and others as -1. Note that each point is defined by 2 values or 2 features. The function will create random sample points for training and test purposes. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">eta</td><td>learning rate (optional, default=0.01) </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;                              {</div>
+<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;    <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(2, eta);  <span class="comment">// 2 features</span></div>
+<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160; </div>
+<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = 50;  <span class="comment">// number of sample points</span></div>
+<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160; </div>
+<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> X[N];</div>
+<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;    <span class="keywordtype">int</span> Y[N];  <span class="comment">// corresponding y-values</span></div>
+<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160; </div>
+<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;    <span class="comment">// generate sample points in the interval</span></div>
+<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;    <span class="comment">// [-range2/100 , (range2-1)/100]</span></div>
+<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;    <span class="keywordtype">int</span> range = 500;          <span class="comment">// sample points full-range</span></div>
+<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;    <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;  <span class="comment">// sample points half-range</span></div>
+<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++) {</div>
+<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;        <span class="keywordtype">double</span> x0 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;        <span class="keywordtype">double</span> x1 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;        X[i] = {x0, x1};</div>
+<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;        Y[i] = (x0 + 3. * x1) &gt; -1 ? 1 : -1;</div>
+<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;    }</div>
+<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160; </div>
+<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 2 -------&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model before fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160; </div>
+<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;    ada.fit(X, Y);</div>
+<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Model after fit: &quot;</span> &lt;&lt; ada &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160; </div>
+<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;    <span class="keywordtype">int</span> N_test_cases = 5;</div>
+<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N_test_cases; i++) {</div>
+<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;        <span class="keywordtype">double</span> x0 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;        <span class="keywordtype">double</span> x1 = ((<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range) - range2) / 100.f;</div>
+<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160; </div>
+<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;        <span class="keywordtype">int</span> predict = ada.predict({x0, x1});</div>
+<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160; </div>
+<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Predict for x=(&quot;</span> &lt;&lt; x0 &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; x1 &lt;&lt; <span class="stringliteral">&quot;): &quot;</span> &lt;&lt; predict;</div>
+<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160; </div>
+<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;        <span class="keywordtype">int</span> expected_val = (x0 + 3. * x1) &gt; -1 ? 1 : -1;</div>
+<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;        assert(predict == expected_val);</div>
+<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; ...passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    }</div>
+<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d5/db0/adaline__learning_8cpp_a379f7488a305f2571f2932b319931f82_cgraph.svg" width="100%" height="544"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a992bdf1fdb0b9d414bcf7981d2d87aa9"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a992bdf1fdb0b9d414bcf7981d2d87aa9">&#9670;&nbsp;</a></span>test3()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test3 </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>eta</em> = <code>0.01</code></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>test function to predict points in a 3D coordinate system lying within the sphere of radius 1 and centre at origin as +1 and others as -1. Note that each point is defined by 3 values but we use 6 features. The function will create random sample points for training and test purposes. The sphere centred at origin and radius 1 is defined as: \(x^2+y^2+z^2=r^2=1\) and if the \(r^2&lt;1\), point lies within the sphere else, outside.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">eta</td><td>learning rate (optional, default=0.01) </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;                              {</div>
+<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;    <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> ada(6, eta);  <span class="comment">// 2 features</span></div>
+<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160; </div>
+<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = 100;  <span class="comment">// number of sample points</span></div>
+<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160; </div>
+<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> X[N];</div>
+<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    <span class="keywordtype">int</span> Y[N];  <span class="comment">// corresponding y-values</span></div>
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+<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    <span class="comment">// generate sample points in the interval</span></div>
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+<div class="title">stairs_pattern.cpp File Reference</div>  </div>
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+<div class="contents">
+
+<p>This program is use to print the following pattern.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for stairs_pattern.cpp:</div>
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/def/stairs__pattern_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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+   \*\*
+   \*\*
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+  <div class="summary">
+<a href="#pub-methods">Public Member Functions</a> &#124;
+<a href="#pri-methods">Private Member Functions</a> &#124;
+<a href="#pri-attribs">Private Attributes</a> &#124;
+<a href="#friends">Friends</a> &#124;
+<a href="../../d9/d21/classmachine__learning_1_1adaline-members.html">List of all members</a>  </div>
+  <div class="headertitle">
+<div class="title">machine_learning::adaline Class Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+<div class="dynheader">
+Collaboration diagram for machine_learning::adaline:</div>
+<div class="dyncontent">
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+</div>
+<center><span class="legend">[<a target="top" href="../../graph_legend.html">legend</a>]</span></center></div>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
+Public Member Functions</h2></td></tr>
+<tr class="memitem:a0acbe32aaab897e7939e5b0454035b8c"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html#a0acbe32aaab897e7939e5b0454035b8c">adaline</a> (int num_features, const double <a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a>=0.01<a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a>, const double <a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a>=1e-5)</td></tr>
+<tr class="separator:a0acbe32aaab897e7939e5b0454035b8c"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ab11242d9ad5b03a75911e29b04f78fd3"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html#ab11242d9ad5b03a75911e29b04f78fd3">predict</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt; &amp;x, double *out=nullptr)</td></tr>
+<tr class="separator:ab11242d9ad5b03a75911e29b04f78fd3"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a74e3c6c037b67895014414c5d75465e5"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html#a74e3c6c037b67895014414c5d75465e5">fit</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt; &amp;x, const int &amp;y)</td></tr>
+<tr class="separator:a74e3c6c037b67895014414c5d75465e5"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a9f1c7cd34252a9ece5bbe7ba36799044"><td class="memTemplParams" colspan="2">template&lt;int N&gt; </td></tr>
+<tr class="memitem:a9f1c7cd34252a9ece5bbe7ba36799044"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html#a9f1c7cd34252a9ece5bbe7ba36799044">fit</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt; const (&amp;X)[N], const int *y)</td></tr>
+<tr class="separator:a9f1c7cd34252a9ece5bbe7ba36799044"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a082f758fb55fe19f22b3df66f89b2325"><td class="memItemLeft" align="right" valign="top"><a id="a082f758fb55fe19f22b3df66f89b2325"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>activation</b> (double x)</td></tr>
+<tr class="separator:a082f758fb55fe19f22b3df66f89b2325"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-methods"></a>
+Private Member Functions</h2></td></tr>
+<tr class="memitem:ac8a9c2aaaa63b0f27ea176857e1e7d56"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html#ac8a9c2aaaa63b0f27ea176857e1e7d56">check_size_match</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt; &amp;x)</td></tr>
+<tr class="separator:ac8a9c2aaaa63b0f27ea176857e1e7d56"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-attribs"></a>
+Private Attributes</h2></td></tr>
+<tr class="memitem:a28160d17e492597a2f112e0d38551cda"><td class="memItemLeft" align="right" valign="top"><a id="a28160d17e492597a2f112e0d38551cda"></a>
+const double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a></td></tr>
+<tr class="memdesc:a28160d17e492597a2f112e0d38551cda"><td class="mdescLeft">&#160;</td><td class="mdescRight">learning rate of the algorithm <br /></td></tr>
+<tr class="separator:a28160d17e492597a2f112e0d38551cda"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aa23d60262f917f35836ef4b1c1d9f7d3"><td class="memItemLeft" align="right" valign="top"><a id="aa23d60262f917f35836ef4b1c1d9f7d3"></a>
+const double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a></td></tr>
+<tr class="memdesc:aa23d60262f917f35836ef4b1c1d9f7d3"><td class="mdescLeft">&#160;</td><td class="mdescRight">model fit convergence accuracy <br /></td></tr>
+<tr class="separator:aa23d60262f917f35836ef4b1c1d9f7d3"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a4cd8fe438032fedaa66f93bfd66f5492"><td class="memItemLeft" align="right" valign="top"><a id="a4cd8fe438032fedaa66f93bfd66f5492"></a>
+<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a></td></tr>
+<tr class="memdesc:a4cd8fe438032fedaa66f93bfd66f5492"><td class="mdescLeft">&#160;</td><td class="mdescRight">weights of the neural network <br /></td></tr>
+<tr class="separator:a4cd8fe438032fedaa66f93bfd66f5492"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="friends"></a>
+Friends</h2></td></tr>
+<tr class="memitem:a1d821a24e1503d468c95d4acedca58b3"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html#a1d821a24e1503d468c95d4acedca58b3">operator&lt;&lt;</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;out, const <a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> &amp;ada)</td></tr>
+<tr class="separator:a1d821a24e1503d468c95d4acedca58b3"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
+<a id="a0acbe32aaab897e7939e5b0454035b8c"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0acbe32aaab897e7939e5b0454035b8c">&#9670;&nbsp;</a></span>adaline()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">machine_learning::adaline::adaline </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>num_features</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const double&#160;</td>
+          <td class="paramname"><em>eta</em> = <code>0.01<a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a></code>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const double&#160;</td>
+          <td class="paramname"><em>accuracy</em> = <code>1e-5</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Default constructor </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">num_features</td><td>number of features present </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">eta</td><td>learning rate (optional, default=0.1) </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">convergence</td><td>accuracy (optional, default= \(1\times10^{-5}\)) </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        : <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a>(<a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a>), <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a>(<a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a>) {</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a> &lt;= 0) {</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;learning rate should be positive and nonzero&quot;</span></div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;                      &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        }</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160; </div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a> = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>(</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;            num_features +</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;            1);  <span class="comment">// additional weight is for the constant bias term</span></div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160; </div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <span class="comment">// initialize with random weights in the range [-50, 49]</span></div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>[i] = 1.<a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a>;</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        <span class="comment">// weights[i] = (static_cast&lt;double&gt;(std::rand() % 100) - 50);</span></div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d30/classmachine__learning_1_1adaline_a0acbe32aaab897e7939e5b0454035b8c_cgraph.svg" width="347" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<h2 class="groupheader">Member Function Documentation</h2>
+<a id="ac8a9c2aaaa63b0f27ea176857e1e7d56"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac8a9c2aaaa63b0f27ea176857e1e7d56">&#9670;&nbsp;</a></span>check_size_match()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool machine_learning::adaline::check_size_match </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt; &amp;&#160;</td>
+          <td class="paramname"><em>x</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">private</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>convenient function to check if input feature vector size matches the model weights size </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>fecture vector to check </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><code>true</code> size matches </dd>
+<dd>
+<code>false</code> size does not match </dd></dl>
+<div class="fragment"><div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;                                                      {</div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;        <span class="keywordflow">if</span> (x.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != (<a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 1)) {</div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;: &quot;</span></div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;                      &lt;&lt; <span class="stringliteral">&quot;Number of features in x does not match the feature &quot;</span></div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;                         <span class="stringliteral">&quot;dimension in model!&quot;</span></div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;                      &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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+<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
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+</div>
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+
+</div>
+</div>
+<a id="a74e3c6c037b67895014414c5d75465e5"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a74e3c6c037b67895014414c5d75465e5">&#9670;&nbsp;</a></span>fit() <span class="overload">[1/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">double machine_learning::adaline::fit </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt; &amp;&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const int &amp;&#160;</td>
+          <td class="paramname"><em>y</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Update the weights of the model using supervised learning for one feature vector</p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>feature vector</td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">y</td><td>known output value </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>correction factor </dd></dl>
+<div class="fragment"><div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                                                         {</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        <span class="keywordflow">if</span> (!<a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#ac8a9c2aaaa63b0f27ea176857e1e7d56">check_size_match</a>(x))</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;            <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160; </div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        <span class="comment">/* output of the model with current weights */</span></div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;        <span class="keywordtype">int</span> p = <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#ab11242d9ad5b03a75911e29b04f78fd3">predict</a>(x);</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;        <span class="keywordtype">int</span> prediction_error = y - p;  <span class="comment">// error in estimation</span></div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;        <span class="keywordtype">double</span> correction_factor = <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">eta</a> * prediction_error;</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160; </div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;        <span class="comment">/* update each weight, the last weight is the bias term */</span></div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; x.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;            <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>[i] += correction_factor * x[i];</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        }</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;        <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>[x.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()] += correction_factor;  <span class="comment">// update bias</span></div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160; </div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;        <span class="keywordflow">return</span> correction_factor;</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d6/d30/classmachine__learning_1_1adaline_a74e3c6c037b67895014414c5d75465e5_cgraph.svg" width="100%" height="530"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
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+</div>
+<a id="a9f1c7cd34252a9ece5bbe7ba36799044"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a9f1c7cd34252a9ece5bbe7ba36799044">&#9670;&nbsp;</a></span>fit() <span class="overload">[2/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;int N&gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void machine_learning::adaline::fit </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt; const (&amp;)&#160;</td>
+          <td class="paramname"><em>X</em>[N], </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const int *&#160;</td>
+          <td class="paramname"><em>y</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Update the weights of the model using supervised learning for an array of vectors.</p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">X</td><td>array of feature vector</td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">y</td><td>known output value for each feature vector </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;                                                            {</div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;        <span class="keywordtype">double</span> avg_pred_error = 1.f;</div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160; </div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;        <span class="keywordtype">int</span> iter;</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;        <span class="keywordflow">for</span> (iter = 0; (iter &lt; MAX_ITER) &amp;&amp; (avg_pred_error &gt; <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">accuracy</a>);</div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;             iter++) {</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;            avg_pred_error = 0.f;</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160; </div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;            <span class="comment">// perform fit for each sample</span></div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++) {</div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;                <span class="keywordtype">double</span> err = <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a74e3c6c037b67895014414c5d75465e5">fit</a>(X[i], y[i]);</div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;                avg_pred_error += std::abs(err);</div>
+<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;            }</div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;            avg_pred_error /= N;</div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160; </div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;            <span class="comment">// Print updates every 200th iteration</span></div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;            <span class="comment">// if (iter % 100 == 0)</span></div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tIter &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot;: Training weights: &quot;</span> &lt;&lt; *<span class="keyword">this</span></div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;                      &lt;&lt; <span class="stringliteral">&quot;\tAvg error: &quot;</span> &lt;&lt; avg_pred_error &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        }</div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160; </div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        <span class="keywordflow">if</span> (iter &lt; MAX_ITER)</div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160; </div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Converged after &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot; iterations.&quot;</span></div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;                      &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;        <span class="keywordflow">else</span></div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Did not converge after &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot; iterations.&quot;</span></div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;                      &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ab11242d9ad5b03a75911e29b04f78fd3"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ab11242d9ad5b03a75911e29b04f78fd3">&#9670;&nbsp;</a></span>predict()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">int machine_learning::adaline::predict </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt; &amp;&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double *&#160;</td>
+          <td class="paramname"><em>out</em> = <code>nullptr</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>predict the output of the model for given set of features </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>input vector </td></tr>
+    <tr><td class="paramdir">[out]</td><td class="paramname">out</td><td>optional argument to return neuron output before applying activation function (optional, <code>nullptr</code> to ignore) </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>model prediction output </dd></dl>
+<div class="fragment"><div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;                                                                   {</div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        <span class="keywordflow">if</span> (!<a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#ac8a9c2aaaa63b0f27ea176857e1e7d56">check_size_match</a>(x))</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;            <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160; </div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;        <span class="keywordtype">double</span> y = <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/back.html">back</a>();  <span class="comment">// assign bias value</span></div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160; </div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;        <span class="comment">// for (int i = 0; i &lt; x.size(); i++) y += x[i] * weights[i];</span></div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        y = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/inner_product.html">std::inner_product</a>(x.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), x.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>(), <a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), y);</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160; </div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;        <span class="keywordflow">if</span> (out != <span class="keyword">nullptr</span>)  <span class="comment">// if out variable is provided</span></div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;            *out = y;</div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160; </div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        <span class="keywordflow">return</span> activation(y);  <span class="comment">// quantizer: apply ADALINE threshold function</span></div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d30/classmachine__learning_1_1adaline_ab11242d9ad5b03a75911e29b04f78fd3_cgraph.svg" width="567" height="256"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<h2 class="groupheader">Friends And Related Function Documentation</h2>
+<a id="a1d821a24e1503d468c95d4acedca58b3"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a1d821a24e1503d468c95d4acedca58b3">&#9670;&nbsp;</a></span>operator&lt;&lt;</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a>&amp; operator&lt;&lt; </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;&#160;</td>
+          <td class="paramname"><em>out</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="el" href="../../d6/d30/classmachine__learning_1_1adaline.html">adaline</a> &amp;&#160;</td>
+          <td class="paramname"><em>ada</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">friend</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Operator to print the weights of the model </p>
+<div class="fragment"><div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;                                                                       {</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;        out &lt;&lt; <span class="stringliteral">&quot;&lt;&quot;</span>;</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; ada.<a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;            out &lt;&lt; ada.<a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>[i];</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;            <span class="keywordflow">if</span> (i &lt; ada.<a class="code" href="../../d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">weights</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 1)</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;                out &lt;&lt; <span class="stringliteral">&quot;, &quot;</span>;</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        }</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        out &lt;&lt; <span class="stringliteral">&quot;&gt;&quot;</span>;</div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;        <span class="keywordflow">return</span> out;</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<hr/>The documentation for this class was generated from the following file:<ul>
+<li>machine_learning/<a class="el" href="../../d5/db0/adaline__learning_8cpp.html">adaline_learning.cpp</a></li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="ainner_product_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/inner_product.html">std::inner_product</a></div><div class="ttdeci">T inner_product(T... args)</div></div>
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+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
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+<div class="title">addition_rule.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Addition rule of probabilities.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for addition_rule.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d26/addition__rule_8cpp__incl.svg" width="142" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a4adfd055c758546456d440ee9133555d"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d4a/addition__rule_8cpp.html#a4adfd055c758546456d440ee9133555d">addition_rule_independent</a> (double A, double B)</td></tr>
+<tr class="separator:a4adfd055c758546456d440ee9133555d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a565ffcbbdbe496ced37250bc8dc36bc0"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d4a/addition__rule_8cpp.html#a565ffcbbdbe496ced37250bc8dc36bc0">addition_rule_dependent</a> (double A, double B, double B_given_A)</td></tr>
+<tr class="separator:a565ffcbbdbe496ced37250bc8dc36bc0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d4a/addition__rule_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Addition rule of probabilities. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a565ffcbbdbe496ced37250bc8dc36bc0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a565ffcbbdbe496ced37250bc8dc36bc0">&#9670;&nbsp;</a></span>addition_rule_dependent()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double addition_rule_dependent </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>B</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>B_given_A</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Calculates the probability of the events A or B for dependent events note that if value of B_given_A is unknown, use chainrule to find it \parama [in] A probability of event A \parama [in] B probability of event B \parama [in] B_given_A probability of event B condition A </p><dl class="section return"><dt>Returns</dt><dd>probability of A and B </dd></dl>
+<div class="fragment"><div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;                                                                     {</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <span class="keywordflow">return</span> (A + B) - (A * B_given_A);</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a4adfd055c758546456d440ee9133555d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a4adfd055c758546456d440ee9133555d">&#9670;&nbsp;</a></span>addition_rule_independent()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double addition_rule_independent </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>B</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>calculates the probability of the independent events A or B for independent events \parama [in] A probability of event A \parama [in] B probability of event B </p><dl class="section return"><dt>Returns</dt><dd>probability of A and B </dd></dl>
+<div class="fragment"><div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;                                                     {</div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;    <span class="keywordflow">return</span> (A + B) - (A * B);</div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;           {</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="keywordtype">double</span> A = 0.5;</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="keywordtype">double</span> B = 0.25;</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="keywordtype">double</span> B_given_A = 0.05;</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160; </div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;independent P(A or B) = &quot;</span> &lt;&lt; <a class="code" href="../../d6/d4a/addition__rule_8cpp.html#a4adfd055c758546456d440ee9133555d">addition_rule_independent</a>(A, B)</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;              &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160; </div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;dependent P(A or B) = &quot;</span></div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;              &lt;&lt; <a class="code" href="../../d6/d4a/addition__rule_8cpp.html#a565ffcbbdbe496ced37250bc8dc36bc0">addition_rule_dependent</a>(A, B, B_given_A) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160; </div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
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+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="aaddition__rule_8cpp_html_a565ffcbbdbe496ced37250bc8dc36bc0"><div class="ttname"><a href="../../d6/d4a/addition__rule_8cpp.html#a565ffcbbdbe496ced37250bc8dc36bc0">addition_rule_dependent</a></div><div class="ttdeci">double addition_rule_dependent(double A, double B, double B_given_A)</div><div class="ttdef"><b>Definition:</b> addition_rule.cpp:25</div></div>
+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
+<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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+<a href="#func-members">Functions</a>  </div>
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+<div class="title">Ordinary Differential Equations</div>  </div>
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+Functions</h2></td></tr>
+<tr class="memitem:gaa197c6b7085ac9ea71abc4c063e6f52f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#gaa197c6b7085ac9ea71abc4c063e6f52f">forward_euler_step</a> (const double dx, const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</td></tr>
+<tr class="memdesc:gaa197c6b7085ac9ea71abc4c063e6f52f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute next step approximation using the forward-Euler method.  <a href="../../d6/d60/group__ode.html#gaa197c6b7085ac9ea71abc4c063e6f52f">More...</a><br /></td></tr>
+<tr class="separator:gaa197c6b7085ac9ea71abc4c063e6f52f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a> (double dx, double x0, double x_max, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, bool save_to_file=false)</td></tr>
+<tr class="memdesc:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute approximation using the forward-Euler method in the given limits.  <a href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">More...</a><br /></td></tr>
+<tr class="separator:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="memdesc:ga8c319db420c3d97a83e9dcca803b6812"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute next step approximation using the midpoint-Euler method.  <a href="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">More...</a><br /></td></tr>
+<tr class="separator:ga8c319db420c3d97a83e9dcca803b6812"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga36ff0710861ca39d957046c0b09b2985"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga36ff0710861ca39d957046c0b09b2985">midpoint_euler</a> (double dx, double x0, double x_max, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, bool save_to_file=false)</td></tr>
+<tr class="memdesc:ga36ff0710861ca39d957046c0b09b2985"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute approximation using the midpoint-Euler method in the given limits.  <a href="../../d6/d60/group__ode.html#ga36ff0710861ca39d957046c0b09b2985">More...</a><br /></td></tr>
+<tr class="separator:ga36ff0710861ca39d957046c0b09b2985"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga827bf009831ddc477c5fa8891d5cb35f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a> (const double dx, const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</td></tr>
+<tr class="memdesc:ga827bf009831ddc477c5fa8891d5cb35f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute next step approximation using the semi-implicit-Euler method.  <a href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">More...</a><br /></td></tr>
+<tr class="separator:ga827bf009831ddc477c5fa8891d5cb35f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga3874d294ab00fe9ce8731c5b7991a089"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga3874d294ab00fe9ce8731c5b7991a089">semi_implicit_euler</a> (double dx, double x0, double x_max, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, bool save_to_file=false)</td></tr>
+<tr class="memdesc:ga3874d294ab00fe9ce8731c5b7991a089"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute approximation using the semi-implicit-Euler method in the given limits.  <a href="../../d6/d60/group__ode.html#ga3874d294ab00fe9ce8731c5b7991a089">More...</a><br /></td></tr>
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+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<p>Integration functions for implementations with solving <a href="https://en.wikipedia.org/wiki/Ordinary_differential_equation">ordinary differential equations</a> (ODEs) of any order and and any number of independent variables. </p>
+<h2 class="groupheader">Function Documentation</h2>
+<a id="gae0509f8843e2bc42de2abbd00a14b7b9"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#gae0509f8843e2bc42de2abbd00a14b7b9">&#9670;&nbsp;</a></span>forward_euler()</h2>
+
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+      <table class="memname">
+        <tr>
+          <td class="memname">double forward_euler </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>dx</em>, </td>
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+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>x0</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>x_max</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>y</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">bool&#160;</td>
+          <td class="paramname"><em>save_to_file</em> = <code>false</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Compute approximation using the forward-Euler method in the given limits. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">dx</td><td>step size </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">x0</td><td>initial value of independent variable </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">x_max</td><td>final value of independent variable </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>take \(y_n\) and compute \(y_{n+1}\) </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">save_to_file</td><td>flag to save results to a CSV file (1) or not (0) </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>time taken for computation in seconds </dd></dl>
+<div class="fragment"><div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;                                                                        {</div>
+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> dy = y[0];</div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160; </div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp;</div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    <span class="keywordflow">if</span> (save_to_file) {</div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;        fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(<span class="stringliteral">&quot;forward_euler.csv&quot;</span>, std::ofstream::out);</div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;        <span class="keywordflow">if</span> (!fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">&quot;Error! &quot;</span>);</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        }</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    }</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160; </div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> L = y-&gt;size();</div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160; </div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    <span class="comment">/* start integration */</span></div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t1 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    <span class="keywordtype">double</span> x = x0;</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160; </div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <span class="keywordflow">do</span> {  <span class="comment">// iterate for each step of independent variable</span></div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;        <span class="keywordflow">if</span> (save_to_file &amp;&amp; fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;            <span class="comment">// write to file</span></div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;            fp &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; L - 1; i++) {</div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;                fp &lt;&lt; y[0][i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;            }</div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;            fp &lt;&lt; y[0][L - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;        }</div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160; </div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;        <a class="code" href="../../d6/d60/group__ode.html#gaa197c6b7085ac9ea71abc4c063e6f52f">forward_euler_step</a>(dx, x, y, &amp;dy);  <span class="comment">// perform integration</span></div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;        x += dx;                            <span class="comment">// update step</span></div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    } <span class="keywordflow">while</span> (x &lt;= x_max);  <span class="comment">// till upper limit of independent variable</span></div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    <span class="comment">/* end of integration */</span></div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t2 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160; </div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    <span class="keywordflow">if</span> (fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;        fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">close</a>();</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160; </div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d60/group__ode_gae0509f8843e2bc42de2abbd00a14b7b9_cgraph.svg" width="427" height="291"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="gaa197c6b7085ac9ea71abc4c063e6f52f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#gaa197c6b7085ac9ea71abc4c063e6f52f">&#9670;&nbsp;</a></span>forward_euler_step()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void forward_euler_step </td>
+          <td>(</td>
+          <td class="paramtype">const double&#160;</td>
+          <td class="paramname"><em>dx</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>y</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>dy</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Compute next step approximation using the forward-Euler method. </p>
+<p class="formulaDsp">
+\[y_{n+1}=y_n + dx\cdot f\left(x_n,y_n\right)\]
+</p>
+ <dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">dx</td><td>step size </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>take \(x_n\) and compute \(x_{n+1}\) </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>take \(y_n\) and compute \(y_{n+1}\) </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">dy</td><td>compute \(f\left(x_n,y_n\right)\) </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;                                                                         {</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <a class="code" href="../../db/dd3/ode__forward__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(x, y, dy);</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    y[0] += dy[0] * dx;</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d60/group__ode_gaa197c6b7085ac9ea71abc4c063e6f52f_cgraph.svg" width="259" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ga36ff0710861ca39d957046c0b09b2985"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ga36ff0710861ca39d957046c0b09b2985">&#9670;&nbsp;</a></span>midpoint_euler()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double midpoint_euler </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>dx</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>x0</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>x_max</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>y</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">bool&#160;</td>
+          <td class="paramname"><em>save_to_file</em> = <code>false</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Compute approximation using the midpoint-Euler method in the given limits. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">dx</td><td>step size </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">x0</td><td>initial value of independent variable </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">x_max</td><td>final value of independent variable </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>take \(y_n\) and compute \(y_{n+1}\) </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">save_to_file</td><td>flag to save results to a CSV file (1) or not (0) </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>time taken for computation in seconds </dd></dl>
+<div class="fragment"><div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                                                                         {</div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> dy = y[0];</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160; </div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp;</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    <span class="keywordflow">if</span> (save_to_file) {</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(<span class="stringliteral">&quot;midpoint_euler.csv&quot;</span>, std::ofstream::out);</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        <span class="keywordflow">if</span> (!fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">&quot;Error! &quot;</span>);</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;        }</div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    }</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160; </div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> L = y-&gt;size();</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160; </div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <span class="comment">/* start integration */</span></div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t1 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    <span class="keywordtype">double</span> x = x0;</div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    <span class="keywordflow">do</span> {  <span class="comment">// iterate for each step of independent variable</span></div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;        <span class="keywordflow">if</span> (save_to_file &amp;&amp; fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;            <span class="comment">// write to file</span></div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;            fp &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; L - 1; i++) {</div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;                fp &lt;&lt; y[0][i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;            }</div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;            fp &lt;&lt; y[0][L - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        }</div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160; </div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;        <a class="code" href="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">midpoint_euler_step</a>(dx, x, y, &amp;dy);  <span class="comment">// perform integration</span></div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;        x += dx;                             <span class="comment">// update step</span></div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    } <span class="keywordflow">while</span> (x &lt;= x_max);  <span class="comment">// till upper limit of independent variable</span></div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    <span class="comment">/* end of integration */</span></div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t2 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160; </div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    <span class="keywordflow">if</span> (fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;        fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">close</a>();</div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160; </div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d60/group__ode_ga36ff0710861ca39d957046c0b09b2985_cgraph.svg" width="434" height="291"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
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+</div>
+</div>
+<a id="ga8c319db420c3d97a83e9dcca803b6812"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ga8c319db420c3d97a83e9dcca803b6812">&#9670;&nbsp;</a></span>midpoint_euler_step()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void midpoint_euler_step </td>
+          <td>(</td>
+          <td class="paramtype">const double&#160;</td>
+          <td class="paramname"><em>dx</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>y</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>dy</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Compute next step approximation using the midpoint-Euler method. </p>
+<p class="formulaDsp">
+\[y_{n+1} = y_n + dx\, f\left(x_n+\frac{1}{2}dx, y_n + \frac{1}{2}dx\,f\left(x_n,y_n\right)\right)\]
+</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">dx</td><td>step size </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>take \(x_n\) and compute \(x_{n+1}\) </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>take \(y_n\) and compute \(y_{n+1}\) </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">dy</td><td>compute \(f\left(x_n,y_n\right)\) </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;                                                                          {</div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <a class="code" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(x, y, dy);</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <span class="keywordtype">double</span> tmp_x = x + 0.5 * dx;</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160; </div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> tmp_y = y[0] + dy[0] * (0.5 * dx);</div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160; </div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    <a class="code" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(tmp_x, &amp;tmp_y, dy);</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160; </div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    y[0] += dy[0] * dx;</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d60/group__ode_ga8c319db420c3d97a83e9dcca803b6812_cgraph.svg" width="266" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
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+
+</div>
+</div>
+<a id="ga3874d294ab00fe9ce8731c5b7991a089"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ga3874d294ab00fe9ce8731c5b7991a089">&#9670;&nbsp;</a></span>semi_implicit_euler()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double semi_implicit_euler </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>dx</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>x0</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>x_max</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>y</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">bool&#160;</td>
+          <td class="paramname"><em>save_to_file</em> = <code>false</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Compute approximation using the semi-implicit-Euler method in the given limits. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">dx</td><td>step size </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">x0</td><td>initial value of independent variable </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">x_max</td><td>final value of independent variable </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>take \(y_n\) and compute \(y_{n+1}\) </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">save_to_file</td><td>flag to save results to a CSV file (1) or not (0) </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>time taken for computation in seconds </dd></dl>
+<div class="fragment"><div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                                                      {</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> dy = y[0];</div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160; </div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp;</div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <span class="keywordflow">if</span> (save_to_file) {</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;        fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(<span class="stringliteral">&quot;semi_implicit_euler.csv&quot;</span>, std::ofstream::out);</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        <span class="keywordflow">if</span> (!fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">&quot;Error! &quot;</span>);</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        }</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    }</div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160; </div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> L = y-&gt;size();</div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160; </div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    <span class="comment">/* start integration */</span></div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t1 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <span class="keywordtype">double</span> x = x0;</div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <span class="keywordflow">do</span> {  <span class="comment">// iterate for each step of independent variable</span></div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        <span class="keywordflow">if</span> (save_to_file &amp;&amp; fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;            <span class="comment">// write to file</span></div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;            fp &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; L - 1; i++) {</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;                fp &lt;&lt; y[0][i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;            }</div>
+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;            fp &lt;&lt; y[0][L - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;        }</div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160; </div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;        <a class="code" href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a>(dx, x, y, &amp;dy);  <span class="comment">// perform integration</span></div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        x += dx;                                  <span class="comment">// update step</span></div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    } <span class="keywordflow">while</span> (x &lt;= x_max);  <span class="comment">// till upper limit of independent variable</span></div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    <span class="comment">/* end of integration */</span></div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t2 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160; </div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    <span class="keywordflow">if</span> (fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;        fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">close</a>();</div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160; </div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d60/group__ode_ga3874d294ab00fe9ce8731c5b7991a089_cgraph.svg" width="474" height="291"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ga827bf009831ddc477c5fa8891d5cb35f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ga827bf009831ddc477c5fa8891d5cb35f">&#9670;&nbsp;</a></span>semi_implicit_euler_step()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void semi_implicit_euler_step </td>
+          <td>(</td>
+          <td class="paramtype">const double&#160;</td>
+          <td class="paramname"><em>dx</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>y</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>dy</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Compute next step approximation using the semi-implicit-Euler method. </p>
+<p class="formulaDsp">
+\[y_{n+1}=y_n + dx\cdot f\left(x_n,y_n\right)\]
+</p>
+ <dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">dx</td><td>step size </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>take \(x_n\) and compute \(x_{n+1}\) </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>take \(y_n\) and compute \(y_{n+1}\) </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">dy</td><td>compute \(f\left(x_n,y_n\right)\) </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;                                                       {</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    <a class="code" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(x, y, dy);         <span class="comment">// update dy once</span></div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    y[0][0] += dx * dy[0][0];  <span class="comment">// update y0</span></div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <a class="code" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(x, y, dy);         <span class="comment">// update dy once more</span></div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160; </div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    dy[0][0] = 0.f;      <span class="comment">// ignore y0</span></div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    y[0] += dy[0] * dx;  <span class="comment">// update remaining using new dy</span></div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d60/group__ode_ga827bf009831ddc477c5fa8891d5cb35f_cgraph.svg" width="292" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="agroup__ode_html_ga827bf009831ddc477c5fa8891d5cb35f"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a></div><div class="ttdeci">void semi_implicit_euler_step(const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the semi-implicit-Euler method.</div><div class="ttdef"><b>Definition:</b> ode_semi_implicit_euler.cpp:82</div></div>
+<div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
+<div class="ttc" id="agroup__ode_html_ga8c319db420c3d97a83e9dcca803b6812"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">midpoint_euler_step</a></div><div class="ttdeci">void midpoint_euler_step(const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the midpoint-Euler method.</div><div class="ttdef"><b>Definition:</b> ode_midpoint_euler.cpp:85</div></div>
+<div class="ttc" id="agroup__ode_html_gaa197c6b7085ac9ea71abc4c063e6f52f"><div class="ttname"><a href="../../d6/d60/group__ode.html#gaa197c6b7085ac9ea71abc4c063e6f52f">forward_euler_step</a></div><div class="ttdeci">void forward_euler_step(const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the forward-Euler method.</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:86</div></div>
+<div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
+<div class="ttc" id="abasic_ofstream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="aclose_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">std::ofstream::close</a></div><div class="ttdeci">T close(T... args)</div></div>
+<div class="ttc" id="aperror_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a></div><div class="ttdeci">T perror(T... args)</div></div>
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+
+<p>Compute factorial of any arbitratily large number/.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cstring&gt;</code><br />
+<code>#include &lt;ctime&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &quot;<a class="el" href="../../d4/d86/large__number_8h_source.html">./large_number.h</a>&quot;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for large_factorial.cpp:</div>
+<div class="dyncontent">
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+Functions</h2></td></tr>
+<tr class="memitem:a3f93b60e229b6683e24c4754a7106ee8"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d9d/large__factorial_8cpp.html#a3f93b60e229b6683e24c4754a7106ee8">test1</a> ()</td></tr>
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+<tr class="memitem:a76aae4778fbe89a3d59fd61fbc050cfa"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d9d/large__factorial_8cpp.html#a76aae4778fbe89a3d59fd61fbc050cfa">test2</a> ()</td></tr>
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+<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d9d/large__factorial_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Compute factorial of any arbitratily large number/. </p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d9/d00/factorial_8cpp.html" title="C++ program to find factorial of given number.">factorial.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a0ddf1224851353fc92bfbff6f499fa97"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
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+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>argc</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char *&#160;</td>
+          <td class="paramname"><em>argv</em>[]&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
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+</div><div class="memdoc">
+<p>Main program </p>
+<div class="fragment"><div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;                                 {</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <span class="keywordtype">int</span> number, i;</div>
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+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;        number = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
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+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; number;</div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    }</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160; </div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> result;</div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160; </div>
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+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d6/d9d/large__factorial_8cpp_a0ddf1224851353fc92bfbff6f499fa97_cgraph.svg" width="100%" height="594"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a3f93b60e229b6683e24c4754a7106ee8"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a3f93b60e229b6683e24c4754a7106ee8">&#9670;&nbsp;</a></span>test1()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool test1 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test implementation for 10! Result must be 3628800. </p><dl class="section return"><dt>Returns</dt><dd>True if test pass else False </dd></dl>
+<div class="fragment"><div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;             {</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;---- Check 1\t&quot;</span>;</div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, number = 10;</div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;    <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> result;</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    <span class="keywordflow">for</span> (i = 2; i &lt;= number; i++) <span class="comment">/* Multiply every number from 2 thru N */</span></div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;        result *= i;</div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160; </div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">char</span> *known_reslt = <span class="stringliteral">&quot;3628800&quot;</span>;</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160; </div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <span class="comment">/* check 1 */</span></div>
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+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot; != &quot;</span> &lt;&lt; result.<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>() &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">size_t</span> N = result.<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>();</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; N; i++) {</div>
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+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;                      &lt;&lt; <span class="stringliteral">&quot; != &quot;</span> &lt;&lt; result.<a class="code" href="../../db/d82/classlarge__number.html#af530d90830d385c76973658ff3214f98">digit_char</a>(i) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d9d/large__factorial_8cpp_a3f93b60e229b6683e24c4754a7106ee8_cgraph.svg" width="656" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
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+</div>
+</div>
+<a id="a76aae4778fbe89a3d59fd61fbc050cfa"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a76aae4778fbe89a3d59fd61fbc050cfa">&#9670;&nbsp;</a></span>test2()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool test2 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test implementation for 100! The result is the 156 digit number: </p><div class="fragment"><div class="line">9332621544394415268169923885626670049071596826438162146859296389521759</div>
+<div class="line">9993229915608941463976156518286253697920827223758251185210916864000000</div>
+<div class="line">000000000000000000</div>
+</div><!-- fragment --><dl class="section return"><dt>Returns</dt><dd>True if test pass else False </dd></dl>
+<div class="fragment"><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;             {</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;---- Check 2\t&quot;</span>;</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i, number = 100;</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> result;</div>
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+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d9d/large__factorial_8cpp_a76aae4778fbe89a3d59fd61fbc050cfa_cgraph.svg" width="656" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="astrlen_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/strlen.html">std::strlen</a></div><div class="ttdeci">T strlen(T... args)</div></div>
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+<div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
+<div class="ttc" id="aclasslarge__number_html"><div class="ttname"><a href="../../db/d82/classlarge__number.html">large_number</a></div><div class="ttdef"><b>Definition:</b> large_number.h:24</div></div>
+<div class="ttc" id="aclasslarge__number_html_af530d90830d385c76973658ff3214f98"><div class="ttname"><a href="../../db/d82/classlarge__number.html#af530d90830d385c76973658ff3214f98">large_number::digit_char</a></div><div class="ttdeci">const char digit_char(size_t i) const</div><div class="ttdef"><b>Definition:</b> large_number.h:248</div></div>
+<div class="ttc" id="aclasslarge__number_html_a2305a82e7b372617419337b2d2119c7d"><div class="ttname"><a href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">large_number::num_digits</a></div><div class="ttdeci">const size_t num_digits() const</div><div class="ttdef"><b>Definition:</b> large_number.h:130</div></div>
+<div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
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+<tr class="memitem:a76ed6ce71415fb400b65f0656cef3d25"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/db0/binomial__dist_8cpp.html#a76ed6ce71415fb400b65f0656cef3d25">binomial_range_successes</a> (double n, double p, double lower_bound, double upper_bound)</td></tr>
+<tr class="separator:a76ed6ce71415fb400b65f0656cef3d25"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/db0/binomial__dist_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Binomial_distribution">Binomial distribution</a> example </p>
+<p>The binomial distribution models the number of successes in a sequence of n independent events</p>
+<p>Summary of variables used:</p><ul>
+<li>n : number of trials</li>
+<li>p : probability of success</li>
+<li>x : desired successes </li>
+</ul>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a4416a7bc7fa87201883c54cdc4c82813"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a4416a7bc7fa87201883c54cdc4c82813">&#9670;&nbsp;</a></span>binomial_expected()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double binomial_expected </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>n</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>p</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>finds the expected value of a binomial distribution </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">n</td><td></td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">p</td><td></td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>\(\mu=np\) </dd></dl>
+<div class="fragment"><div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;{ <span class="keywordflow">return</span> n * p; }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a76ed6ce71415fb400b65f0656cef3d25"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a76ed6ce71415fb400b65f0656cef3d25">&#9670;&nbsp;</a></span>binomial_range_successes()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double binomial_range_successes </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>n</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>p</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>lower_bound</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>upper_bound</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>calculates the probability of a result within a range (inclusive, inclusive) </p><dl class="section return"><dt>Returns</dt><dd>\(\displaystyle \left.P(n,p)\right|_{x_0}^{x_1} = \sum_{i=x_0}^{x_1} P(i) =\sum_{i=x_0}^{x_1} {n\choose i} p^i (1-p)^{n-i}\) </dd></dl>
+<div class="fragment"><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;                                                    {</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <span class="keywordtype">double</span> probability = 0;</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = lower_bound; i &lt;= <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/upper_bound.html">upper_bound</a>; i++) {</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        probability += <a class="code" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, i) * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, i) * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - i);</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    }</div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <span class="keywordflow">return</span> probability;</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/db0/binomial__dist_8cpp_a76ed6ce71415fb400b65f0656cef3d25_cgraph.svg" width="310" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="af09e51f513cee647d41192ab0a872cdc"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af09e51f513cee647d41192ab0a872cdc">&#9670;&nbsp;</a></span>binomial_standard_deviation()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double binomial_standard_deviation </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>n</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>p</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>finds the standard deviation of the binomial distribution </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">n</td><td></td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">p</td><td></td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>\(\sigma = \sqrt{\sigma^2} = \sqrt{n\cdot p\cdot (1-p)}\) </dd></dl>
+<div class="fragment"><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;                                                       {</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(<a class="code" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(n, p));</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/db0/binomial__dist_8cpp_af09e51f513cee647d41192ab0a872cdc_cgraph.svg" width="372" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="acd4dd4558031e4c5d045c801f73d8861"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#acd4dd4558031e4c5d045c801f73d8861">&#9670;&nbsp;</a></span>binomial_variance()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double binomial_variance </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>n</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>p</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>finds the variance of the binomial distribution </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">n</td><td></td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">p</td><td></td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>\(\sigma^2 = n\cdot p\cdot (1-p)\) </dd></dl>
+<div class="fragment"><div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;{ <span class="keywordflow">return</span> n * p * (1 - p); }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a19ae0a6a2bd200fd1eb0e31b2bf4cc76"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a19ae0a6a2bd200fd1eb0e31b2bf4cc76">&#9670;&nbsp;</a></span>binomial_x_successes()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double binomial_x_successes </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>n</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>p</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>x</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>calculates the probability of exactly x successes </p><dl class="section return"><dt>Returns</dt><dd>\(\displaystyle P(n,p,x) = {n\choose x} p^x (1-p)^{n-x}\) </dd></dl>
+<div class="fragment"><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;                                                          {</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <span class="keywordflow">return</span> <a class="code" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, x) * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, x) * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - x);</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/db0/binomial__dist_8cpp_a19ae0a6a2bd200fd1eb0e31b2bf4cc76_cgraph.svg" width="286" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;           {</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;expected value : &quot;</span> &lt;&lt; <a class="code" href="../../d6/db0/binomial__dist_8cpp.html#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a>(100, 0.5)</div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;              &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160; </div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;variance : &quot;</span> &lt;&lt; <a class="code" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(100, 0.5) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160; </div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;standard deviation : &quot;</span></div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;              &lt;&lt; <a class="code" href="../../d6/db0/binomial__dist_8cpp.html#af09e51f513cee647d41192ab0a872cdc">binomial_standard_deviation</a>(100, 0.5) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160; </div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;exactly 30 successes : &quot;</span> &lt;&lt; <a class="code" href="../../d6/db0/binomial__dist_8cpp.html#a19ae0a6a2bd200fd1eb0e31b2bf4cc76">binomial_x_successes</a>(100, 0.5, 30)</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;              &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160; </div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;45 or more successes : &quot;</span></div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;              &lt;&lt; <a class="code" href="../../d6/db0/binomial__dist_8cpp.html#a76ed6ce71415fb400b65f0656cef3d25">binomial_range_successes</a>(100, 0.5, 45, 100) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160; </div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/db0/binomial__dist_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="471" height="291"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a78d36635232e54b5d71fcbf1eac9a49a"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a78d36635232e54b5d71fcbf1eac9a49a">&#9670;&nbsp;</a></span>nCr()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double nCr </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>n</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>r</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Computes n choose r </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">n</td><td></td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">r</td><td></td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>\(\displaystyle {n\choose r} = \frac{n!}{r!(n-r)!} = \frac{n\times(n-1)\times(n-2)\times\cdots(n-r)}{r!} \) </dd></dl>
+<div class="fragment"><div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;                               {</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <span class="keywordtype">double</span> numerator = n;</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    <span class="keywordtype">double</span> denominator = r;</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160; </div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 1; i &gt;= ((n - r) + 1); i--) {</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;        numerator *= i;</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    }</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160; </div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; r; i++) {</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;        denominator *= i;</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    }</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160; </div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    <span class="keywordflow">return</span> numerator / denominator;</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+<!-- Generated by Doxygen 1.8.18 -->
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+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
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+</div>
+
+<div class="PageDoc"><div class="header">
+  <div class="headertitle">
+<div class="title">CONTRIBUTION GUIDELINES </div>  </div>
+</div><!--header-->
+<div class="contents">
+<div class="textblock"><h1><a class="anchor" id="autotoc_md1"></a>
+Before contributing</h1>
+<p>Welcome to <a href="https://github.com/TheAlgorithms/C-Plus-Plus">TheAlgorithms/C-Plus-Plus</a>! Before submitting pull requests, please make sure that you have <b>read the whole guidelines</b>. If you have any doubts about this contribution guide, please open <a href="https://github.com/TheAlgorithms/C-Plus-Plus/issues/new/choose">an issue</a> and clearly state your concerns.</p>
+<h1><a class="anchor" id="autotoc_md2"></a>
+Contributing</h1>
+<h2><a class="anchor" id="autotoc_md3"></a>
+Contributor</h2>
+<p>We are very happy that you consider implementing algorithms and data structures for others! This repository is referred to and used by learners from around the globe. Being one of our contributors, you agree and confirm that:</p><ul>
+<li>You did your own work.<ul>
+<li>No plagiarism allowed. Any plagiarized work will not be merged.</li>
+</ul>
+</li>
+<li>Your work will be distributed under [MIT License](License) once your pull request has been merged.</li>
+<li>You submitted work fulfils or mostly fulfils our styles and standards.</li>
+</ul>
+<p><b>New implementation</b> New implementation are welcome!</p>
+<p><b>Improving comments</b> and <b>adding tests</b> to existing algorithms are much appreciated.</p>
+<p><b>Issues</b> Please avoid opening issues asking to be "assigned” to a particular algorithm. This merely creates unnecessary noise for maintainers. Instead, please submit your implementation in a pull request and it will be evaluated by project maintainers.</p>
+<h2><a class="anchor" id="autotoc_md4"></a>
+Making Changes</h2>
+<h3><a class="anchor" id="autotoc_md5"></a>
+Code</h3>
+<ul>
+<li>Please use the directory structure of the repository.</li>
+<li>File extension for code should be *.h *.cpp.</li>
+<li>Don't use <b>bits/stdc++.h</b> because this is quite Linux specific and slows down the compilation process.</li>
+<li>Avoid using <b>struct</b> and instead use the <b>class</b> keyword.</li>
+<li>You can suggest reasonable changes to existing algorithms.</li>
+<li>Strictly use snake_case (underscore_separated) in filenames.</li>
+<li>If you have added or modified code, please make sure the code compiles before submitting.</li>
+<li>Our automated testing runs <a href="https://github.com/cpplint/cpplint"><b>cpplint</b></a> on all pull requests so please be sure that your code passes before submitting.</li>
+<li><b>Be consistent in use of these guidelines.</b></li>
+</ul>
+<h3><a class="anchor" id="autotoc_md6"></a>
+New File Name guidelines</h3>
+<ul>
+<li>Use lowercase words with <code>"_"</code> as separator</li>
+<li>For instance <div class="fragment"><div class="line">MyNewCppClass.CPP       is incorrect</div>
+<div class="line">my_new_cpp_class.cpp    is correct format</div>
+</div><!-- fragment --></li>
+<li>It will be used to dynamically create a directory of files and implementation.</li>
+<li>File name validation will run on docker to ensure the validity.</li>
+</ul>
+<h3><a class="anchor" id="autotoc_md7"></a>
+New Directory guidelines</h3>
+<ul>
+<li>We recommend adding files to existing directories as much as possible.</li>
+<li>Use lowercase words with <code>"_"</code> as separator ( no spaces or <code>"-"</code> allowed )</li>
+<li>For instance <div class="fragment"><div class="line">SomeNew Fancy-Category          is incorrect</div>
+<div class="line">some_new_fancy_category         is correct</div>
+</div><!-- fragment --></li>
+<li>Filepaths will be used to dynamically create a directory of our algorithms.</li>
+<li>Filepath validation will run on GitHub Actions to ensure compliance.</li>
+</ul>
+<h3><a class="anchor" id="autotoc_md8"></a>
+Commit Guidelines</h3>
+<ul>
+<li>It is recommended to keep your changes grouped logically within individual commits. Maintainers find it easier to understand changes that are logically spilt across multiple commits. Try to modify just one or two files in the same directory. Pull requests that span multiple directories are often rejected. <div class="fragment"><div class="line">git add file_xyz.cpp</div>
+<div class="line">git commit -m &quot;your message&quot;</div>
+</div><!-- fragment --></li>
+</ul>
+<p>Examples of commit messages with semantic prefixes: </p><div class="fragment"><div class="line">fix: xyz algorithm bug</div>
+<div class="line">feat: add xyx algorithm, class xyz</div>
+<div class="line">test: add test for xyz algorithm</div>
+<div class="line">docs: add comments and explanation to xyz algorithm</div>
+</div><!-- fragment --><p>Common prefixes:</p><ul>
+<li>fix: A bug fix</li>
+<li>feat: A new feature</li>
+<li>docs: Documentation changes</li>
+<li>test: Correct existing tests or add new ones</li>
+</ul>
+<h3><a class="anchor" id="autotoc_md9"></a>
+Documentation</h3>
+<ul>
+<li>Make sure you put useful comments in your code. Do not comment things that are obvious.</li>
+<li>Please avoid creating new directories if at all possible. Try to fit your work into the existing directory structure. If you want to create a new directory, then please check if a similar category has been recently suggested or created by other pull requests.</li>
+<li>If you have modified/added documentation, please ensure that your language is concise and contains no grammar errors.</li>
+<li>Do not update README.md along with other changes, first create an issue and then link to that issue in your pull request to suggest specific changes required to README.md</li>
+</ul>
+<h3><a class="anchor" id="autotoc_md10"></a>
+Test</h3>
+<ul>
+<li>Make sure to add examples and test cases in your <a class="el" href="../../d8/dee/avltree_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main()</a> function.</li>
+<li>If you find any algorithm or document without tests, please feel free to create a pull request or issue describing suggested changes.</li>
+</ul>
+<h2><a class="anchor" id="autotoc_md11"></a>
+Pull Requests</h2>
+<ul>
+<li>Checkout our <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/.github/pull_request_template.md">pull request template</a></li>
+</ul>
+<h3><a class="anchor" id="autotoc_md12"></a>
+cpplint</h3>
+<p>To see if <a href="https://github.com/cpplint/cpplint"><b>cpplint</b></a> is already installed, do:</p><ul>
+<li><code>cpplint --version</code> # currently returns "cpplint 1.4.4" If cpplint is ___not___ installed then do:</li>
+<li><code>python3 -m pip install cpplint</code> # If that does not work then try...</li>
+<li><code>py -m pip install cpplint</code> # If that does not work then try...</li>
+<li><code>pip install cpplint</code> Once cpplint is installed, test your file(s) with:</li>
+<li><code>cpplint --filter=-legal my_file.cpp my_other_file.cpp</code> # Fix any issues and try again.</li>
+</ul>
+<p>The <a href="https://clang.llvm.org/docs/ClangFormat.html"><b>clang-format</b></a> tool can fix whitespace related <em>cpplint</em> issues.</p><ul>
+<li>On Macs only: <code>brew install clang-format</code> # Only needs to be installed once.</li>
+<li>All platforms: <code>clang-format -i -style="{IndentWidth: 4}" my_file.cpp</code></li>
+</ul>
+<p>Most importantly,</p><ul>
+<li>Happy coding! </li>
+</ul>
+</div></div><!-- contents -->
+</div><!-- PageDoc -->
+</div><!-- doc-content -->
+<!-- start footer part -->
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+<p>The <a href="https://en.wikipedia.org/wiki/Rabin–Karp_algorithm">Rabin-Karp Algorithm</a> for finding a pattern within a piece of text with complexity O(n + m)  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
+<code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;cstring&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
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+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    assert(<a class="code" href="../../d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">rabin_karp</a>(<span class="stringliteral">&quot;this_is_c++&quot;</span>, <span class="stringliteral">&quot;c++&quot;</span>) == 8);</div>
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+<div class="title">ode_midpoint_euler.cpp File Reference</div>  </div>
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+<div class="contents">
+
+<p>Solve a multivariable first order <a href="https://en.wikipedia.org/wiki/Ordinary_differential_equation">ordinary differential equation (ODEs)</a> using <a href="https://en.wikipedia.org/wiki/Midpoint_method">midpoint Euler method</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;ctime&gt;</code><br />
+<code>#include &lt;fstream&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;valarray&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for ode_midpoint_euler.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/dd5/ode__midpoint__euler_8cpp__incl.svg" width="430" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:abaeae8f62a018d197f0187a1c80a90fe"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a> (const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</td></tr>
+<tr class="memdesc:abaeae8f62a018d197f0187a1c80a90fe"><td class="mdescLeft">&#160;</td><td class="mdescRight">Problem statement for a system with first-order differential equations. Updates the system differential variables.  <a href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">More...</a><br /></td></tr>
+<tr class="separator:abaeae8f62a018d197f0187a1c80a90fe"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:af3adf7b092a87868917ee5fb4255192b"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a> (const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y)</td></tr>
+<tr class="memdesc:af3adf7b092a87868917ee5fb4255192b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Exact solution of the problem. Used for solution comparison.  <a href="../../d6/dd3/ode__midpoint__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">More...</a><br /></td></tr>
+<tr class="separator:af3adf7b092a87868917ee5fb4255192b"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga8c319db420c3d97a83e9dcca803b6812"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">midpoint_euler_step</a> (const double dx, const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</td></tr>
+<tr class="memdesc:ga8c319db420c3d97a83e9dcca803b6812"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute next step approximation using the midpoint-Euler method.  <a href="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">More...</a><br /></td></tr>
+<tr class="separator:ga8c319db420c3d97a83e9dcca803b6812"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga36ff0710861ca39d957046c0b09b2985"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga36ff0710861ca39d957046c0b09b2985">midpoint_euler</a> (double dx, double x0, double x_max, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, bool save_to_file=false)</td></tr>
+<tr class="memdesc:ga36ff0710861ca39d957046c0b09b2985"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute approximation using the midpoint-Euler method in the given limits.  <a href="../../d6/d60/group__ode.html#ga36ff0710861ca39d957046c0b09b2985">More...</a><br /></td></tr>
+<tr class="separator:ga36ff0710861ca39d957046c0b09b2985"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aa13517b8e5de1b75592052db7f7e237f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a> (const double &amp;X0, const double &amp;X_MAX, const double &amp;step_size, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &amp;Y0)</td></tr>
+<tr class="separator:aa13517b8e5de1b75592052db7f7e237f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
+<tr class="separator:a0ddf1224851353fc92bfbff6f499fa97"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Solve a multivariable first order <a href="https://en.wikipedia.org/wiki/Ordinary_differential_equation">ordinary differential equation (ODEs)</a> using <a href="https://en.wikipedia.org/wiki/Midpoint_method">midpoint Euler method</a> </p>
+<dl class="section author"><dt>Authors</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
+<p>The ODE being solved is: </p><p class="formulaDsp">
+\begin{eqnarray*} \dot{u} &amp;=&amp; v\\ \dot{v} &amp;=&amp; -\omega^2 u\\ \omega &amp;=&amp; 1\\ [x_0, u_0, v_0] &amp;=&amp; [0,1,0]\qquad\ldots\text{(initial values)} \end{eqnarray*}
+</p>
+<p> The exact solution for the above problem is: </p><p class="formulaDsp">
+\begin{eqnarray*} u(x) &amp;=&amp; \cos(x)\\ v(x) &amp;=&amp; -\sin(x)\\ \end{eqnarray*}
+</p>
+<p> The computation results are stored to a text file <code>midpoint_euler.csv</code> and the exact soltuion results in <code>exact.csv</code> for comparison. <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/numerical_methods/ode_midpoint_euler.svg" alt="Implementation solution" style="pointer-events: none;" class="inline"/></p>
+<p>To implement <a href="https://en.wikipedia.org/wiki/Van_der_Pol_oscillator">Van der Pol oscillator</a>, change the <a class="el" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe" title="Problem statement for a system with first-order differential equations. Updates the system differenti...">problem</a> function to: </p><div class="fragment"><div class="line"><span class="keyword">const</span> <span class="keywordtype">double</span> mu = 2.0;</div>
+<div class="line">dy[0] = y[1];</div>
+<div class="line">dy[1] = mu * (1.f - y[0] * y[0]) * y[1] - y[0];</div>
+</div><!-- fragment --><dl class="section see"><dt>See also</dt><dd><a class="el" href="../../db/dd3/ode__forward__euler_8cpp.html" title="Solve a multivariable first order ordinary differential equation (ODEs) using forward Euler method">ode_forward_euler.cpp</a>, <a class="el" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html" title="Solve a multivariable first order ordinary differential equation (ODEs) using semi implicit Euler met...">ode_semi_implicit_euler.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="af3adf7b092a87868917ee5fb4255192b"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af3adf7b092a87868917ee5fb4255192b">&#9670;&nbsp;</a></span>exact_solution()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void exact_solution </td>
+          <td>(</td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>y</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Exact solution of the problem. Used for solution comparison. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>independent variable </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>dependent variable </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;                                                             {</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    y[0][0] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(x);</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    y[0][1] = -<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(x);</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/dd3/ode__midpoint__euler_8cpp_af3adf7b092a87868917ee5fb4255192b_cgraph.svg" width="235" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a0ddf1224851353fc92bfbff6f499fa97"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>argc</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char *&#160;</td>
+          <td class="paramname"><em>argv</em>[]&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main Function </p>
+<div class="fragment"><div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;                                 {</div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;    <span class="keywordtype">double</span> X0 = 0.f;                       <span class="comment">/* initial value of x0 */</span></div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;    <span class="keywordtype">double</span> X_MAX = 10.F;                   <span class="comment">/* upper limit of integration */</span></div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> Y0 = {1.f, 0.f}; <span class="comment">/* initial value Y = y(x = x_0) */</span></div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    <span class="keywordtype">double</span> step_size;</div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160; </div>
+<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    <span class="keywordflow">if</span> (argc == 1) {</div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter the step size: &quot;</span>;</div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; step_size;</div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;        <span class="comment">// use commandline argument as independent variable step size</span></div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;        step_size = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[1]);</div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    }</div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160; </div>
+<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    <span class="comment">// get approximate solution</span></div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    <span class="keywordtype">double</span> total_time = <a class="code" href="../../d6/d60/group__ode.html#ga36ff0710861ca39d957046c0b09b2985">midpoint_euler</a>(step_size, X0, X_MAX, &amp;Y0, <span class="keyword">true</span>);</div>
+<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tTime = &quot;</span> &lt;&lt; total_time &lt;&lt; <span class="stringliteral">&quot; ms\n&quot;</span>;</div>
+<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160; </div>
+<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <span class="comment">/* compute exact solution for comparion */</span></div>
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+<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/dd3/ode__midpoint__euler_8cpp_a0ddf1224851353fc92bfbff6f499fa97_cgraph.svg" width="568" height="367"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
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+<a id="abaeae8f62a018d197f0187a1c80a90fe"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#abaeae8f62a018d197f0187a1c80a90fe">&#9670;&nbsp;</a></span>problem()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void problem </td>
+          <td>(</td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>y</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>dy</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Problem statement for a system with first-order differential equations. Updates the system differential variables. </p>
+<dl class="section note"><dt>Note</dt><dd>This function can be updated to and ode of any order.</dd></dl>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>independent variable(s) </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>dependent variable(s) </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">dy</td><td>first-derivative of dependent variable(s) </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;                                      {</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> omega = 1.F;             <span class="comment">// some const for the problem</span></div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    dy[0][0] = y[0][1];                   <span class="comment">// x dot</span></div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    dy[0][1] = -omega * omega * y[0][0];  <span class="comment">// y dot</span></div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="aa13517b8e5de1b75592052db7f7e237f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa13517b8e5de1b75592052db7f7e237f">&#9670;&nbsp;</a></span>save_exact_solution()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void save_exact_solution </td>
+          <td>(</td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>X0</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>X_MAX</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>step_size</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &amp;&#160;</td>
+          <td class="paramname"><em>Y0</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Function to compute and save exact solution for comparison</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">X0</td><td>initial value of independent variable </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">X_MAX</td><td>final value of independent variable </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">step_size</td><td>independent variable step size </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">Y0</td><td>initial values of dependent variables </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;                                                        {</div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <span class="keywordtype">double</span> x = X0;</div>
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+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160; </div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(<span class="stringliteral">&quot;exact.csv&quot;</span>, std::ostream::out);</div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    <span class="keywordflow">if</span> (!fp.is_open()) {</div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">&quot;Error! &quot;</span>);</div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;        <span class="keywordflow">return</span>;</div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    }</div>
+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Finding exact solution\n&quot;</span>;</div>
+<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160; </div>
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+<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;    <span class="keywordflow">do</span> {</div>
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+</div>
+</div>
+
+</div>
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+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="aode__midpoint__euler_8cpp_html_aa13517b8e5de1b75592052db7f7e237f"><div class="ttname"><a href="../../d6/dd3/ode__midpoint__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a></div><div class="ttdeci">void save_exact_solution(const double &amp;X0, const double &amp;X_MAX, const double &amp;step_size, const std::valarray&lt; double &gt; &amp;Y0)</div><div class="ttdef"><b>Definition:</b> ode_midpoint_euler.cpp:156</div></div>
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+<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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+<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt; <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>c</b></td></tr>
+<tr class="separator:ad54b52a703d277babd3f30d20d9d416d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Matrix Exponentiation. </p>
+<p>The problem can be solved with DP but constraints are high. <br  />
+ \(a_i = b_i\) (for \(i &lt;= k\)) <br  />
+ \(a_i = c_1 a_{i-1} + c_2 a_{i-2} + ... + c_k a_{i-k}\) (for \(i &gt; k\)) <br  />
+Taking the example of Fibonacci series, \(k=2\) <br  />
+ \(b_1 = 1,\; b_2=1\) <br  />
+ \(c_1 = 1,\; c_2=1\) <br  />
+ \(a = \begin{bmatrix}0&amp; 1&amp; 1&amp; 2&amp; \ldots\end{bmatrix}\) <br  />
+This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a general way to use it. The program takes the input of B and C matrix.</p>
+<p>Steps for Matrix Expo</p><ol type="1">
+<li>Create vector F1 : which is the copy of B.</li>
+<li>Create transpose matrix (Learn more about it on the internet)</li>
+<li>Perform \(T^{n-1}\) [transpose matrix to the power n-1]</li>
+<li>Multiply with F to get the last matrix of size (1 \(\times\)k).</li>
+</ol>
+<p>The first element of this matrix is the required result. </p>
+</div><h2 class="groupheader">Macro Definition Documentation</h2>
+<a id="a600eaf353befc174637855795f12d258"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a600eaf353befc174637855795f12d258">&#9670;&nbsp;</a></span>endl</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">#define endl&#160;&#160;&#160;std::endl</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>shorthand definition for <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></code> </p>
+
+</div>
+</div>
+<a id="ae1d1ec9482079231e898236e2b23c9ba"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae1d1ec9482079231e898236e2b23c9ba">&#9670;&nbsp;</a></span>ll</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">#define ll&#160;&#160;&#160;int64_t</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>shorthand definition for <code>int64_t</code> </p>
+
+</div>
+</div>
+<a id="a276c5a0e984cf60015b27252fe04fe6b"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a276c5a0e984cf60015b27252fe04fe6b">&#9670;&nbsp;</a></span>pb</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">#define pb&#160;&#160;&#160;push_back</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>shorthand definition for <code>int64_t</code> </p>
+
+</div>
+</div>
+<h2 class="groupheader">Function Documentation</h2>
+<a id="a8bcf0bfddddfd7f6d0848703632d795d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a8bcf0bfddddfd7f6d0848703632d795d">&#9670;&nbsp;</a></span>ab()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> ab </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a>&#160;</td>
+          <td class="paramname"><em>x</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>returns absolute value </p>
+<div class="fragment"><div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;{ <span class="keywordflow">return</span> x &gt; 0LL ? x : -x; }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ad8389ed58fd0ec66df248014775ad1fa"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ad8389ed58fd0ec66df248014775ad1fa">&#9670;&nbsp;</a></span>ans()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> ans </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a>&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Wrapper for Fibonacci </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>\(n^\text{th}\) Fibonacci number </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>\(n^\text{th}\) Fibonacci number </dd></dl>
+<div class="fragment"><div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;             {</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <span class="keywordflow">if</span> (n == 0)</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;        <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    <span class="keywordflow">if</span> (n &lt;= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>)</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        <span class="keywordflow">return</span> b[n - 1];</div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <span class="comment">// F1</span></div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;ll&gt;</a> F1(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> + 1);</div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    <span class="keywordflow">for</span> (ll i = 1; i &lt;= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; i++) F1[i] = b[i - 1];</div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160; </div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    <span class="comment">// Transpose matrix</span></div>
+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;vector&lt;ll&gt;</a>&gt; T(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> + 1, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;ll&gt;</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> + 1));</div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    <span class="keywordflow">for</span> (ll i = 1; i &lt;= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; i++) {</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;        <span class="keywordflow">for</span> (ll j = 1; j &lt;= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; j++) {</div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;            <span class="keywordflow">if</span> (i &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>) {</div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                <span class="keywordflow">if</span> (j == i + 1)</div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;                    T[i][j] = 1;</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                <span class="keywordflow">else</span></div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;                    T[i][j] = 0;</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;                <span class="keywordflow">continue</span>;</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;            }</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;            T[i][j] = c[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> - j];</div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;        }</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    }</div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <span class="comment">// T^n-1</span></div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    T = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a5769b745458157ef2679949155684f3b">power</a>(T, n - 1);</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160; </div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <span class="comment">// T*F1</span></div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    ll res = 0;</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    <span class="keywordflow">for</span> (ll i = 1; i &lt;= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; i++) {</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;        res = (res + (T[1][i] * F1[i]) % MOD) % MOD;</div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    }</div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    <span class="keywordflow">return</span> res;</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;           {</div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a>.tie(0);</div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a>.tie(0);</div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    ll t;</div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; t;</div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    ll i, j, x;</div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    <span class="keywordflow">while</span> (t--) {</div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>;</div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;        <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; i++) {</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; x;</div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;            b.pb(x);</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;        }</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;        <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; i++) {</div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; x;</div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;            c.pb(x);</div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;        }</div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> &gt;&gt; x;</div>
+<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>(x) &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        b.clear();</div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;        c.clear();</div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    }</div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ac62a499b83c7895dd0aa69da1b64c904"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac62a499b83c7895dd0aa69da1b64c904">&#9670;&nbsp;</a></span>multiply()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt;<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a>&gt; &gt; multiply </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt; <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt;&gt; &amp;&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt; <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt;&gt; &amp;&#160;</td>
+          <td class="paramname"><em>B</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>To multiply 2 matrices </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>matrix 1 of size (m \(\times\)n) </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">B</td><td><code>matrix</code> 2 of size (p \(\times\)q)<br  />
+</td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section note"><dt>Note</dt><dd>\(p=n\) </dd></dl>
+<dl class="section return"><dt>Returns</dt><dd>matrix of dimension (m \(\times\)q) </dd></dl>
+<div class="fragment"><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;                                                         {</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;vector&lt;ll&gt;</a>&gt; C(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> + 1, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;ll&gt;</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> + 1));</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="keywordflow">for</span> (ll i = 1; i &lt;= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; i++) {</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <span class="keywordflow">for</span> (ll j = 1; j &lt;= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; j++) {</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;            <span class="keywordflow">for</span> (ll z = 1; z &lt;= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; z++) {</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;                C[i][j] = (C[i][j] + (A[i][z] * B[z][j]) % MOD) % MOD;</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;            }</div>
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+<h2 class="groupheader">Variable Documentation</h2>
+<a id="a9ecd98ce0064e2f7f97bb6a92f58ee72"></a>
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+<div class="ttc" id="amatrix__exponentiation_8cpp_html_a600eaf353befc174637855795f12d258"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a></div><div class="ttdeci">#define endl</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:36</div></div>
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+<a href="#define-members">Macros</a> &#124;
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+  <div class="headertitle">
+<div class="title">bisection_method.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Bisection_method">bisection method</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;limits&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for bisection_method.cpp:</div>
+<div class="dyncontent">
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+#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>&#160;&#160;&#160;50000</td></tr>
+<tr class="memdesc:a0a3abbca80bc98e7abcb3ae73abe0f14"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum number of iterations to check. <br /></td></tr>
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+<tr class="memitem:a2003b5b2dcfff0769b957ab5c968b03d"><td class="memItemLeft" align="right" valign="top">static double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a> (double i)</td></tr>
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+<tr class="memitem:a1ab31b90bc584c635ec159468ceed9b2"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:a1ab31b90bc584c635ec159468ceed9b2"><td class="memTemplItemLeft" align="right" valign="top">int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a> (T val)</td></tr>
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d6a/bisection__method_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Bisection_method">bisection method</a> </p>
+<p>Given two points \(a\) and \(b\) such that \(f(a)&lt;0\) and \(f(b)&gt;0\), then the \((i+1)^\text{th}\) approximation is given by: </p><p class="formulaDsp">
+\[ x_{i+1} = \frac{a_i+b_i}{2} \]
+</p>
+<p> For the next iteration, the interval is selected as: \([a,x]\) if \(x&gt;0\) or \([x,b]\) if \(x&lt;0\). The Process is continued till a close enough approximation is achieved.</p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/dd3/newton__raphson__method_8cpp.html" title="Solve the equation  using Newton-Raphson method for both real and complex solutions.">newton_raphson_method.cpp</a>, <a class="el" href="../../dd/d29/false__position_8cpp.html" title="Solve the equation  using false position method, also known as the Secant method.">false_position.cpp</a>, secant_method.cpp </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a2003b5b2dcfff0769b957ab5c968b03d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a2003b5b2dcfff0769b957ab5c968b03d">&#9670;&nbsp;</a></span>eq()</h2>
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+          <td class="memname">static double eq </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>i</em></td><td>)</td>
+          <td></td>
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+<span class="mlabels"><span class="mlabel">static</span></span>  </td>
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+</div><div class="memdoc">
+<p>define \(f(x)\) to find root for </p>
+<div class="fragment"><div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;                           {</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keywordflow">return</span> (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i, 3) - (4 * i) - 9);  <span class="comment">// original equation</span></div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;           {</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    <span class="keywordtype">double</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = -1, b = 1, x, z;</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keywordtype">int</span> i;</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160; </div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="comment">// loop to find initial intervals a, b</span></div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code" href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        z = <a class="code" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>);</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        x = <a class="code" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(b);</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(z) == <a class="code" href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(x)) {  <span class="comment">// same signs, increase interval</span></div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;            b++;</div>
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+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;        } <span class="keywordflow">else</span> {  <span class="comment">// if opposite signs, we got our interval</span></div>
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+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nSecond initial: &quot;</span> &lt;&lt; b;</div>
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+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\nz: &quot;</span> &lt;&lt; z &lt;&lt; <span class="stringliteral">&quot;\t[&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot; , &quot;</span> &lt;&lt; b</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot; | Bisect: &quot;</span> &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;]&quot;</span>;</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160; </div>
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+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        } <span class="keywordflow">else</span> {</div>
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+</div><!-- fragment -->
+</div>
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+<hr/>The documentation for this struct was generated from the following files:<ul>
+<li>dynamic_programming/bellman_ford.cpp</li>
+<li>graph/cycle_check_directed_graph.cpp</li>
+</ul>
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+<tr class="memitem:aa13bf7c38de112f71921a5525d71a2f2"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d7c/classstatistics_1_1stats__computer1.html#aa13bf7c38de112f71921a5525d71a2f2">new_val</a> (T x)</td></tr>
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+<div class="textblock"><h3>template&lt;typename T&gt;<br />
+class statistics::stats_computer1&lt; T &gt;</h3>
+
+<p>continuous mean and variance computance using first value as an approximation for the mean. If the first number is much far form the mean, the algorithm becomes very inaccurate to compute variance and standard deviation. </p>
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+  </table>
+  </dd>
+</dl>
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+<div class="memitem">
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+<h2 class="memtitle"><span class="permalink"><a href="#ab5b4bfecdf391cae7edb1fe98548b846">&#9670;&nbsp;</a></span>operator&gt;&gt;</h2>
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+<div class="textblock"><p>Prime Factorization is a very important and useful technique to factorize any number into its prime factors. It has various applications in the field of number theory.</p>
+<p>The method of prime factorization involves two function calls. First: Calculating all the prime number up till a certain range using the standard Sieve of Eratosthenes.</p>
+<p>Second: Using the prime numbers to reduce the the given number and thus find all its prime factors.</p>
+<p>The complexity of the solution involves approx. O(n logn) in calculating sieve of eratosthenes O(log n) in calculating the prime factors of the number. So in total approx. O(n logn).</p>
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+<a href="#func-members">Functions</a>  </div>
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+<div class="title">double_factorial.cpp File Reference</div>  </div>
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+<div class="contents">
+
+<p>Compute double factorial: \(n!!\).  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for double_factorial.cpp:</div>
+<div class="dyncontent">
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+<tr class="memitem:a0a3c417360400093891a9ccddaa4be26"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d89/double__factorial_8cpp.html#a0a3c417360400093891a9ccddaa4be26">double_factorial_iterative</a> (uint64_t n)</td></tr>
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+<p>Double factorial of a non-negative integer n, is defined as the product of all the integers from 1 to n that have the same parity (odd or even) as n. <br  />
+It is also called as semifactorial of a number and is denoted by \(n!!\) </p>
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+<h2 class="memtitle"><span class="permalink"><a href="#a0a3c417360400093891a9ccddaa4be26">&#9670;&nbsp;</a></span>double_factorial_iterative()</h2>
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+          <td class="paramname"><em>n</em></td><td>)</td>
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+<div class="fragment"><div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;                                                {</div>
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+<p>Compute double factorial using resursive method. <br  />
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+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
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+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+<div class="title">cll.h</div>  </div>
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+<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/*</span></div>
+<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment"> * Simple data structure CLL (Cicular Linear Linked List)</span></div>
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+<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &lt;cctype&gt;</span></div>
+<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#include &lt;cstdlib&gt;</span></div>
+<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &lt;cstring&gt;</span></div>
+<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div>
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+<div class="ttc" id="aclass_min_heap_html_ae4d358bf063bb196a1945b3fb99b4913"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">MinHeap::heap_size</a></div><div class="ttdeci">int heap_size</div><div class="ttdoc">Current number of elements in min heap.</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:13</div></div>
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+<div class="ttc" id="aavltree_8cpp_html_ae197eb50188fb761346952b9b5f6be59"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#ae197eb50188fb761346952b9b5f6be59">levelOrder</a></div><div class="ttdeci">void levelOrder(node *root)</div><div class="ttdef"><b>Definition:</b> avltree.cpp:119</div></div>
+<div class="ttc" id="aqueue_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue</a></div><div class="ttdoc">STL class.</div></div>
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+<div class="ttc" id="aclass_min_heap_html_aef78f3384f5a0ae880ad0883d2d44b82"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#aef78f3384f5a0ae880ad0883d2d44b82">MinHeap::insertKey</a></div><div class="ttdeci">void insertKey(int k)</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:57</div></div>
+<div class="ttc" id="aavltree_8cpp_html_a1ecfaaea49d452772dbb2b28133e36e0"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#a1ecfaaea49d452772dbb2b28133e36e0">createNode</a></div><div class="ttdeci">node * createNode(int data)</div><div class="ttdef"><b>Definition:</b> avltree.cpp:21</div></div>
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+<div class="ttc" id="aclass_min_heap_html_a34a93a87967308eb516328c0aca3c48e"><div class="ttname"><a href="../../d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">MinHeap::harr</a></div><div class="ttdeci">int * harr</div><div class="ttdoc">pointer to array of elements in heap</div><div class="ttdef"><b>Definition:</b> binaryheap.cpp:11</div></div>
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+   <div id="projectname">Algorithms_in_C++
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+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+<div class="title">stack.h</div>  </div>
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+<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/* This class specifies the basic operation on a stack as a linked list */</span></div>
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+<li>search/<a class="el" href="../../d1/df3/hash__search_8cpp.html">hash_search.cpp</a></li>
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+<a href="#func-members">Functions</a>  </div>
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+<div class="title">bubble_sort.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Bubble sort algorithm.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;vector&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for bubble_sort.cpp:</div>
+<div class="dyncontent">
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Bubble sort algorithm. </p>
+<p>The working principle of the Bubble sort algorithm:</p>
+<p>Bubble sort algorithm is the bubble sorting algorithm. The most important reason for calling the bubble is that the largest number is thrown at the end of this algorithm. This is all about the logic. In each iteration, the largest number is expired and when iterations are completed, the sorting takes place.</p>
+<p>What is Swap?</p>
+<p>Swap in the software means that two variables are displaced. An additional variable is required for this operation. x = 5, y = 10. We want x = 10, y = 5. Here we create the most variable to do it.</p>
+<p>int z; z = x; x = y; y = z;</p>
+<p>The above process is a typical displacement process. When x assigns the value to x, the old value of x is lost. That's why we created a variable z to create the first value of the value of x, and finally, we have assigned to y.</p>
+<p>Bubble Sort Algorithm Analysis (Best Case - Worst Case - Average Case)</p>
+<p>Bubble Sort Worst Case Performance is O (n²). Why is that? Because if you remember Big O Notation, we were calculating the complexity of the algorithms in the nested loops. The n * (n - 1) product gives us O (n²) performance. In the worst case all the steps of the cycle will occur. Bubble Sort (Avarage Case) Performance. Bubble Sort is not an optimal algorithm. in average, O (n²) performance is taken. Bubble Sort Best Case Performance. O (n). However, you can't get the best status in the code we shared above. This happens on the optimized bubble sort algorithm. It's right down there. </p>
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+<div class="title">queue.h</div>  </div>
+</div><!--header-->
+<div class="contents">
+<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/* This class specifies the basic operation on a queue as a linked list */</span></div>
+<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor">#ifndef DATA_STRUCTURES_QUEUE_H_</span></div>
+<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor">#define DATA_STRUCTURES_QUEUE_H_</span></div>
+<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160; </div>
+<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#include &lt;cassert&gt;</span></div>
+<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div>
+<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">/** Definition of the node */</span></div>
+<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> Kind&gt;</div>
+<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="keyword">struct </span><a class="code" href="../../d5/da1/structnode.html">node</a> {</div>
+<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;    Kind data;</div>
+<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;    <a class="code" href="../../d5/da1/structnode.html">node&lt;Kind&gt;</a> *next;</div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;};</div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">/** Definition of the queue class */</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> Kind&gt;</div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="keyword">class </span><a class="code" href="../../d2/d36/structqueue.html">queue</a> {</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; <span class="keyword">public</span>:<span class="comment"></span></div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">    /** Show queue */</span></div>
+<div class="line"><a name="l00020"></a><span class="lineno"><a class="line" href="../../d2/d36/structqueue.html#a26f48801df462ade003b50739196fa4c">   20</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="../../d2/d36/structqueue.html#a26f48801df462ade003b50739196fa4c">display</a>() {</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;        <a class="code" href="../../d5/da1/structnode.html">node&lt;Kind&gt;</a> *current = <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a>;</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Front --&gt; &quot;</span>;</div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;        <span class="keywordflow">while</span> (current != NULL) {</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; current-&gt;data &lt;&lt; <span class="stringliteral">&quot;    &quot;</span>;</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;            current = current-&gt;next;</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;        }</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Size of queue: &quot;</span> &lt;&lt; size &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    }</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="comment">    /** Default constructor*/</span></div>
+<div class="line"><a name="l00032"></a><span class="lineno"><a class="line" href="../../d2/d36/structqueue.html#a21381ee7f95daae0332665914780e970">   32</a></span>&#160;    <a class="code" href="../../d2/d36/structqueue.html#a21381ee7f95daae0332665914780e970">queue</a>() {</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;        <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> = NULL;</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        <a class="code" href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queueRear</a> = NULL;</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;        size = 0;</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    }</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="comment">    /** Destructor */</span></div>
+<div class="line"><a name="l00039"></a><span class="lineno"><a class="line" href="../../d2/d36/structqueue.html#ad215eee654953d25150bb25d5ac12b7c">   39</a></span>&#160;    <a class="code" href="../../d2/d36/structqueue.html#ad215eee654953d25150bb25d5ac12b7c">~queue</a>() {}</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;<span class="comment">    /** Determine whether the queue is empty */</span></div>
+<div class="line"><a name="l00042"></a><span class="lineno"><a class="line" href="../../d2/d36/structqueue.html#ac2fff88dce4d7d2eb7134af382bd1b31">   42</a></span>&#160;    <span class="keywordtype">bool</span> <a class="code" href="../../d2/d36/structqueue.html#ac2fff88dce4d7d2eb7134af382bd1b31">isEmptyQueue</a>() { <span class="keywordflow">return</span> (<a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> == NULL); }</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;<span class="comment">    /** Add new item to the queue */</span></div>
+<div class="line"><a name="l00045"></a><span class="lineno"><a class="line" href="../../d2/d36/structqueue.html#a592c0580551ec0d3b4d43e8198d8a377">   45</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="../../d2/d36/structqueue.html#a592c0580551ec0d3b4d43e8198d8a377">enQueue</a>(Kind item) {</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        <a class="code" href="../../d5/da1/structnode.html">node&lt;Kind&gt;</a> *newNode;</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;        newNode = <span class="keyword">new</span> <a class="code" href="../../d5/da1/structnode.html">node&lt;Kind&gt;</a>;</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;        newNode-&gt;data = item;</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        newNode-&gt;next = NULL;</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> == NULL) {</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;            <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> = newNode;</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;            <a class="code" href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queueRear</a> = newNode;</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;            <a class="code" href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queueRear</a>-&gt;next = newNode;</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;            <a class="code" href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queueRear</a> = <a class="code" href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queueRear</a>-&gt;next;</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;        }</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        size++;</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    }</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;<span class="comment">    /** Return the first element of the queue */</span></div>
+<div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="../../d2/d36/structqueue.html#a36d47fdbedc199609818385110d9f922">   61</a></span>&#160;    Kind <a class="code" href="../../d2/d36/structqueue.html#a36d47fdbedc199609818385110d9f922">front</a>() {</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        assert(<a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> != NULL);</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a>-&gt;data;</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    }</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;<span class="comment">    /** Remove the top element of the queue */</span></div>
+<div class="line"><a name="l00067"></a><span class="lineno"><a class="line" href="../../d2/d36/structqueue.html#a089d4af5532e0a801f560070da6e1f86">   67</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="../../d2/d36/structqueue.html#a089d4af5532e0a801f560070da6e1f86">deQueue</a>() {</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;        <a class="code" href="../../d5/da1/structnode.html">node&lt;Kind&gt;</a> *temp;</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        <span class="keywordflow">if</span> (!<a class="code" href="../../d2/d36/structqueue.html#ac2fff88dce4d7d2eb7134af382bd1b31">isEmptyQueue</a>()) {</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;            temp = <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a>;</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;            <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> = <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a>-&gt;next;</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;            <span class="keyword">delete</span> temp;</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;            size--;</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Queue is empty !&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        }</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    }</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;<span class="comment">    /** Clear queue */</span></div>
+<div class="line"><a name="l00080"></a><span class="lineno"><a class="line" href="../../d2/d36/structqueue.html#ab2019d91e28c06de325fb3076b93a930">   80</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="../../d2/d36/structqueue.html#ab2019d91e28c06de325fb3076b93a930">clear</a>() { <a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a> = NULL; }</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160; <span class="keyword">private</span>:</div>
+<div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">   83</a></span>&#160;    <a class="code" href="../../d5/da1/structnode.html">node&lt;Kind&gt;</a> *<a class="code" href="../../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queueFront</a>; <span class="comment">/**&lt; Pointer to the front of the queue */</span></div>
+<div class="line"><a name="l00084"></a><span class="lineno"><a class="line" href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">   84</a></span>&#160;    <a class="code" href="../../d5/da1/structnode.html">node&lt;Kind&gt;</a> *<a class="code" href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queueRear</a>;  <span class="comment">/**&lt; Pointer to the rear of the queue  */</span></div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    <span class="keywordtype">int</span> size;</div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;};</div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160; </div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="preprocessor">#endif  // DATA_STRUCTURES_QUEUE_H_</span></div>
+</div><!-- fragment --></div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="alist_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list.html">std::list</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="astructqueue_html_a089d4af5532e0a801f560070da6e1f86"><div class="ttname"><a href="../../d2/d36/structqueue.html#a089d4af5532e0a801f560070da6e1f86">queue::deQueue</a></div><div class="ttdeci">void deQueue()</div><div class="ttdef"><b>Definition:</b> queue.h:67</div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
+<div class="ttc" id="asearch_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/search.html">std::search</a></div><div class="ttdeci">T search(T... args)</div></div>
+<div class="ttc" id="ahash__search_8cpp_html_a8ca8dcb494104d273679e219e53d0555"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a></div><div class="ttdeci">struct list node</div></div>
+<div class="ttc" id="astructqueue_html_ae2a7a36270f5d15218a180fa59e5b3a5"><div class="ttname"><a href="../../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queue::queueRear</a></div><div class="ttdeci">node&lt; Kind &gt; * queueRear</div><div class="ttdef"><b>Definition:</b> queue.h:84</div></div>
+<div class="ttc" id="alinkedlist__implentation__usingarray_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d3/dce/linkedlist__implentation__usingarray_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> linkedlist_implentation_usingarray.cpp:79</div></div>
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+<div class="contents">
+
+<p>C++ Program to find the modular inverse using <a href="https://en.wikipedia.org/wiki/Fermat%27s_little_theorem">Fermat's Little Theorem</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;vector&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for modular_inverse_fermat_little_theorem.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d3/d1e/modular__inverse__fermat__little__theorem_8cpp__incl.svg" width="187" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a4c6eefd1254eab3e8d34bf02c205e0f4"><td class="memItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#a4c6eefd1254eab3e8d34bf02c205e0f4">binExpo</a> (int64_t <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, int64_t b, int64_t m)</td></tr>
+<tr class="separator:a4c6eefd1254eab3e8d34bf02c205e0f4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a09660096b134753128952246f4f4e4bd"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#a09660096b134753128952246f4f4e4bd">isPrime</a> (int64_t m)</td></tr>
+<tr class="separator:a09660096b134753128952246f4f4e4bd"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>C++ Program to find the modular inverse using <a href="https://en.wikipedia.org/wiki/Fermat%27s_little_theorem">Fermat's Little Theorem</a> </p>
+<p>Fermat's Little Theorem state that </p><p class="formulaDsp">
+\[ϕ(m) = m-1\]
+</p>
+<p> where \(m\) is a prime number. </p><p class="formulaDsp">
+\begin{eqnarray*} a \cdot x &amp;≡&amp; 1 \;\text{mod}\; m\\ x &amp;≡&amp; a^{-1} \;\text{mod}\; m \end{eqnarray*}
+</p>
+<p> Using Euler's theorem we can modify the equation. </p><p class="formulaDsp">
+\[ a^{ϕ(m)} ≡ 1 \;\text{mod}\; m \]
+</p>
+<p> (Where '^' denotes the exponent operator)</p>
+<p>Here 'ϕ' is Euler's Totient Function. For modular inverse existence 'a' and 'm' must be relatively primes numbers. To apply Fermat's Little Theorem is necessary that 'm' must be a prime number. Generally in many competitive programming competitions 'm' is either 1000000007 (1e9+7) or 998244353.</p>
+<p>We considered m as large prime (1e9+7). \(a^{ϕ(m)} ≡ 1 \;\text{mod}\; m\) (Using Euler's Theorem) \(ϕ(m) = m-1\) using Fermat's Little Theorem. \(a^{m-1} ≡ 1 \;\text{mod}\; m\) Now multiplying both side by \(a^{-1}\). </p><p class="formulaDsp">
+\begin{eqnarray*} a^{m-1} \cdot a^{-1} &amp;≡&amp; a^{-1} \;\text{mod}\; m\\ a^{m-2} &amp;≡&amp; a^{-1} \;\text{mod}\; m \end{eqnarray*}
+</p>
+<p>We will find the exponent using binary exponentiation. Such that the algorithm works in \(O(\log m)\) time.</p>
+<p>Examples: -</p><ul>
+<li>a = 3 and m = 7</li>
+<li>\(a^{-1} \;\text{mod}\; m\) is equivalent to \(a^{m-2} \;\text{mod}\; m\)</li>
+<li>\(3^5 \;\text{mod}\; 7 = 243 \;\text{mod}\; 7 = 5\) <br  />
+Hence, \(3^{-1} \;\text{mod}\; 7 = 5\) or \(3 \times 5 \;\text{mod}\; 7 = 1 \;\text{mod}\; 7\) (as \(a\times a^{-1} = 1\)) </li>
+</ul>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a4c6eefd1254eab3e8d34bf02c205e0f4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a4c6eefd1254eab3e8d34bf02c205e0f4">&#9670;&nbsp;</a></span>binExpo()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int64_t binExpo </td>
+          <td>(</td>
+          <td class="paramtype">int64_t&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int64_t&#160;</td>
+          <td class="paramname"><em>b</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int64_t&#160;</td>
+          <td class="paramname"><em>m</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Recursive function to calculate exponent in \(O(\log n)\) using binary exponent. </p>
+<div class="fragment"><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;                                                 {</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> %= m;</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    int64_t res = 1;</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keywordflow">while</span> (b &gt; 0) {</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;        <span class="keywordflow">if</span> (b % 2) {</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;            res = res * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> % m;</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        }</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> % m;</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        <span class="comment">// Dividing b by 2 is similar to right shift.</span></div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;        b &gt;&gt;= 1;</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    }</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="keywordflow">return</span> res;</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a09660096b134753128952246f4f4e4bd"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a09660096b134753128952246f4f4e4bd">&#9670;&nbsp;</a></span>isPrime()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool isPrime </td>
+          <td>(</td>
+          <td class="paramtype">int64_t&#160;</td>
+          <td class="paramname"><em>m</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Prime check in \(O(\sqrt{m})\) time. </p>
+<div class="fragment"><div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;                        {</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <span class="keywordflow">if</span> (m &lt;= 1) {</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;        <span class="keywordflow">for</span> (int64_t i = 2; i * i &lt;= m; i++) {</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;            <span class="keywordflow">if</span> (m % i == 0) {</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;                <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        }</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    }</div>
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+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;           {</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    int64_t <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, m;</div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    <span class="comment">// Take input of  a and m.</span></div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Computing ((a^(-1))%(m)) using Fermat&#39;s Little Theorem&quot;</span>;</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Give input &#39;a&#39; and &#39;m&#39; space separated : &quot;</span>;</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &gt;&gt; m;</div>
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+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;The modular inverse of a with mod m is (a^(m-2)) : &quot;</span>;</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code" href="../../d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#a4c6eefd1254eab3e8d34bf02c205e0f4">binExpo</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, m - 2, m) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+Here is the call graph for this function:</div>
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+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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+<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
+<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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+<p>check whether two line segments intersect each other or not.  
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+<tr class="memitem:adc731720947b4bc2ab047c141e7d0299"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d77/namespacemachine__learning.html#adc731720947b4bc2ab047c141e7d0299">kohonen_som</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;X, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt;&gt; *W, double alpha_min)</td></tr>
+<tr class="separator:adc731720947b4bc2ab047c141e7d0299"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a361674452869413536ee501f053129a8"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d77/namespacemachine__learning.html#a361674452869413536ee501f053129a8">update_weights</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *W, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *D, double alpha, int R)</td></tr>
+<tr class="separator:a361674452869413536ee501f053129a8"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:acc6a28f40512dbda75ab1a3969248898"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d77/namespacemachine__learning.html#acc6a28f40512dbda75ab1a3969248898">kohonen_som_tracer</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;X, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *W, double alpha_min)</td></tr>
+<tr class="separator:acc6a28f40512dbda75ab1a3969248898"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Machine learning algorithms. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="adc731720947b4bc2ab047c141e7d0299"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#adc731720947b4bc2ab047c141e7d0299">&#9670;&nbsp;</a></span>kohonen_som()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void machine_learning::kohonen_som </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;&#160;</td>
+          <td class="paramname"><em>X</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt;&gt; *&#160;</td>
+          <td class="paramname"><em>W</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>alpha_min</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Apply incremental algorithm with updating neighborhood and learning rates on all samples in the given datset.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">X</td><td>data set </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">W</td><td>weights matrix </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">alpha_min</td><td>terminal value of alpha </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;                                   {</div>
+<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;    <span class="keywordtype">int</span> num_samples = X.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();      <span class="comment">// number of rows</span></div>
+<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;    <span class="keywordtype">int</span> num_features = X[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// number of columns</span></div>
+<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;    <span class="keywordtype">int</span> num_out = W-&gt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();         <span class="comment">// output matrix size</span></div>
+<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;    <span class="keywordtype">int</span> R = num_out &gt;&gt; 2, iter = 0;</div>
+<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;    <span class="keywordtype">double</span> alpha = 1.f;</div>
+<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160; </div>
+<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; D(num_out);</div>
+<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; num_out; i++) D[i] = std::valarray&lt;double&gt;(num_out);</div>
+<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160; </div>
+<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;    <span class="keywordtype">double</span> dmin = 1.f;        <span class="comment">// average minimum distance of all samples</span></div>
+<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;    <span class="keywordtype">double</span> past_dmin = 1.f;   <span class="comment">// average minimum distance of all samples</span></div>
+<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    <span class="keywordtype">double</span> dmin_ratio = 1.f;  <span class="comment">// change per step</span></div>
+<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160; </div>
+<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;    <span class="comment">// Loop alpha from 1 to slpha_min</span></div>
+<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;    <span class="keywordflow">for</span> (; alpha &gt; 0 &amp;&amp; dmin_ratio &gt; 1e-5; alpha -= 1e-4, iter++) {</div>
+<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;        <span class="comment">// Loop for each sample pattern in the data set</span></div>
+<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> sample = 0; sample &lt; num_samples; sample++) {</div>
+<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;            <span class="comment">// update weights for the current input pattern sample</span></div>
+<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;            dmin += <a class="code" href="../../d8/d77/namespacemachine__learning.html#ac4010fe3a52a74e8b5b1aaadfe38b46f">update_weights</a>(X[sample], W, &amp;D, alpha, R);</div>
+<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;        }</div>
+<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160; </div>
+<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;        <span class="comment">// every 100th iteration, reduce the neighborhood range</span></div>
+<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;        <span class="keywordflow">if</span> (iter % 300 == 0 &amp;&amp; R &gt; 1)</div>
+<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;            R--;</div>
+<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160; </div>
+<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;        dmin /= num_samples;</div>
+<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160; </div>
+<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;        <span class="comment">// termination condition variable -&gt; % change in minimum distance</span></div>
+<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;        dmin_ratio = (past_dmin - dmin) / past_dmin;</div>
+<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;        <span class="keywordflow">if</span> (dmin_ratio &lt; 0)</div>
+<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;            dmin_ratio = 1.f;</div>
+<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;        past_dmin = dmin;</div>
+<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160; </div>
+<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;iter: &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot;\t alpha: &quot;</span> &lt;&lt; alpha &lt;&lt; <span class="stringliteral">&quot;\t R: &quot;</span> &lt;&lt; R</div>
+<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;\t d_min: &quot;</span> &lt;&lt; dmin_ratio &lt;&lt; <span class="stringliteral">&quot;\r&quot;</span>;</div>
+<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    }</div>
+<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160; </div>
+<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d8/d77/namespacemachine__learning_adc731720947b4bc2ab047c141e7d0299_cgraph.svg" width="100%" height="499"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="acc6a28f40512dbda75ab1a3969248898"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#acc6a28f40512dbda75ab1a3969248898">&#9670;&nbsp;</a></span>kohonen_som_tracer()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void machine_learning::kohonen_som_tracer </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;&#160;</td>
+          <td class="paramname"><em>X</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>W</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>alpha_min</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Apply incremental algorithm with updating neighborhood and learning rates on all samples in the given datset.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">X</td><td>data set </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">W</td><td>weights matrix </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">alpha_min</td><td>terminal value of alpha </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;                                          {</div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    <span class="keywordtype">int</span> num_samples = X.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();      <span class="comment">// number of rows</span></div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    <span class="keywordtype">int</span> num_features = X[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// number of columns</span></div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="keywordtype">int</span> num_out = W-&gt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();         <span class="comment">// number of rows</span></div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;    <span class="keywordtype">int</span> R = num_out &gt;&gt; 2, iter = 0;</div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    <span class="keywordtype">double</span> alpha = 1.f;</div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160; </div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> D(num_out);</div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160; </div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;    <span class="comment">// Loop alpha from 1 to slpha_min</span></div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    <span class="keywordflow">for</span> (; alpha &gt; alpha_min; alpha -= 0.01, iter++) {</div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;        <span class="comment">// Loop for each sample pattern in the data set</span></div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> sample = 0; sample &lt; num_samples; sample++) {</div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;            <span class="comment">// update weights for the current input pattern sample</span></div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;            <a class="code" href="../../d8/d77/namespacemachine__learning.html#a361674452869413536ee501f053129a8">update_weights</a>(X[sample], W, &amp;D, alpha, R);</div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;        }</div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160; </div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;        <span class="comment">// every 10th iteration, reduce the neighborhood range</span></div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;        <span class="keywordflow">if</span> (iter % 10 == 0 &amp;&amp; R &gt; 1)</div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;            R--;</div>
+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    }</div>
+<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d8/d77/namespacemachine__learning_acc6a28f40512dbda75ab1a3969248898_cgraph.svg" width="100%" height="499"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a1d577f5d95b774ae97eb6838852d0df5"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a1d577f5d95b774ae97eb6838852d0df5">&#9670;&nbsp;</a></span>save_u_matrix()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int machine_learning::save_u_matrix </td>
+          <td>(</td>
+          <td class="paramtype">const char *&#160;</td>
+          <td class="paramname"><em>fname</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt;&gt; &amp;&#160;</td>
+          <td class="paramname"><em>W</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Create the distance matrix or <a href="https://en.wikipedia.org/wiki/U-matrix">U-matrix</a> from the trained 3D weiths matrix and save to disk.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">fname</td><td>filename to save in (gets overwriten without confirmation) </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">W</td><td>model matrix to save </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>0 if all ok </dd>
+<dd>
+-1 if file creation failed </dd></dl>
+<div class="fragment"><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;                                                                      {</div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(fname);</div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    <span class="keywordflow">if</span> (!fp) {  <span class="comment">// error with fopen</span></div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;        <span class="keywordtype">char</span> msg[120];</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">std::snprintf</a>(msg, <span class="keyword">sizeof</span>(msg), <span class="stringliteral">&quot;File error (%s): &quot;</span>, fname);</div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(msg);</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    }</div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160; </div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    <span class="comment">// neighborhood range</span></div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> R = 1;</div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160; </div>
+<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; W.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {         <span class="comment">// for each x</span></div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; W[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) {  <span class="comment">// for each y</span></div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;            <span class="keywordtype">double</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> = 0.f;</div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160; </div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;            <span class="keywordtype">int</span> from_x = std::max&lt;int&gt;(0, i - R);</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;            <span class="keywordtype">int</span> to_x = std::min&lt;int&gt;(W.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), i + R + 1);</div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;            <span class="keywordtype">int</span> from_y = std::max&lt;int&gt;(0, j - R);</div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;            <span class="keywordtype">int</span> to_y = std::min&lt;int&gt;(W[0].size(), j + R + 1);</div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;            <span class="keywordtype">int</span> l, m;</div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="preprocessor">#pragma omp parallel for reduction(+ : distance)</span></div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;            <span class="keywordflow">for</span> (l = from_x; l &lt; to_x; l++) {      <span class="comment">// scan neighborhoor in x</span></div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;                <span class="keywordflow">for</span> (m = from_y; m &lt; to_y; m++) {  <span class="comment">// scan neighborhood in y</span></div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;                    <span class="keyword">auto</span> d = W[i][j] - W[l][m];</div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;                    <span class="keywordtype">double</span> d2 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(d, 2).sum();</div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;                    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> += <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(d2);</div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;                    <span class="comment">// distance += d2;</span></div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;                }</div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;            }</div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160; </div>
+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a> /= R * R;          <span class="comment">// mean distance from neighbors</span></div>
+<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;            fp &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">distance</a>;             <span class="comment">// print the mean separation</span></div>
+<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;            <span class="keywordflow">if</span> (j &lt; W[0].size() - 1) {  <span class="comment">// if not the last column</span></div>
+<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;                fp &lt;&lt; <span class="charliteral">&#39;,&#39;</span>;              <span class="comment">// suffix comma</span></div>
+<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;            }</div>
+<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;        }</div>
+<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;        <span class="keywordflow">if</span> (i &lt; W.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() - 1)  <span class="comment">// if not the last row</span></div>
+<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;            fp &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;        <span class="comment">// start a new line</span></div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    }</div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160; </div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    fp.close();</div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d77/namespacemachine__learning_a1d577f5d95b774ae97eb6838852d0df5_cgraph.svg" width="356" height="240"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a361674452869413536ee501f053129a8"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a361674452869413536ee501f053129a8">&#9670;&nbsp;</a></span>update_weights() <span class="overload">[1/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void machine_learning::update_weights </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &amp;&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>W</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>D</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>alpha</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>R</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Update weights of the SOM using Kohonen algorithm</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">X</td><td>data point </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">W</td><td>weights matrix </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">D</td><td>temporary vector to store distances </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">alpha</td><td>learning rate \(0&lt;\alpha\le1\) </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">R</td><td>neighborhood range </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;                                                                 {</div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    <span class="keywordtype">int</span> j, <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>;</div>
+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    <span class="keywordtype">int</span> num_out = W-&gt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();      <span class="comment">// number of SOM output nodes</span></div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    <span class="keywordtype">int</span> num_features = x.size();  <span class="comment">// number of data features</span></div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160; </div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="comment">// step 1: for each output point</span></div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <span class="keywordflow">for</span> (j = 0; j &lt; num_out; j++) {</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        <span class="comment">// compute Euclidian distance of each output</span></div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        <span class="comment">// point from the current sample</span></div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        (*D)[j] = (((*W)[j] - x) * ((*W)[j] - x)).sum();</div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    }</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160; </div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <span class="comment">// step 2:  get closest node i.e., node with snallest Euclidian distance to</span></div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    <span class="comment">// the current pattern</span></div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    <span class="keyword">auto</span> result = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min_element.html">std::min_element</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(*D), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(*D));</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <span class="keywordtype">double</span> d_min = *result;</div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <span class="keywordtype">int</span> d_min_idx = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">std::distance</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(*D), result);</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160; </div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    <span class="comment">// step 3a: get the neighborhood range</span></div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    <span class="keywordtype">int</span> from_node = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(0, d_min_idx - R);</div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    <span class="keywordtype">int</span> to_node = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(num_out, d_min_idx + R + 1);</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160; </div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    <span class="comment">// step 3b: update the weights of nodes in the</span></div>
+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;    <span class="comment">// neighborhood</span></div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    <span class="keywordflow">for</span> (j = from_node; j &lt; to_node; j++)</div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;        <span class="comment">// update weights of nodes in the neighborhood</span></div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;        (*W)[j] += alpha * (x - (*W)[j]);</div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d77/namespacemachine__learning_a361674452869413536ee501f053129a8_cgraph.svg" width="352" height="291"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ac4010fe3a52a74e8b5b1aaadfe38b46f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac4010fe3a52a74e8b5b1aaadfe38b46f">&#9670;&nbsp;</a></span>update_weights() <span class="overload">[2/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double machine_learning::update_weights </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &amp;&#160;</td>
+          <td class="paramname"><em>X</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt;&gt; *&#160;</td>
+          <td class="paramname"><em>W</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>D</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>alpha</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>R</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Update weights of the SOM using Kohonen algorithm</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">X</td><td>data point - N features </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">W</td><td>weights matrix - PxQxN </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">D</td><td>temporary vector to store distances PxQ </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">alpha</td><td>learning rate \(0&lt;\alpha\le1\) </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">R</td><td>neighborhood range </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>minimum distance of sample and trained weights </dd></dl>
+<div class="fragment"><div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;                             {</div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    <span class="keywordtype">int</span> x, y;</div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    <span class="keywordtype">int</span> num_out_x = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(W-&gt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());       <span class="comment">// output nodes - in X</span></div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;    <span class="keywordtype">int</span> num_out_y = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(W[0][0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());  <span class="comment">// output nodes - in Y</span></div>
+<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    <span class="keywordtype">int</span> num_features = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(W[0][0][0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());  <span class="comment">//  features = in Z</span></div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    <span class="keywordtype">double</span> d_min = 0.f;</div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160; </div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    <span class="comment">// step 1: for each output point</span></div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    <span class="keywordflow">for</span> (x = 0; x &lt; num_out_x; x++) {</div>
+<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;        <span class="keywordflow">for</span> (y = 0; y &lt; num_out_y; y++) {</div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;            (*D)[x][y] = 0.f;</div>
+<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;            <span class="comment">// compute Euclidian distance of each output</span></div>
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+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">exponential_search.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a href="https://en.wikipedia.org/wiki/Exponential_search">Exponential search algorithm</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
+<code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;cstring&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for exponential_search.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d3c/exponential__search_8cpp__incl.svg" width="342" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a0f697e2a3b5193324ab84bd4045088f7"><td class="memTemplParams" colspan="2">template&lt;class Type &gt; </td></tr>
+<tr class="memitem:a0f697e2a3b5193324ab84bd4045088f7"><td class="memTemplItemLeft" align="right" valign="top">Type *&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d8/d8a/exponential__search_8cpp.html#a0f697e2a3b5193324ab84bd4045088f7">binary_s</a> (Type *array, size_t size, Type key)</td></tr>
+<tr class="separator:a0f697e2a3b5193324ab84bd4045088f7"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a67e9c84b4e2eb30e3c5170eabfbb363d"><td class="memTemplParams" colspan="2">template&lt;class Type &gt; </td></tr>
+<tr class="memitem:a67e9c84b4e2eb30e3c5170eabfbb363d"><td class="memTemplItemLeft" align="right" valign="top">Type *&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d8/d8a/exponential__search_8cpp.html#a67e9c84b4e2eb30e3c5170eabfbb363d">struzik_search</a> (Type *array, size_t size, Type key)</td></tr>
+<tr class="separator:a67e9c84b4e2eb30e3c5170eabfbb363d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d8a/exponential__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Exponential_search">Exponential search algorithm</a> </p>
+<dl class="section copyright"><dt>Copyright</dt><dd>2020 Divide-et-impera-11</dd></dl>
+<p>The algorithm try to search the range where the key should be. If it has been found we do a binary search there. The range of the search grows by exponential every time. If the key is larger than the last element of array, the start of block(block_front) will be equal to the end of block(block_size) and the algorithm return null ponter, every other cases the algoritm return fom the loop. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a0f697e2a3b5193324ab84bd4045088f7"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0f697e2a3b5193324ab84bd4045088f7">&#9670;&nbsp;</a></span>binary_s()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Type &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">Type* binary_s </td>
+          <td>(</td>
+          <td class="paramtype">Type *&#160;</td>
+          <td class="paramname"><em>array</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">size_t&#160;</td>
+          <td class="paramname"><em>size</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">Type&#160;</td>
+          <td class="paramname"><em>key</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Binary Search Algorithm (used by <a class="el" href="../../d8/d8a/exponential__search_8cpp.html#a67e9c84b4e2eb30e3c5170eabfbb363d">struzik_search</a>)<br  />
+</p><ul>
+<li>Time Complexity O(log n) where 'n' is the number of elements</li>
+<li>Worst Time Complexity O(log n)</li>
+<li>Best Time Complexity Ω(1)</li>
+<li>Space Complexity O(1)</li>
+<li>Auxiliary Space Complexity O(1) <dl class="section return"><dt>Returns</dt><dd>pointer to value in the array </dd>
+<dd>
+<code>nullptr</code> if value not found </dd></dl>
+</li>
+</ul>
+<div class="fragment"><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;                                                          {</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    int32_t lower_index(0), upper_index(size - 1), middle_index;</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160; </div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="keywordflow">while</span> (lower_index &lt;= upper_index) {</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;        middle_index = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/floor.html">std::floor</a>((lower_index + upper_index) / 2);</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160; </div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        <span class="keywordflow">if</span> (*(array + middle_index) &lt; key)</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;            lower_index = (middle_index + 1);</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (*(array + middle_index) &gt; key)</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;            upper_index = (middle_index - 1);</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        <span class="keywordflow">else</span></div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;            <span class="keywordflow">return</span> (array + middle_index);</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    }</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160; </div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
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+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;           {</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    <span class="comment">// TEST CASES</span></div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <span class="keywordtype">int</span>* sorted_array = <span class="keyword">new</span> <span class="keywordtype">int</span>[7]{7, 10, 15, 23, 70, 105, 203};</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    assert(struzik_search&lt;int&gt;(sorted_array, 7, 0) == <span class="keyword">nullptr</span>);</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    assert(struzik_search&lt;int&gt;(sorted_array, 7, 1000) == <span class="keyword">nullptr</span>);</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    assert(struzik_search&lt;int&gt;(sorted_array, 7, 50) == <span class="keyword">nullptr</span>);</div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    assert(struzik_search&lt;int&gt;(sorted_array, 7, 7) == sorted_array);</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    <span class="comment">// TEST CASES</span></div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    <span class="keyword">delete</span>[] sorted_array;</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a67e9c84b4e2eb30e3c5170eabfbb363d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a67e9c84b4e2eb30e3c5170eabfbb363d">&#9670;&nbsp;</a></span>struzik_search()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class Type &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">Type* struzik_search </td>
+          <td>(</td>
+          <td class="paramtype">Type *&#160;</td>
+          <td class="paramname"><em>array</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">size_t&#160;</td>
+          <td class="paramname"><em>size</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">Type&#160;</td>
+          <td class="paramname"><em>key</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Struzik Search Algorithm(Exponential)</p><ul>
+<li>Time Complexity O(log i) where i is the position of search key in the list</li>
+<li>Worst Time Complexity O(log i)</li>
+<li>Best Time Complexity Ω(1)</li>
+<li>Space Complexity O(1)</li>
+<li>Auxiliary Space Complexity O(1) </li>
+</ul>
+<div class="fragment"><div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;                                                         {</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    uint32_t block_front(0), block_size = size == 0 ? 0 : 1;</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    <span class="keywordflow">while</span> (block_front != block_size) {</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        <span class="keywordflow">if</span> (*(array + block_size - 1) &lt; key) {</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;            block_front = block_size;</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;            (block_size * 2 - 1 &lt; size) ? (block_size *= 2) : block_size = size;</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;            <span class="keywordflow">continue</span>;</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        }</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;        <span class="keywordflow">return</span> binary_s&lt;Type&gt;(array + block_front, (block_size - block_front),</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;                              key);</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    }</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;}</div>
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+</div>
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+<div class="ttc" id="afloor_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/floor.html">std::floor</a></div><div class="ttdeci">T floor(T... args)</div></div>
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+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>data</b> (defined in <a class="el" href="../../db/d8b/struct_node.html">Node</a>)</td><td class="entry"><a class="el" href="../../db/d8b/struct_node.html">Node</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>next</b> (defined in <a class="el" href="../../db/d8b/struct_node.html">Node</a>)</td><td class="entry"><a class="el" href="../../db/d8b/struct_node.html">Node</a></td><td class="entry"></td></tr>
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+  <tr bgcolor="#f0f0f0"><td class="entry"><b>next</b> (defined in <a class="el" href="../../db/d8b/struct_node.html">Node</a>)</td><td class="entry"><a class="el" href="../../db/d8b/struct_node.html">Node</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>Node</b>(int v, Node *n) (defined in <a class="el" href="../../db/d8b/struct_node.html">Node</a>)</td><td class="entry"><a class="el" href="../../db/d8b/struct_node.html">Node</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>val</b> (defined in <a class="el" href="../../db/d8b/struct_node.html">Node</a>)</td><td class="entry"><a class="el" href="../../db/d8b/struct_node.html">Node</a></td><td class="entry"></td></tr>
+</table></div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+<link href="../../doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
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+ <tbody>
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+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
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+<script type="text/javascript">
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+  $(document).ready(function() { init_search(); });
+});
+/* @license-end */</script>
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+<table class="directory">
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>addedge</b>(int src, int dest) (defined in <a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td><td class="entry"><a class="el" href="../../dd/d9b/classgraph.html">graph</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>addEdge</b>(int, int) (defined in <a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td><td class="entry"><a class="el" href="../../dd/d9b/classgraph.html">graph</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>adj</b> (defined in <a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td><td class="entry"><a class="el" href="../../dd/d9b/classgraph.html">graph</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
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+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>bfs</b>(int s) (defined in <a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td><td class="entry"><a class="el" href="../../dd/d9b/classgraph.html">graph</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>connected_components</b> (defined in <a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td><td class="entry"><a class="el" href="../../dd/d9b/classgraph.html">graph</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>depth_first_search</b>() (defined in <a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td><td class="entry"><a class="el" href="../../dd/d9b/classgraph.html">graph</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>explore</b>(int, vector&lt; bool &gt; &amp;) (defined in <a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td><td class="entry"><a class="el" href="../../dd/d9b/classgraph.html">graph</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>getConnectedComponents</b>() (defined in <a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td><td class="entry"><a class="el" href="../../dd/d9b/classgraph.html">graph</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>graph</b>(int v) (defined in <a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td><td class="entry"><a class="el" href="../../dd/d9b/classgraph.html">graph</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>graph</b>(int n) (defined in <a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td><td class="entry"><a class="el" href="../../dd/d9b/classgraph.html">graph</a></td><td class="entry"><span class="mlabel">inline</span><span class="mlabel">explicit</span></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>printgraph</b>() (defined in <a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td><td class="entry"><a class="el" href="../../dd/d9b/classgraph.html">graph</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>v</b> (defined in <a class="el" href="../../dd/d9b/classgraph.html">graph</a>)</td><td class="entry"><a class="el" href="../../dd/d9b/classgraph.html">graph</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+</table></div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
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+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
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+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: statistics::stats_computer2&lt; T &gt; Class Template Reference</title>
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+<script type="text/javascript" src="../../dynsections.js"></script>
+<link href="../../navtree.css" rel="stylesheet" type="text/css"/>
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+<script type="text/javascript" src="../../navtreedata.js"></script>
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+<script type="text/javascript" src="../../search/search.js"></script>
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+<div id="titlearea">
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+   <div id="projectname">Algorithms_in_C++
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+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
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+<script type="text/javascript">
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+</div><!-- top -->
+<div id="side-nav" class="ui-resizable side-nav-resizable">
+  <div id="nav-tree">
+    <div id="nav-tree-contents">
+      <div id="nav-sync" class="sync"></div>
+    </div>
+  </div>
+  <div id="splitbar" style="-moz-user-select:none;" 
+       class="ui-resizable-handle">
+  </div>
+</div>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+/* @license-end */
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+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
+     onmouseout="return searchBox.OnSearchSelectHide()"
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+
+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
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+
+<div class="header">
+  <div class="summary">
+<a href="#pub-methods">Public Member Functions</a> &#124;
+<a href="#pri-attribs">Private Attributes</a> &#124;
+<a href="#friends">Friends</a> &#124;
+<a href="../../d3/da3/classstatistics_1_1stats__computer2-members.html">List of all members</a>  </div>
+  <div class="headertitle">
+<div class="title">statistics::stats_computer2&lt; T &gt; Class Template Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
+Public Member Functions</h2></td></tr>
+<tr class="memitem:ade6de704deea24fdc88077b3d9a0d534"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html#ade6de704deea24fdc88077b3d9a0d534">new_val</a> (T x)</td></tr>
+<tr class="separator:ade6de704deea24fdc88077b3d9a0d534"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a8290966ad468f2a8c266d008bc60720e"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html#a8290966ad468f2a8c266d008bc60720e">mean</a> () const</td></tr>
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+<tr class="memitem:a80099005c6e5f9569b75da0e49b14cf6"><td class="memItemLeft" align="right" valign="top"><a id="a80099005c6e5f9569b75da0e49b14cf6"></a>
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+double&#160;</td><td class="memItemRight" valign="bottom"><b>mu</b> = 0</td></tr>
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+double&#160;</td><td class="memItemRight" valign="bottom"><b>var</b> = 0</td></tr>
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+double&#160;</td><td class="memItemRight" valign="bottom"><b>M</b> = 0</td></tr>
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+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="friends"></a>
+Friends</h2></td></tr>
+<tr class="memitem:a7e7a1a2b0a03df0a70cac40d193421d2"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::istream</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html#a7e7a1a2b0a03df0a70cac40d193421d2">operator&gt;&gt;</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::istream</a> &amp;input, <a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">stats_computer2</a> &amp;stat)</td></tr>
+<tr class="separator:a7e7a1a2b0a03df0a70cac40d193421d2"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><h3>template&lt;typename T&gt;<br />
+class statistics::stats_computer2&lt; T &gt;</h3>
+
+<p>continuous mean and variance computance using Welford's algorithm (very accurate) </p>
+</div><h2 class="groupheader">Member Function Documentation</h2>
+<a id="a8290966ad468f2a8c266d008bc60720e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a8290966ad468f2a8c266d008bc60720e">&#9670;&nbsp;</a></span>mean()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">double <a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2</a>&lt; T &gt;::mean </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td> const</td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>return sample mean computed till last sample </p>
+<div class="fragment"><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;{ <span class="keywordflow">return</span> mu; }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ade6de704deea24fdc88077b3d9a0d534"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ade6de704deea24fdc88077b3d9a0d534">&#9670;&nbsp;</a></span>new_val()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void <a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2</a>&lt; T &gt;::new_val </td>
+          <td>(</td>
+          <td class="paramtype">T&#160;</td>
+          <td class="paramname"><em>x</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Constructor </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>new data sample </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;                      {</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        n++;</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        <span class="keywordtype">double</span> delta = x - mu;</div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;        mu += delta / n;</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;        <span class="keywordtype">double</span> delta2 = x - mu;</div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        M += delta * delta2;</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="acf2e84df4fc386bb3295016ef8fd156e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#acf2e84df4fc386bb3295016ef8fd156e">&#9670;&nbsp;</a></span>std()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
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+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">double <a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2</a>&lt; T &gt;::std </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td> const</td>
+        </tr>
+      </table>
+  </td>
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+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>return sample standard deviation computed till last sample </p>
+<div class="fragment"><div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;{ <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(this-&gt;<a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">variance</a>()); }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
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+</div>
+</div>
+
+</div>
+</div>
+<a id="af6198817084276113b3c064e87ce0555"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af6198817084276113b3c064e87ce0555">&#9670;&nbsp;</a></span>variance()</h2>
+
+<div class="memitem">
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+        <tr>
+          <td class="memname">double <a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2</a>&lt; T &gt;::variance </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td> const</td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>return data variance computed till last sample </p>
+<div class="fragment"><div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;{ <span class="keywordflow">return</span> M / n; }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<h2 class="groupheader">Friends And Related Function Documentation</h2>
+<a id="a7e7a1a2b0a03df0a70cac40d193421d2"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a7e7a1a2b0a03df0a70cac40d193421d2">&#9670;&nbsp;</a></span>operator&gt;&gt;</h2>
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+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
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+<table class="mlabels">
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+  <td class="mlabels-left">
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+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::istream</a>&amp; operator&gt;&gt; </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::istream</a> &amp;&#160;</td>
+          <td class="paramname"><em>input</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="el" href="../../d8/dab/classstatistics_1_1stats__computer2.html">stats_computer2</a>&lt; T &gt; &amp;&#160;</td>
+          <td class="paramname"><em>stat</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">friend</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>short-hand operator to read new sample from input stream <br  />
+ e.g.: <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; stats1;</code> </p>
+<div class="fragment"><div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;                                                           {</div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;        T val;</div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;        input &gt;&gt; val;</div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;        stat.<a class="code" href="../../d8/dab/classstatistics_1_1stats__computer2.html#ade6de704deea24fdc88077b3d9a0d534">new_val</a>(val);</div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        <span class="keywordflow">return</span> input;</div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<hr/>The documentation for this class was generated from the following file:<ul>
+<li>math/<a class="el" href="../../d0/d08/realtime__stats_8cpp.html">realtime_stats.cpp</a></li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
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+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
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+<div class="header">
+  <div class="summary">
+<a href="#pub-methods">Public Member Functions</a> &#124;
+<a href="#pub-attribs">Public Attributes</a> &#124;
+<a href="../../d0/dc4/struct_point-members.html">List of all members</a>  </div>
+  <div class="headertitle">
+<div class="title">Point Struct Reference</div>  </div>
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+<tr class="memitem:ae2d6fb1b3fd3a96169d963d62e37130a"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/dc8/struct_point.html#ae2d6fb1b3fd3a96169d963d62e37130a">Point</a> (double <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>=0.<a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a>, double b=0.<a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a>)</td></tr>
+<tr class="separator:ae2d6fb1b3fd3a96169d963d62e37130a"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="memitem:a8c779e11e694b20e0946105a9f5de842"><td class="memItemLeft" align="right" valign="top"><a id="a8c779e11e694b20e0946105a9f5de842"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>x</b></td></tr>
+<tr class="separator:a8c779e11e694b20e0946105a9f5de842"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a></td></tr>
+<tr class="memdesc:a2e1b5fb2b2a83571f5c0bc0f66a73cf7"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a class="el" href="../../d8/dc8/struct_point.html">Point</a> respect to x coordinate. <br /></td></tr>
+<tr class="separator:a2e1b5fb2b2a83571f5c0bc0f66a73cf7"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ab99c56589bc8ad5fa5071387110a5bc7"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/dc8/struct_point.html#ab99c56589bc8ad5fa5071387110a5bc7">x</a></td></tr>
+<tr class="separator:ab99c56589bc8ad5fa5071387110a5bc7"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:afa38be143ae800e6ad69ce8ed4df62d8"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/dc8/struct_point.html#afa38be143ae800e6ad69ce8ed4df62d8">y</a></td></tr>
+<tr class="separator:afa38be143ae800e6ad69ce8ed4df62d8"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Define a <a class="el" href="../../d8/dc8/struct_point.html">Point</a>.</p>
+<p>Define a point </p>
+</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
+<a id="ae2d6fb1b3fd3a96169d963d62e37130a"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae2d6fb1b3fd3a96169d963d62e37130a">&#9670;&nbsp;</a></span>Point()</h2>
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+<div class="memitem">
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+        </tr>
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+          <td></td>
+          <td class="paramtype">double&#160;</td>
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+          <td></td><td></td>
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+  <td class="mlabels-right">
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+</div><div class="memdoc">
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+    <tr><td class="paramdir">[in]</td><td class="paramname">b</td><td>ordinate (default = 0.0) </td></tr>
+  </table>
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+<div class="fragment"><div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;                                                   {</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;        x = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;        <a class="code" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = b;</div>
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+<h2 class="groupheader">Member Data Documentation</h2>
+<a id="ab99c56589bc8ad5fa5071387110a5bc7"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ab99c56589bc8ad5fa5071387110a5bc7">&#9670;&nbsp;</a></span>x</h2>
+
+<div class="memitem">
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+          <td class="memname">double Point::x</td>
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+</div><div class="memdoc">
+<p>abscissa </p>
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+<h2 class="memtitle"><span class="permalink"><a href="#afa38be143ae800e6ad69ce8ed4df62d8">&#9670;&nbsp;</a></span>y</h2>
+
+<div class="memitem">
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+          <td class="memname">double Point::y</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>ordinate </p>
+
+</div>
+</div>
+<hr/>The documentation for this struct was generated from the following files:<ul>
+<li>geometry/<a class="el" href="../../d8/d6c/line__segment__intersection_8cpp.html">line_segment_intersection.cpp</a></li>
+<li>others/<a class="el" href="../../d0/d01/smallest__circle_8cpp.html">smallest_circle.cpp</a></li>
+</ul>
+</div><!-- contents -->
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+<div class="ttc" id="astruct_point_html_a2e1b5fb2b2a83571f5c0bc0f66a73cf7"><div class="ttname"><a href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">Point::y</a></div><div class="ttdeci">int y</div><div class="ttdoc">Point respect to x coordinate.</div><div class="ttdef"><b>Definition:</b> line_segment_intersection.cpp:14</div></div>
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+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
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+<a href="#var-members">Variables</a>  </div>
+  <div class="headertitle">
+<div class="title">sieve_of_eratosthenes.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Get list of prime numbers using Sieve of Eratosthenes Sieve of Eratosthenes is an algorithm to find the primes that is between 2 to N (as defined in main).  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for sieve_of_eratosthenes.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../da/d35/sieve__of__eratosthenes_8cpp__incl.svg" width="222" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="define-members"></a>
+Macros</h2></td></tr>
+<tr class="memitem:a392fb874e547e582e9c66a08a1f23326"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a>&#160;&#160;&#160;10000000</td></tr>
+<tr class="separator:a392fb874e547e582e9c66a08a1f23326"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:abce89d8999986f085c368969590376b8"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#abce89d8999986f085c368969590376b8">sieve</a> (uint32_t N)</td></tr>
+<tr class="separator:abce89d8999986f085c368969590376b8"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:af50a5c87d27cfd3462745b37fb9b0f46"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#af50a5c87d27cfd3462745b37fb9b0f46">print</a> (uint32_t N)</td></tr>
+<tr class="separator:af50a5c87d27cfd3462745b37fb9b0f46"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a02fd73d861ef2e4aabb38c0c9ff82947"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a02fd73d861ef2e4aabb38c0c9ff82947">init</a> ()</td></tr>
+<tr class="separator:a02fd73d861ef2e4aabb38c0c9ff82947"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="var-members"></a>
+Variables</h2></td></tr>
+<tr class="memitem:a0560e21edb54d5ad8d80b2d80348ce22"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a0560e21edb54d5ad8d80b2d80348ce22">isprime</a> [<a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a692ac7187ee88621a9f78fca78ec498d">MAX</a>]</td></tr>
+<tr class="separator:a0560e21edb54d5ad8d80b2d80348ce22"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Get list of prime numbers using Sieve of Eratosthenes Sieve of Eratosthenes is an algorithm to find the primes that is between 2 to N (as defined in main). </p>
+<p>Time Complexity : \(O(N \cdot\log N)\) <br  />
+Space Complexity : \(O(N)\)</p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d4/d9c/primes__up__to__billion_8cpp.html" title="Compute prime numbers upto 1 billion.">primes_up_to_billion.cpp</a> <a class="el" href="../../de/d9b/prime__numbers_8cpp.html" title="Get list of prime numbers.">prime_numbers.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Macro Definition Documentation</h2>
+<a id="a392fb874e547e582e9c66a08a1f23326"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a392fb874e547e582e9c66a08a1f23326">&#9670;&nbsp;</a></span>MAX</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">#define MAX&#160;&#160;&#160;10000000</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Maximum number of primes </p>
+
+</div>
+</div>
+<h2 class="groupheader">Function Documentation</h2>
+<a id="a02fd73d861ef2e4aabb38c0c9ff82947"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a02fd73d861ef2e4aabb38c0c9ff82947">&#9670;&nbsp;</a></span>init()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void init </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Initialize the array </p>
+<div class="fragment"><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;            {</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <span class="keywordflow">for</span> (uint32_t i = 1; i &lt; <a class="code" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a>; i++) {</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;        <a class="code" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a0560e21edb54d5ad8d80b2d80348ce22">isprime</a>[i] = <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    }</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;           {</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    uint32_t N = 100;</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    <a class="code" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a02fd73d861ef2e4aabb38c0c9ff82947">init</a>();</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <a class="code" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#abce89d8999986f085c368969590376b8">sieve</a>(N);</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <a class="code" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#af50a5c87d27cfd3462745b37fb9b0f46">print</a>(N);</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/ddf/sieve__of__eratosthenes_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="283" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="af50a5c87d27cfd3462745b37fb9b0f46"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af50a5c87d27cfd3462745b37fb9b0f46">&#9670;&nbsp;</a></span>print()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void print </td>
+          <td>(</td>
+          <td class="paramtype">uint32_t&#160;</td>
+          <td class="paramname"><em>N</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>This function prints out the primes to STDOUT </p>
+<div class="fragment"><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;                       {</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keywordflow">for</span> (uint32_t i = 1; i &lt;= N; i++) {</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a0560e21edb54d5ad8d80b2d80348ce22">isprime</a>[i]) {</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="charliteral">&#39; &#39;</span>;</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        }</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    }</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/ddf/sieve__of__eratosthenes_8cpp_af50a5c87d27cfd3462745b37fb9b0f46_cgraph.svg" width="178" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
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+<a id="abce89d8999986f085c368969590376b8"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#abce89d8999986f085c368969590376b8">&#9670;&nbsp;</a></span>sieve()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void sieve </td>
+          <td>(</td>
+          <td class="paramtype">uint32_t&#160;</td>
+          <td class="paramname"><em>N</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>This is the function that finds the primes and eliminates the multiples. </p>
+<div class="fragment"><div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;                       {</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <a class="code" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a0560e21edb54d5ad8d80b2d80348ce22">isprime</a>[0] = <span class="keyword">false</span>;</div>
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+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    <span class="keywordflow">for</span> (uint32_t i = 2; i &lt;= N; i++) {</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a0560e21edb54d5ad8d80b2d80348ce22">isprime</a>[i]) {</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;            <span class="keywordflow">for</span> (uint32_t j = (i &lt;&lt; 1); j &lt;= N; j += i) {</div>
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+</div><!-- fragment -->
+</div>
+</div>
+<h2 class="groupheader">Variable Documentation</h2>
+<a id="a0560e21edb54d5ad8d80b2d80348ce22"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0560e21edb54d5ad8d80b2d80348ce22">&#9670;&nbsp;</a></span>isprime</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool isprime[<a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a692ac7187ee88621a9f78fca78ec498d">MAX</a>]</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>array to store the primes </p>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_af50a5c87d27cfd3462745b37fb9b0f46"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#af50a5c87d27cfd3462745b37fb9b0f46">print</a></div><div class="ttdeci">void print(uint32_t N)</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:40</div></div>
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+<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>A simple tree implementation using nodes. </p>
+<dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000001">Todo:</a></b></dt><dd>update code to use C++ STL library features and OO structure </dd></dl>
+<dl class="section warning"><dt>Warning</dt><dd>This program is a poor implementation and does not utilize any of the C++ STL features. </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a1ecfaaea49d452772dbb2b28133e36e0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a1ecfaaea49d452772dbb2b28133e36e0">&#9670;&nbsp;</a></span>createNode()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d5/da1/structnode.html">node</a>* createNode </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>data</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Create and return a new <a class="el" href="../../db/d8b/struct_node.html">Node</a> </p>
+<div class="fragment"><div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;                           {</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;    <a class="code" href="../../d5/da1/structnode.html">node</a> *nn = <span class="keyword">new</span> <a class="code" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>();</div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    nn-&gt;data = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    nn-&gt;height = 0;</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    nn-&gt;left = NULL;</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    nn-&gt;right = NULL;</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keywordflow">return</span> nn;</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a8286388b0743a716145639df3a33e541"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a8286388b0743a716145639df3a33e541">&#9670;&nbsp;</a></span>deleteNode()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d5/da1/structnode.html">node</a>* deleteNode </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d5/da1/structnode.html">node</a> *&#160;</td>
+          <td class="paramname"><em>root</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>key</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Balanced Deletion </p>
+<div class="fragment"><div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;                                      {</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    <span class="keywordflow">if</span> (root == NULL)</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        <span class="keywordflow">return</span> root;</div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <span class="keywordflow">if</span> (key &lt; root-&gt;<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        root-&gt;left = <a class="code" href="../../d8/dee/avltree_8cpp.html#a8286388b0743a716145639df3a33e541">deleteNode</a>(root-&gt;left, key);</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (key &gt; root-&gt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>)</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;        root-&gt;right = <a class="code" href="../../d8/dee/avltree_8cpp.html#a8286388b0743a716145639df3a33e541">deleteNode</a>(root-&gt;right, key);</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160; </div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        <span class="comment">// Node to be deleted is leaf node or have only one Child</span></div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        <span class="keywordflow">if</span> (!root-&gt;right) {</div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;            <a class="code" href="../../d5/da1/structnode.html">node</a> *temp = root-&gt;left;</div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;            <span class="keyword">delete</span> (root);</div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;            root = NULL;</div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;            <span class="keywordflow">return</span> temp;</div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!root-&gt;left) {</div>
+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;            <a class="code" href="../../d5/da1/structnode.html">node</a> *temp = root-&gt;right;</div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;            <span class="keyword">delete</span> (root);</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;            root = NULL;</div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;            <span class="keywordflow">return</span> temp;</div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;        }</div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;        <span class="comment">// Node to be deleted have both left and right subtrees</span></div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;        <a class="code" href="../../d5/da1/structnode.html">node</a> *temp = <a class="code" href="../../d8/dee/avltree_8cpp.html#adb8e952bf1c266bae84111b9d6a12015">minValue</a>(root-&gt;right);</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        root-&gt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a> = temp-&gt;data;</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        root-&gt;right = <a class="code" href="../../d8/dee/avltree_8cpp.html#a8286388b0743a716145639df3a33e541">deleteNode</a>(root-&gt;right, temp-&gt;data);</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    }</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    <span class="comment">// Balancing Tree after deletion</span></div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    <span class="keywordflow">return</span> root;</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/dee/avltree_8cpp_a8286388b0743a716145639df3a33e541_cgraph.svg" width="264" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="aaa457ffec24c9643f2768e7a65e96546"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aaa457ffec24c9643f2768e7a65e96546">&#9670;&nbsp;</a></span>getBalance()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int getBalance </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d5/da1/structnode.html">node</a> *&#160;</td>
+          <td class="paramname"><em>root</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Returns difference between height of left and right subtree </p>
+<div class="fragment"><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;{ <span class="keywordflow">return</span> <a class="code" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>(root-&gt;left) - <a class="code" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>(root-&gt;right); }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/dee/avltree_8cpp_aaa457ffec24c9643f2768e7a65e96546_cgraph.svg" width="324" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ae4a66d8b0c2b0d626aea45977e358c83"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae4a66d8b0c2b0d626aea45977e358c83">&#9670;&nbsp;</a></span>height()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int height </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d5/da1/structnode.html">node</a> *&#160;</td>
+          <td class="paramname"><em>root</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Returns height of tree </p>
+<div class="fragment"><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;                       {</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="keywordflow">if</span> (root == NULL)</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;        <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <span class="keywordflow">return</span> 1 + <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(<a class="code" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>(root-&gt;left), <a class="code" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>(root-&gt;right));</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/dee/avltree_8cpp_ae4a66d8b0c2b0d626aea45977e358c83_cgraph.svg" width="190" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="aa7cd8a68075fae1c33df41233c1bed6a"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa7cd8a68075fae1c33df41233c1bed6a">&#9670;&nbsp;</a></span>insert()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d5/da1/structnode.html">node</a>* insert </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d5/da1/structnode.html">node</a> *&#160;</td>
+          <td class="paramname"><em>root</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>item</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Balanced Insertion </p>
+<div class="fragment"><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;                                   {</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    <a class="code" href="../../d5/da1/structnode.html">node</a> *nn = <a class="code" href="../../d8/dee/avltree_8cpp.html#a1ecfaaea49d452772dbb2b28133e36e0">createNode</a>(item);</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keywordflow">if</span> (root == NULL)</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        <span class="keywordflow">return</span> nn;</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <span class="keywordflow">if</span> (item &lt; root-&gt;<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;        root-&gt;left = <a class="code" href="../../d8/dee/avltree_8cpp.html#aa7cd8a68075fae1c33df41233c1bed6a">insert</a>(root-&gt;left, item);</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <span class="keywordflow">else</span></div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;        root-&gt;right = <a class="code" href="../../d8/dee/avltree_8cpp.html#aa7cd8a68075fae1c33df41233c1bed6a">insert</a>(root-&gt;right, item);</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    <span class="keywordtype">int</span> b = <a class="code" href="../../d8/dee/avltree_8cpp.html#aaa457ffec24c9643f2768e7a65e96546">getBalance</a>(root);</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    <span class="keywordflow">if</span> (b &gt; 1) {</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d8/dee/avltree_8cpp.html#aaa457ffec24c9643f2768e7a65e96546">getBalance</a>(root-&gt;left) &lt; 0)</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;            root-&gt;left = <a class="code" href="../../d8/dee/avltree_8cpp.html#aed58f3cea338a9d7bdcb9a4cfc6c7a78">leftRotate</a>(root-&gt;left);  <span class="comment">// Left-Right Case</span></div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../d8/dee/avltree_8cpp.html#a4d93589966920b2756b84f8b92c54d1c">rightRotate</a>(root);                 <span class="comment">// Left-Left Case</span></div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (b &lt; -1) {</div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d8/dee/avltree_8cpp.html#aaa457ffec24c9643f2768e7a65e96546">getBalance</a>(root-&gt;right) &gt; 0)</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;            root-&gt;right = <a class="code" href="../../d8/dee/avltree_8cpp.html#a4d93589966920b2756b84f8b92c54d1c">rightRotate</a>(root-&gt;right);  <span class="comment">// Right-Left Case</span></div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../d8/dee/avltree_8cpp.html#aed58f3cea338a9d7bdcb9a4cfc6c7a78">leftRotate</a>(root);                     <span class="comment">// Right-Right Case</span></div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    }</div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    <span class="keywordflow">return</span> root;</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/dee/avltree_8cpp_aa7cd8a68075fae1c33df41233c1bed6a_cgraph.svg" width="203" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="aed58f3cea338a9d7bdcb9a4cfc6c7a78"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aed58f3cea338a9d7bdcb9a4cfc6c7a78">&#9670;&nbsp;</a></span>leftRotate()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d5/da1/structnode.html">node</a>* leftRotate </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d5/da1/structnode.html">node</a> *&#160;</td>
+          <td class="paramname"><em>root</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Returns <a class="el" href="../../db/d8b/struct_node.html">Node</a> after Left Rotation </p>
+<div class="fragment"><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;                             {</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    <a class="code" href="../../d5/da1/structnode.html">node</a> *t = root-&gt;right;</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    <a class="code" href="../../d5/da1/structnode.html">node</a> *u = t-&gt;left;</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    t-&gt;left = root;</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    root-&gt;right = u;</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keywordflow">return</span> t;</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae197eb50188fb761346952b9b5f6be59"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae197eb50188fb761346952b9b5f6be59">&#9670;&nbsp;</a></span>levelOrder()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void levelOrder </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d5/da1/structnode.html">node</a> *&#160;</td>
+          <td class="paramname"><em>root</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>LevelOrder (Breadth First Search) </p>
+<div class="fragment"><div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;                            {</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;node *&gt;</a> q;</div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    q.push(root);</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    <span class="keywordflow">while</span> (!q.empty()) {</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;        root = q.front();</div>
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+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;        q.pop();</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;        <span class="keywordflow">if</span> (root-&gt;left)</div>
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+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;        <span class="keywordflow">if</span> (root-&gt;right)</div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;            q.push(root-&gt;right);</div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    }</div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;           {</div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    <span class="comment">// Testing AVL Tree</span></div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    <a class="code" href="../../d5/da1/structnode.html">node</a> *root = NULL;</div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    <span class="keywordtype">int</span> i;</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    <span class="keywordflow">for</span> (i = 1; i &lt;= 7; i++) root = <a class="code" href="../../d8/dee/avltree_8cpp.html#aa7cd8a68075fae1c33df41233c1bed6a">insert</a>(root, i);</div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;LevelOrder: &quot;</span>;</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    <a class="code" href="../../d8/dee/avltree_8cpp.html#ae197eb50188fb761346952b9b5f6be59">levelOrder</a>(root);</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    root = <a class="code" href="../../d8/dee/avltree_8cpp.html#a8286388b0743a716145639df3a33e541">deleteNode</a>(root, 1);  <span class="comment">// Deleting key with value 1</span></div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nLevelOrder: &quot;</span>;</div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    <a class="code" href="../../d8/dee/avltree_8cpp.html#ae197eb50188fb761346952b9b5f6be59">levelOrder</a>(root);</div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;    root = <a class="code" href="../../d8/dee/avltree_8cpp.html#a8286388b0743a716145639df3a33e541">deleteNode</a>(root, 4);  <span class="comment">// Deletin key with value 4</span></div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nLevelOrder: &quot;</span>;</div>
+<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    <a class="code" href="../../d8/dee/avltree_8cpp.html#ae197eb50188fb761346952b9b5f6be59">levelOrder</a>(root);</div>
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+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/dee/avltree_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="363" height="190"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="adb8e952bf1c266bae84111b9d6a12015"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#adb8e952bf1c266bae84111b9d6a12015">&#9670;&nbsp;</a></span>minValue()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d5/da1/structnode.html">node</a>* minValue </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d5/da1/structnode.html">node</a> *&#160;</td>
+          <td class="paramname"><em>root</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Returns node with minimum value in the tree </p>
+<div class="fragment"><div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;                           {</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="keywordflow">if</span> (root-&gt;left == NULL)</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;        <span class="keywordflow">return</span> root;</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <span class="keywordflow">return</span> <a class="code" href="../../d8/dee/avltree_8cpp.html#adb8e952bf1c266bae84111b9d6a12015">minValue</a>(root-&gt;left);</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a4d93589966920b2756b84f8b92c54d1c"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a4d93589966920b2756b84f8b92c54d1c">&#9670;&nbsp;</a></span>rightRotate()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../d5/da1/structnode.html">node</a>* rightRotate </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d5/da1/structnode.html">node</a> *&#160;</td>
+          <td class="paramname"><em>root</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Returns <a class="el" href="../../db/d8b/struct_node.html">Node</a> after Right Rotation </p>
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+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="atower__of__hanoi_8cpp_html_af4cfc41e546f1f8d25f01e0804e8b61d"><div class="ttname"><a href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a></div><div class="ttdeci">void mov(tower *From, tower *To)</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:39</div></div>
+<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
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+<div class="ttc" id="aternary__search_8cpp_html_aef655a27eb82efa299bf9d0becf6e9c8"><div class="ttname"><a href="../../dc/dfe/ternary__search_8cpp.html#aef655a27eb82efa299bf9d0becf6e9c8">ternary_search</a></div><div class="ttdeci">void ternary_search(int N, int A[], int target)</div><div class="ttdef"><b>Definition:</b> ternary_search.cpp:127</div></div>
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+<div class="ttc" id="adecimal__to__binary_8cpp_html_a10df57491019f0ac39b492740fb388f7"><div class="ttname"><a href="../../df/d06/decimal__to__binary_8cpp.html#a10df57491019f0ac39b492740fb388f7">method2</a></div><div class="ttdeci">void method2(int number)</div><div class="ttdef"><b>Definition:</b> decimal_to_binary.cpp:27</div></div>
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+<div class="ttc" id="astairs__pattern_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d5/def/stairs__pattern_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> stairs_pattern.cpp:17</div></div>
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+<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div><div class="ttdoc">STL class.</div></div>
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+<div class="ttc" id="ashell__sort2_8cpp_html_a22ea0d1f7943ebb4371d31e44b465b6d"><div class="ttname"><a href="../../d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">test_f</a></div><div class="ttdeci">void test_f(const int NUM_DATA)</div><div class="ttdef"><b>Definition:</b> shell_sort2.cpp:145</div></div>
+<div class="ttc" id="anamespacestring__search_html"><div class="ttname"><a href="../../d9/d03/namespacestring__search.html">string_search</a></div><div class="ttdoc">String search algorithms.</div><div class="ttdef"><b>Definition:</b> brute_force_string_searching.cpp:13</div></div>
+<div class="ttc" id="ashell__sort2_8cpp_html_a951127aea9d7e1e53ea9ae0868633246"><div class="ttname"><a href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a></div><div class="ttdeci">void show_data(T *arr, size_t LEN)</div><div class="ttdef"><b>Definition:</b> shell_sort2.cpp:18</div></div>
+<div class="ttc" id="alist_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list.html">std::list</a></div><div class="ttdoc">STL class.</div></div>
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+<div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
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+<div class="ttc" id="aclass_bit_html"><div class="ttname"><a href="../../df/d27/class_bit.html">Bit</a></div><div class="ttdef"><b>Definition:</b> bit.cpp:6</div></div>
+<div class="ttc" id="apair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a></div></div>
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+<div class="ttc" id="aternary__search_8cpp_html_ae01eda5098801bb6b5b778828fb4fddc"><div class="ttname"><a href="../../dc/dfe/ternary__search_8cpp.html#ae01eda5098801bb6b5b778828fb4fddc">absolutePrecision</a></div><div class="ttdeci">#define absolutePrecision</div><div class="ttdef"><b>Definition:</b> ternary_search.cpp:22</div></div>
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+<div class="ttc" id="anamespacesorting_html_a7e7f25f31c50523990437abf2ac3907e"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#a7e7f25f31c50523990437abf2ac3907e">sorting::partition</a></div><div class="ttdeci">int partition(int arr[], int low, int high)</div><div class="ttdef"><b>Definition:</b> quick_sort.cpp:37</div></div>
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+<div class="ttc" id="astruct_point_html_afa38be143ae800e6ad69ce8ed4df62d8"><div class="ttname"><a href="../../d8/dc8/struct_point.html#afa38be143ae800e6ad69ce8ed4df62d8">Point::y</a></div><div class="ttdeci">double y</div><div class="ttdef"><b>Definition:</b> smallest_circle.cpp:17</div></div>
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+<div class="ttc" id="afscanf_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/fscanf.html">std::scanf</a></div><div class="ttdeci">T scanf(T... args)</div></div>
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+<div class="ttc" id="aavltree_8cpp_html_ae197eb50188fb761346952b9b5f6be59"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#ae197eb50188fb761346952b9b5f6be59">levelOrder</a></div><div class="ttdeci">void levelOrder(node *root)</div><div class="ttdef"><b>Definition:</b> avltree.cpp:119</div></div>
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+<div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
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+<p>C++ program to find factorial of given number.  
+<a href="#details">More...</a></p>
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+</div><div class="textblock"><div class="dynheader">
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+</div><!--header-->
+<div class="contents">
+
+<p><a href="https://en.wikipedia.org/wiki/Linear_search">Linear search algorithm</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for linear_search.cpp:</div>
+<div class="dyncontent">
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+<h2 class="memtitle"><span class="permalink"><a href="#a84ac3988a534eb60ca351ed6caf56d84">&#9670;&nbsp;</a></span>LinearSearch()</h2>
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+        <tr>
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+        </tr>
+        <tr>
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+          <td>)</td>
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+    <tr><td class="paramdir">[in]</td><td class="paramname">size</td><td>length of array </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">key</td><td>key value to search for </td></tr>
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+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+</div>
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+<!-- Generated by Doxygen 1.8.18 -->
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+        name="MSearchResults" id="MSearchResults">
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+
+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">string_search Namespace Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>String search algorithms.  
+<a href="../../d9/d03/namespacestring__search.html#details">More...</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:aeb2cd81064717aedd62bfb096b1a73d8"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d03/namespacestring__search.html#aeb2cd81064717aedd62bfb096b1a73d8">brute_force</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;text, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;pattern)</td></tr>
+<tr class="separator:aeb2cd81064717aedd62bfb096b1a73d8"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aa422aab133d4ed5e5d6022a7f701271f"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d03/namespacestring__search.html#aa422aab133d4ed5e5d6022a7f701271f">getFailureArray</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;pattern)</td></tr>
+<tr class="separator:aa422aab133d4ed5e5d6022a7f701271f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a26a58225ce7d3fa9d4c2f5349a65ed93"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d03/namespacestring__search.html#a26a58225ce7d3fa9d4c2f5349a65ed93">kmp</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;pattern, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;text)</td></tr>
+<tr class="separator:a26a58225ce7d3fa9d4c2f5349a65ed93"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a8fb0bc932ba8b582c9f4c71338d050f8"><td class="memItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d03/namespacestring__search.html#a8fb0bc932ba8b582c9f4c71338d050f8">create_hash</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;s, int n)</td></tr>
+<tr class="separator:a8fb0bc932ba8b582c9f4c71338d050f8"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aed769d565b705a9b3e0eb1ec74088893"><td class="memItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d03/namespacestring__search.html#aed769d565b705a9b3e0eb1ec74088893">recalculate_hash</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;s, int old_index, int new_index, int64_t old_hash, int patLength)</td></tr>
+<tr class="separator:aed769d565b705a9b3e0eb1ec74088893"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aebe07cea289a13142503d98be7df11fd"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d03/namespacestring__search.html#aebe07cea289a13142503d98be7df11fd">check_if_equal</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;str1, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;str2, int start1, int end1, int start2, int end2)</td></tr>
+<tr class="separator:aebe07cea289a13142503d98be7df11fd"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a21c673d56cbf67b1d2ee4d869185b7d9"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">rabin_karp</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;str, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;pat)</td></tr>
+<tr class="separator:a21c673d56cbf67b1d2ee4d869185b7d9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>String search algorithms. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="aeb2cd81064717aedd62bfb096b1a73d8"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aeb2cd81064717aedd62bfb096b1a73d8">&#9670;&nbsp;</a></span>brute_force()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int string_search::brute_force </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>text</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>pattern</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Find a pattern in a string by comparing the pattern to every substring. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">text</td><td>Any string that might contain the pattern. </td></tr>
+    <tr><td class="paramname">pattern</td><td>String that we are searching for. </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>Index where the pattern starts in the text </dd>
+<dd>
+-1 if the pattern was not found. </dd></dl>
+<div class="fragment"><div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;                                                                 {</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;    <span class="keywordtype">size_t</span> pat_l = pattern.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    <span class="keywordtype">size_t</span> txt_l = text.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>();</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    <span class="keywordtype">int</span> index = -1;</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <span class="keywordflow">if</span> (pat_l &lt;= txt_l) {</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; txt_l - pat_l + 1; i++) {</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s = text.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(i, pat_l);</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;            <span class="keywordflow">if</span> (s == pattern) {</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;                index = i;</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;                <span class="keywordflow">break</span>;</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;            }</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;        }</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    }</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <span class="keywordflow">return</span> index;</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d03/namespacestring__search_aeb2cd81064717aedd62bfb096b1a73d8_cgraph.svg" width="320" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="aebe07cea289a13142503d98be7df11fd"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aebe07cea289a13142503d98be7df11fd">&#9670;&nbsp;</a></span>check_if_equal()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool string_search::check_if_equal </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>str1</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>str2</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>start1</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>end1</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>start2</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>end2</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>compare if two sub-strings are equal </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">str1</td><td>string pattern to search </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">str2</td><td>text in which to search </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">start1,end1</td><td>start and end indices for substring in str1 </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">start2,end2</td><td>start and end indices for substring in str2 </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><code>true</code> if pattern was found </dd>
+<dd>
+<code>false</code> if pattern was not found </dd></dl>
+<dl class="section note"><dt>Note</dt><dd>can this be replaced by <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/compare.html">std::string::compare</a>? </dd></dl>
+<div class="fragment"><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;                                                                {</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <span class="keywordflow">if</span> (end1 - start1 != end2 - start2) {</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    }</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <span class="keywordflow">while</span> (start1 &lt;= end1 &amp;&amp; start2 &lt;= end2) {</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        <span class="keywordflow">if</span> (str1[start1] != str2[start2]) {</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;        }</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        start1++;</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        start2++;</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    }</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a8fb0bc932ba8b582c9f4c71338d050f8"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a8fb0bc932ba8b582c9f4c71338d050f8">&#9670;&nbsp;</a></span>create_hash()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int64_t string_search::create_hash </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>s</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>convert a string to an intger - called as hashing function </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">s</td><td>source of string to hash </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>length of substring to hash </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>hash integer </dd></dl>
+<div class="fragment"><div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;                                               {</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    int64_t result = 0;</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;        result += (int64_t)(s[i] * (int64_t)<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(<a class="code" href="../../d6/dce/rabin__karp_8cpp.html#ac4add2a227a10511e0128d63952030e8">PRIME</a>, i));</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    }</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="keywordflow">return</span> result;</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="aa422aab133d4ed5e5d6022a7f701271f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa422aab133d4ed5e5d6022a7f701271f">&#9670;&nbsp;</a></span>getFailureArray()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;int&gt; string_search::getFailureArray </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>pattern</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Generate the partial match table aka failure function for a pattern to search. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">pattern</td><td>text for which to create the partial match table </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>the partial match table as a vector array </dd></dl>
+<div class="fragment"><div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;                                                         {</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <span class="keywordtype">int</span> pattern_length = pattern.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> failure(pattern_length + 1);</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    failure[0] = -1;</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="keywordtype">int</span> j = -1;</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160; </div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; pattern_length; i++) {</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        <span class="keywordflow">while</span> (j != -1 &amp;&amp; pattern[j] != pattern[i]) {</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;            j = failure[j];</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        }</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        j++;</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        failure[i + 1] = j;</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    }</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    <span class="keywordflow">return</span> failure;</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d03/namespacestring__search_aa422aab133d4ed5e5d6022a7f701271f_cgraph.svg" width="336" height="52"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a26a58225ce7d3fa9d4c2f5349a65ed93"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a26a58225ce7d3fa9d4c2f5349a65ed93">&#9670;&nbsp;</a></span>kmp()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool string_search::kmp </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>pattern</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>text</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>KMP algorithm to find a pattern in a text </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">pattern</td><td>string pattern to search </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">text</td><td>text in which to search </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><code>true</code> if pattern was found </dd>
+<dd>
+<code>false</code> if pattern was not found </dd></dl>
+<div class="fragment"><div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;                                                          {</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keywordtype">int</span> text_length = text.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(), pattern_length = pattern.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> failure = <a class="code" href="../../d9/d03/namespacestring__search.html#aa422aab133d4ed5e5d6022a7f701271f">getFailureArray</a>(pattern);</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160; </div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = 0;</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; text_length; j++) {</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        <span class="keywordflow">while</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> != -1 &amp;&amp; pattern[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] != text[j]) {</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;            <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = failure[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>];</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        }</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++;</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> == pattern_length)</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    }</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d03/namespacestring__search_a26a58225ce7d3fa9d4c2f5349a65ed93_cgraph.svg" width="518" height="75"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a21c673d56cbf67b1d2ee4d869185b7d9"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a21c673d56cbf67b1d2ee4d869185b7d9">&#9670;&nbsp;</a></span>rabin_karp()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int string_search::rabin_karp </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>str</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>pat</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Perform string pattern search using Rabin-Karp algorithm </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">str</td><td>string to search in </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">pat</td><td>pattern to search for </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>index of first occurrence of pattern </dd>
+<dd>
+-1 if pattern not found </dd></dl>
+<div class="fragment"><div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;                                                           {</div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    int64_t pat_hash = <a class="code" href="../../d9/d03/namespacestring__search.html#a8fb0bc932ba8b582c9f4c71338d050f8">create_hash</a>(pat, pat.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    int64_t str_hash = <a class="code" href="../../d9/d03/namespacestring__search.html#a8fb0bc932ba8b582c9f4c71338d050f8">create_hash</a>(str, pat.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= str.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - pat.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(); ++i) {</div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;        <span class="keywordflow">if</span> (pat_hash == str_hash &amp;&amp;</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;            <a class="code" href="../../d9/d03/namespacestring__search.html#aebe07cea289a13142503d98be7df11fd">check_if_equal</a>(str, pat, i, i + pat.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1, 0,</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;                           pat.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - 1)) {</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;            <span class="keywordflow">return</span> i;</div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        }</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        <span class="keywordflow">if</span> (i &lt; str.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() - pat.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>()) {</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;            str_hash =</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;                <a class="code" href="../../d9/d03/namespacestring__search.html#aed769d565b705a9b3e0eb1ec74088893">recalculate_hash</a>(str, i, i + pat.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(), str_hash, pat.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>());</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;        }</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    }</div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    <span class="keywordflow">return</span> -1;  <span class="comment">// return -1 if given pattern not found</span></div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d03/namespacestring__search_a21c673d56cbf67b1d2ee4d869185b7d9_cgraph.svg" width="434" height="206"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="aed769d565b705a9b3e0eb1ec74088893"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aed769d565b705a9b3e0eb1ec74088893">&#9670;&nbsp;</a></span>recalculate_hash()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int64_t string_search::recalculate_hash </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>s</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>old_index</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>new_index</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int64_t&#160;</td>
+          <td class="paramname"><em>old_hash</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>patLength</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>re-hash a string using known existing hash </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">s</td><td>source of string to hash </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">old_index</td><td>previous index of string </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">new_index</td><td>new index of string </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">old_hash</td><td>previous hash of substring </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">patLength</td><td>length of substring to hash </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>new hash integer </dd></dl>
+<div class="fragment"><div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;                                                          {</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    int64_t new_hash = old_hash - s[old_index];</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    new_hash /= <a class="code" href="../../d6/dce/rabin__karp_8cpp.html#ac4add2a227a10511e0128d63952030e8">PRIME</a>;</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    new_hash += (int64_t)(s[new_index] * (int64_t)<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(<a class="code" href="../../d6/dce/rabin__karp_8cpp.html#ac4add2a227a10511e0128d63952030e8">PRIME</a>, patLength - 1));</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    <span class="keywordflow">return</span> new_hash;</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int &gt;</a></div></div>
+<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::length</a></div><div class="ttdeci">T length(T... args)</div></div>
+<div class="ttc" id="arabin__karp_8cpp_html_ac4add2a227a10511e0128d63952030e8"><div class="ttname"><a href="../../d6/dce/rabin__karp_8cpp.html#ac4add2a227a10511e0128d63952030e8">PRIME</a></div><div class="ttdeci">#define PRIME</div><div class="ttdoc">Prime modulus for hash functions.</div><div class="ttdef"><b>Definition:</b> rabin_karp.cpp:16</div></div>
+<div class="ttc" id="anamespacestring__search_html_a8fb0bc932ba8b582c9f4c71338d050f8"><div class="ttname"><a href="../../d9/d03/namespacestring__search.html#a8fb0bc932ba8b582c9f4c71338d050f8">string_search::create_hash</a></div><div class="ttdeci">int64_t create_hash(const std::string &amp;s, int n)</div><div class="ttdef"><b>Definition:</b> rabin_karp.cpp:25</div></div>
+<div class="ttc" id="anamespacestring__search_html_aed769d565b705a9b3e0eb1ec74088893"><div class="ttname"><a href="../../d9/d03/namespacestring__search.html#aed769d565b705a9b3e0eb1ec74088893">string_search::recalculate_hash</a></div><div class="ttdeci">int64_t recalculate_hash(const std::string &amp;s, int old_index, int new_index, int64_t old_hash, int patLength)</div><div class="ttdef"><b>Definition:</b> rabin_karp.cpp:42</div></div>
+<div class="ttc" id="amatrix__exponentiation_8cpp_html_afcf0d19607cd0edd8ae333d2b9c220c0"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a></div><div class="ttdeci">ll k</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:48</div></div>
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+<div class="ttc" id="asubstr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">std::string::substr</a></div><div class="ttdeci">T substr(T... args)</div></div>
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+<a href="#func-members">Functions</a>  </div>
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+<div class="title">poisson_dist.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a href="https://en.wikipedia.org/wiki/Poisson_distribution">Poisson statistics</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for poisson_dist.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/df5/poisson__dist_8cpp__incl.svg" width="166" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ac217ab9a06291f360d816700a6958ca8"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d24/poisson__dist_8cpp.html#ac217ab9a06291f360d816700a6958ca8">poisson_rate</a> (double events, double timeframe)</td></tr>
+<tr class="separator:ac217ab9a06291f360d816700a6958ca8"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ad0aa718023ce802dd5899f0e03a7ac71"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d24/poisson__dist_8cpp.html#ad0aa718023ce802dd5899f0e03a7ac71">poisson_expected</a> (double rate, double time)</td></tr>
+<tr class="separator:ad0aa718023ce802dd5899f0e03a7ac71"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a63ffd347e75d5ed7a518cbcfbfeec71a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d24/poisson__dist_8cpp.html#a63ffd347e75d5ed7a518cbcfbfeec71a">fact</a> (double x)</td></tr>
+<tr class="separator:a63ffd347e75d5ed7a518cbcfbfeec71a"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a69a136b32707bdc7950fb9057b5fa1e1"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d24/poisson__dist_8cpp.html#a69a136b32707bdc7950fb9057b5fa1e1">poisson_x_successes</a> (double expected, double x)</td></tr>
+<tr class="separator:a69a136b32707bdc7950fb9057b5fa1e1"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ad9c9e74079278ca10e3b97a8d5391c9a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d24/poisson__dist_8cpp.html#ad9c9e74079278ca10e3b97a8d5391c9a">poisson_range_successes</a> (double expected, double lower, double upper)</td></tr>
+<tr class="separator:ad9c9e74079278ca10e3b97a8d5391c9a"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d24/poisson__dist_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Poisson_distribution">Poisson statistics</a> </p>
+<p>The Poisson distribution counts how many events occur over a set time interval. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a63ffd347e75d5ed7a518cbcfbfeec71a"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a63ffd347e75d5ed7a518cbcfbfeec71a">&#9670;&nbsp;</a></span>fact()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double fact </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>x</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Compute factorial of a given number </p>
+<div class="fragment"><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;                      {</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="keywordtype">double</span> x_fact = x;</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = x - 1; i &gt; 0; i--) {</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;        x_fact *= i;</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    }</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160; </div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <span class="keywordflow">if</span> (x_fact &lt;= 0) {</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;        x_fact = 1;</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    }</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keywordflow">return</span> x_fact;</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;           {</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <span class="keywordtype">double</span> rate, expected;</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    rate = <a class="code" href="../../d9/d24/poisson__dist_8cpp.html#ac217ab9a06291f360d816700a6958ca8">poisson_rate</a>(3, 1);</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Poisson rate : &quot;</span> &lt;&lt; rate &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160; </div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    expected = <a class="code" href="../../d9/d24/poisson__dist_8cpp.html#ad0aa718023ce802dd5899f0e03a7ac71">poisson_expected</a>(rate, 2);</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Poisson expected : &quot;</span> &lt;&lt; expected &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160; </div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Poisson 0 successes : &quot;</span> &lt;&lt; <a class="code" href="../../d9/d24/poisson__dist_8cpp.html#a69a136b32707bdc7950fb9057b5fa1e1">poisson_x_successes</a>(expected, 0)</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;              &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Poisson 0-8 successes : &quot;</span></div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;              &lt;&lt; <a class="code" href="../../d9/d24/poisson__dist_8cpp.html#ad9c9e74079278ca10e3b97a8d5391c9a">poisson_range_successes</a>(expected, 0, 8) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160; </div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d24/poisson__dist_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="604" height="240"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ad0aa718023ce802dd5899f0e03a7ac71"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ad0aa718023ce802dd5899f0e03a7ac71">&#9670;&nbsp;</a></span>poisson_expected()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double poisson_expected </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>rate</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>time</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>calculate the expected value over a time e.g rate of 2.5 over 10 mins = 2.5 x 10 = 25 </p>
+<div class="fragment"><div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;{ <span class="keywordflow">return</span> rate * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a>; }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ad9c9e74079278ca10e3b97a8d5391c9a"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ad9c9e74079278ca10e3b97a8d5391c9a">&#9670;&nbsp;</a></span>poisson_range_successes()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double poisson_range_successes </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>expected</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>lower</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>upper</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>probability of a success in range for Poisson dist (inclusive, inclusive) </p><p class="formulaDsp">
+\[P = \sum_i p(\mu,i)\]
+</p>
+ <div class="fragment"><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;                                                                            {</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keywordtype">double</span> probability = 0;</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = lower; i &lt;= upper; i++) {</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        probability += <a class="code" href="../../d9/d24/poisson__dist_8cpp.html#a69a136b32707bdc7950fb9057b5fa1e1">poisson_x_successes</a>(expected, i);</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    }</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    <span class="keywordflow">return</span> probability;</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d24/poisson__dist_8cpp_ad9c9e74079278ca10e3b97a8d5391c9a_cgraph.svg" width="506" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ac217ab9a06291f360d816700a6958ca8"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac217ab9a06291f360d816700a6958ca8">&#9670;&nbsp;</a></span>poisson_rate()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double poisson_rate </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>events</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>timeframe</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>poisson rate:<br  />
+calculate the events per unit time<br  />
+e.g 5 dollars every 2 mins = 5 / 2 = 2.5 </p>
+<div class="fragment"><div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;                                                     {</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;    <span class="keywordflow">return</span> events / timeframe;</div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a69a136b32707bdc7950fb9057b5fa1e1"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a69a136b32707bdc7950fb9057b5fa1e1">&#9670;&nbsp;</a></span>poisson_x_successes()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double poisson_x_successes </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>expected</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>x</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Find the probability of x successes in a Poisson dist. </p><p class="formulaDsp">
+\[p(\mu,x) = \frac{\mu^x e^{-\mu}}{x!}\]
+</p>
+ <div class="fragment"><div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;                                                      {</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    <span class="keywordflow">return</span> (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(expected, x) * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(-expected)) / <a class="code" href="../../d9/d24/poisson__dist_8cpp.html#a63ffd347e75d5ed7a518cbcfbfeec71a">fact</a>(x);</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d24/poisson__dist_8cpp_a69a136b32707bdc7950fb9057b5fa1e1_cgraph.svg" width="282" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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+<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
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+<tr class="separator:a361674452869413536ee501f053129a8"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:acc6a28f40512dbda75ab1a3969248898"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d77/namespacemachine__learning.html#acc6a28f40512dbda75ab1a3969248898">machine_learning::kohonen_som_tracer</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;X, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *W, double alpha_min)</td></tr>
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+<tr class="separator:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a412b7afa156306b1f8788643c91a1c60"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d49/kohonen__som__trace_8cpp.html#a412b7afa156306b1f8788643c91a1c60">test_lamniscate</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *<a class="el" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</td></tr>
+<tr class="separator:a412b7afa156306b1f8788643c91a1c60"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="separator:a0283886819c7c140a023582b7269e2d0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a9ab8c79ffb674a63f151f282faeb723b"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d49/kohonen__som__trace_8cpp.html#a9ab8c79ffb674a63f151f282faeb723b">test_3d_classes</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *<a class="el" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</td></tr>
+<tr class="separator:a9ab8c79ffb674a63f151f282faeb723b"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a6d0455dd5c30adda100e95f0423c786e"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d49/kohonen__som__trace_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a> ()</td></tr>
+<tr class="separator:a6d0455dd5c30adda100e95f0423c786e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a2256c10b16edba377b64a44b6c656908"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d49/kohonen__som__trace_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a> (clock_t start_t, clock_t end_t)</td></tr>
+<tr class="separator:a2256c10b16edba377b64a44b6c656908"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d49/kohonen__som__trace_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
+<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Self-organizing_map">Kohonen self organizing map</a> (data tracing) </p>
+<p>This example implements a powerful self organizing map algorithm. The algorithm creates a connected network of weights that closely follows the given data points. This this creates a chain of nodes that resembles the given input shape.</p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
+<dl class="section note"><dt>Note</dt><dd>This C++ version of the program is considerable slower than its <a href="https://github.com/kvedala/C/blob/master/machine_learning/kohonen_som_trace.c">C counterpart</a> </dd>
+<dd>
+The compiled code is much slower when compiled with MS Visual C++ 2019 than with GCC on windows </dd></dl>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d4/def/kohonen__som__topology_8cpp.html" title="Kohonen self organizing map (topological map)">kohonen_som_topology.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a2256c10b16edba377b64a44b6c656908"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a2256c10b16edba377b64a44b6c656908">&#9670;&nbsp;</a></span>get_clock_diff()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double get_clock_diff </td>
+          <td>(</td>
+          <td class="paramtype">clock_t&#160;</td>
+          <td class="paramname"><em>start_t</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">clock_t&#160;</td>
+          <td class="paramname"><em>end_t</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Convert clock cycle difference to time in seconds</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">start_t</td><td>start clock </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">end_t</td><td>end clock </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>time difference in seconds </dd></dl>
+<div class="fragment"><div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;                                                      {</div>
+<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_t - start_t) / CLOCKS_PER_SEC;</div>
+<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>argc</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char **&#160;</td>
+          <td class="paramname"><em>argv</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;                                {</div>
+<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Using OpenMP based parallelization\n&quot;</span>;</div>
+<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;<span class="preprocessor">#else</span></div>
+<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;NOT using OpenMP based parallelization\n&quot;</span>;</div>
+<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160; </div>
+<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
+<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160; </div>
+<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;    <a class="code" href="../../d9/d49/kohonen__som__trace_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
+<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;    <span class="keyword">auto</span> end_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 completed in &quot;</span> &lt;&lt; <a class="code" href="../../d9/d49/kohonen__som__trace_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
+<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160; </div>
+<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;    start_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;    <a class="code" href="../../d9/d49/kohonen__som__trace_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
+<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;    end_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 completed in &quot;</span> &lt;&lt; <a class="code" href="../../d9/d49/kohonen__som__trace_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
+<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160; </div>
+<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;    start_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;    <a class="code" href="../../d9/d49/kohonen__som__trace_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
+<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;    end_clk = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 completed in &quot;</span> &lt;&lt; <a class="code" href="../../d9/d49/kohonen__som__trace_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a>(start_clk, end_clk)</div>
+<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160; </div>
+<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
+<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;        &lt;&lt; <span class="stringliteral">&quot;(Note: Calculated times include: creating test sets, training &quot;</span></div>
+<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;           <span class="stringliteral">&quot;model and writing files to disk.)\n\n&quot;</span>;</div>
+<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d9/d49/kohonen__som__trace_8cpp_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="100%" height="600"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a1440a7779ac56f47a3f355ce4a8c7da0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">&#9670;&nbsp;</a></span>test1()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test1 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test that creates a random set of points distributed <em>near</em> the circumference of a circle and trains an SOM that finds that circular pattern. The following <a href="https://en.wikipedia.org/wiki/Comma-separated_values">CSV</a> files are created to validate the execution:</p><ul>
+<li><code>test1.csv</code>: random test samples points with a circular pattern</li>
+<li><code>w11.csv</code>: initial random map</li>
+<li><code>w12.csv</code>: trained SOM map</li>
+</ul>
+<p>The outputs can be readily plotted in <a href="https:://gnuplot.info">gnuplot</a> using the following snippet </p><div class="fragment"><div class="line">set datafile separator &#39;,&#39;</div>
+<div class="line">plot &quot;test1.csv&quot; title &quot;original&quot;, \</div>
+<div class="line">     &quot;w11.csv&quot; title &quot;w1&quot;, \</div>
+<div class="line">     &quot;w12.csv&quot; title &quot;w2&quot;</div>
+</div><!-- fragment --><p><img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/machine_learning/kohonen/test1.svg" alt="Sample execution
+output" style="pointer-events: none;" class="inline"/> </p>
+<div class="fragment"><div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;             {</div>
+<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;    <span class="keywordtype">int</span> j, N = 500;</div>
+<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    <span class="keywordtype">int</span> features = 2;</div>
+<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;    <span class="keywordtype">int</span> num_out = 50;</div>
+<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; W(num_out);</div>
+<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;        <span class="keywordflow">if</span> (i &lt; N)  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;            X[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;            W[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160; </div>
+<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;            <span class="keywordflow">for</span> (j = 0; j &lt; features; j++)</div>
+<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;                <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;                W[i][j] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-1, 1);</div>
+<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;        }</div>
+<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;    }</div>
+<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160; </div>
+<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;    <a class="code" href="../../d9/d49/kohonen__som__trace_8cpp.html#ab47fb569e63648bd76e7edfdacc02dbd">test_circle</a>(&amp;X);  <span class="comment">// create test data around circumference of a circle</span></div>
+<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga72699c805c19a6cc47a937a6f3378afa">save_nd_data</a>(<span class="stringliteral">&quot;test1.csv&quot;</span>, X);    <span class="comment">// save test data points</span></div>
+<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga72699c805c19a6cc47a937a6f3378afa">save_nd_data</a>(<span class="stringliteral">&quot;w11.csv&quot;</span>, W);      <span class="comment">// save initial random weights</span></div>
+<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#acc6a28f40512dbda75ab1a3969248898">kohonen_som_tracer</a>(X, &amp;W, 0.1);  <span class="comment">// train the SOM</span></div>
+<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga72699c805c19a6cc47a937a6f3378afa">save_nd_data</a>(<span class="stringliteral">&quot;w12.csv&quot;</span>, W);      <span class="comment">// save the resultant weights</span></div>
+<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d9/d49/kohonen__som__trace_8cpp_a1440a7779ac56f47a3f355ce4a8c7da0_cgraph.svg" width="100%" height="597"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a0283886819c7c140a023582b7269e2d0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0283886819c7c140a023582b7269e2d0">&#9670;&nbsp;</a></span>test2()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test2 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test that creates a random set of points distributed <em>near</em> the locus of the <a href="https://en.wikipedia.org/wiki/Lemniscate_of_Gerono">Lamniscate of Gerono</a> and trains an SOM that finds that circular pattern. The following <a href="https://en.wikipedia.org/wiki/Comma-separated_values">CSV</a> files are created to validate the execution:</p><ul>
+<li><code>test2.csv</code>: random test samples points with a lamniscate pattern</li>
+<li><code>w21.csv</code>: initial random map</li>
+<li><code>w22.csv</code>: trained SOM map</li>
+</ul>
+<p>The outputs can be readily plotted in <a href="https:://gnuplot.info">gnuplot</a> using the following snippet </p><div class="fragment"><div class="line">set datafile separator &#39;,&#39;</div>
+<div class="line">plot &quot;test2.csv&quot; title &quot;original&quot;, \</div>
+<div class="line">     &quot;w21.csv&quot; title &quot;w1&quot;, \</div>
+<div class="line">     &quot;w22.csv&quot; title &quot;w2&quot;</div>
+</div><!-- fragment --><p><img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/machine_learning/kohonen/test2.svg" alt="Sample execution
+output" style="pointer-events: none;" class="inline"/> </p>
+<div class="fragment"><div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;             {</div>
+<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;    <span class="keywordtype">int</span> j, N = 500;</div>
+<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    <span class="keywordtype">int</span> features = 2;</div>
+<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;    <span class="keywordtype">int</span> num_out = 20;</div>
+<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; W(num_out);</div>
+<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;        <span class="keywordflow">if</span> (i &lt; N)  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;            X[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;            W[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160; </div>
+<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;            <span class="keywordflow">for</span> (j = 0; j &lt; features; j++)</div>
+<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;                <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;                W[i][j] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-1, 1);</div>
+<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;        }</div>
+<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;    }</div>
+<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160; </div>
+<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;    <a class="code" href="../../d9/d49/kohonen__som__trace_8cpp.html#a412b7afa156306b1f8788643c91a1c60">test_lamniscate</a>(&amp;X);              <span class="comment">// create test data around the lamniscate</span></div>
+<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga72699c805c19a6cc47a937a6f3378afa">save_nd_data</a>(<span class="stringliteral">&quot;test2.csv&quot;</span>, X);     <span class="comment">// save test data points</span></div>
+<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga72699c805c19a6cc47a937a6f3378afa">save_nd_data</a>(<span class="stringliteral">&quot;w21.csv&quot;</span>, W);       <span class="comment">// save initial random weights</span></div>
+<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#acc6a28f40512dbda75ab1a3969248898">kohonen_som_tracer</a>(X, &amp;W, 0.01);  <span class="comment">// train the SOM</span></div>
+<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga72699c805c19a6cc47a937a6f3378afa">save_nd_data</a>(<span class="stringliteral">&quot;w22.csv&quot;</span>, W);       <span class="comment">// save the resultant weights</span></div>
+<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d9/d49/kohonen__som__trace_8cpp_a0283886819c7c140a023582b7269e2d0_cgraph.svg" width="100%" height="597"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a6d0455dd5c30adda100e95f0423c786e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a6d0455dd5c30adda100e95f0423c786e">&#9670;&nbsp;</a></span>test3()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test3 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Test that creates a random set of points distributed in six clusters in 3D space. The following <a href="https://en.wikipedia.org/wiki/Comma-separated_values">CSV</a> files are created to validate the execution:</p><ul>
+<li><code>test3.csv</code>: random test samples points with a circular pattern</li>
+<li><code>w31.csv</code>: initial random map</li>
+<li><code>w32.csv</code>: trained SOM map</li>
+</ul>
+<p>The outputs can be readily plotted in <a href="https:://gnuplot.info">gnuplot</a> using the following snippet </p><div class="fragment"><div class="line">set datafile separator &#39;,&#39;</div>
+<div class="line">plot &quot;test3.csv&quot; title &quot;original&quot;, \</div>
+<div class="line">     &quot;w31.csv&quot; title &quot;w1&quot;, \</div>
+<div class="line">     &quot;w32.csv&quot; title &quot;w2&quot;</div>
+</div><!-- fragment --><p><img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/machine_learning/kohonen/test3.svg" alt="Sample execution
+output" style="pointer-events: none;" class="inline"/> </p>
+<div class="fragment"><div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;             {</div>
+<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;    <span class="keywordtype">int</span> j, N = 200;</div>
+<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;    <span class="keywordtype">int</span> features = 3;</div>
+<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;    <span class="keywordtype">int</span> num_out = 20;</div>
+<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; X(N);</div>
+<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;double&gt;</a>&gt; W(num_out);</div>
+<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(num_out, N); i++) {</div>
+<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;        <span class="comment">// loop till max(N, num_out)</span></div>
+<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;        <span class="keywordflow">if</span> (i &lt; N)  <span class="comment">// only add new arrays if i &lt; N</span></div>
+<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;            X[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;        <span class="keywordflow">if</span> (i &lt; num_out) {  <span class="comment">// only add new arrays if i &lt; num_out</span></div>
+<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;            W[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(features);</div>
+<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160; </div>
+<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;            <span class="keywordflow">for</span> (j = 0; j &lt; features; j++)</div>
+<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;                <span class="comment">// preallocate with random initial weights</span></div>
+<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;                W[i][j] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-1, 1);</div>
+<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;        }</div>
+<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;    }</div>
+<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160; </div>
+<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;    <a class="code" href="../../d9/d49/kohonen__som__trace_8cpp.html#a9ab8c79ffb674a63f151f282faeb723b">test_3d_classes</a>(&amp;X);              <span class="comment">// create test data around the lamniscate</span></div>
+<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga72699c805c19a6cc47a937a6f3378afa">save_nd_data</a>(<span class="stringliteral">&quot;test3.csv&quot;</span>, X);     <span class="comment">// save test data points</span></div>
+<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga72699c805c19a6cc47a937a6f3378afa">save_nd_data</a>(<span class="stringliteral">&quot;w31.csv&quot;</span>, W);       <span class="comment">// save initial random weights</span></div>
+<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;    <a class="code" href="../../d8/d77/namespacemachine__learning.html#acc6a28f40512dbda75ab1a3969248898">kohonen_som_tracer</a>(X, &amp;W, 0.01);  <span class="comment">// train the SOM</span></div>
+<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;    <a class="code" href="../../d9/d66/group__machine__learning.html#ga72699c805c19a6cc47a937a6f3378afa">save_nd_data</a>(<span class="stringliteral">&quot;w32.csv&quot;</span>, W);       <span class="comment">// save the resultant weights</span></div>
+<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d9/d49/kohonen__som__trace_8cpp_a6d0455dd5c30adda100e95f0423c786e_cgraph.svg" width="100%" height="600"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a9ab8c79ffb674a63f151f282faeb723b"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a9ab8c79ffb674a63f151f282faeb723b">&#9670;&nbsp;</a></span>test_3d_classes()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test_3d_classes </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>data</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Creates a random set of points distributed in six clusters in 3D space with centroids at the points</p><ul>
+<li>\({0.5, 0.5, 0.5}\)</li>
+<li>\({0.5, 0.5, -0.5}\)</li>
+<li>\({0.5, -0.5, 0.5}\)</li>
+<li>\({0.5, -0.5, -0.5}\)</li>
+<li>\({-0.5, 0.5, 0.5}\)</li>
+<li>\({-0.5, 0.5, -0.5}\)</li>
+<li>\({-0.5, -0.5, 0.5}\)</li>
+<li>\({-0.5, -0.5, -0.5}\)</li>
+</ul>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[out]</td><td class="paramname">data</td><td>matrix to store data in </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;                                                           {</div>
+<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
+<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.1;  <span class="comment">// radius of cluster</span></div>
+<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;    <span class="keywordtype">int</span> i;</div>
+<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> num_classes = 8;</div>
+<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> centres[][3] = {</div>
+<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;        <span class="comment">// centres of each class cluster</span></div>
+<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;        {.5, .5, .5},    <span class="comment">// centre of class 0</span></div>
+<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;        {.5, .5, -.5},   <span class="comment">// centre of class 1</span></div>
+<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;        {.5, -.5, .5},   <span class="comment">// centre of class 2</span></div>
+<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;        {.5, -.5, -.5},  <span class="comment">// centre of class 3</span></div>
+<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;        {-.5, .5, .5},   <span class="comment">// centre of class 4</span></div>
+<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;        {-.5, .5, -.5},  <span class="comment">// centre of class 5</span></div>
+<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;        {-.5, -.5, .5},  <span class="comment">// centre of class 6</span></div>
+<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;        {-.5, -.5, -.5}  <span class="comment">// centre of class 7</span></div>
+<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;    };</div>
+<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160; </div>
+<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; N; i++) {</div>
+<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;        <span class="keywordtype">int</span> cls =</div>
+<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % num_classes;  <span class="comment">// select a random class for the point</span></div>
+<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160; </div>
+<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;        <span class="comment">// create random coordinates (x,y,z) around the centre of the class</span></div>
+<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][0] - R, centres[cls][0] + R);</div>
+<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][1] - R, centres[cls][1] + R);</div>
+<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][2] = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(centres[cls][2] - R, centres[cls][2] + R);</div>
+<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160; </div>
+<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;        <span class="comment">/* The follosing can also be used</span></div>
+<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;<span class="comment">        for (int j = 0; j &lt; 3; j++)</span></div>
+<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;<span class="comment">            data[0][i][j] = _random(centres[cls][j] - R, centres[cls][j] + R);</span></div>
+<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;<span class="comment">        */</span></div>
+<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;    }</div>
+<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d49/kohonen__som__trace_8cpp_a9ab8c79ffb674a63f151f282faeb723b_cgraph.svg" width="250" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ab47fb569e63648bd76e7edfdacc02dbd"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ab47fb569e63648bd76e7edfdacc02dbd">&#9670;&nbsp;</a></span>test_circle()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test_circle </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>data</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Creates a random set of points distributed <em>near</em> the circumference of a circle and trains an SOM that finds that circular pattern. The generating function is </p><p class="formulaDsp">
+\begin{eqnarray*} r &amp;\in&amp; [1-\delta r, 1+\delta r)\\ \theta &amp;\in&amp; [0, 2\pi)\\ x &amp;=&amp; r\cos\theta\\ y &amp;=&amp; r\sin\theta \end{eqnarray*}
+</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[out]</td><td class="paramname">data</td><td>matrix to store data in </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;                                                       {</div>
+<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
+<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> R = 0.75, dr = 0.3;</div>
+<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    <span class="keywordtype">double</span> a_t = 0., b_t = 2.f * M_PI;  <span class="comment">// theta random between 0 and 2*pi</span></div>
+<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    <span class="keywordtype">double</span> a_r = R - dr, b_r = R + dr;  <span class="comment">// radius random between R-dr and R+dr</span></div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;    <span class="keywordtype">int</span> i;</div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160; </div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; N; i++) {</div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;        <span class="keywordtype">double</span> r = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(a_r, b_r);      <span class="comment">// random radius</span></div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;        <span class="keywordtype">double</span> theta = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(a_t, b_t);  <span class="comment">// random theta</span></div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = r * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(theta);    <span class="comment">// convert from polar to cartesian</span></div>
+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = r * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">sin</a>(theta);</div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    }</div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d49/kohonen__som__trace_8cpp_ab47fb569e63648bd76e7edfdacc02dbd_cgraph.svg" width="214" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a412b7afa156306b1f8788643c91a1c60"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a412b7afa156306b1f8788643c91a1c60">&#9670;&nbsp;</a></span>test_lamniscate()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test_lamniscate </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>data</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Creates a random set of points distributed <em>near</em> the locus of the <a href="https://en.wikipedia.org/wiki/Lemniscate_of_Gerono">Lamniscate of Gerono</a>. </p><p class="formulaDsp">
+\begin{eqnarray*} \delta r &amp;=&amp; 0.2\\ \delta x &amp;\in&amp; [-\delta r, \delta r)\\ \delta y &amp;\in&amp; [-\delta r, \delta r)\\ \theta &amp;\in&amp; [0, \pi)\\ x &amp;=&amp; \delta x + \cos\theta\\ y &amp;=&amp; \delta y + \frac{\sin(2\theta)}{2} \end{eqnarray*}
+</p>
+ <dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[out]</td><td class="paramname">data</td><td>matrix to store data in </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;                                                           {</div>
+<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> N = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>-&gt;size();</div>
+<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> dr = 0.2;</div>
+<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;    <span class="keywordtype">int</span> i;</div>
+<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160; </div>
+<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; N; i++) {</div>
+<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;        <span class="keywordtype">double</span> dx = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-dr, dr);     <span class="comment">// random change in x</span></div>
+<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;        <span class="keywordtype">double</span> dy = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(-dr, dr);     <span class="comment">// random change in y</span></div>
+<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;        <span class="keywordtype">double</span> theta = <a class="code" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a>(0, M_PI);  <span class="comment">// random theta</span></div>
+<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][0] = dx + <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(theta);  <span class="comment">// convert from polar to cartesian</span></div>
+<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;        <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[0][i][1] = dy + <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">sin</a>(2. * theta) / 2.f;</div>
+<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;    }</div>
+<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d49/kohonen__som__trace_8cpp_a412b7afa156306b1f8788643c91a1c60_cgraph.svg" width="246" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
+<div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
+<div class="ttc" id="acos_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a></div><div class="ttdeci">T cos(T... args)</div></div>
+<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="akohonen__som__trace_8cpp_html_a9ab8c79ffb674a63f151f282faeb723b"><div class="ttname"><a href="../../d9/d49/kohonen__som__trace_8cpp.html#a9ab8c79ffb674a63f151f282faeb723b">test_3d_classes</a></div><div class="ttdeci">void test_3d_classes(std::vector&lt; std::valarray&lt; double &gt;&gt; *data)</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:347</div></div>
+<div class="ttc" id="agroup__machine__learning_html_ga72699c805c19a6cc47a937a6f3378afa"><div class="ttname"><a href="../../d9/d66/group__machine__learning.html#ga72699c805c19a6cc47a937a6f3378afa">save_nd_data</a></div><div class="ttdeci">int save_nd_data(const char *fname, const std::vector&lt; std::valarray&lt; double &gt;&gt; &amp;X)</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:57</div></div>
+<div class="ttc" id="akohonen__som__trace_8cpp_html_a2256c10b16edba377b64a44b6c656908"><div class="ttname"><a href="../../d9/d49/kohonen__som__trace_8cpp.html#a2256c10b16edba377b64a44b6c656908">get_clock_diff</a></div><div class="ttdeci">double get_clock_diff(clock_t start_t, clock_t end_t)</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:438</div></div>
+<div class="ttc" id="akohonen__som__trace_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../d9/d49/kohonen__som__trace_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:225</div></div>
+<div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
+<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="akohonen__som__trace_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../d9/d49/kohonen__som__trace_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:305</div></div>
+<div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
+<div class="ttc" id="akohonen__som__trace_8cpp_html_a412b7afa156306b1f8788643c91a1c60"><div class="ttname"><a href="../../d9/d49/kohonen__som__trace_8cpp.html#a412b7afa156306b1f8788643c91a1c60">test_lamniscate</a></div><div class="ttdeci">void test_lamniscate(std::vector&lt; std::valarray&lt; double &gt;&gt; *data)</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:267</div></div>
+<div class="ttc" id="asin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a></div><div class="ttdeci">T sin(T... args)</div></div>
+<div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
+<div class="ttc" id="akohonen__som__trace_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="../../d9/d49/kohonen__som__trace_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdef"><b>Definition:</b> kohonen_som_trace.cpp:402</div></div>
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">extended_euclid_algorithm.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>GCD using <a href="https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm">extended Euclid's algorithm</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for extended_euclid_algorithm.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/dc7/extended__euclid__algorithm_8cpp__incl.svg" width="182" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:abe92d63a0ff9bda7e304df510d5dd217"><td class="memTemplParams" colspan="2">template&lt;typename T , typename T2 &gt; </td></tr>
+<tr class="memitem:abe92d63a0ff9bda7e304df510d5dd217"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a> (T *r, T *r0, const T2 quotient)</td></tr>
+<tr class="separator:abe92d63a0ff9bda7e304df510d5dd217"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a1792ac7c33aaf26b860ab55f5652ab25"><td class="memTemplParams" colspan="2">template&lt;typename T1 , typename T2 &gt; </td></tr>
+<tr class="memitem:a1792ac7c33aaf26b860ab55f5652ab25"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#a1792ac7c33aaf26b860ab55f5652ab25">extendedEuclid_1</a> (T1 A, T1 B, T1 *GCD, T2 *x, T2 *y)</td></tr>
+<tr class="separator:a1792ac7c33aaf26b860ab55f5652ab25"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:acba15ca55b3e7dcb91f3c65d72ba052d"><td class="memTemplParams" colspan="2">template&lt;typename T , typename T2 &gt; </td></tr>
+<tr class="memitem:acba15ca55b3e7dcb91f3c65d72ba052d"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d">extendedEuclid</a> (T A, T B, T *GCD, T2 *x, T2 *y)</td></tr>
+<tr class="separator:acba15ca55b3e7dcb91f3c65d72ba052d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top"><a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>GCD using <a href="https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm">extended Euclid's algorithm</a> </p>
+<p>Finding coefficients of a and b ie x and y in Bézout's identity </p><p class="formulaDsp">
+\[\text{gcd}(a, b) = a \times x + b \times y \]
+</p>
+<p> This is also used in finding Modular multiplicative inverse of a number. (A * B)M == 1 Here B is the MMI of A for given M, so extendedEuclid (A, M) gives B. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="acba15ca55b3e7dcb91f3c65d72ba052d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#acba15ca55b3e7dcb91f3c65d72ba052d">&#9670;&nbsp;</a></span>extendedEuclid()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T , typename T2 &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">void extendedEuclid </td>
+          <td>(</td>
+          <td class="paramtype">T&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">T&#160;</td>
+          <td class="paramname"><em>B</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">T *&#160;</td>
+          <td class="paramname"><em>GCD</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">T2 *&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">T2 *&#160;</td>
+          <td class="paramname"><em>y</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Implementation using recursive algorithm</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>unsigned </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">B</td><td>unsigned </td></tr>
+    <tr><td class="paramdir">[out]</td><td class="paramname">GCD</td><td>unsigned </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">x</td><td>signed </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>signed </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;                                                    {</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    <span class="keywordflow">if</span> (B &gt; A)</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(A, B);  <span class="comment">// Ensure that A &gt;= B</span></div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160; </div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    <span class="keywordflow">if</span> (B == 0) {</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        *GCD = A;</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        *x = 1;</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        *y = 0;</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        <a class="code" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d">extendedEuclid</a>(B, A % B, GCD, x, y);</div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;        T2 temp = *x;</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;        *x = *y;</div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        *y = temp - (A / B) * (*y);</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    }</div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
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+<h2 class="memtitle"><span class="permalink"><a href="#a1792ac7c33aaf26b860ab55f5652ab25">&#9670;&nbsp;</a></span>extendedEuclid_1()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T1 , typename T2 &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">void extendedEuclid_1 </td>
+          <td>(</td>
+          <td class="paramtype">T1&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">T1&#160;</td>
+          <td class="paramname"><em>B</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">T1 *&#160;</td>
+          <td class="paramname"><em>GCD</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">T2 *&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">T2 *&#160;</td>
+          <td class="paramname"><em>y</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Implementation using iterative algorithm from <a href="https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Pseudocode">Wikipedia</a></p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>unsigned </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">B</td><td>unsigned </td></tr>
+    <tr><td class="paramdir">[out]</td><td class="paramname">GCD</td><td>unsigned </td></tr>
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+<tr class="memdesc:d5/db0/adaline__learning_8cpp"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a href="https://en.wikipedia.org/wiki/ADALINE">Adaptive Linear Neuron (ADALINE)</a> implementation <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="memdesc:d4/def/kohonen__som__topology_8cpp"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a href="https://en.wikipedia.org/wiki/Self-organizing_map">Kohonen self organizing map</a> (topological map) <br /></td></tr>
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+<tr class="memdesc:d9/d49/kohonen__som__trace_8cpp"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a href="https://en.wikipedia.org/wiki/Self-organizing_map">Kohonen self organizing map</a> (data tracing) <br /></td></tr>
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+<tr class="memdesc:d8/d77/namespacemachine__learning"><td class="mdescLeft">&#160;</td><td class="mdescRight">Machine learning algorithms. <br /></td></tr>
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+#define&#160;</td><td class="memItemRight" valign="bottom"><b>MAX_ITER</b>&#160;&#160;&#160;500</td></tr>
+<tr class="separator:gacd517c6f195c75b9dd0f3aad65326f3b"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+#define&#160;</td><td class="memItemRight" valign="bottom"><b>_USE_MATH_DEFINES</b></td></tr>
+<tr class="separator:ga525335710b53cb064ca56b936120431e"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+#define&#160;</td><td class="memItemRight" valign="bottom"><b>_USE_MATH_DEFINES</b></td></tr>
+<tr class="separator:ga525335710b53cb064ca56b936120431e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:gaf5ce14f026d6d231bef29161bac2b485"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">_random</a> (double <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, double b)</td></tr>
+<tr class="separator:gaf5ce14f026d6d231bef29161bac2b485"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga6c606bc85a3e9fd9d010f874ad760336"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336">save_2d_data</a> (const char *fname, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;X)</td></tr>
+<tr class="separator:ga6c606bc85a3e9fd9d010f874ad760336"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gab53c14440b2b2dd3172c66afc5c2f63f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d66/group__machine__learning.html#gab53c14440b2b2dd3172c66afc5c2f63f">get_min_2d</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;X, double *val, int *x_idx, int *y_idx)</td></tr>
+<tr class="separator:gab53c14440b2b2dd3172c66afc5c2f63f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ga72699c805c19a6cc47a937a6f3378afa"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d66/group__machine__learning.html#ga72699c805c19a6cc47a937a6f3378afa">save_nd_data</a> (const char *fname, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;X)</td></tr>
+<tr class="separator:ga72699c805c19a6cc47a937a6f3378afa"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<h2 class="groupheader">Function Documentation</h2>
+<a id="gaf5ce14f026d6d231bef29161bac2b485"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#gaf5ce14f026d6d231bef29161bac2b485">&#9670;&nbsp;</a></span>_random()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">double _random </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>b</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Helper function to generate a random number in a given interval. <br  />
+ Steps:</p><ol type="1">
+<li><code>r1 = rand() % 100</code> gets a random number between 0 and 99</li>
+<li><code>r2 = r1 / 100</code> converts random number to be between 0 and 0.99</li>
+<li>scale and offset the random number to given range of \([a,b]\)</li>
+</ol>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">a</td><td>lower limit </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">b</td><td>upper limit </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>random number in the range \([a,b]\) </dd></dl>
+<div class="fragment"><div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;                                   {</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    <span class="keywordflow">return</span> ((b - <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>) * (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100) / 100.<a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a>) + <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="gab53c14440b2b2dd3172c66afc5c2f63f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#gab53c14440b2b2dd3172c66afc5c2f63f">&#9670;&nbsp;</a></span>get_min_2d()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void get_min_2d </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;&#160;</td>
+          <td class="paramname"><em>X</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">double *&#160;</td>
+          <td class="paramname"><em>val</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int *&#160;</td>
+          <td class="paramname"><em>x_idx</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int *&#160;</td>
+          <td class="paramname"><em>y_idx</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Get minimum value and index of the value in a matrix </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">X</td><td>matrix to search </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">N</td><td>number of points in the vector </td></tr>
+    <tr><td class="paramdir">[out]</td><td class="paramname">val</td><td>minimum value found </td></tr>
+    <tr><td class="paramdir">[out]</td><td class="paramname">idx_x</td><td>x-index where minimum value was found </td></tr>
+    <tr><td class="paramdir">[out]</td><td class="paramname">idx_y</td><td>y-index where minimum value was found </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;                                        {</div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    val[0] = INFINITY;  <span class="comment">// initial min value</span></div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;    <span class="keywordtype">int</span> N = X.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160; </div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++) {  <span class="comment">// traverse each x-index</span></div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;        <span class="keyword">auto</span> result = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min_element.html">std::min_element</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(X[i]), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(X[i]));</div>
+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        <span class="keywordtype">double</span> d_min = *result;</div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;        <span class="keywordtype">int</span> j = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/distance.html">std::distance</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(X[i]), result);</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160; </div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        <span class="keywordflow">if</span> (d_min &lt; val[0]) {  <span class="comment">// if a lower value is found</span></div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                               <span class="comment">// save the value and its index</span></div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;            x_idx[0] = i;</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;            y_idx[0] = j;</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;            val[0] = d_min;</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        }</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    }</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d66/group__machine__learning_gab53c14440b2b2dd3172c66afc5c2f63f_cgraph.svg" width="271" height="190"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ga6c606bc85a3e9fd9d010f874ad760336"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ga6c606bc85a3e9fd9d010f874ad760336">&#9670;&nbsp;</a></span>save_2d_data()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int save_2d_data </td>
+          <td>(</td>
+          <td class="paramtype">const char *&#160;</td>
+          <td class="paramname"><em>fname</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;&#160;</td>
+          <td class="paramname"><em>X</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Save a given n-dimensional data martix to file.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">fname</td><td>filename to save in (gets overwriten without confirmation) </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">X</td><td>matrix to save </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>0 if all ok </dd>
+<dd>
+-1 if file creation failed </dd></dl>
+<div class="fragment"><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;                                                          {</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <span class="keywordtype">size_t</span> num_points = X.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();       <span class="comment">// number of rows</span></div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="keywordtype">size_t</span> num_features = X[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();  <span class="comment">// number of columns</span></div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160; </div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp;</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(fname);</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    <span class="keywordflow">if</span> (!fp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;        <span class="comment">// error with opening file to write</span></div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Error opening file &quot;</span> &lt;&lt; fname &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    }</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160; </div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="comment">// for each point in the array</span></div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; num_points; i++) {</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        <span class="comment">// for each feature in the array</span></div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; num_features; j++) {</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;            fp &lt;&lt; X[i][j];             <span class="comment">// print the feature value</span></div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;            <span class="keywordflow">if</span> (j &lt; num_features - 1)  <span class="comment">// if not the last feature</span></div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;                fp &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;             <span class="comment">// suffix comma</span></div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;        }</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;        <span class="keywordflow">if</span> (i &lt; num_points - 1)  <span class="comment">// if not the last row</span></div>
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+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int save_nd_data </td>
+          <td>(</td>
+          <td class="paramtype">const char *&#160;</td>
+          <td class="paramname"><em>fname</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;&#160;</td>
+          <td class="paramname"><em>X</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
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+<p>Save a given n-dimensional data martix to file.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">fname</td><td>filename to save in (gets overwriten without confirmation) </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">X</td><td>matrix to save </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>0 if all ok </dd>
+<dd>
+-1 if file creation failed </dd></dl>
+<div class="fragment"><div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;                                                          {</div>
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+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;        <span class="comment">// for each feature in the array</span></div>
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+<p><a href="https://en.wikipedia.org/wiki/Median_search">Median search</a> algorithm  
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+<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
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+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; *&#160;</td>
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+<div class="dyncontent">
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
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+      </table>
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+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;           {</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> v{25, 21, 98, 100, 76, 22, 43, 60, 89, 87};</div>
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+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    <span class="comment">// creates an array of random numbers</span></div>
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+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    <span class="comment">//     v.push_back(r);</span></div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <span class="comment">//     std::cout &lt;&lt; r &lt;&lt; &quot; &quot;;</span></div>
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+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">fibonacci.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Generate fibonacci sequence.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for fibonacci.cpp:</div>
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+int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d89/fibonacci_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Generate fibonacci sequence. </p>
+<p>Calculate the the value on Fibonacci's sequence given an integer as input. </p><p class="formulaDsp">
+\[\text{fib}(n) = \text{fib}(n-1) + \text{fib}(n-2)\]
+</p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/de4/fibonacci__large_8cpp.html" title="Computes N^th Fibonacci number given as input argument. Uses custom build arbitrary integers library ...">fibonacci_large.cpp</a>, <a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html" title="Faster computation of Fibonacci series.">fibonacci_fast.cpp</a>, <a class="el" href="../../de/d47/string__fibonacci_8cpp.html" title="This Programme returns the Nth fibonacci as a string.">string_fibonacci.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a4bc27e88a3da5cc590f1f78622019a7b"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a4bc27e88a3da5cc590f1f78622019a7b">&#9670;&nbsp;</a></span>fibonacci()</h2>
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+          <td class="memname">int fibonacci </td>
+          <td>(</td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
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+      </table>
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+<p>Recursively compute sequences </p>
+<div class="fragment"><div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;                              {</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;    <span class="comment">/* If the input is 0 or 1 just return the same</span></div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">       This will set the first 2 values of the sequence */</span></div>
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">interpolation_search.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a href="https://en.wikipedia.org/wiki/Interpolation_search">Interpolation search</a> algorithm  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for interpolation_search.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/dab/interpolation__search_8cpp__incl.svg" width="146" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
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+Functions</h2></td></tr>
+<tr class="memitem:a9805865b5c5ca6b0fdf95fd86132625a"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/dd7/interpolation__search_8cpp.html#a9805865b5c5ca6b0fdf95fd86132625a">interpolation_search</a> (int arr[], int value, int len)</td></tr>
+<tr class="separator:a9805865b5c5ca6b0fdf95fd86132625a"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/dd7/interpolation__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Interpolation_search">Interpolation search</a> algorithm </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a9805865b5c5ca6b0fdf95fd86132625a"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a9805865b5c5ca6b0fdf95fd86132625a">&#9670;&nbsp;</a></span>interpolation_search()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int interpolation_search </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>arr</em>[], </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>value</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>len</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>function to search the value in an array using interpolation search </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">arr</td><td>array to search in </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">value</td><td>value to search for </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">len</td><td>length of array </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>index where the value is found </dd>
+<dd>
+0 if not found </dd></dl>
+<div class="fragment"><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;                                                        {</div>
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+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (arr[mid] &lt; value)</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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+<div class="memitem">
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+          <td>(</td>
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+      </table>
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+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;           {</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    <span class="keywordtype">int</span> n, value, re;</div>
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+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
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+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160; </div>
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+</div><!--header-->
+<div class="contents">
+
+<p>C++ Program to find <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function">Euler's Totient</a> function.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cstdlib&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
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+<tr class="memitem:a35e4874a3e1d67eb708dc57944c8aea0"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d23/eulers__totient__function_8cpp.html#a35e4874a3e1d67eb708dc57944c8aea0">phiFunction</a> (uint64_t n)</td></tr>
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+<p>Euler Totient Function is also known as phi function. </p><p class="formulaDsp">
+\[\phi(n) = \phi\left({p_1}^{a_1}\right)\cdot\phi\left({p_2}^{a_2}\right)\ldots\]
+</p>
+<p> where \(p_1\), \(p_2\), \(\ldots\) are prime factors of n. <br  />
+3 Euler's properties:</p><ol type="1">
+<li>\(\phi(n) = n-1\)</li>
+<li>\(\phi(n^k) = n^k - n^{k-1}\)</li>
+<li>\(\phi(a,b) = \phi(a)\cdot\phi(b)\) where a and b are relative primes.</li>
+</ol>
+<p>Applying this 3 properties on the first equation. </p><p class="formulaDsp">
+\[\phi(n) = n\cdot\left(1-\frac{1}{p_1}\right)\cdot\left(1-\frac{1}{p_2}\right)\cdots\]
+</p>
+<p> where \(p_1\), \(p_2\)... are prime factors. Hence Implementation in \(O\left(\sqrt{n}\right)\). <br  />
+Some known values are:</p><ul>
+<li>\(\phi(100) = 40\)</li>
+<li>\(\phi(1) = 1\)</li>
+<li>\(\phi(17501) = 15120\)</li>
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+          <td>(</td>
+          <td class="paramtype">uint64_t&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
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+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">sqrt_double.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Calculate the square root of any positive real number in \(O(\log N)\) time, with precision fixed using <a href="https://en.wikipedia.org/wiki/Bisection_method">bisection method</a> of root-finding.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d24/sqrt__double_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Calculate the square root of any positive real number in \(O(\log N)\) time, with precision fixed using <a href="https://en.wikipedia.org/wiki/Bisection_method">bisection method</a> of root-finding. </p>
+<dl class="section see"><dt>See also</dt><dd>Can be implemented using faster and better algorithms like <a class="el" href="../../de/dd3/newton__raphson__method_8cpp.html" title="Solve the equation  using Newton-Raphson method for both real and complex solutions.">newton_raphson_method.cpp</a> and <a class="el" href="../../dd/d29/false__position_8cpp.html" title="Solve the equation  using false position method, also known as the Secant method.">false_position.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;           {</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <span class="keywordtype">double</span> n{};</div>
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+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    assert(n &gt;= 0);</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    <span class="comment">// Change this line for a better precision</span></div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>.precision(12);</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/fixed.html">std::fixed</a> &lt;&lt; <a class="code" href="../../da/d24/sqrt__double_8cpp.html#ae662282ad0740d2063ac404ca3bd74fc">Sqrt</a>(n);</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
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+</div>
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+          <td class="paramname"><em>a</em></td><td>)</td>
+          <td></td>
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+<p>Bisection method implemented for the function \(x^2-a=0\) whose roots are \(\pm\sqrt{a}\) and only the positive root is returned. </p>
+<div class="fragment"><div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;                      {</div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;    <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &gt; 0 &amp;&amp; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt; 1) {</div>
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+<div class="title">primality_test.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a href="https://en.wikipedia.org/wiki/Primality_test">Primality test</a> implementation.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for primality_test.cpp:</div>
+<div class="dyncontent">
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+Functions</h2></td></tr>
+<tr class="memitem:a2bfa6adead2bdcbf1dac94cbe08d7eaf"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d7b/primality__test_8cpp.html#a2bfa6adead2bdcbf1dac94cbe08d7eaf">IsPrime</a> (int number)</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Primality_test">Primality test</a> implementation. </p>
+<p>A simple and efficient implementation of a function to test if a number is prime, based on the fact that </p><blockquote class="doxtable">
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+          <td class="paramname"><em>number</em></td><td>)</td>
+          <td></td>
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+<p>Check if a number is prime </p><dl class="params"><dt>Parameters</dt><dd>
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+  </table>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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+&#160;</td><td class="memItemRight" valign="bottom"><b>Graph</b> (const int V)</td></tr>
+<tr class="separator:acfa457b5f6f7eb480fd469fb980a01ea"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a6dc4dd4ce49c4052ad2a5d27523881f4"><td class="memItemLeft" align="right" valign="top"><a id="a6dc4dd4ce49c4052ad2a5d27523881f4"></a>
+void&#160;</td><td class="memItemRight" valign="bottom"><b>addEdge</b> (int src, int dst, int weight)</td></tr>
+<tr class="separator:a6dc4dd4ce49c4052ad2a5d27523881f4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-attribs"></a>
+Public Attributes</h2></td></tr>
+<tr class="memitem:a6afcd41564ea00294a4c089414979ca1"><td class="memItemLeft" align="right" valign="top"><a id="a6afcd41564ea00294a4c089414979ca1"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>vertexNum</b></td></tr>
+<tr class="separator:a6afcd41564ea00294a4c089414979ca1"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a10ff9c6c323cf435f18e424dbb62235e"><td class="memItemLeft" align="right" valign="top"><a id="a10ff9c6c323cf435f18e424dbb62235e"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>edgeNum</b></td></tr>
+<tr class="separator:a10ff9c6c323cf435f18e424dbb62235e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a3535be2ce0d62152e54395951330da81"><td class="memItemLeft" align="right" valign="top"><a id="a3535be2ce0d62152e54395951330da81"></a>
+<a class="el" href="../../d7/d77/class_edge.html">Edge</a> *&#160;</td><td class="memItemRight" valign="bottom"><b>edges</b></td></tr>
+<tr class="separator:a3535be2ce0d62152e54395951330da81"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a268ba18d421817ad8713c2e92f19d82a"><td class="memItemLeft" align="right" valign="top"><a id="a268ba18d421817ad8713c2e92f19d82a"></a>
+int **&#160;</td><td class="memItemRight" valign="bottom"><b>edges</b></td></tr>
+<tr class="separator:a268ba18d421817ad8713c2e92f19d82a"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-methods"></a>
+Private Member Functions</h2></td></tr>
+<tr class="memitem:acfd6fbc5243626bfb7b7116b76fedab0"><td class="memItemLeft" align="right" valign="top"><a id="acfd6fbc5243626bfb7b7116b76fedab0"></a>
+bool&#160;</td><td class="memItemRight" valign="bottom"><b>bfs</b> (int source, int sink)</td></tr>
+<tr class="separator:acfd6fbc5243626bfb7b7116b76fedab0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-attribs"></a>
+Private Attributes</h2></td></tr>
+<tr class="memitem:a61943646676002a5e75f7b6493c25713"><td class="memItemLeft" align="right" valign="top"><a id="a61943646676002a5e75f7b6493c25713"></a>
+unsigned int&#160;</td><td class="memItemRight" valign="bottom"><b>m_vertices</b></td></tr>
+<tr class="separator:a61943646676002a5e75f7b6493c25713"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a13697caf8be6275ebb7b9497c9a9d6e5"><td class="memItemLeft" align="right" valign="top"><a id="a13697caf8be6275ebb7b9497c9a9d6e5"></a>
+<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map.html">AdjList</a>&#160;</td><td class="memItemRight" valign="bottom"><b>m_adjList</b></td></tr>
+<tr class="separator:a13697caf8be6275ebb7b9497c9a9d6e5"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:af0e8f10f05298718b830d7c01a7cd69c"><td class="memItemLeft" align="right" valign="top"><a id="af0e8f10f05298718b830d7c01a7cd69c"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>residual_capacity</b> [MAXN][MAXN]</td></tr>
+<tr class="separator:af0e8f10f05298718b830d7c01a7cd69c"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ada0d96b867fe317f251c5a025a1ee8b3"><td class="memItemLeft" align="right" valign="top"><a id="ada0d96b867fe317f251c5a025a1ee8b3"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>capacity</b> [MAXN][MAXN]</td></tr>
+<tr class="separator:ada0d96b867fe317f251c5a025a1ee8b3"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae93ae98711b868af601d424954fe94ac"><td class="memItemLeft" align="right" valign="top"><a id="ae93ae98711b868af601d424954fe94ac"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>total_nodes</b></td></tr>
+<tr class="separator:ae93ae98711b868af601d424954fe94ac"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ad621c5393837c21780ff3477431707ac"><td class="memItemLeft" align="right" valign="top"><a id="ad621c5393837c21780ff3477431707ac"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>total_edges</b></td></tr>
+<tr class="separator:ad621c5393837c21780ff3477431707ac"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a9912e31b32405d21a4c22a9ab8dece30"><td class="memItemLeft" align="right" valign="top"><a id="a9912e31b32405d21a4c22a9ab8dece30"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>source</b></td></tr>
+<tr class="separator:a9912e31b32405d21a4c22a9ab8dece30"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a47336f7cfe4698ef887a34e03f1a3856"><td class="memItemLeft" align="right" valign="top"><a id="a47336f7cfe4698ef887a34e03f1a3856"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>sink</b></td></tr>
+<tr class="separator:a47336f7cfe4698ef887a34e03f1a3856"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a08e82d027824859388cd85c83bfbc314"><td class="memItemLeft" align="right" valign="top"><a id="a08e82d027824859388cd85c83bfbc314"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>parent</b> [MAXN]</td></tr>
+<tr class="separator:a08e82d027824859388cd85c83bfbc314"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a73268574e2528b8e760191113ef6d1eb"><td class="memItemLeft" align="right" valign="top"><a id="a73268574e2528b8e760191113ef6d1eb"></a>
+<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/tuple.html">std::tuple</a>&lt; int, int, int &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>edge_participated</b></td></tr>
+<tr class="separator:a73268574e2528b8e760191113ef6d1eb"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:af1abf6ea5346e12dea4df46262ff35aa"><td class="memItemLeft" align="right" valign="top"><a id="af1abf6ea5346e12dea4df46262ff35aa"></a>
+<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/bitset.html">std::bitset</a>&lt; MAXN &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>visited</b></td></tr>
+<tr class="separator:af1abf6ea5346e12dea4df46262ff35aa"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aa0aaff1a0c13bdf209ea40b83ac01ae6"><td class="memItemLeft" align="right" valign="top"><a id="aa0aaff1a0c13bdf209ea40b83ac01ae6"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>max_flow</b> = 0</td></tr>
+<tr class="separator:aa0aaff1a0c13bdf209ea40b83ac01ae6"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Implementation of graph class.</p>
+<p>The graph will be represented using Adjacency List representation. This class contains 2 data members "m_vertices" &amp; "m_adjList" used to represent the number of vertices and adjacency list of the graph respectively. The vertices are labelled 0 - (m_vertices - 1). </p>
+</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
+<a id="ae30edce9b4e7c6347e67edc343f366d8"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae30edce9b4e7c6347e67edc343f366d8">&#9670;&nbsp;</a></span>Graph() <span class="overload">[1/3]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">Graph::Graph </td>
+          <td>(</td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>vertices</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map.html">AdjList</a> const &amp;&#160;</td>
+          <td class="paramname"><em>adjList</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Create a graph from vertices and adjacency list.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">vertices</td><td>specify the number of vertices the graph would contain. </td></tr>
+    <tr><td class="paramname">adjList</td><td>is the adjacency list representation of graph. </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;        : m_vertices(vertices), m_adjList(adjList) {}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a8c95e00effaea0cd9404dd74cd802ae3"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a8c95e00effaea0cd9404dd74cd802ae3">&#9670;&nbsp;</a></span>Graph() <span class="overload">[2/3]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">Graph::Graph </td>
+          <td>(</td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>vertices</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map.html">AdjList</a> &amp;&amp;&#160;</td>
+          <td class="paramname"><em>adjList</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Create a graph from vertices and adjacency list.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">vertices</td><td>specify the number of vertices the graph would contain. </td></tr>
+    <tr><td class="paramname">adjList</td><td>is the adjacency list representation of graph. </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        : m_vertices(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(vertices)), m_adjList(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(adjList)) {}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="aa99d44d3179d5bbbfa84a5031cf80cb1"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa99d44d3179d5bbbfa84a5031cf80cb1">&#9670;&nbsp;</a></span>Graph() <span class="overload">[3/3]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">Graph::Graph </td>
+          <td>(</td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>vertices</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="el" href="../../d7/d77/class_edge.html">Edge</a> &gt; const &amp;&#160;</td>
+          <td class="paramname"><em>edges</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Create a graph from vertices and a set of edges.</p>
+<p>Adjacency list of the graph would be created from the set of edges. If the source or destination of any edge has a value greater or equal to number of vertices, then it would throw a range_error.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">vertices</td><td>specify the number of vertices the graph would contain. </td></tr>
+    <tr><td class="paramname">edges</td><td>is a vector of edges. </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        : m_vertices(vertices) {</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        <span class="keywordflow">for</span> (<span class="keyword">auto</span> <span class="keyword">const</span>&amp; edge : edges) {</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;            <span class="keywordflow">if</span> (edge.src &gt;= vertices || edge.dest &gt;= vertices) {</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;                <span class="keywordflow">throw</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/range_error.html">std::range_error</a>(</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;                    <span class="stringliteral">&quot;Either src or dest of edge out of range&quot;</span>);</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;            }</div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;            m_adjList[edge.src].emplace_back(edge.dest);</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        }</div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<h2 class="groupheader">Member Function Documentation</h2>
+<a id="af765dda8f21280e1cecea19e129f1bc5"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af765dda8f21280e1cecea19e129f1bc5">&#9670;&nbsp;</a></span>addEdge() <span class="overload">[1/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void Graph::addEdge </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d7/d77/class_edge.html">Edge</a> const &amp;&#160;</td>
+          <td class="paramname"><em>edge</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Add an edge in the graph.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">edge</td><td>that needs to be added. </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;                                   {</div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;        <span class="keywordflow">if</span> (edge.src &gt;= m_vertices || edge.dest &gt;= m_vertices) {</div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;            <span class="keywordflow">throw</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/range_error.html">std::range_error</a>(<span class="stringliteral">&quot;Either src or dest of edge out of range&quot;</span>);</div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;        }</div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        m_adjList[edge.src].emplace_back(edge.dest);</div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ac85c63bcca4764a621f9f8609a8e5910"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac85c63bcca4764a621f9f8609a8e5910">&#9670;&nbsp;</a></span>addEdge() <span class="overload">[2/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void Graph::addEdge </td>
+          <td>(</td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>source</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>destination</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Add an <a class="el" href="../../d7/d77/class_edge.html">Edge</a> in the graph</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">source</td><td>is source vertex of the edge. </td></tr>
+    <tr><td class="paramname">destination</td><td>is the destination vertex of the edge. </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;                                                                {</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;        <span class="keywordflow">if</span> (source &gt;= m_vertices || destination &gt;= m_vertices) {</div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;            <span class="keywordflow">throw</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/range_error.html">std::range_error</a>(</div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;                <span class="stringliteral">&quot;Either source or destination of edge out of range&quot;</span>);</div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;        }</div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;        m_adjList[source].emplace_back(destination);</div>
+<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ac5a4d9a4f894a179198936042c778413"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac5a4d9a4f894a179198936042c778413">&#9670;&nbsp;</a></span>addVertices()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
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+          <td>(</td>
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+          <td class="paramname"><em>num</em> = <code>1</code></td><td>)</td>
+          <td></td>
+        </tr>
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+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
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+<p>Add vertices in the graph.</p>
+<dl class="params"><dt>Parameters</dt><dd>
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+    <tr><td class="paramname">num</td><td>is the number of vertices to be added. It adds 1 vertex by default. </td></tr>
+  </table>
+  </dd>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae8959064e179573cc48f8cee99115c07">&#9670;&nbsp;</a></span>getAdjList()</h2>
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+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td> const</td>
+        </tr>
+      </table>
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+<p>Return a const reference of the adjacency list.</p>
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+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td> const</td>
+        </tr>
+      </table>
+  </td>
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+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
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+<dl class="section return"><dt>Returns</dt><dd>number of vertices in the graph. </dd></dl>
+<div class="fragment"><div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;                                                                   {</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        <span class="keywordflow">return</span> m_vertices;</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<hr/>The documentation for this class was generated from the following files:<ul>
+<li>dynamic_programming/bellman_ford.cpp</li>
+<li>dynamic_programming/floyd_warshall.cpp</li>
+<li>graph/cycle_check_directed_graph.cpp</li>
+<li>graph/max_flow_with_ford_fulkerson_and_edmond_karp_algo.cpp</li>
+<li>greedy_algorithms/dijkstra.cpp</li>
+</ul>
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+</div><!-- doc-content -->
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">palindrome_of_number.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Check if a number is <a href="https://en.wikipedia.org/wiki/Palindrome">palindrome</a> or not.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;cstring&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for palindrome_of_number.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d6c/palindrome__of__number_8cpp__incl.svg" width="267" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
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+Functions</h2></td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d9a/palindrome__of__number_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Check if a number is <a href="https://en.wikipedia.org/wiki/Palindrome">palindrome</a> or not. </p>
+<p>This program cheats by using the STL library's <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/reverse.html">std::reverse</a> function. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
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+          <td>(</td>
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+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;           {</div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;    <span class="keywordtype">int</span> num;</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number = &quot;</span>;</div>
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+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s1 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(num);  <span class="comment">// convert number to string</span></div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s2 = s1;</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160; </div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/reverse.html">std::reverse</a>(s1.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(), s1.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">end</a>());  <span class="comment">// reverse the string</span></div>
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+<tr class="memitem:a840291bc02cba5474a4cb46a9b9566fe"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/de7/decimal__to__hexadecimal_8cpp.html#a840291bc02cba5474a4cb46a9b9566fe">main</a> (void)</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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+<h2 class="memtitle"><span class="permalink"><a href="#a840291bc02cba5474a4cb46a9b9566fe">&#9670;&nbsp;</a></span>main()</h2>
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+          <td class="memname">int main </td>
+          <td>(</td>
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+          <td class="paramname"></td><td>)</td>
+          <td></td>
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+<p>Main program </p>
+<div class="fragment"><div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;               {</div>
+<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;    <span class="keywordtype">int</span> valueToConvert = 0;  <span class="comment">// Holds user input</span></div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;    <span class="keywordtype">int</span> hexArray[8];         <span class="comment">// Contains hex values backwards</span></div>
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+<a href="#define-members">Macros</a> &#124;
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+<div class="title">durand_kerner_roots.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
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+<p>Compute all possible approximate roots of any given polynomial using <a href="https://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method">Durand Kerner algorithm</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
+<code>#include &lt;cassert&gt;</code><br />
+<code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;complex&gt;</code><br />
+<code>#include &lt;cstdlib&gt;</code><br />
+<code>#include &lt;ctime&gt;</code><br />
+<code>#include &lt;fstream&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
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+<tr class="memitem:ac38b9cfd2a39d856e0feba3b5d241ded"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; uint32_t, double &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/df2/durand__kerner__roots_8cpp.html#ac38b9cfd2a39d856e0feba3b5d241ded">durand_kerner_algo</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &amp;coeffs, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; double &gt;&gt; *roots, bool write_log=false)</td></tr>
+<tr class="separator:ac38b9cfd2a39d856e0feba3b5d241ded"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/df2/durand__kerner__roots_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a> ()</td></tr>
+<tr class="separator:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a0283886819c7c140a023582b7269e2d0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a> ()</td></tr>
+<tr class="separator:a0283886819c7c140a023582b7269e2d0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top"><a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>main</b> (int argc, char **argv)</td></tr>
+<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Compute all possible approximate roots of any given polynomial using <a href="https://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method">Durand Kerner algorithm</a> </p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
+<p>Test the algorithm online: <a href="https://gist.github.com/kvedala/27f1b0b6502af935f6917673ec43bcd7">https://gist.github.com/kvedala/27f1b0b6502af935f6917673ec43bcd7</a></p>
+<p>Try the highly unstable Wilkinson's polynomial: </p><div class="fragment"><div class="line">./numerical_methods/durand_kerner_roots 1 -210 20615 -1256850 53327946</div>
+<div class="line">-1672280820 40171771630 -756111184500 11310276995381 -135585182899530</div>
+<div class="line">1307535010540395 -10142299865511450 63030812099294896 -311333643161390640</div>
+<div class="line">1206647803780373360 -3599979517947607200 8037811822645051776</div>
+<div class="line">-12870931245150988800 13803759753640704000 -8752948036761600000</div>
+<div class="line">2432902008176640000</div>
+</div><!-- fragment --><p>Sample implementation results to compute approximate roots of the equation \(x^4-1=0\):<br  />
+<img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/numerical_methods/durand_kerner_error.svg" alt="Error evolution during root approximations computed every
+iteration." style="pointer-events: none;" width="400" class="inline"/> <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/numerical_methods/durand_kerner_roots.svg" alt="Roots evolution - shows the initial approximation of the
+roots and their convergence to a final approximation along with the iterative
+approximations" style="pointer-events: none;" width="400" class="inline"/> </p>
+</div><h2 class="groupheader">Macro Definition Documentation</h2>
+<a id="af270a96662132d0385cb6b4637c5a689"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af270a96662132d0385cb6b4637c5a689">&#9670;&nbsp;</a></span>ACCURACY</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">#define ACCURACY&#160;&#160;&#160;1e-10</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>maximum accuracy limit </p>
+
+</div>
+</div>
+<h2 class="groupheader">Function Documentation</h2>
+<a id="a024b8bc4755863315456d573a6732377"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a024b8bc4755863315456d573a6732377">&#9670;&nbsp;</a></span>check_termination()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool check_termination </td>
+          <td>(</td>
+          <td class="paramtype">long double&#160;</td>
+          <td class="paramname"><em>delta</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>check for termination condition </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">delta</td><td>point at which to evaluate the polynomial </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><code>false</code> if termination not reached </dd>
+<dd>
+<code>true</code> if termination reached </dd></dl>
+<div class="fragment"><div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;                                          {</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    <span class="keyword">static</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> past_delta = INFINITY;</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="keywordflow">if</span> (std::abs(past_delta - delta) &lt;= <a class="code" href="../../da/df2/durand__kerner__roots_8cpp.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a> || delta &lt; <a class="code" href="../../da/df2/durand__kerner__roots_8cpp.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a>)</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    past_delta = delta;</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a3bada3e58ad8d1b00918db2ffe83a740"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a3bada3e58ad8d1b00918db2ffe83a740">&#9670;&nbsp;</a></span>complex_str()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">const char* complex_str </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; double &gt; &amp;&#160;</td>
+          <td class="paramname"><em>x</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>create a textual form of complex number </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>point at which to evaluate the polynomial </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>pointer to converted string </dd></dl>
+<div class="fragment"><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;                                                     {</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;<span class="preprocessor">#define MAX_BUFF_SIZE 50</span></div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <span class="keyword">static</span> <span class="keywordtype">char</span> msg[MAX_BUFF_SIZE];</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160; </div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">std::snprintf</a>(msg, MAX_BUFF_SIZE, <span class="stringliteral">&quot;% 7.04g%+7.04gj&quot;</span>, x.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>(), x.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>());</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    <span class="keywordflow">return</span> msg;</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ac38b9cfd2a39d856e0feba3b5d241ded"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac38b9cfd2a39d856e0feba3b5d241ded">&#9670;&nbsp;</a></span>durand_kerner_algo()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt;uint32_t, double&gt; durand_kerner_algo </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &amp;&#160;</td>
+          <td class="paramname"><em>coeffs</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>roots</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">bool&#160;</td>
+          <td class="paramname"><em>write_log</em> = <code>false</code>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Implements Durand Kerner iterative algorithm to compute all roots of a polynomial.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">coeffs</td><td>coefficients of the polynomial </td></tr>
+    <tr><td class="paramdir">[out]</td><td class="paramname">roots</td><td>the computed roots of the polynomial </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">write_log</td><td>flag whether to save the log file (default = <code>false</code>) </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>pair of values - number of iterations taken and final accuracy achieved </dd></dl>
+<div class="fragment"><div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;                                                                    {</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    <span class="keywordtype">long</span> <span class="keywordtype">double</span> tol_condition = 1;</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    uint32_t iter = 0;</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    <span class="keywordtype">int</span> n;</div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> log_file;</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160; </div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <span class="keywordflow">if</span> (write_log) {</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;        <span class="comment">/*</span></div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;<span class="comment">         * store intermediate values to a CSV file</span></div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;<span class="comment">         */</span></div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;        log_file.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(<span class="stringliteral">&quot;durand_kerner.log.csv&quot;</span>);</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        <span class="keywordflow">if</span> (!log_file.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">perror</a>(<span class="stringliteral">&quot;Unable to create a storage log file!&quot;</span>);</div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;        }</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;        log_file &lt;&lt; <span class="stringliteral">&quot;iter#,&quot;</span>;</div>
+<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160; </div>
+<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;        <span class="keywordflow">for</span> (n = 0; n &lt; roots-&gt;size(); n++) log_file &lt;&lt; <span class="stringliteral">&quot;root_&quot;</span> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160; </div>
+<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;        log_file &lt;&lt; <span class="stringliteral">&quot;avg. correction&quot;</span>;</div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;        log_file &lt;&lt; <span class="stringliteral">&quot;\n0,&quot;</span>;</div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        <span class="keywordflow">for</span> (n = 0; n &lt; roots-&gt;size(); n++)</div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;            log_file &lt;&lt; <a class="code" href="../../da/df2/durand__kerner__roots_8cpp.html#a3bada3e58ad8d1b00918db2ffe83a740">complex_str</a>((*roots)[n]) &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    }</div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160; </div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    <span class="keywordtype">bool</span> break_loop = <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    <span class="keywordflow">while</span> (!<a class="code" href="../../da/df2/durand__kerner__roots_8cpp.html#a024b8bc4755863315456d573a6732377">check_termination</a>(tol_condition) &amp;&amp; iter &lt; INT16_MAX &amp;&amp;</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;           !break_loop) {</div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;        tol_condition = 0;</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;        iter++;</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;        break_loop = <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160; </div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;        <span class="keywordflow">if</span> (log_file.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;            log_file &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160; </div>
+<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;<span class="preprocessor">#pragma omp parallel for shared(break_loop, tol_condition)</span></div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        <span class="keywordflow">for</span> (n = 0; n &lt; roots-&gt;size(); n++) {</div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;            <span class="keywordflow">if</span> (break_loop)</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;                <span class="keywordflow">continue</span>;</div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160; </div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> numerator, denominator;</div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;            numerator = <a class="code" href="../../da/df2/durand__kerner__roots_8cpp.html#a51637ff89e55ca749993d3e84b95d153">poly_function</a>(coeffs, (*roots)[n]);</div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;            denominator = 1.0;</div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; roots-&gt;size(); i++)</div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;                <span class="keywordflow">if</span> (i != n)</div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;                    denominator *= (*roots)[n] - (*roots)[i];</div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160; </div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a> delta = numerator / denominator;</div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160; </div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;            <span class="keywordflow">if</span> (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isnan.html">std::isnan</a>(std::abs(delta)) || <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isinf.html">std::isinf</a>(std::abs(delta))) {</div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;                <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\n\nOverflow/underrun error - got value = &quot;</span></div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;                          &lt;&lt; std::abs(delta) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;                <span class="comment">// return std::pair&lt;uint32_t, double&gt;(iter, tol_condition);</span></div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;                break_loop = <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;            }</div>
+<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160; </div>
+<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;            (*roots)[n] -= delta;</div>
+<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160; </div>
+<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;<span class="preprocessor">#pragma omp critical</span></div>
+<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;            tol_condition = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(tol_condition, std::abs(std::abs(delta)));</div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;        }</div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;        <span class="comment">// tol_condition /= (degree - 1);</span></div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160; </div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;        <span class="keywordflow">if</span> (break_loop)</div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;            <span class="keywordflow">break</span>;</div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160; </div>
+<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;        <span class="keywordflow">if</span> (log_file.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
+<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;            <span class="keywordflow">for</span> (n = 0; n &lt; roots-&gt;size(); n++)</div>
+<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;                log_file &lt;&lt; <a class="code" href="../../da/df2/durand__kerner__roots_8cpp.html#a3bada3e58ad8d1b00918db2ffe83a740">complex_str</a>((*roots)[n]) &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;        }</div>
+<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160; </div>
+<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;<span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
+<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;        <span class="keywordflow">if</span> (iter % 500 == 0) {</div>
+<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Iter: &quot;</span> &lt;&lt; iter &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
+<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;            <span class="keywordflow">for</span> (n = 0; n &lt; roots-&gt;size(); n++)</div>
+<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;                <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span> &lt;&lt; <a class="code" href="../../da/df2/durand__kerner__roots_8cpp.html#a3bada3e58ad8d1b00918db2ffe83a740">complex_str</a>((*roots)[n]);</div>
+<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t\tabsolute average change: &quot;</span> &lt;&lt; tol_condition</div>
+<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;                      &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;        }</div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160; </div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;        <span class="keywordflow">if</span> (log_file.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;            log_file &lt;&lt; tol_condition;</div>
+<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    }</div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160; </div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;uint32_t, long double&gt;</a>(iter, tol_condition);</div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../da/df2/durand__kerner__roots_8cpp_ac38b9cfd2a39d856e0feba3b5d241ded_cgraph.svg" width="527" height="494"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a51637ff89e55ca749993d3e84b95d153"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a51637ff89e55ca749993d3e84b95d153">&#9670;&nbsp;</a></span>poly_function()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt;double&gt; poly_function </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &amp;&#160;</td>
+          <td class="paramname"><em>coeffs</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; double &gt;&#160;</td>
+          <td class="paramname"><em>x</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Evaluate the value of a polynomial with given coefficients </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">coeffs</td><td>coefficients of the polynomial </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>point at which to evaluate the polynomial </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>\(f(x)\) </dd></dl>
+<div class="fragment"><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;                                                         {</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keywordtype">double</span> real = 0.f, imag = 0.f;</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keywordtype">int</span> n;</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160; </div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="comment">// #ifdef _OPENMP</span></div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    <span class="comment">// #pragma omp target teams distribute reduction(+ : real, imag)</span></div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="comment">// #endif</span></div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    <span class="keywordflow">for</span> (n = 0; n &lt; coeffs.size(); n++) {</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> tmp =</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;            coeffs[n] * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, coeffs.size() - n - 1);</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        real += tmp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>();</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        imag += tmp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>();</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    }</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160; </div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(real, imag);</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../da/df2/durand__kerner__roots_8cpp_a51637ff89e55ca749993d3e84b95d153_cgraph.svg" width="291" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a1440a7779ac56f47a3f355ce4a8c7da0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">&#9670;&nbsp;</a></span>test1()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test1 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Self test the algorithm by checking the roots for \(x^2+4=0\) to which the roots are \(0 \pm 2i\) </p>
+<div class="fragment"><div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;             {</div>
+<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;    <span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> coeffs = {1, 0, 4};  <span class="comment">// x^2 - 2 = 0</span></div>
+<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; roots(2);</div>
+<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; expected = {</div>
+<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(0., 2.),</div>
+<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(0., -2.)  <span class="comment">// known expected roots</span></div>
+<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;    };</div>
+<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160; </div>
+<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    <span class="comment">/* initialize root approximations with random values */</span></div>
+<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n &lt; roots.size(); n++) {</div>
+<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;        roots[n] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100);</div>
+<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;        roots[n] -= 50.f;</div>
+<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;        roots[n] /= 25.f;</div>
+<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    }</div>
+<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160; </div>
+<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    <span class="keyword">auto</span> result = <a class="code" href="../../da/df2/durand__kerner__roots_8cpp.html#ac38b9cfd2a39d856e0feba3b5d241ded">durand_kerner_algo</a>(coeffs, &amp;roots, <span class="keyword">false</span>);</div>
+<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160; </div>
+<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; roots.size(); i++) {</div>
+<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;        <span class="comment">// check if approximations are have &lt; 0.1% error with one of the</span></div>
+<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;        <span class="comment">// expected roots</span></div>
+<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;        <span class="keywordtype">bool</span> err1 = <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; roots.size(); j++)</div>
+<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;            err1 |= std::abs(std::abs(roots[i] - expected[j])) &lt; 1e-3;</div>
+<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;        assert(err1);</div>
+<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;    }</div>
+<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160; </div>
+<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 passed! - &quot;</span> &lt;&lt; result.first &lt;&lt; <span class="stringliteral">&quot; iterations, &quot;</span></div>
+<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;              &lt;&lt; result.second &lt;&lt; <span class="stringliteral">&quot; accuracy&quot;</span></div>
+<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../da/df2/durand__kerner__roots_8cpp_a1440a7779ac56f47a3f355ce4a8c7da0_cgraph.svg" width="626" height="494"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a0283886819c7c140a023582b7269e2d0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0283886819c7c140a023582b7269e2d0">&#9670;&nbsp;</a></span>test2()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test2 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Self test the algorithm by checking the roots for \(0.015625x^3-1=0\) to which the roots are \((4+0i),\,(-2\pm3.464i)\) </p>
+<div class="fragment"><div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;             {</div>
+<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;    <span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> coeffs = {<span class="comment">// 0.015625 x^3 - 1 = 0</span></div>
+<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;                                          1. / 64., 0., 0., -1.};</div>
+<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; roots(3);</div>
+<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;    <span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::complex&lt;double&gt;</a>&gt; expected = {</div>
+<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(4., 0.), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(-2., 3.46410162),</div>
+<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(-2., -3.46410162)  <span class="comment">// known expected roots</span></div>
+<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;    };</div>
+<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160; </div>
+<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;    <span class="comment">/* initialize root approximations with random values */</span></div>
+<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n &lt; roots.size(); n++) {</div>
+<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;        roots[n] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100);</div>
+<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;        roots[n] -= 50.f;</div>
+<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;        roots[n] /= 25.f;</div>
+<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    }</div>
+<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160; </div>
+<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;    <span class="keyword">auto</span> result = <a class="code" href="../../da/df2/durand__kerner__roots_8cpp.html#ac38b9cfd2a39d856e0feba3b5d241ded">durand_kerner_algo</a>(coeffs, &amp;roots, <span class="keyword">false</span>);</div>
+<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160; </div>
+<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; roots.size(); i++) {</div>
+<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;        <span class="comment">// check if approximations are have &lt; 0.1% error with one of the</span></div>
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+<a href="#func-members">Functions</a>  </div>
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+</div><!--header-->
+<div class="contents">
+
+<p>Print the elements of a matrix traversing it spirally.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for spiral_print.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d7/d4c/spiral__print_8cpp__incl.svg" width="162" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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+</div>
+</div><table class="memberdecls">
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+Functions</h2></td></tr>
+<tr class="memitem:acfff36db81326fb990a643ab198ee8a5"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d07/spiral__print_8cpp.html#acfff36db81326fb990a643ab198ee8a5">genArray</a> (int **<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, int r, int c)</td></tr>
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d07/spiral__print_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Print the elements of a matrix traversing it spirally. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="acfff36db81326fb990a643ab198ee8a5"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#acfff36db81326fb990a643ab198ee8a5">&#9670;&nbsp;</a></span>genArray()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void genArray </td>
+          <td>(</td>
+          <td class="paramtype">int **&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>r</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>c</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Arrange sequence of numbers from '1' in a matrix form </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[out]</td><td class="paramname">a</td><td>matrix to fill </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">r</td><td>number of rows </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">c</td><td>number of columns </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;                                     {</div>
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+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    }</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
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+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;           {</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <span class="keywordtype">int</span> r, c;</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; r &gt;&gt; c;</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <span class="keywordtype">int</span> **<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = <span class="keyword">new</span> <span class="keywordtype">int</span> *[r];</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; r; i++) <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>[i] = <span class="keyword">new</span> <span class="keywordtype">int</span>[c];</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160; </div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    <a class="code" href="../../db/d07/spiral__print_8cpp.html#acfff36db81326fb990a643ab198ee8a5">genArray</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, r, c);</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <a class="code" href="../../db/d07/spiral__print_8cpp.html#a850d3f55e1a8d227176cdcc67352c197">spiralPrint</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, r, c);</div>
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+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    <span class="keyword">delete</span>[] <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a850d3f55e1a8d227176cdcc67352c197"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a850d3f55e1a8d227176cdcc67352c197">&#9670;&nbsp;</a></span>spiralPrint()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void spiralPrint </td>
+          <td>(</td>
+          <td class="paramtype">int **&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>r</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>c</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Traverse the matrix spirally and print the sequence of elements </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">a</td><td>matrix to read from </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">r</td><td>number of rows </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">c</td><td>number of columns </td></tr>
+  </table>
+  </dd>
+</dl>
+<p>Print start row</p>
+<p>Print the end col</p>
+<p>Print the end row</p>
+<p>Print the start Col</p>
+<div class="fragment"><div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;                                        {</div>
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+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>[startRow][i] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;        }</div>
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+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;<span class="comment">        /// Print the end col</span></div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="comment"></span>        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = startRow; i &lt;= endRow; i++, cnt++) {</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>[i][endCol] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        }</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;        endCol--;</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="comment"></span> </div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="comment">        /// Print the end row</span></div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;<span class="comment"></span>        <span class="keywordflow">if</span> (cnt == r * c) {</div>
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+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160; </div>
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+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;        }</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;        endRow--;</div>
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+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="comment">        /// Print the start Col</span></div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;<span class="comment"></span>        <span class="keywordflow">if</span> (cnt == r * c) {</div>
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+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a> &#124;
+<a href="#var-members">Variables</a>  </div>
+  <div class="headertitle">
+<div class="title">prime_factorization.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Prime factorization of positive integers.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
+<code>#include &lt;cstring&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;vector&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for prime_factorization.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/def/prime__factorization_8cpp__incl.svg" width="350" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:affe577b9bce8f604f5e2f861c63c7099"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">SieveOfEratosthenes</a> (int N)</td></tr>
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+<tr class="separator:a0ece0145fb29a5cf48378c23dde2da46"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d0d/prime__factorization_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="memitem:a7fe38b570a51e448430d6a0f072c2f23"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a> [1000006]</td></tr>
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+<tr class="memitem:af097796783684712b8326e5b82bfd4fe"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a></td></tr>
+<tr class="separator:af097796783684712b8326e5b82bfd4fe"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:acfb0df439a4beae5a34ef131ce737c1b"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; int, int &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">factors</a></td></tr>
+<tr class="separator:acfb0df439a4beae5a34ef131ce737c1b"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Prime factorization of positive integers. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main program </p>
+<div class="fragment"><div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;           {</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="keywordtype">int</span> num;</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t\tComputes the prime factorization\n\n&quot;</span>;</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Type in a number: &quot;</span>;</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; num;</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160; </div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">SieveOfEratosthenes</a>(num);</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160; </div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a0ece0145fb29a5cf48378c23dde2da46">prime_factorization</a>(num);</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160; </div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <span class="comment">// Prime factors with their powers in the given number in new line</span></div>
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+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    }</div>
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+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d0d/prime__factorization_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="459" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
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+</div>
+</div>
+<a id="a0ece0145fb29a5cf48378c23dde2da46"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0ece0145fb29a5cf48378c23dde2da46">&#9670;&nbsp;</a></span>prime_factorization()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void prime_factorization </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>num</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Prime factorization of a number </p>
+<div class="fragment"><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;                                  {</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keywordtype">int</span> number = num;</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160; </div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i] &lt;= num; i++) {</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        <span class="keywordtype">int</span> count = 0;</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160; </div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        <span class="comment">// termination condition</span></div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;        <span class="keywordflow">if</span> (number == 1) {</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;            <span class="keywordflow">break</span>;</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        }</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160; </div>
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+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;            count++;</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;            number = number / <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i];</div>
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+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160; </div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;        <span class="keywordflow">if</span> (count)</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;            <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">factors</a>.push_back(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(<a class="code" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i], count));</div>
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+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
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+</div>
+</div>
+
+</div>
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+<a id="affe577b9bce8f604f5e2f861c63c7099"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#affe577b9bce8f604f5e2f861c63c7099">&#9670;&nbsp;</a></span>SieveOfEratosthenes()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void SieveOfEratosthenes </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>N</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Calculating prime number upto a given range </p>
+<div class="fragment"><div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;                                {</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    <span class="comment">// initializes the array isprime</span></div>
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+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[i])</div>
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+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d0d/prime__factorization_8cpp_affe577b9bce8f604f5e2f861c63c7099_cgraph.svg" width="360" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<h2 class="groupheader">Variable Documentation</h2>
+<a id="acfb0df439a4beae5a34ef131ce737c1b"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#acfb0df439a4beae5a34ef131ce737c1b">&#9670;&nbsp;</a></span>factors</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt;int, int&gt; &gt; factors</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>list of prime factor-pairs </p>
+
+</div>
+</div>
+<a id="a7fe38b570a51e448430d6a0f072c2f23"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a7fe38b570a51e448430d6a0f072c2f23">&#9670;&nbsp;</a></span>isprime</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool isprime[1000006]</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Declaring variables for maintaing prime numbers and to check whether a number is prime or not </p>
+
+</div>
+</div>
+<a id="af097796783684712b8326e5b82bfd4fe"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af097796783684712b8326e5b82bfd4fe">&#9670;&nbsp;</a></span>prime_numbers</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;int&gt; prime_numbers</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>list of prime numbers </p>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
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+<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
+<div class="ttc" id="amemset_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/memset.html">std::memset</a></div><div class="ttdeci">T memset(T... args)</div></div>
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+  <ul>
+    <li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../db/d0d/prime__factorization_8cpp.html">prime_factorization.cpp</a></li>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:44 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+    [ "SieveOfEratosthenes", "db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099", null ],
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+    [ "isprime", "db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23", null ],
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+</div>
+
+<div class="header">
+  <div class="summary">
+<a href="#nested-classes">Classes</a> &#124;
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">tower_of_hanoi.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Solve the <a href="https://en.wikipedia.org/wiki/Tower_of_Hanoi">Tower of Hanoi</a> problem.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for tower_of_hanoi.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/ddb/tower__of__hanoi_8cpp__incl.svg" width="186" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="nested-classes"></a>
+Classes</h2></td></tr>
+<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d2c/structtower.html">tower</a></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a746d9a3984bba88fd6dd91978f6931ed"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">show</a> (const struct <a class="el" href="../../d2/d2c/structtower.html">tower</a> *const F, const struct <a class="el" href="../../d2/d2c/structtower.html">tower</a> *const T, const struct <a class="el" href="../../d2/d2c/structtower.html">tower</a> *const U)</td></tr>
+<tr class="separator:a746d9a3984bba88fd6dd91978f6931ed"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:af4cfc41e546f1f8d25f01e0804e8b61d"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a> (<a class="el" href="../../d2/d2c/structtower.html">tower</a> *From, <a class="el" href="../../d2/d2c/structtower.html">tower</a> *To)</td></tr>
+<tr class="separator:af4cfc41e546f1f8d25f01e0804e8b61d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ab037f72a5eac476535a6cfbbcb965417"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a> (int n, <a class="el" href="../../d2/d2c/structtower.html">tower</a> *From, <a class="el" href="../../d2/d2c/structtower.html">tower</a> *Using, <a class="el" href="../../d2/d2c/structtower.html">tower</a> *To)</td></tr>
+<tr class="separator:ab037f72a5eac476535a6cfbbcb965417"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d3c/tower__of__hanoi_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Solve the <a href="https://en.wikipedia.org/wiki/Tower_of_Hanoi">Tower of Hanoi</a> problem. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;           {</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <span class="keyword">struct </span><a class="code" href="../../d2/d2c/structtower.html">tower</a> F, U, T;</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160; </div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    F.<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a> = 0;</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    U.top = 0;</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    T.top = 0;</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160; </div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <span class="keywordtype">int</span> no;</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160; </div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter number of discs : &quot;</span>;</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; no;</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160; </div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = no; i &gt; 0; i--) {</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        F.values[F.top++] = i;</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    }</div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160; </div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">show</a>(&amp;F, &amp;T, &amp;U);</div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a>(no, &amp;F, &amp;U, &amp;T);</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160; </div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d3c/tower__of__hanoi_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="251" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="af4cfc41e546f1f8d25f01e0804e8b61d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af4cfc41e546f1f8d25f01e0804e8b61d">&#9670;&nbsp;</a></span>mov()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void mov </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../d2/d2c/structtower.html">tower</a> *&#160;</td>
+          <td class="paramname"><em>From</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="el" href="../../d2/d2c/structtower.html">tower</a> *&#160;</td>
+          <td class="paramname"><em>To</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Move one disc from one tower to another </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">From</td><td>tower to move disk <em>from</em> </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">To</td><td>tower to move disk <em>to</em> </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;                                 {</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    --From-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>;</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    To-&gt;<a class="code" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[To-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>] = From-&gt;<a class="code" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[From-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>];</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    ++To-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>;</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a746d9a3984bba88fd6dd91978f6931ed"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a746d9a3984bba88fd6dd91978f6931ed">&#9670;&nbsp;</a></span>show()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void show </td>
+          <td>(</td>
+          <td class="paramtype">const struct <a class="el" href="../../d2/d2c/structtower.html">tower</a> *const&#160;</td>
+          <td class="paramname"><em>F</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const struct <a class="el" href="../../d2/d2c/structtower.html">tower</a> *const&#160;</td>
+          <td class="paramname"><em>T</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const struct <a class="el" href="../../d2/d2c/structtower.html">tower</a> *const&#160;</td>
+          <td class="paramname"><em>U</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Display the towers </p>
+<div class="fragment"><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;                                       {</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\n\tF : &quot;</span>;</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; F-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; F-&gt;<a class="code" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    }</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\tU : &quot;</span>;</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; U-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; U-&gt;<a class="code" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    }</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\tT : &quot;</span>;</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; T-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; T-&gt;<a class="code" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
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+</div><!-- fragment -->
+</div>
+</div>
+<a id="ab037f72a5eac476535a6cfbbcb965417"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ab037f72a5eac476535a6cfbbcb965417">&#9670;&nbsp;</a></span>TH()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void TH </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="el" href="../../d2/d2c/structtower.html">tower</a> *&#160;</td>
+          <td class="paramname"><em>From</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="el" href="../../d2/d2c/structtower.html">tower</a> *&#160;</td>
+          <td class="paramname"><em>Using</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="el" href="../../d2/d2c/structtower.html">tower</a> *&#160;</td>
+          <td class="paramname"><em>To</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Recursive algorithm to solve the puzzle </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>starting number of disks </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">From</td><td>tower to move disks from </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">Using</td><td>temporary tower for the puzzle </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">To</td><td>tower to move disk to </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;                                                     {</div>
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+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a>(n - 1, From, To, Using);</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a>(From, To);</div>
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+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    }</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
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+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="atower__of__hanoi_8cpp_html_af4cfc41e546f1f8d25f01e0804e8b61d"><div class="ttname"><a href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a></div><div class="ttdeci">void mov(tower *From, tower *To)</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:39</div></div>
+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
+<div class="ttc" id="astructtower_html"><div class="ttname"><a href="../../d2/d2c/structtower.html">tower</a></div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:11</div></div>
+<div class="ttc" id="atower__of__hanoi_8cpp_html_a746d9a3984bba88fd6dd91978f6931ed"><div class="ttname"><a href="../../db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">show</a></div><div class="ttdeci">void show(const struct tower *const F, const struct tower *const T, const struct tower *const U)</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:19</div></div>
+<div class="ttc" id="astructtower_html_a3ebb75c13c57d51a8a1ba1ea54a515e9"><div class="ttname"><a href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">tower::values</a></div><div class="ttdeci">int values[10]</div><div class="ttdoc">Values in the tower.</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:13</div></div>
+<div class="ttc" id="astructtower_html_acb535964abd34c47678a4ade0628223d"><div class="ttname"><a href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">tower::top</a></div><div class="ttdeci">int top</div><div class="ttdoc">top tower ID</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:15</div></div>
+<div class="ttc" id="atower__of__hanoi_8cpp_html_ab037f72a5eac476535a6cfbbcb965417"><div class="ttname"><a href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a></div><div class="ttdeci">void TH(int n, tower *From, tower *Using, tower *To)</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:52</div></div>
+<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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+    <li class="footer">Generated on Fri Jun 19 2020 16:06:44 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+    [ "show", "db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed", null ],
+    [ "TH", "db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417", null ]
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+const unsigned char &amp;&#160;</td><td class="memItemRight" valign="bottom"><b>operator[]</b> (size_t n) const</td></tr>
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+<tr class="separator:a622d84883180ff42f04955909adea5a9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ac4fafa6289295419d48d444f0ae4b706"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d82/classlarge__number.html#ac4fafa6289295419d48d444f0ae4b706">operator++</a> (int)</td></tr>
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+<a class="el" href="../../db/d82/classlarge__number.html">large_number</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><b>operator+=</b> (int n)</td></tr>
+<tr class="separator:aad394466f3207b21b5d3e994b3a8ed72"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="separator:aeb22d2aae39d1b1e0bd39c7f47b333eb"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ab1af3e0f425cdf7ea2039c9dcfe22f0b"><td class="memTemplParams" colspan="2">template&lt;class T &gt; </td></tr>
+<tr class="memitem:ab1af3e0f425cdf7ea2039c9dcfe22f0b"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a> &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/d82/classlarge__number.html#ab1af3e0f425cdf7ea2039c9dcfe22f0b">operator*=</a> (const T n)</td></tr>
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+<tr class="separator:af530d90830d385c76973658ff3214f98"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-methods"></a>
+Static Public Member Functions</h2></td></tr>
+<tr class="memitem:a959c5c1a982949bbf98e1ea0f9afe6a9"><td class="memItemLeft" align="right" valign="top">static bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d82/classlarge__number.html#a959c5c1a982949bbf98e1ea0f9afe6a9">test</a> ()</td></tr>
+<tr class="separator:a959c5c1a982949bbf98e1ea0f9afe6a9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-methods"></a>
+Private Member Functions</h2></td></tr>
+<tr class="memitem:a2f5571e66305cf68bb8283e4aeda58bc"><td class="memTemplParams" colspan="2">template&lt;class T &gt; </td></tr>
+<tr class="memitem:a2f5571e66305cf68bb8283e4aeda58bc"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/d82/classlarge__number.html#a2f5571e66305cf68bb8283e4aeda58bc">multiply</a> (const T n)</td></tr>
+<tr class="separator:a2f5571e66305cf68bb8283e4aeda58bc"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-attribs"></a>
+Private Attributes</h2></td></tr>
+<tr class="memitem:af2b3ec9c35842d3a46ac7326f268af57"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; unsigned char &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a></td></tr>
+<tr class="separator:af2b3ec9c35842d3a46ac7326f268af57"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="friends"></a>
+Friends</h2></td></tr>
+<tr class="memitem:a778428c4761b6ea5e7770743f0eab5ab"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d82/classlarge__number.html#a778428c4761b6ea5e7770743f0eab5ab">operator&lt;&lt;</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;out, const <a class="el" href="../../db/d82/classlarge__number.html">large_number</a> &amp;<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>)</td></tr>
+<tr class="separator:a778428c4761b6ea5e7770743f0eab5ab"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a7ba872b9a3ce1f3da6c06c5409663cca"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d82/classlarge__number.html#a7ba872b9a3ce1f3da6c06c5409663cca">operator==</a> (<a class="el" href="../../db/d82/classlarge__number.html">large_number</a> const &amp;<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, <a class="el" href="../../db/d82/classlarge__number.html">large_number</a> const &amp;b)</td></tr>
+<tr class="separator:a7ba872b9a3ce1f3da6c06c5409663cca"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a72ae1ef050c4c28c50952ecab22d4b94"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d82/classlarge__number.html#a72ae1ef050c4c28c50952ecab22d4b94">operator!=</a> (<a class="el" href="../../db/d82/classlarge__number.html">large_number</a> const &amp;<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, <a class="el" href="../../db/d82/classlarge__number.html">large_number</a> const &amp;b)</td></tr>
+<tr class="separator:a72ae1ef050c4c28c50952ecab22d4b94"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a70d23d67535e67030db570e56c00e16d"><td class="memTemplParams" colspan="2">template&lt;class T &gt; </td></tr>
+<tr class="memitem:a70d23d67535e67030db570e56c00e16d"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a> &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/d82/classlarge__number.html#a70d23d67535e67030db570e56c00e16d">operator+</a> (const <a class="el" href="../../db/d82/classlarge__number.html">large_number</a> &amp;<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, const T &amp;b)</td></tr>
+<tr class="separator:a70d23d67535e67030db570e56c00e16d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Store large unsigned numbers as a C++ vector The class provides convenience functions to add a digit to the number, perform multiplication of large number with long unsigned integers. </p>
+</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
+<a id="a10119a83839e65962621b73df46a5337"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a10119a83839e65962621b73df46a5337">&#9670;&nbsp;</a></span>large_number() <span class="overload">[1/4]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">large_number::large_number </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>&lt; initializer with value = 1 </p>
+<div class="fragment"><div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;{ <a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(1); }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_a10119a83839e65962621b73df46a5337_cgraph.svg" width="350" height="52"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="af4598f1f2794b5e17e10c25e0501e41a"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af4598f1f2794b5e17e10c25e0501e41a">&#9670;&nbsp;</a></span>large_number() <span class="overload">[2/4]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">large_number::large_number </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">explicit</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>&lt; initializer from an integer initializer from another <a class="el" href="../../db/d82/classlarge__number.html">large_number</a> </p>
+<div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_af4598f1f2794b5e17e10c25e0501e41a_cgraph.svg" width="558" height="52"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a0b1efd203274e38a67b78937dfb9b872"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0b1efd203274e38a67b78937dfb9b872">&#9670;&nbsp;</a></span>large_number() <span class="overload">[3/4]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">large_number::large_number </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="el" href="../../db/d82/classlarge__number.html">large_number</a> &amp;&#160;</td>
+          <td class="paramname"><em>a</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>initializer from a vector </p>
+
+</div>
+</div>
+<a id="a76ddf1ed1b00fb8c107ea56f7f91e42f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a76ddf1ed1b00fb8c107ea56f7f91e42f">&#9670;&nbsp;</a></span>large_number() <span class="overload">[4/4]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">large_number::large_number </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; unsigned char &gt; &amp;&#160;</td>
+          <td class="paramname"><em>vec</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">explicit</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>initializer from a string </p>
+
+</div>
+</div>
+<h2 class="groupheader">Member Function Documentation</h2>
+<a id="a60c436d1a1c5e3795d6177d3815ad615"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a60c436d1a1c5e3795d6177d3815ad615">&#9670;&nbsp;</a></span>add_digit()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void large_number::add_digit </td>
+          <td>(</td>
+          <td class="paramtype">unsigned int&#160;</td>
+          <td class="paramname"><em>value</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>add a digit at MSB to the large number </p>
+<div class="fragment"><div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;                                       {</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;        <span class="keywordflow">if</span> (value &gt; 9) {</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;digit &gt; 9!!\n&quot;</span>;</div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">exit</a>(EXIT_FAILURE);</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        }</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160; </div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;        <a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(value);</div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_a60c436d1a1c5e3795d6177d3815ad615_cgraph.svg" width="374" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="af530d90830d385c76973658ff3214f98"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af530d90830d385c76973658ff3214f98">&#9670;&nbsp;</a></span>digit_char()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">const char large_number::digit_char </td>
+          <td>(</td>
+          <td class="paramtype">size_t&#160;</td>
+          <td class="paramname"><em>i</em></td><td>)</td>
+          <td> const</td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>returns i^th digit as an ASCII character </p>
+<div class="fragment"><div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;                                          {</div>
+<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>[<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>() - i - 1] + <span class="charliteral">&#39;0&#39;</span>;</div>
+<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_af530d90830d385c76973658ff3214f98_cgraph.svg" width="558" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a2f5571e66305cf68bb8283e4aeda58bc"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a2f5571e66305cf68bb8283e4aeda58bc">&#9670;&nbsp;</a></span>multiply()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class T &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void large_number::multiply </td>
+          <td>(</td>
+          <td class="paramtype">const T&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">private</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>multiply large number with another integer and store the result in the same large number </p>
+<div class="fragment"><div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;                             {</div>
+<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;        static_assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/is_integral.html">std::is_integral&lt;T&gt;::value</a>,</div>
+<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;                      <span class="stringliteral">&quot;Can only have integer types.&quot;</span>);</div>
+<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;        <span class="comment">// assert(!(std::is_signed&lt;T&gt;::value)); //, &quot;Implemented only for</span></div>
+<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;        <span class="comment">// unsigned integer types.&quot;);</span></div>
+<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160; </div>
+<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;        <span class="keywordtype">size_t</span> i;</div>
+<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;        uint64_t carry = 0, temp;</div>
+<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;        <span class="keywordflow">for</span> (i = 0; i &lt; this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>(); i++) {</div>
+<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;            temp = (*this)[i] * n;</div>
+<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;            temp += carry;</div>
+<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;            <span class="keywordflow">if</span> (temp &lt; 10) {</div>
+<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;                carry = 0;</div>
+<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;            } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;                carry = temp / 10;</div>
+<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;                temp = temp % 10;</div>
+<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;            }</div>
+<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;            (*this)[i] = temp;</div>
+<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;        }</div>
+<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160; </div>
+<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;        <span class="keywordflow">while</span> (carry != 0) {</div>
+<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;            this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">add_digit</a>(carry % 10);</div>
+<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;            carry /= 10;</div>
+<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;        }</div>
+<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_a2f5571e66305cf68bb8283e4aeda58bc_cgraph.svg" width="586" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a2305a82e7b372617419337b2d2119c7d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a2305a82e7b372617419337b2d2119c7d">&#9670;&nbsp;</a></span>num_digits()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">const size_t large_number::num_digits </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td> const</td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Get number of digits in the number </p>
+<div class="fragment"><div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;{ <span class="keywordflow">return</span> <a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_a2305a82e7b372617419337b2d2119c7d_cgraph.svg" width="346" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ab1af3e0f425cdf7ea2039c9dcfe22f0b"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ab1af3e0f425cdf7ea2039c9dcfe22f0b">&#9670;&nbsp;</a></span>operator*=()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class T &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a>&amp; large_number::operator*= </td>
+          <td>(</td>
+          <td class="paramtype">const T&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>operator overload to increment </p>
+<div class="fragment"><div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;                                        {</div>
+<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;        static_assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/is_integral.html">std::is_integral&lt;T&gt;::value</a>,</div>
+<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;                      <span class="stringliteral">&quot;Must be integer addition unsigned integer types.&quot;</span>);</div>
+<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;        this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2f5571e66305cf68bb8283e4aeda58bc">multiply</a>(n);</div>
+<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_ab1af3e0f425cdf7ea2039c9dcfe22f0b_cgraph.svg" width="100%" height="366"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a622d84883180ff42f04955909adea5a9"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a622d84883180ff42f04955909adea5a9">&#9670;&nbsp;</a></span>operator++() <span class="overload">[1/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a>&amp; large_number::operator++ </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>operator overload to increment (prefix) </p>
+<div class="fragment"><div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;                               {</div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;        (*this) += 1;</div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ac4fafa6289295419d48d444f0ae4b706"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac4fafa6289295419d48d444f0ae4b706">&#9670;&nbsp;</a></span>operator++() <span class="overload">[2/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a>&amp; large_number::operator++ </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>operator overload to increment (postfix) </p>
+<div class="fragment"><div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;                                  {</div>
+<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;        <span class="keyword">static</span> <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> tmp(<a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>);</div>
+<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;        ++(*this);</div>
+<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;        <span class="keywordflow">return</span> tmp;</div>
+<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ac27b399ed872731758ec33ebb102730e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac27b399ed872731758ec33ebb102730e">&#9670;&nbsp;</a></span>operator+=()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a>&amp; large_number::operator+= </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a>&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>operator overload to add </p>
+<div class="fragment"><div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;                                             {</div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;        <span class="comment">// if adding with another large_number</span></div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;        <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> *b = <span class="keyword">reinterpret_cast&lt;</span><a class="code" href="../../db/d82/classlarge__number.html">large_number</a> *<span class="keyword">&gt;</span>(&amp;n);</div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;        <span class="keyword">const</span> <span class="keywordtype">size_t</span> max_L = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>(), b-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>());</div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> carry = 0;</div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;        <span class="keywordtype">size_t</span> i;</div>
+<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;        <span class="keywordflow">for</span> (i = 0; i &lt; max_L || carry != 0; i++) {</div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;            <span class="keywordflow">if</span> (i &lt; b-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>())</div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;                carry += (*b)[i];</div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;            <span class="keywordflow">if</span> (i &lt; this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>())</div>
+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;                carry += (*this)[i];</div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;            <span class="keywordflow">if</span> (i &lt; this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">num_digits</a>())</div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;                (*this)[i] = carry % 10;</div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;            <span class="keywordflow">else</span></div>
+<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;                this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">add_digit</a>(carry % 10);</div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;            carry /= 10;</div>
+<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;        }</div>
+<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="aeb22d2aae39d1b1e0bd39c7f47b333eb"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aeb22d2aae39d1b1e0bd39c7f47b333eb">&#9670;&nbsp;</a></span>operator=()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a>&amp; large_number::operator= </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="el" href="../../db/d82/classlarge__number.html">large_number</a> &amp;&#160;</td>
+          <td class="paramname"><em>b</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>assignment operator </p>
+<div class="fragment"><div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;                                                   {</div>
+<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;        this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a> = b.<a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>;</div>
+<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
+<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ace19126cf343a09efc0010735f6e3a8d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ace19126cf343a09efc0010735f6e3a8d">&#9670;&nbsp;</a></span>operator[]()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">unsigned char&amp; large_number::operator[] </td>
+          <td>(</td>
+          <td class="paramtype">size_t&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>operator over load to access the i^th digit conveniently and also assign value to it </p>
+<div class="fragment"><div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;{ <span class="keywordflow">return</span> this-&gt;<a class="code" href="../../db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">_digits</a>[n]; }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a959c5c1a982949bbf98e1ea0f9afe6a9"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a959c5c1a982949bbf98e1ea0f9afe6a9">&#9670;&nbsp;</a></span>test()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">static bool large_number::test </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">static</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Function to check implementation </p>
+<div class="fragment"><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;                       {</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------ Checking `large_number` class implementations\t&quot;</span></div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;                  &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;        <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>(40);</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        <span class="comment">// 1. test multiplication</span></div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> *= 10;</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> != <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(400)) {</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 1/6 (&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot;!=400)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 1/6...&quot;</span>;</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        <span class="comment">// 2. test compound addition with integer</span></div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> += 120;</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> != <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(520)) {</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 2/6 (&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot;!=520)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 2/6...&quot;</span>;</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        <span class="comment">// 3. test compound multiplication again</span></div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> *= 10;</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> != <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(5200)) {</div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;\tFailed 3/6 (&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot;!=5200)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tPassed 3/6...&quot;</span>;</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        <span class="comment">// 4. test increment (prefix)</span></div>
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+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> != <a class="code" href="../../db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>(5201)) {</div>
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+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        <span class="comment">// 5. test increment (postfix)</span></div>
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+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        }</div>
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+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        <span class="comment">// 6. test addition with another large number</span></div>
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+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d82/classlarge__number_a959c5c1a982949bbf98e1ea0f9afe6a9_cgraph.svg" width="528" height="104"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<h2 class="groupheader">Friends And Related Function Documentation</h2>
+<a id="a72ae1ef050c4c28c50952ecab22d4b94"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a72ae1ef050c4c28c50952ecab22d4b94">&#9670;&nbsp;</a></span>operator!=</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool operator!= </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a> const &amp;&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a> const &amp;&#160;</td>
+          <td class="paramname"><em>b</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">friend</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>operator overload to compare two numbers </p>
+<div class="fragment"><div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;                                                                         {</div>
+<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;        <span class="keywordflow">return</span> !(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> == b);</div>
+<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a70d23d67535e67030db570e56c00e16d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a70d23d67535e67030db570e56c00e16d">&#9670;&nbsp;</a></span>operator+</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;class T &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a>&amp; operator+ </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="el" href="../../db/d82/classlarge__number.html">large_number</a> &amp;&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const T &amp;&#160;</td>
+          <td class="paramname"><em>b</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">friend</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>operator overload to perform addition </p>
+<div class="fragment"><div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;                                                                      {</div>
+<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;        <span class="keyword">static</span> <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> c = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;        c += b;</div>
+<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;        <span class="keywordflow">return</span> c;</div>
+<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a778428c4761b6ea5e7770743f0eab5ab"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a778428c4761b6ea5e7770743f0eab5ab">&#9670;&nbsp;</a></span>operator&lt;&lt;</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a>&amp; operator&lt;&lt; </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;&#160;</td>
+          <td class="paramname"><em>out</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="el" href="../../db/d82/classlarge__number.html">large_number</a> &amp;&#160;</td>
+          <td class="paramname"><em>a</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">friend</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>operator overload to compare two numbers </p>
+<div class="fragment"><div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;                                                                          {</div>
+<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>.num_digits(); i &gt; 0; i--)</div>
+<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;            out &lt;&lt; static_cast&lt;int&gt;(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>[i - 1]);</div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        <span class="keywordflow">return</span> out;</div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a7ba872b9a3ce1f3da6c06c5409663cca"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a7ba872b9a3ce1f3da6c06c5409663cca">&#9670;&nbsp;</a></span>operator==</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool operator== </td>
+          <td>(</td>
+          <td class="paramtype"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a> const &amp;&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a> const &amp;&#160;</td>
+          <td class="paramname"><em>b</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">friend</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>operator overload to compare two numbers </p>
+<div class="fragment"><div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;                                                                         {</div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;        <span class="keywordtype">size_t</span> N = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>.num_digits();</div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;        <span class="keywordflow">if</span> (N != b.num_digits())</div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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+<a href="#func-members">Functions</a>  </div>
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+<div class="title">check_prime.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Reduced all possibilities of a number which cannot be prime. Eg: No even number, except 2 can be a prime number, hence we will increment our loop with i+2 jumping on all odd numbers only. If number is &lt;= 1 or if it is even except 2, break the loop and return false telling number is not prime.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for check_prime.cpp:</div>
+<div class="dyncontent">
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+Functions</h2></td></tr>
+<tr class="memitem:aa18b3517017d99bb4024853bddba5532"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:aa18b3517017d99bb4024853bddba5532"><td class="memTemplItemLeft" align="right" valign="top">bool&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/d93/check__prime_8cpp.html#aa18b3517017d99bb4024853bddba5532">is_prime</a> (T num)</td></tr>
+<tr class="separator:aa18b3517017d99bb4024853bddba5532"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d93/check__prime_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Reduced all possibilities of a number which cannot be prime. Eg: No even number, except 2 can be a prime number, hence we will increment our loop with i+2 jumping on all odd numbers only. If number is &lt;= 1 or if it is even except 2, break the loop and return false telling number is not prime. </p>
+<p>Copyright 2020 </p><dl class="section author"><dt>Author</dt><dd>omkarlanghe</dd></dl>
+<p>A simple program to check if the given number if prime or not. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="aa18b3517017d99bb4024853bddba5532"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa18b3517017d99bb4024853bddba5532">&#9670;&nbsp;</a></span>is_prime()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname">bool is_prime </td>
+          <td>(</td>
+          <td class="paramtype">T&#160;</td>
+          <td class="paramname"><em>num</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Function to check if the given number is prime or not. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">num</td><td>number to be checked. </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>if number is prime, it returns @ true, else it returns @ false. </dd></dl>
+<div class="fragment"><div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;                     {</div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    <span class="keywordtype">bool</span> result = <span class="keyword">true</span>;</div>
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+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    }</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="keywordflow">if</span> (num &gt;= 3) {</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;        <span class="keywordflow">for</span> (T i = 3; (i * i) &lt; (num); i = (i + 2)) {</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;            <span class="keywordflow">if</span> ((num % i) == 0) {</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;                result = <span class="keyword">false</span>;</div>
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">ode_forward_euler.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Solve a multivariable first order <a href="https://en.wikipedia.org/wiki/Ordinary_differential_equation">ordinary differential equation (ODEs)</a> using <a href="https://en.wikipedia.org/wiki/Numerical_methods_for_ordinary_differential_equations#Euler_method">forward Euler method</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;ctime&gt;</code><br />
+<code>#include &lt;fstream&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;valarray&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for ode_forward_euler.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/dc5/ode__forward__euler_8cpp__incl.svg" width="430" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
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+<tr class="memitem:abaeae8f62a018d197f0187a1c80a90fe"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/dd3/ode__forward__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a> (const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</td></tr>
+<tr class="memdesc:abaeae8f62a018d197f0187a1c80a90fe"><td class="mdescLeft">&#160;</td><td class="mdescRight">Problem statement for a system with first-order differential equations. Updates the system differential variables.  <a href="../../db/dd3/ode__forward__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">More...</a><br /></td></tr>
+<tr class="separator:abaeae8f62a018d197f0187a1c80a90fe"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:af3adf7b092a87868917ee5fb4255192b"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/dd3/ode__forward__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a> (const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y)</td></tr>
+<tr class="memdesc:af3adf7b092a87868917ee5fb4255192b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Exact solution of the problem. Used for solution comparison.  <a href="../../db/dd3/ode__forward__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">More...</a><br /></td></tr>
+<tr class="separator:af3adf7b092a87868917ee5fb4255192b"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gaa197c6b7085ac9ea71abc4c063e6f52f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#gaa197c6b7085ac9ea71abc4c063e6f52f">forward_euler_step</a> (const double dx, const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</td></tr>
+<tr class="memdesc:gaa197c6b7085ac9ea71abc4c063e6f52f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute next step approximation using the forward-Euler method.  <a href="../../d6/d60/group__ode.html#gaa197c6b7085ac9ea71abc4c063e6f52f">More...</a><br /></td></tr>
+<tr class="separator:gaa197c6b7085ac9ea71abc4c063e6f52f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a> (double dx, double x0, double x_max, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, bool save_to_file=false)</td></tr>
+<tr class="memdesc:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute approximation using the forward-Euler method in the given limits.  <a href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">More...</a><br /></td></tr>
+<tr class="separator:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aa13517b8e5de1b75592052db7f7e237f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/dd3/ode__forward__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a> (const double &amp;X0, const double &amp;X_MAX, const double &amp;step_size, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &amp;Y0)</td></tr>
+<tr class="separator:aa13517b8e5de1b75592052db7f7e237f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/dd3/ode__forward__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
+<tr class="separator:a0ddf1224851353fc92bfbff6f499fa97"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Solve a multivariable first order <a href="https://en.wikipedia.org/wiki/Ordinary_differential_equation">ordinary differential equation (ODEs)</a> using <a href="https://en.wikipedia.org/wiki/Numerical_methods_for_ordinary_differential_equations#Euler_method">forward Euler method</a> </p>
+<dl class="section author"><dt>Authors</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
+<p>The ODE being solved is: </p><p class="formulaDsp">
+\begin{eqnarray*} \dot{u} &amp;=&amp; v\\ \dot{v} &amp;=&amp; -\omega^2 u\\ \omega &amp;=&amp; 1\\ [x_0, u_0, v_0] &amp;=&amp; [0,1,0]\qquad\ldots\text{(initial values)} \end{eqnarray*}
+</p>
+<p> The exact solution for the above problem is: </p><p class="formulaDsp">
+\begin{eqnarray*} u(x) &amp;=&amp; \cos(x)\\ v(x) &amp;=&amp; -\sin(x)\\ \end{eqnarray*}
+</p>
+<p> The computation results are stored to a text file <code>forward_euler.csv</code> and the exact soltuion results in <code>exact.csv</code> for comparison. <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/numerical_methods/ode_forward_euler.svg" alt="Implementation solution" style="pointer-events: none;" class="inline"/></p>
+<p>To implement <a href="https://en.wikipedia.org/wiki/Van_der_Pol_oscillator">Van der Pol oscillator</a>, change the <a class="el" href="../../db/dd3/ode__forward__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe" title="Problem statement for a system with first-order differential equations. Updates the system differenti...">problem</a> function to: </p><div class="fragment"><div class="line"><span class="keyword">const</span> <span class="keywordtype">double</span> mu = 2.0;</div>
+<div class="line">dy[0] = y[1];</div>
+<div class="line">dy[1] = mu * (1.f - y[0] * y[0]) * y[1] - y[0];</div>
+</div><!-- fragment --><dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d6/dd3/ode__midpoint__euler_8cpp.html" title="Solve a multivariable first order ordinary differential equation (ODEs) using midpoint Euler method">ode_midpoint_euler.cpp</a>, <a class="el" href="../../d3/d06/ode__semi__implicit__euler_8cpp.html" title="Solve a multivariable first order ordinary differential equation (ODEs) using semi implicit Euler met...">ode_semi_implicit_euler.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="af3adf7b092a87868917ee5fb4255192b"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af3adf7b092a87868917ee5fb4255192b">&#9670;&nbsp;</a></span>exact_solution()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void exact_solution </td>
+          <td>(</td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>y</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Exact solution of the problem. Used for solution comparison. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>independent variable </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>dependent variable </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;                                                             {</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    y[0][0] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(x);</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    y[0][1] = -<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(x);</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/dd3/ode__forward__euler_8cpp_af3adf7b092a87868917ee5fb4255192b_cgraph.svg" width="235" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a0ddf1224851353fc92bfbff6f499fa97"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>argc</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char *&#160;</td>
+          <td class="paramname"><em>argv</em>[]&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main Function </p>
+<div class="fragment"><div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;                                 {</div>
+<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <span class="keywordtype">double</span> X0 = 0.f;                       <span class="comment">/* initial value of x0 */</span></div>
+<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    <span class="keywordtype">double</span> X_MAX = 10.F;                   <span class="comment">/* upper limit of integration */</span></div>
+<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> Y0 = {1.f, 0.f}; <span class="comment">/* initial value Y = y(x = x_0) */</span></div>
+<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    <span class="keywordtype">double</span> step_size;</div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160; </div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;    <span class="keywordflow">if</span> (argc == 1) {</div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter the step size: &quot;</span>;</div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; step_size;</div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;    } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;        <span class="comment">// use commandline argument as independent variable step size</span></div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;        step_size = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a>(argv[1]);</div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    }</div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160; </div>
+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;    <span class="comment">// get approximate solution</span></div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    <span class="keywordtype">double</span> total_time = <a class="code" href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a>(step_size, X0, X_MAX, &amp;Y0, <span class="keyword">true</span>);</div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tTime = &quot;</span> &lt;&lt; total_time &lt;&lt; <span class="stringliteral">&quot; ms\n&quot;</span>;</div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160; </div>
+<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    <span class="comment">/* compute exact solution for comparion */</span></div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    <a class="code" href="../../db/dd3/ode__forward__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a>(X0, X_MAX, step_size, Y0);</div>
+<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160; </div>
+<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/dd3/ode__forward__euler_8cpp_a0ddf1224851353fc92bfbff6f499fa97_cgraph.svg" width="568" height="367"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="abaeae8f62a018d197f0187a1c80a90fe"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#abaeae8f62a018d197f0187a1c80a90fe">&#9670;&nbsp;</a></span>problem()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void problem </td>
+          <td>(</td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>y</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
+          <td class="paramname"><em>dy</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Problem statement for a system with first-order differential equations. Updates the system differential variables. </p>
+<dl class="section note"><dt>Note</dt><dd>This function can be updated to and ode of any order.</dd></dl>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>independent variable(s) </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">y</td><td>dependent variable(s) </td></tr>
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">dy</td><td>first-derivative of dependent variable(s) </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;                                      {</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> omega = 1.F;             <span class="comment">// some const for the problem</span></div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    dy[0][0] = y[0][1];                   <span class="comment">// x dot</span></div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    dy[0][1] = -omega * omega * y[0][0];  <span class="comment">// y dot</span></div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="aa13517b8e5de1b75592052db7f7e237f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa13517b8e5de1b75592052db7f7e237f">&#9670;&nbsp;</a></span>save_exact_solution()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void save_exact_solution </td>
+          <td>(</td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>X0</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>X_MAX</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const double &amp;&#160;</td>
+          <td class="paramname"><em>step_size</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &amp;&#160;</td>
+          <td class="paramname"><em>Y0</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Function to compute and save exact solution for comparison</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">X0</td><td>initial value of independent variable </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">X_MAX</td><td>final value of independent variable </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">step_size</td><td>independent variable step size </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">Y0</td><td>initial values of dependent variables </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;                                                        {</div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;    <span class="keywordtype">double</span> x = X0;</div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> y = Y0;</div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160; </div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(<span class="stringliteral">&quot;exact.csv&quot;</span>, std::ostream::out);</div>
+<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <span class="keywordflow">if</span> (!fp.is_open()) {</div>
+<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a>(<span class="stringliteral">&quot;Error! &quot;</span>);</div>
+<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;        <span class="keywordflow">return</span>;</div>
+<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    }</div>
+<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Finding exact solution\n&quot;</span>;</div>
+<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160; </div>
+<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t1 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    <span class="keywordflow">do</span> {</div>
+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;        fp &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; y.size() - 1; i++) {</div>
+<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;            fp &lt;&lt; y[i] &lt;&lt; <span class="stringliteral">&quot;,&quot;</span>;</div>
+<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;        }</div>
+<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;        fp &lt;&lt; y[y.size() - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160; </div>
+<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;        <a class="code" href="../../db/dd3/ode__forward__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a>(x, &amp;y);</div>
+<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160; </div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;        x += step_size;</div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    } <span class="keywordflow">while</span> (x &lt;= X_MAX);</div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160; </div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> t2 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    <span class="keywordtype">double</span> total_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\tTime = &quot;</span> &lt;&lt; total_time &lt;&lt; <span class="stringliteral">&quot; ms\n&quot;</span>;</div>
+<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160; </div>
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+<p>A happy number is a number whose sum of digits is calculated until the sum is a single digit, and this sum turns out to be 1.  
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+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">pascal_triangle.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Pascal's triangle implementation.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cstring&gt;</code><br />
+<code>#include &lt;iomanip&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for pascal_triangle.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/d1d/pascal__triangle_8cpp__incl.svg" width="259" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:ad7a31d9cb2818d21b1ba12aead7f4c5c"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d1a/pascal__triangle_8cpp.html#ad7a31d9cb2818d21b1ba12aead7f4c5c">show_pascal</a> (int **arr, int n)</td></tr>
+<tr class="separator:ad7a31d9cb2818d21b1ba12aead7f4c5c"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:afd3f52dd56ddedbf7af5d26a202a199e"><td class="memItemLeft" align="right" valign="top">int **&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d1a/pascal__triangle_8cpp.html#afd3f52dd56ddedbf7af5d26a202a199e">pascal_triangle</a> (int **arr, int n)</td></tr>
+<tr class="separator:afd3f52dd56ddedbf7af5d26a202a199e"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d1a/pascal__triangle_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Pascal's triangle implementation. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;           {</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <span class="keywordtype">int</span> n = 0;</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160; </div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Set Pascal&#39;s Triangle Height&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160; </div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="comment">// memory allocation (Assign two-dimensional array to store Pascal triangle)</span></div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    <span class="keywordtype">int</span> **arr = <span class="keyword">new</span> <span class="keywordtype">int</span> *[n];</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;        arr[i] = <span class="keyword">new</span> <span class="keywordtype">int</span>[2 * n - 1];</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/memset.html">memset</a>(arr[i], 0, <span class="keyword">sizeof</span>(<span class="keywordtype">int</span>) * (2 * n - 1));</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    }</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160; </div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <a class="code" href="../../dc/d1a/pascal__triangle_8cpp.html#afd3f52dd56ddedbf7af5d26a202a199e">pascal_triangle</a>(arr, n);</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <a class="code" href="../../dc/d1a/pascal__triangle_8cpp.html#ad7a31d9cb2818d21b1ba12aead7f4c5c">show_pascal</a>(arr, n);</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160; </div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="comment">// deallocation</span></div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        <span class="keyword">delete</span>[] arr[i];</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    }</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <span class="keyword">delete</span>[] arr;</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160; </div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
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+</div>
+</div>
+
+</div>
+</div>
+<a id="afd3f52dd56ddedbf7af5d26a202a199e"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#afd3f52dd56ddedbf7af5d26a202a199e">&#9670;&nbsp;</a></span>pascal_triangle()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int** pascal_triangle </td>
+          <td>(</td>
+          <td class="paramtype">int **&#160;</td>
+          <td class="paramname"><em>arr</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Print the triangle </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in,out]</td><td class="paramname">arr</td><td>array containing Pascal numbers </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>depth of Pascal triangle to print </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>arr pointer returned </dd></dl>
+<div class="fragment"><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;                                        {</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = n - i - 1; j &lt; n + i; ++j) {</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;            <span class="keywordflow">if</span> (j == n - i - 1 || j == n + i - 1)</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;                arr[i][j] = 1;  <span class="comment">// The edge of the Pascal triangle goes in 1</span></div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;            <span class="keywordflow">else</span></div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;                arr[i][j] = arr[i - 1][j - 1] + arr[i - 1][j + 1];</div>
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+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    }</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160; </div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    <span class="keywordflow">return</span> arr;</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ad7a31d9cb2818d21b1ba12aead7f4c5c"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ad7a31d9cb2818d21b1ba12aead7f4c5c">&#9670;&nbsp;</a></span>show_pascal()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void show_pascal </td>
+          <td>(</td>
+          <td class="paramtype">int **&#160;</td>
+          <td class="paramname"><em>arr</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Print the triangle </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">arr</td><td>2D-array containing Pascal numbers </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>depth of Pascal triangle to print </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;                                   {</div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n + i; ++j) {</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;            <span class="keywordflow">if</span> (arr[i][j] == 0)</div>
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+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;        }</div>
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+Here is the call graph for this function:</div>
+<div class="dyncontent">
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+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="apascal__triangle_8cpp_html_afd3f52dd56ddedbf7af5d26a202a199e"><div class="ttname"><a href="../../dc/d1a/pascal__triangle_8cpp.html#afd3f52dd56ddedbf7af5d26a202a199e">pascal_triangle</a></div><div class="ttdeci">int ** pascal_triangle(int **arr, int n)</div><div class="ttdef"><b>Definition:</b> pascal_triangle.cpp:36</div></div>
+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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+    <li class="footer">Generated on Fri Jun 19 2020 16:06:44 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">ordinary_least_squares_regressor.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Linear regression example using <a href="https://en.wikipedia.org/wiki/Ordinary_least_squares">Ordinary least squares</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iomanip&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;vector&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for ordinary_least_squares_regressor.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/d4b/ordinary__least__squares__regressor_8cpp__incl.svg" width="256" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
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+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a98eb5807f21b783c341cab402ced6732"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
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+<tr class="separator:a31be3fe36e76b87d5616ff8e7918cd24"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a67249e31221231cf3aaf3cfd870372d0"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:a67249e31221231cf3aaf3cfd870372d0"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a67249e31221231cf3aaf3cfd870372d0">operator+</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;A, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;B)</td></tr>
+<tr class="separator:a67249e31221231cf3aaf3cfd870372d0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a98ab8f75d981088369b89b8be2182483"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:a98ab8f75d981088369b89b8be2182483"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; float &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a98ab8f75d981088369b89b8be2182483">get_inverse</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;A)</td></tr>
+<tr class="separator:a98ab8f75d981088369b89b8be2182483"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a889f9de199fa793497c864d8e493af05"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:a889f9de199fa793497c864d8e493af05"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a889f9de199fa793497c864d8e493af05">get_transpose</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;A)</td></tr>
+<tr class="separator:a889f9de199fa793497c864d8e493af05"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a38ff1d954e9b7de93eb20e2dd101a045"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:a38ff1d954e9b7de93eb20e2dd101a045"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; float &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a38ff1d954e9b7de93eb20e2dd101a045">fit_OLS_regressor</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;X, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;Y)</td></tr>
+<tr class="separator:a38ff1d954e9b7de93eb20e2dd101a045"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="memitem:a4bcaaf41c66da4d3a471dacef133def7"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; float &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4bcaaf41c66da4d3a471dacef133def7">predict_OLS_regressor</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;X, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; float &gt; const &amp;beta)</td></tr>
+<tr class="separator:a4bcaaf41c66da4d3a471dacef133def7"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Linear regression example using <a href="https://en.wikipedia.org/wiki/Ordinary_least_squares">Ordinary least squares</a> </p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> Program that gets the number of data samples and number of features per sample along with output per sample. It applies OLS regression to compute the regression output for additional test data samples. </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a38ff1d954e9b7de93eb20e2dd101a045"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a38ff1d954e9b7de93eb20e2dd101a045">&#9670;&nbsp;</a></span>fit_OLS_regressor()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;float&gt; fit_OLS_regressor </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
+          <td class="paramname"><em>X</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
+          <td class="paramname"><em>Y</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Perform Ordinary Least Squares curve fit. This operation is defined as </p><p class="formulaDsp">
+\[\beta = \left(X^TXX^T\right)Y\]
+</p>
+ <dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">X</td><td>feature matrix with rows representing sample vector of features </td></tr>
+    <tr><td class="paramname">Y</td><td>known regression value for each sample </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>fitted regression model polynomial coefficients </dd></dl>
+<div class="fragment"><div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;                                                            {</div>
+<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    <span class="comment">// NxF</span></div>
+<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; X2 = X;</div>
+<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; X2.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++)</div>
+<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;        <span class="comment">// add Y-intercept -&gt; Nx(F+1)</span></div>
+<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;        X2[i].push_back(1);</div>
+<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;    <span class="comment">// (F+1)xN</span></div>
+<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; Xt = <a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a889f9de199fa793497c864d8e493af05">get_transpose</a>(X2);</div>
+<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;    <span class="comment">// (F+1)x(F+1)</span></div>
+<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; tmp = <a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a98ab8f75d981088369b89b8be2182483">get_inverse</a>(Xt * X2);</div>
+<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;    <span class="comment">// (F+1)xN</span></div>
+<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; out = tmp * Xt;</div>
+<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;    <span class="comment">// cout &lt;&lt; endl</span></div>
+<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;    <span class="comment">//      &lt;&lt; &quot;Projection matrix: &quot; &lt;&lt; X2 * out &lt;&lt; endl;</span></div>
+<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160; </div>
+<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;    <span class="comment">// Fx1,1    -&gt; (F+1)^th element is the independent constant</span></div>
+<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;    <span class="keywordflow">return</span> out * Y;</div>
+<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d38/ordinary__least__squares__regressor_8cpp_a38ff1d954e9b7de93eb20e2dd101a045_cgraph.svg" width="428" height="164"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a98ab8f75d981088369b89b8be2182483"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a98ab8f75d981088369b89b8be2182483">&#9670;&nbsp;</a></span>get_inverse()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;float&gt; &gt; get_inverse </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
+          <td class="paramname"><em>A</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Get matrix inverse using Row-trasnformations. Given matrix must be a square and non-singular. </p><dl class="section return"><dt>Returns</dt><dd>inverse matrix </dd></dl>
+<div class="fragment"><div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;                                      {</div>
+<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <span class="comment">// Assuming A is square matrix</span></div>
+<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    <span class="keywordtype">size_t</span> N = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160; </div>
+<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; inverse(N);</div>
+<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) {</div>
+<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;        <span class="comment">// preallocatae a resultant identity matrix</span></div>
+<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;        inverse[row] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a>(N);</div>
+<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; N; col++)</div>
+<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;            inverse[row][col] = (row == col) ? 1.f : 0.f;</div>
+<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;    }</div>
+<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160; </div>
+<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    <span class="keywordflow">if</span> (!<a class="code" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4921874435266592b222e3f2eda0e01f">is_square</a>(A)) {</div>
+<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;A must be a square matrix!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;        <span class="keywordflow">return</span> inverse;</div>
+<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;    }</div>
+<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160; </div>
+<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;    <span class="comment">// preallocatae a temporary matrix identical to A</span></div>
+<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;float&gt;</a>&gt; temp(N);</div>
+<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) {</div>
+<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> v(N);</div>
+<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; N; col++)</div>
+<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;            v[col] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(A[row][col]);</div>
+<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;        temp[row] = v;</div>
+<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;    }</div>
+<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160; </div>
+<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;    <span class="comment">// start transformations</span></div>
+<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) {</div>
+<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = row; row2 &lt; N &amp;&amp; temp[row][row] == 0; row2++) {</div>
+<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;            <span class="comment">// this to ensure diagonal elements are not 0</span></div>
+<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;            temp[row] = temp[row] + temp[row2];</div>
+<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;            inverse[row] = inverse[row] + inverse[row2];</div>
+<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;        }</div>
+<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160; </div>
+<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col2 = row; col2 &lt; N &amp;&amp; temp[row][row] == 0; col2++) {</div>
+<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;            <span class="comment">// this to further ensure diagonal elements are not 0</span></div>
+<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; N; row2++) {</div>
+<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;                temp[row2][row] = temp[row2][row] + temp[row2][col2];</div>
+<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;                inverse[row2][row] = inverse[row2][row] + inverse[row2][col2];</div>
+<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;            }</div>
+<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;        }</div>
+<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160; </div>
+<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;        <span class="keywordflow">if</span> (temp[row][row] == 0) {</div>
+<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;            <span class="comment">// Probably a low-rank matrix and hence singular</span></div>
+<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;            <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Low-rank matrix, no inverse!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;            <span class="keywordflow">return</span> inverse;</div>
+<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;        }</div>
+<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160; </div>
+<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;        <span class="comment">// set diagonal to 1</span></div>
+<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;        <span class="keywordtype">float</span> divisor = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(temp[row][row]);</div>
+<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;        temp[row] = temp[row] / divisor;</div>
+<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;        inverse[row] = inverse[row] / divisor;</div>
+<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;        <span class="comment">// Row transformations</span></div>
+<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row2 = 0; row2 &lt; N; row2++) {</div>
+<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;            <span class="keywordflow">if</span> (row2 == row)</div>
+<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;                <span class="keywordflow">continue</span>;</div>
+<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;            <span class="keywordtype">float</span> factor = temp[row2][row];</div>
+<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;            temp[row2] = temp[row2] - factor * temp[row];</div>
+<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;            inverse[row2] = inverse[row2] - factor * inverse[row];</div>
+<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;        }</div>
+<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;    }</div>
+<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160; </div>
+<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;    <span class="keywordflow">return</span> inverse;</div>
+<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d38/ordinary__least__squares__regressor_8cpp_a98ab8f75d981088369b89b8be2182483_cgraph.svg" width="227" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a889f9de199fa793497c864d8e493af05"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a889f9de199fa793497c864d8e493af05">&#9670;&nbsp;</a></span>get_transpose()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;T&gt; &gt; get_transpose </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
+          <td class="paramname"><em>A</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>matrix transpose </p><dl class="section return"><dt>Returns</dt><dd>resultant matrix </dd></dl>
+<div class="fragment"><div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;                                      {</div>
+<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; result(A[0].size());</div>
+<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160; </div>
+<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; A[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); row++) {</div>
+<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> v(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>());</div>
+<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); col++) v[col] = A[col][row];</div>
+<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160; </div>
+<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;        result[row] = v;</div>
+<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    }</div>
+<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;    <span class="keywordflow">return</span> result;</div>
+<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a4921874435266592b222e3f2eda0e01f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a4921874435266592b222e3f2eda0e01f">&#9670;&nbsp;</a></span>is_square()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool is_square </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
+          <td class="paramname"><em>A</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>function to check if given matrix is a square matrix </p><dl class="section return"><dt>Returns</dt><dd>1 if true, 0 if false </dd></dl>
+<div class="fragment"><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;                                                        {</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="comment">// Assuming A is square matrix</span></div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keywordtype">size_t</span> N = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; N; i++)</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        <span class="keywordflow">if</span> (A[i].size() != N)</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;           {</div>
+<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;    <span class="keywordtype">size_t</span> N, F;</div>
+<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160; </div>
+<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of features: &quot;</span>;</div>
+<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;    <span class="comment">// number of features = columns</span></div>
+<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; F;</div>
+<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter number of samples: &quot;</span>;</div>
+<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;    <span class="comment">// number of samples = rows</span></div>
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+<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d38/ordinary__least__squares__regressor_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="555" height="190"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a9b2b5da35a6ba8ae203c33739ef0b91d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a9b2b5da35a6ba8ae203c33739ef0b91d">&#9670;&nbsp;</a></span>operator*() <span class="overload">[1/4]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;float&gt; operator* </td>
+          <td>(</td>
+          <td class="paramtype">float const&#160;</td>
+          <td class="paramname"><em>scalar</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
+          <td class="paramname"><em>A</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>pre-multiplication of a vector by a scalar </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
+<div class="fragment"><div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                                                                      {</div>
+<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    <span class="comment">// Number of rows in A</span></div>
+<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    <span class="keywordtype">size_t</span> N_A = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160; </div>
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+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160; </div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;        result[row] += A[row] * <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(scalar);</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    }</div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160; </div>
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+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d38/ordinary__least__squares__regressor_8cpp_a9b2b5da35a6ba8ae203c33739ef0b91d_cgraph.svg" width="250" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ab6171f4db68a5e50ae0f3500a63acd26"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ab6171f4db68a5e50ae0f3500a63acd26">&#9670;&nbsp;</a></span>operator*() <span class="overload">[2/4]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;T&gt; &gt; operator* </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
+          <td class="paramname"><em>B</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Matrix multiplication such that if A is size (mxn) and B is of size (pxq) then the multiplication is defined only when n = p and the resultant matrix is of size (mxq)</p>
+<dl class="section return"><dt>Returns</dt><dd>resultant matrix </dd></dl>
+<div class="fragment"><div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;                                                                        {</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="comment">// Number of rows in A</span></div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    <span class="keywordtype">size_t</span> N_A = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    <span class="comment">// Number of columns in B</span></div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <span class="keywordtype">size_t</span> N_B = B[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160; </div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a>&gt; result(N_A);</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160; </div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <span class="keywordflow">if</span> (A[0].size() != B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {</div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Number of columns in A != Number of rows in B (&quot;</span></div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;                  &lt;&lt; A[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        <span class="keywordflow">return</span> result;</div>
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+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160; </div>
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+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> v(N_B);</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; N_B; col++) {</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;            v[col] = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(0);</div>
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+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d38/ordinary__least__squares__regressor_8cpp_ab6171f4db68a5e50ae0f3500a63acd26_cgraph.svg" width="206" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#a64d9dd5c5816d6d907b00e5f4b0372a5">&#9670;&nbsp;</a></span>operator*() <span class="overload">[3/4]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;T&gt; operator* </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
+          <td class="paramname"><em>B</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
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+      </table>
+</div><div class="memdoc">
+<p>multiplication of a matrix with a column vector </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
+<div class="fragment"><div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                                                {</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <span class="comment">// Number of rows in A</span></div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    <span class="keywordtype">size_t</span> N_A = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160; </div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> result(N_A);</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160; </div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <span class="keywordflow">if</span> (A[0].size() != B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) {</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Number of columns in A != Number of rows in B (&quot;</span></div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;                  &lt;&lt; A[0].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;&lt; <span class="stringliteral">&quot;)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        <span class="keywordflow">return</span> result;</div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    }</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160; </div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++) {</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;        result[row] = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(0);</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); j++) result[row] += A[row][j] * B[j];</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    }</div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160; </div>
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+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d38/ordinary__least__squares__regressor_8cpp_a64d9dd5c5816d6d907b00e5f4b0372a5_cgraph.svg" width="250" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="aecef32c2a4f39a3f7398949256d180a6"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aecef32c2a4f39a3f7398949256d180a6">&#9670;&nbsp;</a></span>operator*() <span class="overload">[4/4]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;float&gt; operator* </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">float const&#160;</td>
+          <td class="paramname"><em>scalar</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>post-multiplication of a vector by a scalar </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
+<div class="fragment"><div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;                                                                      {</div>
+<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    <span class="comment">// Number of rows in A</span></div>
+<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="keywordtype">size_t</span> N_A = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160; </div>
+<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> result(N_A);</div>
+<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160; </div>
+<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N_A; row++)</div>
+<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        result[row] = A[row] * <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(scalar);</div>
+<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160; </div>
+<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    <span class="keywordflow">return</span> result;</div>
+<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d38/ordinary__least__squares__regressor_8cpp_aecef32c2a4f39a3f7398949256d180a6_cgraph.svg" width="250" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a67249e31221231cf3aaf3cfd870372d0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a67249e31221231cf3aaf3cfd870372d0">&#9670;&nbsp;</a></span>operator+()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;T&gt; operator+ </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
+          <td class="paramname"><em>B</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>addition of two vectors of identical lengths </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
+<div class="fragment"><div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;                                                                     {</div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    <span class="comment">// Number of rows in A</span></div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;    <span class="keywordtype">size_t</span> N = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160; </div>
+<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> result(N);</div>
+<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160; </div>
+<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    <span class="keywordflow">if</span> (B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != N) {</div>
+<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Vector dimensions shouldbe identical!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;        <span class="keywordflow">return</span> A;</div>
+<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    }</div>
+<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160; </div>
+<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) result[row] = A[row] + B[row];</div>
+<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160; </div>
+<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;    <span class="keywordflow">return</span> result;</div>
+<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d38/ordinary__least__squares__regressor_8cpp_a67249e31221231cf3aaf3cfd870372d0_cgraph.svg" width="252" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a31be3fe36e76b87d5616ff8e7918cd24"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a31be3fe36e76b87d5616ff8e7918cd24">&#9670;&nbsp;</a></span>operator-()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;T&gt; operator- </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
+          <td class="paramname"><em>B</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>subtraction of two vectors of identical lengths </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
+<div class="fragment"><div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;                                                                     {</div>
+<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <span class="comment">// Number of rows in A</span></div>
+<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    <span class="keywordtype">size_t</span> N = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160; </div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> result(N);</div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160; </div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    <span class="keywordflow">if</span> (B.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() != N) {</div>
+<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Vector dimensions shouldbe identical!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;        <span class="keywordflow">return</span> A;</div>
+<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    }</div>
+<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160; </div>
+<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; N; row++) result[row] = A[row] - B[row];</div>
+<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160; </div>
+<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    <span class="keywordflow">return</span> result;</div>
+<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d38/ordinary__least__squares__regressor_8cpp_a31be3fe36e76b87d5616ff8e7918cd24_cgraph.svg" width="248" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a30acf52af3184bc22274234ef5a73536"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a30acf52af3184bc22274234ef5a73536">&#9670;&nbsp;</a></span>operator/()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;float&gt; operator/ </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">float const&#160;</td>
+          <td class="paramname"><em>scalar</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>division of a vector by a scalar </p><dl class="section return"><dt>Returns</dt><dd>resultant vector </dd></dl>
+<div class="fragment"><div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;                                                                      {</div>
+<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    <span class="keywordflow">return</span> (1.<a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a> / scalar) * A;</div>
+<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a98eb5807f21b783c341cab402ced6732"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a98eb5807f21b783c341cab402ced6732">&#9670;&nbsp;</a></span>operator&lt;&lt;() <span class="overload">[1/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a>&amp; operator&lt;&lt; </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;&#160;</td>
+          <td class="paramname"><em>out</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
+          <td class="paramname"><em>v</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>operator to print a matrix </p>
+<div class="fragment"><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;                                                           {</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
+<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
+<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160; </div>
+<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++) {</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; v[row].size(); col++)</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;            out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;                &lt;&lt; v[row][col];</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;        out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    }</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160; </div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="keywordflow">return</span> out;</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
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+<h2 class="memtitle"><span class="permalink"><a href="#aa799b4cec1681219887d89d037cfab50">&#9670;&nbsp;</a></span>operator&lt;&lt;() <span class="overload">[2/2]</span></h2>
+
+<div class="memitem">
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+template&lt;typename T &gt; </div>
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+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a>&amp; operator&lt;&lt; </td>
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+          <td class="paramkey"></td>
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+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; const &amp;&#160;</td>
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+<p>operator to print a vector </p>
+<div class="fragment"><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;                                                               {</div>
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+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;            &lt;&lt; v[row];</div>
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+<p>Given data and OLS model coeffficients, predict regression estimates. This operation is defined as </p><p class="formulaDsp">
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+</p>
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+    <tr><td class="paramname">beta</td><td>fitted regression model </td></tr>
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">text_search.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Search for words in a long textual paragraph.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cstdlib&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;cstring&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/db5/text__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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+<div class="memitem">
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+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
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+<p>Main function </p>
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+<a href="#define-members">Macros</a> &#124;
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">paranthesis_matching.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Perform paranthesis matching.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;cstring&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for paranthesis_matching.cpp:</div>
+<div class="dyncontent">
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+void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/dc5/paranthesis__matching_8cpp.html#aae41c72130114bf31204cde6873b6095">push</a> (char ch)</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Perform paranthesis matching. </p>
+<dl class="section note"><dt>Note</dt><dd>Do not know the application of this, however. </dd>
+<dd>
+Implementation is C-type and does not utilize the C++ constructs </dd></dl>
+<dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000005">Todo:</a></b></dt><dd>implement as a C++ class </dd></dl>
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+<h2 class="memtitle"><span class="permalink"><a href="#a392fb874e547e582e9c66a08a1f23326">&#9670;&nbsp;</a></span>MAX</h2>
+
+<div class="memitem">
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+          <td class="memname">#define MAX&#160;&#160;&#160;100</td>
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+<p>check number </p>
+
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+<a id="ade525d33459755a32ba21e1b6910ff21"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ade525d33459755a32ba21e1b6910ff21">&#9670;&nbsp;</a></span>opening()</h2>
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+          <td>(</td>
+          <td class="paramtype">char&#160;</td>
+          <td class="paramname"><em>ch</em></td><td>)</td>
+          <td></td>
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+<p>return opening paranthesis corresponding to the close paranthesis </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">ch</td><td>closed paranthesis character </td></tr>
+  </table>
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+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;        <span class="keywordflow">return</span> <span class="charliteral">&#39;[&#39;</span>;</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    <span class="keywordflow">case</span> <span class="charliteral">&#39;)&#39;</span>:</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        <span class="keywordflow">return</span> <span class="charliteral">&#39;(&#39;</span>;</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#aa37d24a036d239b3b528f13b9de880c7">&#9670;&nbsp;</a></span>stack</h2>
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+<tr class="memitem:a7f7d866eccdabe51bb16818a792618b1"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/dfe/ternary__search_8cpp.html#a7f7d866eccdabe51bb16818a792618b1">get_input</a> ()</td></tr>
+<tr class="separator:a7f7d866eccdabe51bb16818a792618b1"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae30dfe2894191bfeffe5b3b1854b95b0"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/dfe/ternary__search_8cpp.html#ae30dfe2894191bfeffe5b3b1854b95b0">it_ternary_search</a> (int left, int right, int A[], int target)</td></tr>
+<tr class="separator:ae30dfe2894191bfeffe5b3b1854b95b0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a93d0099db95022f1eb90ddfd68f73ead"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/dfe/ternary__search_8cpp.html#a93d0099db95022f1eb90ddfd68f73ead">rec_ternary_search</a> (int left, int right, int A[], int target)</td></tr>
+<tr class="separator:a93d0099db95022f1eb90ddfd68f73ead"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aef655a27eb82efa299bf9d0becf6e9c8"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/dfe/ternary__search_8cpp.html#aef655a27eb82efa299bf9d0becf6e9c8">ternary_search</a> (int N, int A[], int target)</td></tr>
+<tr class="separator:aef655a27eb82efa299bf9d0becf6e9c8"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/dfe/ternary__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Ternary_search">Ternary search</a> algorithm </p>
+<p>This is a divide and conquer algorithm. It does this by dividing the search space by 3 parts and using its property (usually monotonic property) to find the desired index.</p>
+<ul>
+<li>Time Complexity : O(log3 n)</li>
+<li>Space Complexity : O(1) (without the array) </li>
+</ul>
+</div><h2 class="groupheader">Macro Definition Documentation</h2>
+<a id="a23ad617bfce1e7cf4591059c85c1a027"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a23ad617bfce1e7cf4591059c85c1a027">&#9670;&nbsp;</a></span>_target</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">#define _target&#160;&#160;&#160;10</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>The value of _target should be decided or can be decided later by using the variable of the function. </p>
+
+</div>
+</div>
+<a id="ae01eda5098801bb6b5b778828fb4fddc"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae01eda5098801bb6b5b778828fb4fddc">&#9670;&nbsp;</a></span>absolutePrecision</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">#define absolutePrecision&#160;&#160;&#160;10</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>The absolutePrecision can be modified to fit preference but it is recommended to not go lower than 10 due to errors that may occur. </p>
+
+</div>
+</div>
+<h2 class="groupheader">Function Documentation</h2>
+<a id="a7f7d866eccdabe51bb16818a792618b1"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a7f7d866eccdabe51bb16818a792618b1">&#9670;&nbsp;</a></span>get_input()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void get_input </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>get_input function is to receive input from standard IO </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000010">Todo:</a></b></dt><dd>@christianbender Get input from STDIO or write input to memory as done above. </dd></dl>
+<div class="fragment"><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;{}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae30dfe2894191bfeffe5b3b1854b95b0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae30dfe2894191bfeffe5b3b1854b95b0">&#9670;&nbsp;</a></span>it_ternary_search()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int it_ternary_search </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>left</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>right</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>A</em>[], </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>target</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>This is the iterative method of the ternary search which returns the index of the element. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">left</td><td>lower interval limit </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">right</td><td>upper interval limit </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>array to search in </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">target</td><td>value to search for </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>index where the target value was found </dd>
+<dd>
+-1 if target value not found </dd></dl>
+<div class="fragment"><div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;                                                                {</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    <span class="keywordflow">while</span> (1) {</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        <span class="keywordflow">if</span> (left &lt; right) {</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;            <span class="keywordflow">if</span> (right - left &lt; <a class="code" href="../../dc/dfe/ternary__search_8cpp.html#ae01eda5098801bb6b5b778828fb4fddc">absolutePrecision</a>) {</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = left; i &lt;= <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>; i++)</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;                    <span class="keywordflow">if</span> (A[i] == target)</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;                        <span class="keywordflow">return</span> i;</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160; </div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;                <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;            }</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160; </div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;            <span class="keywordtype">int</span> oneThird = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> + <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>) / 3 + 1;</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;            <span class="keywordtype">int</span> twoThird = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> + <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>) * 2 / 3 + 1;</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160; </div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;            <span class="keywordflow">if</span> (A[oneThird] == target)</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;                <span class="keywordflow">return</span> oneThird;</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (A[twoThird] == target)</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;                <span class="keywordflow">return</span> twoThird;</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160; </div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (target &gt; A[twoThird])</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;                <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = twoThird + 1;</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (target &lt; A[oneThird])</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;                <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = oneThird - 1;</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160; </div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;            <span class="keywordflow">else</span></div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;                <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> = oneThird + 1, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> = twoThird - 1;</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;            <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        }</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    }</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;           {</div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    <span class="keywordtype">int</span> N = 21;</div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    <span class="keywordtype">int</span> A[] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 10};</div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    <a class="code" href="../../dc/dfe/ternary__search_8cpp.html#a7f7d866eccdabe51bb16818a792618b1">get_input</a>();</div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    <a class="code" href="../../dc/dfe/ternary__search_8cpp.html#aef655a27eb82efa299bf9d0becf6e9c8">ternary_search</a>(N, A, <a class="code" href="../../dc/dfe/ternary__search_8cpp.html#a23ad617bfce1e7cf4591059c85c1a027">_target</a>);</div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/dfe/ternary__search_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="399" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a93d0099db95022f1eb90ddfd68f73ead"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a93d0099db95022f1eb90ddfd68f73ead">&#9670;&nbsp;</a></span>rec_ternary_search()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int rec_ternary_search </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>left</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>right</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>A</em>[], </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>target</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>This is the recursive method of the ternary search which returns the index of the element. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">left</td><td>lower interval limit </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">right</td><td>upper interval limit </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>array to search in </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">target</td><td>value to search for </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>index where the target value was found </dd>
+<dd>
+-1 if target value not found </dd></dl>
+<div class="fragment"><div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;                                                                 {</div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <span class="keywordflow">if</span> (left &lt; right) {</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        <span class="keywordflow">if</span> (right - left &lt; <a class="code" href="../../dc/dfe/ternary__search_8cpp.html#ae01eda5098801bb6b5b778828fb4fddc">absolutePrecision</a>) {</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = left; i &lt;= <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>; i++)</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;                <span class="keywordflow">if</span> (A[i] == target)</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;                    <span class="keywordflow">return</span> i;</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160; </div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;            <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        }</div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160; </div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;        <span class="keywordtype">int</span> oneThird = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> + <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>) / 3 + 1;</div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;        <span class="keywordtype">int</span> twoThird = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a> + <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>) * 2 / 3 + 1;</div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160; </div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;        <span class="keywordflow">if</span> (A[oneThird] == target)</div>
+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;            <span class="keywordflow">return</span> oneThird;</div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;        <span class="keywordflow">if</span> (A[twoThird] == target)</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;            <span class="keywordflow">return</span> twoThird;</div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160; </div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;        <span class="keywordflow">if</span> (target &lt; A[oneThird])</div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;            <span class="keywordflow">return</span> <a class="code" href="../../dc/dfe/ternary__search_8cpp.html#a93d0099db95022f1eb90ddfd68f73ead">rec_ternary_search</a>(left, oneThird - 1, A, target);</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;        <span class="keywordflow">if</span> (target &gt; A[twoThird])</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;            <span class="keywordflow">return</span> <a class="code" href="../../dc/dfe/ternary__search_8cpp.html#a93d0099db95022f1eb90ddfd68f73ead">rec_ternary_search</a>(twoThird + 1, right, A, target);</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160; </div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../dc/dfe/ternary__search_8cpp.html#a93d0099db95022f1eb90ddfd68f73ead">rec_ternary_search</a>(oneThird + 1, twoThird - 1, A, target);</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    }</div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="aef655a27eb82efa299bf9d0becf6e9c8"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aef655a27eb82efa299bf9d0becf6e9c8">&#9670;&nbsp;</a></span>ternary_search()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void ternary_search </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>N</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>A</em>[], </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>target</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
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+<p>ternary_search is a template function You could either use it_ternary_search or rec_ternary_search according to preference. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">N</td><td>length of array </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>array to search in </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">target</td><td>value to search for </td></tr>
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+  </dd>
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+Public Attributes</h2></td></tr>
+<tr class="memitem:aedd873fb96eb4f83fb4289b1c58ce794"><td class="memItemLeft" align="right" valign="top"><a id="aedd873fb96eb4f83fb4289b1c58ce794"></a>
+int&#160;</td><td class="memItemRight" valign="bottom"><b>l</b></td></tr>
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+<tr class="memitem:a748f5dfd8faf440897bab39091f0a5ca"><td class="memItemLeft" align="right" valign="top"><a id="a748f5dfd8faf440897bab39091f0a5ca"></a>
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+int&#160;</td><td class="memItemRight" valign="bottom"><b>i</b></td></tr>
+<tr class="separator:a1442afb70f26fd0655914632c0dcadcd"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<hr/>The documentation for this struct was generated from the following file:<ul>
+<li>range_queries/mo.cpp</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
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+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+   <div id="projectname">Algorithms_in_C++
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+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+<div class="header">
+  <div class="summary">
+<a href="#define-members">Macros</a> &#124;
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">false_position.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Regula_falsi">false position method</a>, also known as the Secant method.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;cstdlib&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;limits&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for false_position.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/de2/false__position_8cpp__incl.svg" width="328" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="define-members"></a>
+Macros</h2></td></tr>
+<tr class="memitem:a002b2f4894492820fe708b1b7e7c5e70"><td class="memItemLeft" align="right" valign="top"><a id="a002b2f4894492820fe708b1b7e7c5e70"></a>
+#define&#160;</td><td class="memItemRight" valign="bottom"><b>EPSILON</b>&#160;&#160;&#160;1e-6</td></tr>
+<tr class="separator:a002b2f4894492820fe708b1b7e7c5e70"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a0a3abbca80bc98e7abcb3ae73abe0f14"><td class="memItemLeft" align="right" valign="top"><a id="a0a3abbca80bc98e7abcb3ae73abe0f14"></a>
+#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>&#160;&#160;&#160;50000</td></tr>
+<tr class="memdesc:a0a3abbca80bc98e7abcb3ae73abe0f14"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum number of iterations to check. <br /></td></tr>
+<tr class="separator:a0a3abbca80bc98e7abcb3ae73abe0f14"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a2003b5b2dcfff0769b957ab5c968b03d"><td class="memItemLeft" align="right" valign="top">static double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a> (double i)</td></tr>
+<tr class="separator:a2003b5b2dcfff0769b957ab5c968b03d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a1ab31b90bc584c635ec159468ceed9b2"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:a1ab31b90bc584c635ec159468ceed9b2"><td class="memTemplItemLeft" align="right" valign="top">int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a> (T val)</td></tr>
+<tr class="separator:a1ab31b90bc584c635ec159468ceed9b2"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Regula_falsi">false position method</a>, also known as the Secant method. </p>
+<p>Given two points \(a\) and \(b\) such that \(f(a)&lt;0\) and \(f(b)&gt;0\), then the \((i+1)^\text{th}\) approximation is given by: </p><p class="formulaDsp">
+\[ x_{i+1} = \frac{a_i\cdot f(b_i) - b_i\cdot f(a_i)}{f(b_i) - f(a_i)} \]
+</p>
+<p> For the next iteration, the interval is selected as: \([a,x]\) if \(x&gt;0\) or \([x,b]\) if \(x&lt;0\). The Process is continued till a close enough approximation is achieved.</p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/dd3/newton__raphson__method_8cpp.html" title="Solve the equation  using Newton-Raphson method for both real and complex solutions.">newton_raphson_method.cpp</a>, <a class="el" href="../../d7/d6a/bisection__method_8cpp.html" title="Solve the equation  using bisection method">bisection_method.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a2003b5b2dcfff0769b957ab5c968b03d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a2003b5b2dcfff0769b957ab5c968b03d">&#9670;&nbsp;</a></span>eq()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">static double eq </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>i</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">static</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>define \(f(x)\) to find root for </p>
+<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;                           {</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <span class="keywordflow">return</span> (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i, 3) - (4 * i) - 9);  <span class="comment">// origial equation</span></div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d29/false__position_8cpp_a2003b5b2dcfff0769b957ab5c968b03d_cgraph.svg" width="170" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;           {</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <span class="keywordtype">double</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = -1, b = 1, x, z, m, n, c;</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keywordtype">int</span> i;</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160; </div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <span class="comment">// loop to find initial intervals a, b</span></div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code" href="../../dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;        z = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>);</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        x = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(b);</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;        <span class="keywordflow">if</span> (<a class="code" href="../../dd/d29/false__position_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(z) == <a class="code" href="../../dd/d29/false__position_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(x)) {  <span class="comment">// same signs, increase interval</span></div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;            b++;</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;            <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>--;</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        } <span class="keywordflow">else</span> {  <span class="comment">// if opposite signs, we got our interval</span></div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;            <span class="keywordflow">break</span>;</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;        }</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    }</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160; </div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nFirst initial: &quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nSecond initial: &quot;</span> &lt;&lt; b;</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160; </div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code" href="../../dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        m = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>);</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        n = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(b);</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160; </div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        c = ((<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> * n) - (b * m)) / (n - m);</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160; </div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = c;</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        z = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(c);</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160; </div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;        <span class="keywordflow">if</span> (std::abs(z) &lt; EPSILON) {  <span class="comment">// stoping criteria</span></div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;            <span class="keywordflow">break</span>;</div>
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+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
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+<div class="header">
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+<a href="#nested-classes">Classes</a> &#124;
+<a href="#pub-methods">Public Member Functions</a> &#124;
+<a href="#pri-methods">Private Member Functions</a> &#124;
+<a href="#pri-static-methods">Static Private Member Functions</a> &#124;
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+<a href="#pri-static-attribs">Static Private Attributes</a> &#124;
+<a href="../../de/d8a/class_trie-members.html">List of all members</a>  </div>
+  <div class="headertitle">
+<div class="title">Trie Class Reference</div>  </div>
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+<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d48/struct_trie_1_1_trie_node.html">TrieNode</a></td></tr>
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+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
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+<tr class="memitem:afd8b79959009b554e98ea7128b2886f2"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d2f/class_trie.html#afd8b79959009b554e98ea7128b2886f2">insert</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;word)</td></tr>
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+<tr class="memitem:a6d10eb1669453395d1900ebd401954fb"><td class="memItemLeft" align="right" valign="top">static bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d2f/class_trie.html#a6d10eb1669453395d1900ebd401954fb">hasChildren</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a>&lt; <a class="el" href="../../de/d48/struct_trie_1_1_trie_node.html">TrieNode</a> &gt; <a class="el" href="../../d5/da1/structnode.html">node</a>)</td></tr>
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+<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a>&lt; <a class="el" href="../../de/d48/struct_trie_1_1_trie_node.html">TrieNode</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>m_root</b></td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>A basic implementation of trie class to store only lower-case strings. You can extend the implementation to all the ASCII characters by changing the value of @ ALPHABETS to 128. </p>
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+          <td>(</td>
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+<p>Function to check if a node has some children which can form words. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">node</td><td>whose character array of pointers need to be checked for children. </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><code>true</code> if a child is found </dd>
+<dd>
+<code>false</code> if a child is not found </dd></dl>
+<div class="fragment"><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;                                                                 {</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; ALPHABETS; i++) {</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;            <span class="keywordflow">if</span> (<a class="code" href="../../d5/da1/structnode.html">node</a>-&gt;character[i]) {</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;            }</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        }</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="afd8b79959009b554e98ea7128b2886f2"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#afd8b79959009b554e98ea7128b2886f2">&#9670;&nbsp;</a></span>insert()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">void Trie::insert </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>word</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Insert a word into the trie. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">word</td><td>which needs to be inserted into the string. </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;                                       {</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;        <span class="keyword">auto</span> curr = m_root;</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">char</span> ch : word) {</div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;            <span class="keywordtype">size_t</span> index = ch - <span class="charliteral">&#39;a&#39;</span>;</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160; </div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;            <span class="comment">// if a node for current word is not already present in trie, create</span></div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;            <span class="comment">// a new node for it.</span></div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;            <span class="keywordflow">if</span> (!curr-&gt;character[index]) {</div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;                curr-&gt;character[index] = std::make_shared&lt;TrieNode&gt;();</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;            }</div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160; </div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;            curr = curr-&gt;character[index];</div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;        }</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        curr-&gt;isEndOfWord = <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a95216ffc56cb9f8cede982cecb872af4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a95216ffc56cb9f8cede982cecb872af4">&#9670;&nbsp;</a></span>removeWordHelper()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a>&lt;<a class="el" href="../../de/d48/struct_trie_1_1_trie_node.html">TrieNode</a>&gt; Trie::removeWordHelper </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>word</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a>&lt; <a class="el" href="../../de/d48/struct_trie_1_1_trie_node.html">TrieNode</a> &gt;&#160;</td>
+          <td class="paramname"><em>curr</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">size_t&#160;</td>
+          <td class="paramname"><em>index</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">private</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>A recursive helper function to remove a word from the trie. First, it recursively traverses to the location of last character of word in the trie. However, if the word is not found, the function returns a runtime error. Upon successfully reaching the last character of word in trie, if sets the isEndOfWord to false and deletes the node if and only if it has no children, else it returns the current node. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">word</td><td>is the string which needs to be removed from trie. </td></tr>
+    <tr><td class="paramname">curr</td><td>is the current node we are at. </td></tr>
+    <tr><td class="paramname">index</td><td>is the index of the @word we are at. </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>if current node has childern, it returns @ curr, else it returns nullptr. </dd></dl>
+<dl class="exception"><dt>Exceptions</dt><dd>
+  <table class="exception">
+    <tr><td class="paramname">a</td><td>runtime error in case @ word is not found in the trie. </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;                                                             {</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;        <span class="keywordflow">if</span> (word.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>() == index) {</div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;            <span class="keywordflow">if</span> (curr-&gt;isEndOfWord) {</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;                curr-&gt;isEndOfWord = <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;            }</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;            <span class="keywordflow">if</span> (<a class="code" href="../../dd/d2f/class_trie.html#a6d10eb1669453395d1900ebd401954fb">hasChildren</a>(curr)) {</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;                <span class="keywordflow">return</span> curr;</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;            }</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        }</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160; </div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        <span class="keywordtype">size_t</span> idx = word[index] - <span class="charliteral">&#39;a&#39;</span>;</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160; </div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        <span class="comment">// Throw a runtime error in case the user enters a word which is not</span></div>
+<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;        <span class="comment">// present in the trie.</span></div>
+<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;        <span class="keywordflow">if</span> (!curr-&gt;character[idx]) {</div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;            <span class="keywordflow">throw</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/runtime_error.html">std::runtime_error</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;Word not found.&quot;</span>)));</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        }</div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160; </div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;        curr-&gt;character[idx] =</div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;            <a class="code" href="../../dd/d2f/class_trie.html#a95216ffc56cb9f8cede982cecb872af4">removeWordHelper</a>(word, curr-&gt;character[idx], index + 1);</div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160; </div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;        <span class="comment">// This if condition checks if the node has some childern.</span></div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        <span class="comment">// The 1st if check, i.e. (curr-&gt;character[idx]) is checked specifically</span></div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        <span class="comment">// because if the older string is a prefix of some other string, then,</span></div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        <span class="comment">// there would be no need to check all 26 characters. Example- str1 =</span></div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        <span class="comment">// abbey, str2 = abbex and we want to delete string &quot;abbey&quot;, then in</span></div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;        <span class="comment">// this case, there would be no need to check all characters for the</span></div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;        <span class="comment">// chars a,b,b.</span></div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;        <span class="keywordflow">if</span> (curr-&gt;character[idx] || <a class="code" href="../../dd/d2f/class_trie.html#a6d10eb1669453395d1900ebd401954fb">hasChildren</a>(curr)) {</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;            <span class="keywordflow">return</span> curr;</div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        }</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    }</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d2f/class_trie_a95216ffc56cb9f8cede982cecb872af4_cgraph.svg" width="343" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a411e77126930a0942dd7b65e96b15206"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a411e77126930a0942dd7b65e96b15206">&#9670;&nbsp;</a></span>search()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
+        <tr>
+          <td class="memname">bool Trie::search </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>word</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">inline</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>Search if a word is present in trie or not. </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">word</td><td>which is needed to be searched in the trie. </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>True if the word is found in trie and isEndOfWord is set to true. </dd>
+<dd>
+False if word is not found in trie or isEndOfWord is set to false. </dd></dl>
+<div class="fragment"><div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;                                       {</div>
+<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;        <span class="keyword">auto</span> curr = m_root;</div>
+<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">char</span> ch : word) {</div>
+<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;            <span class="keywordtype">size_t</span> index = ch - <span class="charliteral">&#39;a&#39;</span>;</div>
+<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160; </div>
+<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;            <span class="comment">// if any node for a character is not found, then return that the</span></div>
+<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;            <span class="comment">// word cannot be formed.</span></div>
+<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;            <span class="keywordflow">if</span> (!curr-&gt;character[index]) {</div>
+<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;                <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;            }</div>
+<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;            curr = curr-&gt;character[index];</div>
+<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;        }</div>
+<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;        <span class="keywordflow">return</span> curr-&gt;isEndOfWord;</div>
+<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    }</div>
+</div><!-- fragment -->
+</div>
+</div>
+<hr/>The documentation for this class was generated from the following file:<ul>
+<li>data_structures/<a class="el" href="../../dc/d93/trie__modern_8cpp.html">trie_modern.cpp</a></li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="amove_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/move.html">std::move</a></div><div class="ttdeci">T move(T... args)</div></div>
+<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::size</a></div><div class="ttdeci">T size(T... args)</div></div>
+<div class="ttc" id="aclass_trie_html_a6d10eb1669453395d1900ebd401954fb"><div class="ttname"><a href="../../dd/d2f/class_trie.html#a6d10eb1669453395d1900ebd401954fb">Trie::hasChildren</a></div><div class="ttdeci">static bool hasChildren(std::shared_ptr&lt; TrieNode &gt; node)</div><div class="ttdef"><b>Definition:</b> trie_modern.cpp:41</div></div>
+<div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
+<div class="ttc" id="aruntime_error_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/runtime_error.html">std::runtime_error</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="aclass_trie_html_a95216ffc56cb9f8cede982cecb872af4"><div class="ttname"><a href="../../dd/d2f/class_trie.html#a95216ffc56cb9f8cede982cecb872af4">Trie::removeWordHelper</a></div><div class="ttdeci">std::shared_ptr&lt; TrieNode &gt; removeWordHelper(const std::string &amp;word, std::shared_ptr&lt; TrieNode &gt; curr, size_t index)</div><div class="ttdef"><b>Definition:</b> trie_modern.cpp:64</div></div>
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="navelem"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></li>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
diff --git a/dd/d2f/class_trie.js b/dd/d2f/class_trie.js
new file mode 100644
index 000000000..2661e64da
--- /dev/null
+++ b/dd/d2f/class_trie.js
@@ -0,0 +1,12 @@
+var class_trie =
+[
+    [ "TrieNode", "de/d48/struct_trie_1_1_trie_node.html", "de/d48/struct_trie_1_1_trie_node" ],
+    [ "Trie", "dd/d2f/class_trie.html#a6af57e9f25d0d0a2d59eea5a4a802908", null ],
+    [ "hasChildren", "dd/d2f/class_trie.html#a6d10eb1669453395d1900ebd401954fb", null ],
+    [ "insert", "dd/d2f/class_trie.html#afd8b79959009b554e98ea7128b2886f2", null ],
+    [ "removeWord", "dd/d2f/class_trie.html#a734a08b52b8ad73bdd1f36ae8348056e", null ],
+    [ "removeWordHelper", "dd/d2f/class_trie.html#a95216ffc56cb9f8cede982cecb872af4", null ],
+    [ "search", "dd/d2f/class_trie.html#a411e77126930a0942dd7b65e96b15206", null ],
+    [ "ALPHABETS", "dd/d2f/class_trie.html#a7c3ba4caf24378826a789848629177bd", null ],
+    [ "m_root", "dd/d2f/class_trie.html#a58b359fad33ca0064bd75a0d41a7b66d", null ]
+];
\ No newline at end of file
diff --git a/dd/d2f/class_trie_a95216ffc56cb9f8cede982cecb872af4_cgraph.map b/dd/d2f/class_trie_a95216ffc56cb9f8cede982cecb872af4_cgraph.map
new file mode 100644
index 000000000..ca1931122
--- /dev/null
+++ b/dd/d2f/class_trie_a95216ffc56cb9f8cede982cecb872af4_cgraph.map
@@ -0,0 +1,6 @@
+<map id="Trie::removeWordHelper" name="Trie::removeWordHelper">
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+<a href="#func-members">Functions</a>  </div>
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+</div><!--header-->
+<div class="contents">
+
+<p><a href="https://en.wikipedia.org/wiki/LU_decompositon">LU decomposition</a> of a square matrix  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;ctime&gt;</code><br />
+<code>#include &lt;iomanip&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;vector&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for lu_decompose.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d37/lu__decompose_8cpp__incl.svg" width="336" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:af703fd0afe349e567d7a82350e03cace"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d65/lu__decompose_8cpp.html#af703fd0afe349e567d7a82350e03cace">lu_decomposition</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt;&gt; &amp;A, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt;&gt; *L, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt;&gt; *U)</td></tr>
+<tr class="separator:af703fd0afe349e567d7a82350e03cace"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a98eb5807f21b783c341cab402ced6732"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
+<tr class="memitem:a98eb5807f21b783c341cab402ced6732"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d65/lu__decompose_8cpp.html#a98eb5807f21b783c341cab402ced6732">operator&lt;&lt;</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;out, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;v)</td></tr>
+<tr class="separator:a98eb5807f21b783c341cab402ced6732"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d65/lu__decompose_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
+<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/LU_decompositon">LU decomposition</a> of a square matrix </p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="af703fd0afe349e567d7a82350e03cace"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#af703fd0afe349e567d7a82350e03cace">&#9670;&nbsp;</a></span>lu_decomposition()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int lu_decomposition </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt;&gt; &amp;&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>L</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>U</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Perform LU decomposition on matrix </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>matrix to decompose </td></tr>
+    <tr><td class="paramdir">[out]</td><td class="paramname">L</td><td>output L matrix </td></tr>
+    <tr><td class="paramdir">[out]</td><td class="paramname">U</td><td>output U matrix </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>0 if no errors </dd>
+<dd>
+negative if error occurred </dd></dl>
+<div class="fragment"><div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;                                                      {</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <span class="keywordtype">int</span> row, col, j;</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <span class="keywordtype">int</span> mat_size = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160; </div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    <span class="keywordflow">if</span> (mat_size != A[0].size()) {</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;        <span class="comment">// check matrix is a square matrix</span></div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Not a square matrix!\n&quot;</span>;</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    }</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160; </div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <span class="comment">// regularize each row</span></div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keywordflow">for</span> (row = 0; row &lt; mat_size; row++) {</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;        <span class="comment">// Upper triangular matrix</span></div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        <span class="keywordflow">for</span> (col = row; col &lt; mat_size; col++) {</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;            <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;            <span class="keywordtype">double</span> lu_sum = 0.;</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;            <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) lu_sum += L[0][row][j] * U[0][j][col];</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160; </div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;            <span class="comment">// Evaluate U[i,k]</span></div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;            U[0][row][col] = A[row][col] - lu_sum;</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;        }</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160; </div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        <span class="comment">// Lower triangular matrix</span></div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        <span class="keywordflow">for</span> (col = row; col &lt; mat_size; col++) {</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;            <span class="keywordflow">if</span> (row == col) {</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;                L[0][row][col] = 1.;</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;                <span class="keywordflow">continue</span>;</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;            }</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160; </div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;            <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;            <span class="keywordtype">double</span> lu_sum = 0.;</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;            <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) lu_sum += L[0][col][j] * U[0][j][row];</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160; </div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;            <span class="comment">// Evaluate U[i,k]</span></div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;            L[0][col][row] = (A[col][row] - lu_sum) / U[0][row][row];</div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        }</div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    }</div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160; </div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>argc</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char **&#160;</td>
+          <td class="paramname"><em>argv</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;                                {</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    <span class="keywordtype">int</span> mat_size = 3;  <span class="comment">// default matrix size</span></div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> range = 50;</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160; </div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <span class="keywordflow">if</span> (argc == 2)</div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        mat_size = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160; </div>
+<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(NULL));  <span class="comment">// random number initializer</span></div>
+<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160; </div>
+<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    <span class="comment">/* Create a square matrix with random values */</span></div>
+<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;double&gt;</a>&gt; A(mat_size);</div>
+<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;double&gt;</a>&gt; L(mat_size);  <span class="comment">// output</span></div>
+<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;double&gt;</a>&gt; U(mat_size);  <span class="comment">// output</span></div>
+<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; mat_size; i++) {</div>
+<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;        <span class="comment">// calloc so that all valeus are &#39;0&#39; by default</span></div>
+<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        A[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>(mat_size);</div>
+<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;        L[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>(mat_size);</div>
+<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;        U[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>(mat_size);</div>
+<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; mat_size; j++)</div>
+<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;            <span class="comment">/* create random values in the limits [-range2, range-1] */</span></div>
+<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;            A[i][j] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range - range2);</div>
+<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    }</div>
+<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
+<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start_t = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    <a class="code" href="../../dd/d65/lu__decompose_8cpp.html#af703fd0afe349e567d7a82350e03cace">lu_decomposition</a>(A, &amp;L, &amp;U);</div>
+<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> end_t = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
+<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time taken: &quot;</span></div>
+<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;              &lt;&lt; <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_t - start_t) / CLOCKS_PER_SEC &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160; </div>
+<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;A = \n&quot;</span> &lt;&lt; A &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;L = \n&quot;</span> &lt;&lt; L &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;U = \n&quot;</span> &lt;&lt; U &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160; </div>
+<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d65/lu__decompose_8cpp_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="232" height="240"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
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+</div>
+</div>
+<a id="a98eb5807f21b783c341cab402ced6732"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a98eb5807f21b783c341cab402ced6732">&#9670;&nbsp;</a></span>operator&lt;&lt;()</h2>
+
+<div class="memitem">
+<div class="memproto">
+<div class="memtemplate">
+template&lt;typename T &gt; </div>
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a>&amp; operator&lt;&lt; </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;&#160;</td>
+          <td class="paramname"><em>out</em>, </td>
+        </tr>
+        <tr>
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+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
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+<div class="title">Todo List </div>  </div>
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+<div class="textblock"><dl class="reflist">
+<dt>File <a class="el" href="../../d8/dee/avltree_8cpp.html">avltree.cpp</a>  </dt>
+<dd><a class="anchor" id="_todo000001"></a>update code to use C++ STL library features and OO structure  </dd>
+<dt>File <a class="el" href="../../d3/d26/binary__search__tree_8cpp.html">binary_search_tree.cpp</a>  </dt>
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+<dt>Member <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>  </dt>
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+<dt>File <a class="el" href="../../dc/dc5/paranthesis__matching_8cpp.html">paranthesis_matching.cpp</a>  </dt>
+<dd><a class="anchor" id="_todo000005"></a>implement as a C++ class  </dd>
+<dt>Member <a class="el" href="../../d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>  ()</dt>
+<dd><a class="anchor" id="_todo000006"></a>This test fails  </dd>
+<dt>File <a class="el" href="../../d1/df3/hash__search_8cpp.html">hash_search.cpp</a>  </dt>
+<dd><a class="anchor" id="_todo000007"></a>fix the program for memory leaks and better structure in C++ and not C fashion  </dd>
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+<dt>Member <a class="el" href="../../dc/dfe/ternary__search_8cpp.html#a7f7d866eccdabe51bb16818a792618b1">get_input</a>  ()</dt>
+<dd><a class="anchor" id="_todo000010"></a>@christianbender Get input from STDIO or write input to memory as done above. </dd>
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">string_fibonacci.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>This Programme returns the Nth fibonacci as a string.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;cstring&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for string_fibonacci.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/da1/string__fibonacci_8cpp__incl.svg" width="182" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a28052eee05d43c2ebc5147c52bd50c35"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d47/string__fibonacci_8cpp.html#a28052eee05d43c2ebc5147c52bd50c35">add</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> b)</td></tr>
+<tr class="separator:a28052eee05d43c2ebc5147c52bd50c35"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ad8055ee368a5d5b24de01bdde6bf8fca"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d47/string__fibonacci_8cpp.html#ad8055ee368a5d5b24de01bdde6bf8fca">fib_Accurate</a> (uint64_t n)</td></tr>
+<tr class="separator:ad8055ee368a5d5b24de01bdde6bf8fca"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d47/string__fibonacci_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>This Programme returns the Nth fibonacci as a string. </p>
+<p>The method used is manual addition with carry and placing it in a string which is called string addition This makes it have no bounds or limits</p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/de4/fibonacci__large_8cpp.html" title="Computes N^th Fibonacci number given as input argument. Uses custom build arbitrary integers library ...">fibonacci_large.cpp</a>, <a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html" title="Faster computation of Fibonacci series.">fibonacci_fast.cpp</a>, <a class="el" href="../../d9/d89/fibonacci_8cpp.html" title="Generate fibonacci sequence.">fibonacci.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a28052eee05d43c2ebc5147c52bd50c35"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a28052eee05d43c2ebc5147c52bd50c35">&#9670;&nbsp;</a></span>add()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> add </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td>
+          <td class="paramname"><em>b</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>function to add two string numbers </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">a</td><td>first number in string to add </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">b</td><td>second number in string to add </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>sum as a <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html" title="STL class.">std::string</a> </dd></dl>
+<div class="fragment"><div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;                                        {</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> temp = <span class="stringliteral">&quot;&quot;</span>;</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160; </div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="comment">// carry flag</span></div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    <span class="keywordtype">int</span> carry = 0;</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160; </div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="comment">// fills up with zeros</span></div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="keywordflow">while</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>.length() &lt; b.length()) {</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = <span class="stringliteral">&quot;0&quot;</span> + <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    }</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160; </div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="comment">// fills up with zeros</span></div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <span class="keywordflow">while</span> (b.length() &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>.length()) {</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;        b = <span class="stringliteral">&quot;0&quot;</span> + b;</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    }</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160; </div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <span class="comment">// adds the numbers a and b</span></div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>.length() - 1; i &gt;= 0; i--) {</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        <span class="keywordtype">char</span> val = <span class="keyword">static_cast&lt;</span><span class="keywordtype">char</span><span class="keyword">&gt;</span>(((<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>[i] - 48) + (b[i] - 48)) + 48 + carry);</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        <span class="keywordflow">if</span> (val &gt; 57) {</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;            carry = 1;</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;            val -= 10;</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;            carry = 0;</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;        }</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        temp = val + temp;</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    }</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160; </div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    <span class="comment">// processes the carry flag</span></div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <span class="keywordflow">if</span> (carry == 1) {</div>
+<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;        temp = <span class="stringliteral">&quot;1&quot;</span> + temp;</div>
+<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    }</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160; </div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="comment">// removes leading zeros.</span></div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="keywordflow">while</span> (temp[0] == <span class="charliteral">&#39;0&#39;</span> &amp;&amp; temp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>() &gt; 1) {</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        temp = temp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(1);</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    }</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160; </div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <span class="keywordflow">return</span> temp;</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ad8055ee368a5d5b24de01bdde6bf8fca"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ad8055ee368a5d5b24de01bdde6bf8fca">&#9670;&nbsp;</a></span>fib_Accurate()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void fib_Accurate </td>
+          <td>(</td>
+          <td class="paramtype">uint64_t&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Fibonacci iterator </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>n^th Fibonacci number </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;                              {</div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> tmp = <span class="stringliteral">&quot;&quot;</span>;</div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> fibMinus1 = <span class="stringliteral">&quot;1&quot;</span>;</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> fibMinus2 = <span class="stringliteral">&quot;0&quot;</span>;</div>
+<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
+<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;        tmp = <a class="code" href="../../de/d47/string__fibonacci_8cpp.html#a28052eee05d43c2ebc5147c52bd50c35">add</a>(fibMinus1, fibMinus2);</div>
+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        fibMinus2 = fibMinus1;</div>
+<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        fibMinus1 = tmp;</div>
+<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    }</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; fibMinus2;</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d47/string__fibonacci_8cpp_ad8055ee368a5d5b24de01bdde6bf8fca_cgraph.svg" width="196" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;           {</div>
+<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    <span class="keywordtype">int</span> n;</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter whatever number N you want to find the fibonacci of\n&quot;</span>;</div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; th Fibonacci is \n&quot;</span>;</div>
+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    <a class="code" href="../../de/d47/string__fibonacci_8cpp.html#ad8055ee368a5d5b24de01bdde6bf8fca">fib_Accurate</a>(n);</div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160; </div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d47/string__fibonacci_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="295" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div><div class="ttdoc">STL class.</div></div>
+<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::length</a></div><div class="ttdeci">T length(T... args)</div></div>
+<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
+<div class="ttc" id="amatrix__exponentiation_8cpp_html_a9ecd98ce0064e2f7f97bb6a92f58ee72"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a></div><div class="ttdeci">vector&lt; ll &gt; a</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:53</div></div>
+<div class="ttc" id="asubstr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">std::string::substr</a></div><div class="ttdeci">T substr(T... args)</div></div>
+<div class="ttc" id="astring__fibonacci_8cpp_html_a28052eee05d43c2ebc5147c52bd50c35"><div class="ttname"><a href="../../de/d47/string__fibonacci_8cpp.html#a28052eee05d43c2ebc5147c52bd50c35">add</a></div><div class="ttdeci">std::string add(std::string a, std::string b)</div><div class="ttdef"><b>Definition:</b> string_fibonacci.cpp:24</div></div>
+<div class="ttc" id="astring__fibonacci_8cpp_html_ad8055ee368a5d5b24de01bdde6bf8fca"><div class="ttname"><a href="../../de/d47/string__fibonacci_8cpp.html#ad8055ee368a5d5b24de01bdde6bf8fca">fib_Accurate</a></div><div class="ttdeci">void fib_Accurate(uint64_t n)</div><div class="ttdef"><b>Definition:</b> string_fibonacci.cpp:68</div></div>
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+
+<p>The <a href="https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm">Knuth-Morris-Pratt Algorithm</a> for finding a pattern within a piece of text with complexity O(n + m)  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;cstring&gt;</code><br />
+<code>#include &lt;vector&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for knuth_morris_pratt.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d69/knuth__morris__pratt_8cpp__incl.svg" width="251" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
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+<tr class="memitem:d9/d03/namespacestring__search"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d03/namespacestring__search.html">string_search</a></td></tr>
+<tr class="memdesc:d9/d03/namespacestring__search"><td class="mdescLeft">&#160;</td><td class="mdescRight">String search algorithms. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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+<tr class="memitem:aa422aab133d4ed5e5d6022a7f701271f"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d03/namespacestring__search.html#aa422aab133d4ed5e5d6022a7f701271f">string_search::getFailureArray</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;pattern)</td></tr>
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+<tr class="memitem:a26a58225ce7d3fa9d4c2f5349a65ed93"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d03/namespacestring__search.html#a26a58225ce7d3fa9d4c2f5349a65ed93">string_search::kmp</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;pattern, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;text)</td></tr>
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d6a/knuth__morris__pratt_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>The <a href="https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm">Knuth-Morris-Pratt Algorithm</a> for finding a pattern within a piece of text with complexity O(n + m) </p>
+<ol type="1">
+<li>Preprocess pattern to identify any suffixes that are identical to prefixes. This tells us where to continue from if we get a mismatch between a character in our pattern and the text.</li>
+<li>Step through the text one character at a time and compare it to a character in the pattern updating our location within the pattern if necessary </li>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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+<div class="memitem">
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+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
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+      </table>
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+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;           {</div>
+<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text = <span class="stringliteral">&quot;alskfjaldsabc1abc1abc12k23adsfabcabc&quot;</span>;</div>
+<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern = <span class="stringliteral">&quot;abc1abc12l&quot;</span>;</div>
+<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160; </div>
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+<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    text = <span class="stringliteral">&quot;abcabc&quot;</span>;</div>
+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    pattern = <span class="stringliteral">&quot;bca&quot;</span>;</div>
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+Functions</h2></td></tr>
+<tr class="memitem:a33cb0a68c36aa26fd599c7c66da86ed7"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a33cb0a68c36aa26fd599c7c66da86ed7">create_matrix</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *A)</td></tr>
+<tr class="separator:a33cb0a68c36aa26fd599c7c66da86ed7"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a7558fd7779bf207157ced66f275951a0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a7558fd7779bf207157ced66f275951a0">mat_mul</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;A, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;B, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *OUT)</td></tr>
+<tr class="separator:a7558fd7779bf207157ced66f275951a0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a763896dbb4a7e95c4a1e614ac0819d66"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *A, bool print_intermediates=false)</td></tr>
+<tr class="separator:a763896dbb4a7e95c4a1e614ac0819d66"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a> ()</td></tr>
+<tr class="separator:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a0283886819c7c140a023582b7269e2d0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a> ()</td></tr>
+<tr class="separator:a0283886819c7c140a023582b7269e2d0"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
+<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Compute real eigen values and eigen vectors of a symmetric matrix using <a href="https://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</a> method. </p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
+</div><h2 class="groupheader">Macro Definition Documentation</h2>
+<a id="aee57a411f07599034f5ceb8cc7d65b40"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aee57a411f07599034f5ceb8cc7d65b40">&#9670;&nbsp;</a></span>LIMS</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">#define LIMS&#160;&#160;&#160;9</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>limit of range of matrix values </p>
+
+</div>
+</div>
+<h2 class="groupheader">Function Documentation</h2>
+<a id="a33cb0a68c36aa26fd599c7c66da86ed7"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a33cb0a68c36aa26fd599c7c66da86ed7">&#9670;&nbsp;</a></span>create_matrix()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void create_matrix </td>
+          <td>(</td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>A</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>create a symmetric square matrix of given size with random elements. A symmetric square matrix will <em>always</em> have real eigen values.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[out]</td><td class="paramname">A</td><td>matrix to create (must be pre-allocated in memory) </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;                                                        {</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <span class="keywordtype">int</span> i, j, tmp, lim2 = <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a> &gt;&gt; 1;</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="keywordtype">int</span> N = A-&gt;size();</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160; </div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="preprocessor">#endif</span></div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; N; i++) {</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;        A[0][i][i] = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;        <span class="keywordflow">for</span> (j = i + 1; j &lt; N; j++) {</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;            tmp = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;            A[0][i][j] = tmp;  <span class="comment">// summetrically distribute random values</span></div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;            A[0][j][i] = tmp;</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;        }</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    }</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d75/qr__eigen__values_8cpp_a33cb0a68c36aa26fd599c7c66da86ed7_cgraph.svg" width="234" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>argc</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char **&#160;</td>
+          <td class="paramname"><em>argv</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;                                {</div>
+<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;    <span class="keywordtype">int</span> mat_size = 5;</div>
+<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;    <span class="keywordflow">if</span> (argc == 2) {</div>
+<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;        mat_size = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
+<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;    } <span class="keywordflow">else</span> {  <span class="comment">// if invalid input argument is given run tests</span></div>
+<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;        <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
+<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;        <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
+<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Usage: ./qr_eigen_values [mat_size]\n&quot;</span>;</div>
+<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;        <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;    }</div>
+<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160; </div>
+<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    <span class="keywordflow">if</span> (mat_size &lt; 2) {</div>
+<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">fprintf</a>(stderr, <span class="stringliteral">&quot;Matrix size should be &gt; 2\n&quot;</span>);</div>
+<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;        <span class="keywordflow">return</span> -1;</div>
+<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;    }</div>
+<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160; </div>
+<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;    <span class="comment">// initialize random number generator</span></div>
+<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
+<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160; </div>
+<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;    <span class="keywordtype">int</span> i, rows = mat_size, columns = mat_size;</div>
+<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160; </div>
+<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; A(rows);</div>
+<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160; </div>
+<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; rows; i++) {</div>
+<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;        A[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(columns);</div>
+<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;    }</div>
+<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160; </div>
+<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;    <span class="comment">/* create a random matrix */</span></div>
+<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;    <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a33cb0a68c36aa26fd599c7c66da86ed7">create_matrix</a>(&amp;A);</div>
+<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160; </div>
+<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; A &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160; </div>
+<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;    clock_t t1 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
+<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eigen_vals = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a>(&amp;A);</div>
+<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;    <span class="keywordtype">double</span> dtime = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>() - t1) / CLOCKS_PER_SEC;</div>
+<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160; </div>
+<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Eigen vals: &quot;</span>;</div>
+<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;    <span class="keywordflow">for</span> (i = 0; i &lt; mat_size; i++) <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; eigen_vals[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
+<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTime taken to compute: &quot;</span> &lt;&lt; dtime &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
+<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160; </div>
+<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../de/d75/qr__eigen__values_8cpp_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="100%" height="518"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a7558fd7779bf207157ced66f275951a0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a7558fd7779bf207157ced66f275951a0">&#9670;&nbsp;</a></span>mat_mul()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void mat_mul </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;&#160;</td>
+          <td class="paramname"><em>A</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;&#160;</td>
+          <td class="paramname"><em>B</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
+          <td class="paramname"><em>OUT</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Perform multiplication of two matrices.</p><ul>
+<li>R2 must be equal to C1</li>
+<li>Resultant matrix size should be R1xC2 <dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>first matrix to multiply </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">B</td><td>second matrix to multiply </td></tr>
+    <tr><td class="paramdir">[out]</td><td class="paramname">OUT</td><td>output matrix (must be pre-allocated) </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>pointer to resultant matrix </dd></dl>
+</li>
+</ul>
+<div class="fragment"><div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;                                                    {</div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keywordtype">int</span> R1 = A.size();</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="keywordtype">int</span> C1 = A[0].size();</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    <span class="keywordtype">int</span> R2 = B.size();</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="keywordtype">int</span> C2 = B[0].size();</div>
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+<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a1440a7779ac56f47a3f355ce4a8c7da0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">&#9670;&nbsp;</a></span>test1()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test1 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
+\[\begin{bmatrix} 5 &amp; 7\\ 7 &amp; 11 \end{bmatrix}\]
+</p>
+<p> which are approximately, {15.56158, 0.384227} </p>
+<div class="fragment"><div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;             {</div>
+<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; X = {{5, 7}, {7, 11}};</div>
+<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    <span class="keywordtype">double</span> y[] = {15.56158, 0.384227};  <span class="comment">// corresponding y-values</span></div>
+<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160; </div>
+<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 1 -------&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eig_vals = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a>(&amp;X);</div>
+<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160; </div>
+<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; i++) {</div>
+<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i + 1 &lt;&lt; <span class="stringliteral">&quot;/2 Checking for &quot;</span> &lt;&lt; y[i] &lt;&lt; <span class="stringliteral">&quot; --&gt; &quot;</span>;</div>
+<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;        <span class="keywordtype">bool</span> result = <span class="keyword">false</span>;</div>
+<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 2 &amp;&amp; !result; j++) {</div>
+<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;            <span class="keywordflow">if</span> (std::abs(y[i] - eig_vals[j]) &lt; 0.1) {</div>
+<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;                result = <span class="keyword">true</span>;</div>
+<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;                <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; eig_vals[j] &lt;&lt; <span class="stringliteral">&quot;) &quot;</span>;</div>
+<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;            }</div>
+<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;        }</div>
+<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;        assert(result);  <span class="comment">// ensure that i^th expected eigen value was computed</span></div>
+<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;found\n&quot;</span>;</div>
+<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    }</div>
+<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed\n\n&quot;</span>;</div>
+<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../de/d75/qr__eigen__values_8cpp_a1440a7779ac56f47a3f355ce4a8c7da0_cgraph.svg" width="100%" height="391"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a0283886819c7c140a023582b7269e2d0"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0283886819c7c140a023582b7269e2d0">&#9670;&nbsp;</a></span>test2()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void test2 </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
+\[\begin{bmatrix} -4&amp; 4&amp; 2&amp; 0&amp; -3\\ 4&amp; -4&amp; 4&amp; -3&amp; -1\\ 2&amp; 4&amp; 4&amp; 3&amp; -3\\ 0&amp; -3&amp; 3&amp; -1&amp;-1\\ -3&amp; -1&amp; -3&amp; -3&amp; 0 \end{bmatrix}\]
+</p>
+<p> which are approximately, {9.27648, -9.26948, 2.0181, -1.03516, -5.98994} </p>
+<div class="fragment"><div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;             {</div>
+<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; X = {{-4, 4, 2, 0, -3},</div>
+<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;                                              {4, -4, 4, -3, -1},</div>
+<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;                                              {2, 4, 4, 3, -3},</div>
+<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;                                              {0, -3, 3, -1, -3},</div>
+<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;                                              {-3, -1, -3, -3, 0}};</div>
+<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    <span class="keywordtype">double</span> y[] = {9.27648, -9.26948, 2.0181, -1.03516,</div>
+<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;                  -5.98994};  <span class="comment">// corresponding y-values</span></div>
+<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160; </div>
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+<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eig_vals = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a>(&amp;X);</div>
+<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160; </div>
+<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; X &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span></div>
+<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;              &lt;&lt; <span class="stringliteral">&quot;Eigen values: &quot;</span> &lt;&lt; eig_vals &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160; </div>
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+<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;        <span class="keywordtype">bool</span> result = <span class="keyword">false</span>;</div>
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+<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;            <span class="keywordflow">if</span> (std::abs(y[i] - eig_vals[j]) &lt; 0.1) {</div>
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+<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;            }</div>
+<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;        }</div>
+<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;        assert(result);  <span class="comment">// ensure that i^th expected eigen value was computed</span></div>
+<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;found\n&quot;</span>;</div>
+<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;    }</div>
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+<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../de/d75/qr__eigen__values_8cpp_a0283886819c7c140a023582b7269e2d0_cgraph.svg" width="100%" height="391"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
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+<div class="ttc" id="anamespaceqr__algorithm_html_a763896dbb4a7e95c4a1e614ac0819d66"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a></div><div class="ttdeci">std::valarray&lt; double &gt; eigen_values(std::valarray&lt; std::valarray&lt; double &gt;&gt; *A, bool print_intermediates=false)</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:98</div></div>
+<div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
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+<div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
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+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html">qr_eigen_values.cpp</a></li>
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new file mode 100644
index 000000000..efcc5d814
--- /dev/null
+++ b/de/d75/qr__eigen__values_8cpp.js
@@ -0,0 +1,10 @@
+var qr__eigen__values_8cpp =
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+    [ "create_matrix", "de/d75/qr__eigen__values_8cpp.html#a33cb0a68c36aa26fd599c7c66da86ed7", null ],
+    [ "eigen_values", "de/d75/qr__eigen__values_8cpp.html#a763896dbb4a7e95c4a1e614ac0819d66", null ],
+    [ "main", "de/d75/qr__eigen__values_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627", null ],
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+$(document).ready(function(){initNavTree('de/d85/decimal__to__roman__numeral_8cpp.html','../../'); initResizable(); });
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">decimal_to_roman_numeral.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>This Programme Converts a given decimal number in the range [0,4000) to both Lower case and Upper case Roman Numeral.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;cstdio&gt;</code><br />
+<code>#include &lt;cstring&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for decimal_to_roman_numeral.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d43/decimal__to__roman__numeral_8cpp__incl.svg" width="334" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a88203bd297e8405160c132faa1187780"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a> (char c, int n)</td></tr>
+<tr class="separator:a88203bd297e8405160c132faa1187780"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a003fb4e1b08279fe4cd50fbbc2782c2d"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a> (int n)</td></tr>
+<tr class="separator:a003fb4e1b08279fe4cd50fbbc2782c2d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a214743638eff1336f835310049aef979"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a> (int n)</td></tr>
+<tr class="separator:a214743638eff1336f835310049aef979"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>This Programme Converts a given decimal number in the range [0,4000) to both Lower case and Upper case Roman Numeral. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a88203bd297e8405160c132faa1187780"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a88203bd297e8405160c132faa1187780">&#9670;&nbsp;</a></span>fill()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> fill </td>
+          <td>(</td>
+          <td class="paramtype">char&#160;</td>
+          <td class="paramname"><em>c</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>This functions fills a string with character c, n times and returns it </p><dl class="section note"><dt>Note</dt><dd>This can probably be replace by <code>memcpy</code> function. </dd></dl>
+<div class="fragment"><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;                              {</div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s = <span class="stringliteral">&quot;&quot;</span>;</div>
+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;    <span class="keywordflow">while</span> (n--) s += c;</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;    <span class="keywordflow">return</span> s;</div>
+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;           {</div>
+<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <span class="keywordtype">int</span> n;</div>
+<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t\tRoman numbers converter\n\n&quot;</span>;</div>
+<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Type in decimal number between 0 up to 4000 (exclusive): &quot;</span>;</div>
+<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; in Upper Roman Numerals is &quot;</span> &lt;&lt; <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; in Lower Roman Numerals is &quot;</span> &lt;&lt; <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
+<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d85/decimal__to__roman__numeral_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="303" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a003fb4e1b08279fe4cd50fbbc2782c2d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a003fb4e1b08279fe4cd50fbbc2782c2d">&#9670;&nbsp;</a></span>tolowerRoman()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> tolowerRoman </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>to convert to lowercase Roman Numeral the function works recursively </p>
+<div class="fragment"><div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;                              {</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <span class="keywordflow">if</span> (n &lt; 4)</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, n);</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keywordflow">if</span> (n &lt; 6)</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, 5 - n) + <span class="stringliteral">&quot;v&quot;</span>;</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <span class="keywordflow">if</span> (n &lt; 9)</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;        <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;v&quot;</span>) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, n - 5);</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="keywordflow">if</span> (n &lt; 11)</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, 10 - n) + <span class="stringliteral">&quot;x&quot;</span>;</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="keywordflow">if</span> (n &lt; 40)</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, n / 10) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keywordflow">if</span> (n &lt; 60)</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, 5 - n / 10) + <span class="charliteral">&#39;l&#39;</span> + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="keywordflow">if</span> (n &lt; 90)</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;        <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;l&quot;</span>) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, n / 10 - 5) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keywordflow">if</span> (n &lt; 110)</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, 10 - n / 10) + <span class="stringliteral">&quot;c&quot;</span> + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keywordflow">if</span> (n &lt; 400)</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, n / 100) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <span class="keywordflow">if</span> (n &lt; 600)</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, 5 - n / 100) + <span class="charliteral">&#39;d&#39;</span> + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    <span class="keywordflow">if</span> (n &lt; 900)</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;d&quot;</span>) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, n / 100 - 5) +</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;               <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <span class="keywordflow">if</span> (n &lt; 1100)</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, 10 - n / 100) + <span class="stringliteral">&quot;m&quot;</span> + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    <span class="keywordflow">if</span> (n &lt; 4000)</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;m&#39;</span>, n / 1000) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 1000);</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    <span class="keywordflow">return</span> <span class="stringliteral">&quot;?&quot;</span>;</div>
+<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d85/decimal__to__roman__numeral_8cpp_a003fb4e1b08279fe4cd50fbbc2782c2d_cgraph.svg" width="204" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a214743638eff1336f835310049aef979"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a214743638eff1336f835310049aef979">&#9670;&nbsp;</a></span>toupperRoman()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> toupperRoman </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>to convert to uppercase Roman Numeral the function works recursively </p>
+<div class="fragment"><div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;                              {</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    <span class="keywordflow">if</span> (n &lt; 4)</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, n);</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    <span class="keywordflow">if</span> (n &lt; 6)</div>
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+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="keywordflow">if</span> (n &lt; 9)</div>
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+<link href="../../doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
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+<div class="header">
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+<div class="title">Trie Member List</div>  </div>
+</div><!--header-->
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+
+<p>This is the complete list of members for <a class="el" href="../../dd/d2f/class_trie.html">Trie</a>, including all inherited members.</p>
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+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>ALPHABETS</b> (defined in <a class="el" href="../../dd/d2f/class_trie.html">Trie</a>)</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">private</span><span class="mlabel">static</span></td></tr>
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+  <tr bgcolor="#f0f0f0"><td class="entry"><b>m_root</b> (defined in <a class="el" href="../../dd/d2f/class_trie.html">Trie</a>)</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>removeWord</b>(const std::string &amp;word) (defined in <a class="el" href="../../dd/d2f/class_trie.html">Trie</a>)</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html#a95216ffc56cb9f8cede982cecb872af4">removeWordHelper</a>(const std::string &amp;word, std::shared_ptr&lt; TrieNode &gt; curr, size_t index)</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">inline</span><span class="mlabel">private</span></td></tr>
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+  <tr><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html#a6af57e9f25d0d0a2d59eea5a4a802908">Trie</a>()</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+</table></div><!-- contents -->
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+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
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+<div class="contents">
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+<p>This is the complete list of members for <a class="el" href="../../d0/dd2/class_queue___array.html">Queue_Array</a>, including all inherited members.</p>
+<table class="directory">
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>arr</b> (defined in <a class="el" href="../../d0/dd2/class_queue___array.html">Queue_Array</a>)</td><td class="entry"><a class="el" href="../../d0/dd2/class_queue___array.html">Queue_Array</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>dequeue</b>() (defined in <a class="el" href="../../d0/dd2/class_queue___array.html">Queue_Array</a>)</td><td class="entry"><a class="el" href="../../d0/dd2/class_queue___array.html">Queue_Array</a></td><td class="entry"></td></tr>
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+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>front</b> (defined in <a class="el" href="../../d0/dd2/class_queue___array.html">Queue_Array</a>)</td><td class="entry"><a class="el" href="../../d0/dd2/class_queue___array.html">Queue_Array</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
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+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>rear</b> (defined in <a class="el" href="../../d0/dd2/class_queue___array.html">Queue_Array</a>)</td><td class="entry"><a class="el" href="../../d0/dd2/class_queue___array.html">Queue_Array</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
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+</table></div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
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+<script type="text/javascript" src="../../jquery.js"></script>
+<script type="text/javascript" src="../../dynsections.js"></script>
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+<script type="text/javascript" src="../../search/search.js"></script>
+<script type="text/x-mathjax-config">
+  MathJax.Hub.Config({
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+<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
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+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
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+</div><!--header-->
+<div class="contents">
+
+<p>Get list of prime numbers.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;vector&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for prime_numbers.cpp:</div>
+<div class="dyncontent">
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+Functions</h2></td></tr>
+<tr class="memitem:a3b91f208e8365c95a295cfe3e67df5c3"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d9b/prime__numbers_8cpp.html#a3b91f208e8365c95a295cfe3e67df5c3">primes</a> (int max)</td></tr>
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d9b/prime__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Get list of prime numbers. </p>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d4/d9c/primes__up__to__billion_8cpp.html" title="Compute prime numbers upto 1 billion.">primes_up_to_billion.cpp</a> <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html" title="Get list of prime numbers using Sieve of Eratosthenes Sieve of Eratosthenes is an algorithm to find t...">sieve_of_eratosthenes.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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+<div class="memitem">
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+          <td class="memname">int main </td>
+          <td>(</td>
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+
+<div class="memitem">
+<div class="memproto">
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+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;int&gt; primes </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>max</em></td><td>)</td>
+          <td></td>
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+<p>Generate an increasingly large number of primes and store in a list </p>
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+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>operator=</b>(Edge &amp;&amp;)=default (defined in <a class="el" href="../../d7/d77/class_edge.html">Edge</a>)</td><td class="entry"><a class="el" href="../../d7/d77/class_edge.html">Edge</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>operator=</b>(Edge const &amp;)=default (defined in <a class="el" href="../../d7/d77/class_edge.html">Edge</a>)</td><td class="entry"><a class="el" href="../../d7/d77/class_edge.html">Edge</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>src</b> (defined in <a class="el" href="../../d7/d77/class_edge.html">Edge</a>)</td><td class="entry"><a class="el" href="../../d7/d77/class_edge.html">Edge</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>src</b> (defined in <a class="el" href="../../d7/d77/class_edge.html">Edge</a>)</td><td class="entry"><a class="el" href="../../d7/d77/class_edge.html">Edge</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>weight</b> (defined in <a class="el" href="../../d7/d77/class_edge.html">Edge</a>)</td><td class="entry"><a class="el" href="../../d7/d77/class_edge.html">Edge</a></td><td class="entry"></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>~Edge</b>()=default (defined in <a class="el" href="../../d7/d77/class_edge.html">Edge</a>)</td><td class="entry"><a class="el" href="../../d7/d77/class_edge.html">Edge</a></td><td class="entry"></td></tr>
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+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+  <div class="summary">
+<a href="#nested-classes">Classes</a> &#124;
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">binaryheap.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>A C++ program to demonstrate common Binary Heap Operations.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;climits&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
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+<div class="textblock"><p>A C++ program to demonstrate common Binary Heap Operations. </p>
+</div></div><!-- contents -->
+</div><!-- doc-content -->
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+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+  <tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>operator+=</b>(int n) (defined in <a class="el" href="../../db/d82/classlarge__number.html">large_number</a>)</td><td class="entry"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr><td class="entry"><a class="el" href="../../db/d82/classlarge__number.html#a778428c4761b6ea5e7770743f0eab5ab">operator&lt;&lt;</a>(std::ostream &amp;out, const large_number &amp;a)</td><td class="entry"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a></td><td class="entry"><span class="mlabel">friend</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="../../db/d82/classlarge__number.html#aeb22d2aae39d1b1e0bd39c7f47b333eb">operator=</a>(const large_number &amp;b)</td><td class="entry"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr><td class="entry"><a class="el" href="../../db/d82/classlarge__number.html#a7ba872b9a3ce1f3da6c06c5409663cca">operator==</a>(large_number const &amp;a, large_number const &amp;b)</td><td class="entry"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a></td><td class="entry"><span class="mlabel">friend</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="../../db/d82/classlarge__number.html#ace19126cf343a09efc0010735f6e3a8d">operator[]</a>(size_t n)</td><td class="entry"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr bgcolor="#f0f0f0"><td class="entry"><b>operator[]</b>(size_t n) const (defined in <a class="el" href="../../db/d82/classlarge__number.html">large_number</a>)</td><td class="entry"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
+  <tr class="even"><td class="entry"><a class="el" href="../../db/d82/classlarge__number.html#a959c5c1a982949bbf98e1ea0f9afe6a9">test</a>()</td><td class="entry"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a></td><td class="entry"><span class="mlabel">inline</span><span class="mlabel">static</span></td></tr>
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+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">binary_exponent.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>C++ Program to find Binary Exponent Iteratively and Recursively.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for binary_exponent.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d36/binary__exponent_8cpp__incl.svg" width="186" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:aeb48dce0725e63d19147944f41843c73"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dcf/binary__exponent_8cpp.html#aeb48dce0725e63d19147944f41843c73">binExpo</a> (int <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, int b)</td></tr>
+<tr class="separator:aeb48dce0725e63d19147944f41843c73"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a31dbf5f7ceb9c9eec831ef9f7782291f"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dcf/binary__exponent_8cpp.html#a31dbf5f7ceb9c9eec831ef9f7782291f">binExpo_alt</a> (int <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, int b)</td></tr>
+<tr class="separator:a31dbf5f7ceb9c9eec831ef9f7782291f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dcf/binary__exponent_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function.  <a href="../../de/dcf/binary__exponent_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>C++ Program to find Binary Exponent Iteratively and Recursively. </p>
+<p>Calculate \(a^b\) in \(O(\log(b))\) by converting \(b\) to a binary number. Binary exponentiation is also known as exponentiation by squaring. </p><dl class="section note"><dt>Note</dt><dd>This is a far better approach compared to naive method which provide \(O(b)\) operations.</dd></dl>
+<p>Example: 10 in base 2 is 1010. </p><p class="formulaDsp">
+\begin{eqnarray*} 2^{10_d} &amp;=&amp; 2^{1010_b} = 2^8 * 2^2\\ 2^1 &amp;=&amp; 2\\ 2^2 &amp;=&amp; (2^1)^2 = 2^2 = 4\\ 2^4 &amp;=&amp; (2^2)^2 = 4^2 = 16\\ 2^8 &amp;=&amp; (2^4)^2 = 16^2 = 256\\ \end{eqnarray*}
+</p>
+<p> Hence to calculate 2^10 we only need to multiply \(2^8\) and \(2^2\) skipping \(2^1\) and \(2^4\). </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="aeb48dce0725e63d19147944f41843c73"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aeb48dce0725e63d19147944f41843c73">&#9670;&nbsp;</a></span>binExpo()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int binExpo </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>b</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Recursive function to calculate exponent in \(O(\log(n))\) using binary exponent. </p>
+<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;                          {</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <span class="keywordflow">if</span> (b == 0) {</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;        <span class="keywordflow">return</span> 1;</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    }</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="keywordtype">int</span> res = <a class="code" href="../../de/dcf/binary__exponent_8cpp.html#aeb48dce0725e63d19147944f41843c73">binExpo</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b / 2);</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="keywordflow">if</span> (b % 2) {</div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        <span class="keywordflow">return</span> res * res * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;        <span class="keywordflow">return</span> res * res;</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    }</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="a31dbf5f7ceb9c9eec831ef9f7782291f"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a31dbf5f7ceb9c9eec831ef9f7782291f">&#9670;&nbsp;</a></span>binExpo_alt()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int binExpo_alt </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>a</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>b</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Iterative function to calculate exponent in \(O(\log(n))\) using binary exponent. </p>
+<div class="fragment"><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;                              {</div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <span class="keywordtype">int</span> res = 1;</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    <span class="keywordflow">while</span> (b &gt; 0) {</div>
+<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;        <span class="keywordflow">if</span> (b % 2) {</div>
+<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;            res = res * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;        }</div>
+<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;        <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
+<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        b /= 2;</div>
+<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    }</div>
+<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    <span class="keywordflow">return</span> res;</div>
+<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+
+<p>Main function. </p>
+<p>Give two numbers a, b</p>
+<p>int resIterate = binExpo_alt(a, b);</p>
+<p>Result of a^b (where '^' denotes exponentiation)</p>
+<p><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; resIterate &lt;&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</p>
+<div class="fragment"><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;           {</div>
+<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b;<span class="comment"></span></div>
+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="comment">    /// Give two numbers a, b</span></div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;<span class="comment"></span>    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &gt;&gt; b;</div>
+<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> == 0 &amp;&amp; b == 0) {</div>
+<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Math error&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (b &lt; 0) {</div>
+<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Exponent must be positive !!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    } <span class="keywordflow">else</span> {</div>
+<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <span class="keywordtype">int</span> resRecurse = <a class="code" href="../../de/dcf/binary__exponent_8cpp.html#aeb48dce0725e63d19147944f41843c73">binExpo</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b);<span class="comment"></span></div>
+<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;<span class="comment">        /// int resIterate = binExpo_alt(a, b);</span></div>
+<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;<span class="comment"></span><span class="comment"></span> </div>
+<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="comment">        /// Result of a^b (where &#39;^&#39; denotes exponentiation)</span></div>
+<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;<span class="comment"></span>        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; resRecurse &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;<span class="comment"></span></div>
+<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;<span class="comment">        /// std::cout &lt;&lt; resIterate &lt;&lt; std::endl;</span></div>
+<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="comment"></span>    }</div>
+<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;}</div>
+</div><!-- fragment -->
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
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+  <div class="summary">
+<a href="#define-members">Macros</a> &#124;
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">newton_raphson_method.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Newton%27s_method">Newton-Raphson method</a> for both real and complex solutions.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;ctime&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+<code>#include &lt;limits&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for newton_raphson_method.cpp:</div>
+<div class="dyncontent">
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+<tr class="memdesc:a0a3abbca80bc98e7abcb3ae73abe0f14"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum number of iterations to check. <br /></td></tr>
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+Functions</h2></td></tr>
+<tr class="memitem:a2003b5b2dcfff0769b957ab5c968b03d"><td class="memItemLeft" align="right" valign="top">static double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dd3/newton__raphson__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a> (double i)</td></tr>
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+<tr class="memitem:a3d3f7f41977394680af6ebbed96f3386"><td class="memItemLeft" align="right" valign="top">static double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dd3/newton__raphson__method_8cpp.html#a3d3f7f41977394680af6ebbed96f3386">eq_der</a> (double i)</td></tr>
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dd3/newton__raphson__method_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Newton%27s_method">Newton-Raphson method</a> for both real and complex solutions. </p>
+<p>The \((i+1)^\text{th}\) approximation is given by: </p><p class="formulaDsp">
+\[ x_{i+1} = x_i - \frac{f(x_i)}{f&#39;(x_i)} \]
+</p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d7/d6a/bisection__method_8cpp.html" title="Solve the equation  using bisection method">bisection_method.cpp</a>, <a class="el" href="../../dd/d29/false__position_8cpp.html" title="Solve the equation  using false position method, also known as the Secant method.">false_position.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a2003b5b2dcfff0769b957ab5c968b03d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a2003b5b2dcfff0769b957ab5c968b03d">&#9670;&nbsp;</a></span>eq()</h2>
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+  <td class="mlabels-left">
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+          <td class="memname">static double eq </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>i</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
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+<span class="mlabels"><span class="mlabel">static</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>define \(f(x)\) to find root for </p>
+<div class="fragment"><div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;                           {</div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keywordflow">return</span> (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i, 3) - (4 * i) - 9);  <span class="comment">// original equation</span></div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;}</div>
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+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/dd3/newton__raphson__method_8cpp_a2003b5b2dcfff0769b957ab5c968b03d_cgraph.svg" width="170" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
+<a id="a3d3f7f41977394680af6ebbed96f3386"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a3d3f7f41977394680af6ebbed96f3386">&#9670;&nbsp;</a></span>eq_der()</h2>
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+<div class="memitem">
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+          <td class="memname">static double eq_der </td>
+          <td>(</td>
+          <td class="paramtype">double&#160;</td>
+          <td class="paramname"><em>i</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+  </td>
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+<span class="mlabels"><span class="mlabel">static</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>define the derivative function \(f&#39;(x)\) </p>
+<div class="fragment"><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;                               {</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="keywordflow">return</span> ((3 * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i, 2)) - 4);  <span class="comment">// derivative of equation</span></div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/dd3/newton__raphson__method_8cpp_a3d3f7f41977394680af6ebbed96f3386_cgraph.svg" width="192" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
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+
+<div class="memitem">
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+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
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+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;           {</div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));  <span class="comment">// initialize randomizer</span></div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160; </div>
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+<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\nRoot: &quot;</span> &lt;&lt; z &lt;&lt; <span class="stringliteral">&quot;\t\tSteps: &quot;</span> &lt;&lt; i &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="keywordflow">return</span> 0;</div>
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+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
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+</div>
+</div>
+
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
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+<p>Computes N^th Fibonacci number given as input argument. Uses custom build arbitrary integers library to perform additions and other operations.  
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+<div class="textblock"><code>#include &lt;cinttypes&gt;</code><br />
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+Include dependency graph for fibonacci_large.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/de0/fibonacci__large_8cpp__incl.svg" width="646" height="187"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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+</div>
+</div><table class="memberdecls">
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+<tr class="memitem:adf3e906875ab257f7fab3bc1370aa2db"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/de4/fibonacci__large_8cpp.html#adf3e906875ab257f7fab3bc1370aa2db">fib</a> (uint64_t n)</td></tr>
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+<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top"><a id="a0ddf1224851353fc92bfbff6f499fa97"></a>
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+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Computes N^th Fibonacci number given as input argument. Uses custom build arbitrary integers library to perform additions and other operations. </p>
+<p>Took 0.608246 seconds to compute 50,000^th Fibonacci number that contains 10450 digits!</p>
+<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
+<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d9/d89/fibonacci_8cpp.html" title="Generate fibonacci sequence.">fibonacci.cpp</a>, <a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html" title="Faster computation of Fibonacci series.">fibonacci_fast.cpp</a>, <a class="el" href="../../de/d47/string__fibonacci_8cpp.html" title="This Programme returns the Nth fibonacci as a string.">string_fibonacci.cpp</a> </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="adf3e906875ab257f7fab3bc1370aa2db"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#adf3e906875ab257f7fab3bc1370aa2db">&#9670;&nbsp;</a></span>fib()</h2>
+
+<div class="memitem">
+<div class="memproto">
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+        <tr>
+          <td class="memname"><a class="el" href="../../db/d82/classlarge__number.html">large_number</a> fib </td>
+          <td>(</td>
+          <td class="paramtype">uint64_t&#160;</td>
+          <td class="paramname"><em>n</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Compute fibonacci numbers using the relation </p><p class="formulaDsp">
+\[f(n)=f(n-1)+f(n-2)\]
+</p>
+<p> and returns the result as a <a class="el" href="../../db/d82/classlarge__number.html">large_number</a> type. </p>
+<div class="fragment"><div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;                             {</div>
+<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <a class="code" href="../../db/d82/classlarge__number.html">large_number</a> f0(1);</div>
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+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;        f1 += f0;</div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;        f0 = f2;</div>
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+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    } <span class="keywordflow">while</span> (n &gt; 2);  <span class="comment">// since we start from 2</span></div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160; </div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keywordflow">return</span> f1;</div>
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+</div><!-- fragment -->
+</div>
+</div>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="aclasslarge__number_html"><div class="ttname"><a href="../../db/d82/classlarge__number.html">large_number</a></div><div class="ttdef"><b>Definition:</b> large_number.h:24</div></div>
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+    <li class="footer">Generated on Fri Jun 19 2020 16:06:44 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">decimal_to_binary.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Function to convert decimal number to binary representation.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for decimal_to_binary.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d7/dae/decimal__to__binary_8cpp__incl.svg" width="202" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a9240f2e79074a2a248395258aebbfa11"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d06/decimal__to__binary_8cpp.html#a9240f2e79074a2a248395258aebbfa11">method1</a> (int number)</td></tr>
+<tr class="separator:a9240f2e79074a2a248395258aebbfa11"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a10df57491019f0ac39b492740fb388f7"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d06/decimal__to__binary_8cpp.html#a10df57491019f0ac39b492740fb388f7">method2</a> (int number)</td></tr>
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+int&#160;</td><td class="memItemRight" valign="bottom"><b>main</b> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Function to convert decimal number to binary representation. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a9240f2e79074a2a248395258aebbfa11"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a9240f2e79074a2a248395258aebbfa11">&#9670;&nbsp;</a></span>method1()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void method1 </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>number</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>This method converts the bit representation and stores it as a decimal number. </p>
+<div class="fragment"><div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;                         {</div>
+<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;    <span class="keywordtype">int</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/remainder.html">remainder</a>, binary = 0, var = 1;</div>
+<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
+<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;    <span class="keywordflow">do</span> {</div>
+<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/remainder.html">remainder</a> = number % 2;</div>
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+<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;        binary = binary + (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/remainder.html">remainder</a> * var);</div>
+<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;        var = var * 10;</div>
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+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d06/decimal__to__binary_8cpp_a9240f2e79074a2a248395258aebbfa11_cgraph.svg" width="203" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+
+</div>
+</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#a10df57491019f0ac39b492740fb388f7">&#9670;&nbsp;</a></span>method2()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">void method2 </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>number</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>This method stores each bit value from LSB to MSB and then prints them back from MSB to LSB </p>
+<div class="fragment"><div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;                         {</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    <span class="keywordtype">int</span> num_bits = 0;</div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <span class="keywordtype">char</span> bit_string[50];</div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160; </div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="keywordflow">do</span> {</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;        <span class="keywordtype">bool</span> bit = number &amp; 0x01;  <span class="comment">// get last bit</span></div>
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+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;            bit_string[num_bits++] = <span class="charliteral">&#39;1&#39;</span>;</div>
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+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;            bit_string[num_bits++] = <span class="charliteral">&#39;0&#39;</span>;</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;        number &gt;&gt;= 1;  <span class="comment">// right shift bit 1 bit</span></div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    } <span class="keywordflow">while</span> (number &gt; 0);</div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160; </div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Method 2 : &quot;</span>;</div>
+<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keywordflow">while</span> (num_bits &gt;= 0)</div>
+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; bit_string[num_bits--];  <span class="comment">// print from MSB to LSB</span></div>
+<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
+<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d06/decimal__to__binary_8cpp_a10df57491019f0ac39b492740fb388f7_cgraph.svg" width="203" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
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+</div>
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+</div><!-- contents -->
+</div><!-- doc-content -->
+<div class="ttc" id="aremainder_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/remainder.html">std::remainder</a></div><div class="ttdeci">T remainder(T... args)</div></div>
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+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">interpolation_search2.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a href="https://en.wikipedia.org/wiki/Interpolation_search">Interpolation search</a> algorithm  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for interpolation_search2.cpp:</div>
+<div class="dyncontent">
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+Functions</h2></td></tr>
+<tr class="memitem:aa3ec659ec8394d186c761df81ad1f629"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d39/interpolation__search2_8cpp.html#aa3ec659ec8394d186c761df81ad1f629">InterpolationSearch</a> (int A[], int n, int x)</td></tr>
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d39/interpolation__search2_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Interpolation_search">Interpolation search</a> algorithm </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="aa3ec659ec8394d186c761df81ad1f629"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa3ec659ec8394d186c761df81ad1f629">&#9670;&nbsp;</a></span>InterpolationSearch()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int InterpolationSearch </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>A</em>[], </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>x</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>function to search the value in an array using interpolation search </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">arr</td><td>array to search in </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">value</td><td>value to search for </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">len</td><td>length of array </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>index where the value is found </dd>
+<dd>
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+<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;        <span class="keywordtype">int</span> mid = low + (((high - 1) * (x - A[low])) / (A[high] - A[low]));</div>
+<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;        <span class="keywordflow">if</span> (x == A[mid])</div>
+<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;            <span class="keywordflow">return</span> mid;  <span class="comment">// Found x, return (exit)</span></div>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
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+          <td>(</td>
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+<p>main function </p>
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+</div><!--header-->
+<div class="contents">
+
+<p>Method of successive approximations using <a href="https://en.wikipedia.org/wiki/Fixed-point_iteration">fixed-point iteration</a> method.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
+<code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for successive_approximation.cpp:</div>
+<div class="dyncontent">
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+</div>
+</div><table class="memberdecls">
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+Functions</h2></td></tr>
+<tr class="memitem:a79c1d08919ff7780a5d7723172602389"><td class="memItemLeft" align="right" valign="top">static float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dc8/successive__approximation_8cpp.html#a79c1d08919ff7780a5d7723172602389">eq</a> (float y)</td></tr>
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+<tr class="memitem:ae89c36add7c55298c5195d0a83de1456"><td class="memItemLeft" align="right" valign="top">static float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dc8/successive__approximation_8cpp.html#ae89c36add7c55298c5195d0a83de1456">eqd</a> (float y)</td></tr>
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+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dc8/successive__approximation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Method of successive approximations using <a href="https://en.wikipedia.org/wiki/Fixed-point_iteration">fixed-point iteration</a> method. </p>
+</div><h2 class="groupheader">Function Documentation</h2>
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+<h2 class="memtitle"><span class="permalink"><a href="#a79c1d08919ff7780a5d7723172602389">&#9670;&nbsp;</a></span>eq()</h2>
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+  <tr>
+  <td class="mlabels-left">
+      <table class="memname">
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+          <td>(</td>
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+          <td class="paramname"><em>y</em></td><td>)</td>
+          <td></td>
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+<span class="mlabels"><span class="mlabel">static</span></span>  </td>
+  </tr>
+</table>
+</div><div class="memdoc">
+<p>equation 1 </p><p class="formulaDsp">
+\[f(y) = 3y - \cos y -2\]
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+</div><!-- fragment -->
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+        <tr>
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+          <td>(</td>
+          <td class="paramtype">float&#160;</td>
+          <td class="paramname"><em>y</em></td><td>)</td>
+          <td></td>
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+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">static</span></span>  </td>
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+</div><div class="memdoc">
+<p>equation 2 </p><p class="formulaDsp">
+\[f(y) = \frac{\cos y+2}{2}\]
+</p>
+ <div class="fragment"><div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;{ <span class="keywordflow">return</span> 0.5 * (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(y) + 2); }</div>
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+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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+          <td class="memname">int main </td>
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+          <td class="paramname"></td><td>)</td>
+          <td></td>
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+<p>Main function </p>
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+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="header">
+  <div class="summary">
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">binary_search.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p><a href="https://en.wikipedia.org/wiki/Binary_search_algorithm">Binary search algorithm</a>  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for binary_search.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d66/binary__search_8cpp__incl.svg" width="182" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
+</div>
+</div>
+</div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a78df202b718cfe3c2c9216979b08298d"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dd5/binary__search_8cpp.html#a78df202b718cfe3c2c9216979b08298d">binary_search</a> (int <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>[], int r, int key)</td></tr>
+<tr class="separator:a78df202b718cfe3c2c9216979b08298d"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:abf9e6b7e6f15df4b525a2e7705ba3089"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dd5/binary__search_8cpp.html#abf9e6b7e6f15df4b525a2e7705ba3089">main</a> (int argc, char const *argv[])</td></tr>
+<tr class="separator:abf9e6b7e6f15df4b525a2e7705ba3089"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Binary_search_algorithm">Binary search algorithm</a> </p>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="a78df202b718cfe3c2c9216979b08298d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a78df202b718cfe3c2c9216979b08298d">&#9670;&nbsp;</a></span>binary_search()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int binary_search </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>a</em>[], </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>r</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>key</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>binary_search function </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramdir">[in]</td><td class="paramname">a</td><td>array to sort </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">r</td><td>right hand limit = \(n-1\) </td></tr>
+    <tr><td class="paramdir">[in]</td><td class="paramname">key</td><td>value to find </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>index if T is found </dd>
+<dd>
+-1 if T is not found </dd></dl>
+<div class="fragment"><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;                                           {</div>
+<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;    <span class="keywordtype">int</span> l = 0;</div>
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+</div><!-- fragment -->
+</div>
+</div>
+<a id="abf9e6b7e6f15df4b525a2e7705ba3089"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#abf9e6b7e6f15df4b525a2e7705ba3089">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>argc</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">char const *&#160;</td>
+          <td class="paramname"><em>argv</em>[]&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>main function </p>
+<div class="fragment"><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;                                       {</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="keywordtype">int</span> n, key;</div>
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+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter array elements: &quot;</span>;</div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160; </div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="keywordtype">int</span>* <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = <span class="keyword">new</span> <span class="keywordtype">int</span>[n];</div>
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+  <div class="summary">
+<a href="#define-members">Macros</a> &#124;
+<a href="#func-members">Functions</a>  </div>
+  <div class="headertitle">
+<div class="title">power_for_huge_numbers.cpp File Reference</div>  </div>
+</div><!--header-->
+<div class="contents">
+
+<p>Compute powers of large numbers.  
+<a href="#details">More...</a></p>
+<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
+</div><div class="textblock"><div class="dynheader">
+Include dependency graph for power_for_huge_numbers.cpp:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d7/d8e/power__for__huge__numbers_8cpp__incl.svg" width="158" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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+Macros</h2></td></tr>
+<tr class="memitem:a392fb874e547e582e9c66a08a1f23326"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/def/power__for__huge__numbers_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a>&#160;&#160;&#160;100000</td></tr>
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+Functions</h2></td></tr>
+<tr class="memitem:aa141a7904f0c4668bac112d652a3acf9"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/def/power__for__huge__numbers_8cpp.html#aa141a7904f0c4668bac112d652a3acf9">multiply</a> (int x, int res[], int res_size)</td></tr>
+<tr class="separator:aa141a7904f0c4668bac112d652a3acf9"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae249a2af508aa94266023ce8aa81426f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a> (int x, int n)</td></tr>
+<tr class="separator:ae249a2af508aa94266023ce8aa81426f"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/def/power__for__huge__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<div class="textblock"><p>Compute powers of large numbers. </p>
+</div><h2 class="groupheader">Macro Definition Documentation</h2>
+<a id="a392fb874e547e582e9c66a08a1f23326"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a392fb874e547e582e9c66a08a1f23326">&#9670;&nbsp;</a></span>MAX</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">#define MAX&#160;&#160;&#160;100000</td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Maximum number of digits in output \(x^n\) where \(1 &lt;= x,\; n &lt;= 10000\) and overflow may happen </p>
+
+</div>
+</div>
+<h2 class="groupheader">Function Documentation</h2>
+<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int main </td>
+          <td>(</td>
+          <td class="paramname"></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>Main function </p>
+<div class="fragment"><div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;           {</div>
+<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <span class="keywordtype">int</span> exponent, base;</div>
+<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter base &quot;</span>;</div>
+<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; base;</div>
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+<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; exponent;</div>
+<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <a class="code" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a>(base, exponent);</div>
+<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;}</div>
+</div><!-- fragment --><div class="dynheader">
+Here is the call graph for this function:</div>
+<div class="dyncontent">
+<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/def/power__for__huge__numbers_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="282" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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+<h2 class="memtitle"><span class="permalink"><a href="#aa141a7904f0c4668bac112d652a3acf9">&#9670;&nbsp;</a></span>multiply()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname">int multiply </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>res</em>[], </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>res_size</em>&#160;</td>
+        </tr>
+        <tr>
+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
+        </tr>
+      </table>
+</div><div class="memdoc">
+<p>This function multiplies x with the number represented by res[]. res_size is size of res[] or number of digits in the number represented by res[]. This function uses simple school mathematics for multiplication. This function may value of res_size and returns the new value of res_size </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">x</td><td>multiplicand </td></tr>
+    <tr><td class="paramname">res</td><td>large number representation using array </td></tr>
+    <tr><td class="paramname">res_size</td><td>number of digits in <code>res</code> </td></tr>
+  </table>
+  </dd>
+</dl>
+<div class="fragment"><div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;                                             {</div>
+<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <span class="comment">// Initialize carry</span></div>
+<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keywordtype">int</span> carry = 0;</div>
+<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160; </div>
+<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <span class="comment">// One by one multiply n with</span></div>
+<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="comment">// individual digits of res[]</span></div>
+<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; res_size; i++) {</div>
+<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;        <span class="keywordtype">int</span> prod = res[i] * x + carry;</div>
+<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160; </div>
+<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        <span class="comment">// Store last digit of</span></div>
+<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;        <span class="comment">// &#39;prod&#39; in res[]</span></div>
+<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;        res[i] = prod % 10;</div>
+<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160; </div>
+<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;        <span class="comment">// Put rest in carry</span></div>
+<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;        carry = prod / 10;</div>
+<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    }</div>
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+<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    <span class="comment">// Put carry in res and</span></div>
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+<div class="memitem">
+<div class="memproto">
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+        <tr>
+          <td class="memname">void power </td>
+          <td>(</td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>x</em>, </td>
+        </tr>
+        <tr>
+          <td class="paramkey"></td>
+          <td></td>
+          <td class="paramtype">int&#160;</td>
+          <td class="paramname"><em>n</em>&#160;</td>
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+          <td></td>
+          <td>)</td>
+          <td></td><td></td>
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+<p>This function finds power of a number x and print \(x^n\) </p><dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">x</td><td>base </td></tr>
+    <tr><td class="paramname">n</td><td>exponent </td></tr>
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+	text-shadow: none;
+	color: white;
+	margin-right: 4px;
+	padding: 2px 3px;
+	border-radius: 3px;
+	font-size: 7pt;
+	white-space: nowrap;
+	vertical-align: middle;
+}
+
+
+
+/* @end */
+
+/* these are for tree view inside a (index) page */
+
+div.directory {
+        margin: 10px 0px;
+        border-top: 1px solid #9CAFD4;
+        border-bottom: 1px solid #9CAFD4;
+        width: 100%;
+}
+
+.directory table {
+        border-collapse:collapse;
+}
+
+.directory td {
+        margin: 0px;
+        padding: 0px;
+	vertical-align: top;
+}
+
+.directory td.entry {
+        white-space: nowrap;
+        padding-right: 6px;
+	padding-top: 3px;
+}
+
+.directory td.entry a {
+        outline:none;
+}
+
+.directory td.entry a img {
+        border: none;
+}
+
+.directory td.desc {
+        width: 100%;
+        padding-left: 6px;
+	padding-right: 6px;
+	padding-top: 3px;
+	border-left: 1px solid rgba(0,0,0,0.05);
+}
+
+.directory tr.even {
+	padding-left: 6px;
+	background-color: #F7F8FB;
+}
+
+.directory img {
+	vertical-align: -30%;
+}
+
+.directory .levels {
+        white-space: nowrap;
+        width: 100%;
+        text-align: right;
+        font-size: 9pt;
+}
+
+.directory .levels span {
+        cursor: pointer;
+        padding-left: 2px;
+        padding-right: 2px;
+	color: #3D578C;
+}
+
+.arrow {
+    color: #9CAFD4;
+    -webkit-user-select: none;
+    -khtml-user-select: none;
+    -moz-user-select: none;
+    -ms-user-select: none;
+    user-select: none;
+    cursor: pointer;
+    font-size: 80%;
+    display: inline-block;
+    width: 16px;
+    height: 22px;
+}
+
+.icon {
+    font-family: Arial, Helvetica;
+    font-weight: bold;
+    font-size: 12px;
+    height: 14px;
+    width: 16px;
+    display: inline-block;
+    background-color: #728DC1;
+    color: white;
+    text-align: center;
+    border-radius: 4px;
+    margin-left: 2px;
+    margin-right: 2px;
+}
+
+.icona {
+    width: 24px;
+    height: 22px;
+    display: inline-block;
+}
+
+.iconfopen {
+    width: 24px;
+    height: 18px;
+    margin-bottom: 4px;
+    background-image:url('folderopen.png');
+    background-position: 0px -4px;
+    background-repeat: repeat-y;
+    vertical-align:top;
+    display: inline-block;
+}
+
+.iconfclosed {
+    width: 24px;
+    height: 18px;
+    margin-bottom: 4px;
+    background-image:url('folderclosed.png');
+    background-position: 0px -4px;
+    background-repeat: repeat-y;
+    vertical-align:top;
+    display: inline-block;
+}
+
+.icondoc {
+    width: 24px;
+    height: 18px;
+    margin-bottom: 4px;
+    background-image:url('doc.png');
+    background-position: 0px -4px;
+    background-repeat: repeat-y;
+    vertical-align:top;
+    display: inline-block;
+}
+
+table.directory {
+    font: 400 14px Roboto,sans-serif;
+}
+
+/* @end */
+
+div.dynheader {
+        margin-top: 8px;
+	-webkit-touch-callout: none;
+	-webkit-user-select: none;
+	-khtml-user-select: none;
+	-moz-user-select: none;
+	-ms-user-select: none;
+	user-select: none;
+}
+
+address {
+	font-style: normal;
+	color: #2A3D61;
+}
+
+table.doxtable caption {
+	caption-side: top;
+}
+
+table.doxtable {
+	border-collapse:collapse;
+        margin-top: 4px;
+        margin-bottom: 4px;
+}
+
+table.doxtable td, table.doxtable th {
+	border: 1px solid #2D4068;
+	padding: 3px 7px 2px;
+}
+
+table.doxtable th {
+	background-color: #374F7F;
+	color: #FFFFFF;
+	font-size: 110%;
+	padding-bottom: 4px;
+	padding-top: 5px;
+}
+
+table.fieldtable {
+        /*width: 100%;*/
+        margin-bottom: 10px;
+        border: 1px solid #A8B8D9;
+        border-spacing: 0px;
+        -moz-border-radius: 4px;
+        -webkit-border-radius: 4px;
+        border-radius: 4px;
+        -moz-box-shadow: rgba(0, 0, 0, 0.15) 2px 2px 2px;
+        -webkit-box-shadow: 2px 2px 2px rgba(0, 0, 0, 0.15);
+        box-shadow: 2px 2px 2px rgba(0, 0, 0, 0.15);
+}
+
+.fieldtable td, .fieldtable th {
+        padding: 3px 7px 2px;
+}
+
+.fieldtable td.fieldtype, .fieldtable td.fieldname {
+        white-space: nowrap;
+        border-right: 1px solid #A8B8D9;
+        border-bottom: 1px solid #A8B8D9;
+        vertical-align: top;
+}
+
+.fieldtable td.fieldname {
+        padding-top: 3px;
+}
+
+.fieldtable td.fielddoc {
+        border-bottom: 1px solid #A8B8D9;
+        /*width: 100%;*/
+}
+
+.fieldtable td.fielddoc p:first-child {
+        margin-top: 0px;
+}       
+        
+.fieldtable td.fielddoc p:last-child {
+        margin-bottom: 2px;
+}
+
+.fieldtable tr:last-child td {
+        border-bottom: none;
+}
+
+.fieldtable th {
+        background-image:url('nav_f.png');
+        background-repeat:repeat-x;
+        background-color: #E2E8F2;
+        font-size: 90%;
+        color: #253555;
+        padding-bottom: 4px;
+        padding-top: 5px;
+        text-align:left;
+        font-weight: 400;
+        -moz-border-radius-topleft: 4px;
+        -moz-border-radius-topright: 4px;
+        -webkit-border-top-left-radius: 4px;
+        -webkit-border-top-right-radius: 4px;
+        border-top-left-radius: 4px;
+        border-top-right-radius: 4px;
+        border-bottom: 1px solid #A8B8D9;
+}
+
+
+.tabsearch {
+	top: 0px;
+	left: 10px;
+	height: 36px;
+	background-image: url('tab_b.png');
+	z-index: 101;
+	overflow: hidden;
+	font-size: 13px;
+}
+
+.navpath ul
+{
+	font-size: 11px;
+	background-image:url('tab_b.png');
+	background-repeat:repeat-x;
+	background-position: 0 -5px;
+	height:30px;
+	line-height:30px;
+	color:#8AA0CC;
+	border:solid 1px #C2CDE4;
+	overflow:hidden;
+	margin:0px;
+	padding:0px;
+}
+
+.navpath li
+{
+	list-style-type:none;
+	float:left;
+	padding-left:10px;
+	padding-right:15px;
+	background-image:url('bc_s.png');
+	background-repeat:no-repeat;
+	background-position:right;
+	color:#364D7C;
+}
+
+.navpath li.navelem a
+{
+	height:32px;
+	display:block;
+	text-decoration: none;
+	outline: none;
+	color: #283A5D;
+	font-family: 'Lucida Grande',Geneva,Helvetica,Arial,sans-serif;
+	text-shadow: 0px 1px 1px rgba(255, 255, 255, 0.9);
+	text-decoration: none;        
+}
+
+.navpath li.navelem a:hover
+{
+	color:#6884BD;
+}
+
+.navpath li.footer
+{
+        list-style-type:none;
+        float:right;
+        padding-left:10px;
+        padding-right:15px;
+        background-image:none;
+        background-repeat:no-repeat;
+        background-position:right;
+        color:#364D7C;
+        font-size: 8pt;
+}
+
+
+div.summary
+{
+	float: right;
+	font-size: 8pt;
+	padding-right: 5px;
+	width: 50%;
+	text-align: right;
+}       
+
+div.summary a
+{
+	white-space: nowrap;
+}
+
+table.classindex
+{
+        margin: 10px;
+        white-space: nowrap;
+        margin-left: 3%;
+        margin-right: 3%;
+        width: 94%;
+        border: 0;
+        border-spacing: 0; 
+        padding: 0;
+}
+
+div.ingroups
+{
+	font-size: 8pt;
+	width: 50%;
+	text-align: left;
+}
+
+div.ingroups a
+{
+	white-space: nowrap;
+}
+
+div.header
+{
+        background-image:url('nav_h.png');
+        background-repeat:repeat-x;
+	background-color: #F9FAFC;
+	margin:  0px;
+	border-bottom: 1px solid #C4CFE5;
+}
+
+div.headertitle
+{
+	padding: 5px 5px 5px 10px;
+}
+
+.PageDocRTL-title div.headertitle {
+  text-align: right;
+  direction: rtl;
+}
+
+dl {
+        padding: 0 0 0 0;
+}
+
+/* dl.note, dl.warning, dl.attention, dl.pre, dl.post, dl.invariant, dl.deprecated, dl.todo, dl.test, dl.bug, dl.examples */
+dl.section {
+	margin-left: 0px;
+	padding-left: 0px;
+}
+
+dl.section.DocNodeRTL {
+  margin-right: 0px;
+  padding-right: 0px;
+}
+
+dl.note {
+  margin-left: -7px;
+  padding-left: 3px;
+  border-left: 4px solid;
+  border-color: #D0C000;
+}
+
+dl.note.DocNodeRTL {
+  margin-left: 0;
+  padding-left: 0;
+  border-left: 0;
+  margin-right: -7px;
+  padding-right: 3px;
+  border-right: 4px solid;
+  border-color: #D0C000;
+}
+
+dl.warning, dl.attention {
+  margin-left: -7px;
+  padding-left: 3px;
+  border-left: 4px solid;
+  border-color: #FF0000;
+}
+
+dl.warning.DocNodeRTL, dl.attention.DocNodeRTL {
+  margin-left: 0;
+  padding-left: 0;
+  border-left: 0;
+  margin-right: -7px;
+  padding-right: 3px;
+  border-right: 4px solid;
+  border-color: #FF0000;
+}
+
+dl.pre, dl.post, dl.invariant {
+  margin-left: -7px;
+  padding-left: 3px;
+  border-left: 4px solid;
+  border-color: #00D000;
+}
+
+dl.pre.DocNodeRTL, dl.post.DocNodeRTL, dl.invariant.DocNodeRTL {
+  margin-left: 0;
+  padding-left: 0;
+  border-left: 0;
+  margin-right: -7px;
+  padding-right: 3px;
+  border-right: 4px solid;
+  border-color: #00D000;
+}
+
+dl.deprecated {
+  margin-left: -7px;
+  padding-left: 3px;
+  border-left: 4px solid;
+  border-color: #505050;
+}
+
+dl.deprecated.DocNodeRTL {
+  margin-left: 0;
+  padding-left: 0;
+  border-left: 0;
+  margin-right: -7px;
+  padding-right: 3px;
+  border-right: 4px solid;
+  border-color: #505050;
+}
+
+dl.todo {
+  margin-left: -7px;
+  padding-left: 3px;
+  border-left: 4px solid;
+  border-color: #00C0E0;
+}
+
+dl.todo.DocNodeRTL {
+  margin-left: 0;
+  padding-left: 0;
+  border-left: 0;
+  margin-right: -7px;
+  padding-right: 3px;
+  border-right: 4px solid;
+  border-color: #00C0E0;
+}
+
+dl.test {
+  margin-left: -7px;
+  padding-left: 3px;
+  border-left: 4px solid;
+  border-color: #3030E0;
+}
+
+dl.test.DocNodeRTL {
+  margin-left: 0;
+  padding-left: 0;
+  border-left: 0;
+  margin-right: -7px;
+  padding-right: 3px;
+  border-right: 4px solid;
+  border-color: #3030E0;
+}
+
+dl.bug {
+  margin-left: -7px;
+  padding-left: 3px;
+  border-left: 4px solid;
+  border-color: #C08050;
+}
+
+dl.bug.DocNodeRTL {
+  margin-left: 0;
+  padding-left: 0;
+  border-left: 0;
+  margin-right: -7px;
+  padding-right: 3px;
+  border-right: 4px solid;
+  border-color: #C08050;
+}
+
+dl.section dd {
+	margin-bottom: 6px;
+}
+
+
+#projectlogo
+{
+	text-align: center;
+	vertical-align: bottom;
+	border-collapse: separate;
+}
+ 
+#projectlogo img
+{ 
+	border: 0px none;
+}
+ 
+#projectalign
+{
+        vertical-align: middle;
+}
+
+#projectname
+{
+	font: 300% Tahoma, Arial,sans-serif;
+	margin: 0px;
+	padding: 2px 0px;
+}
+    
+#projectbrief
+{
+	font: 120% Tahoma, Arial,sans-serif;
+	margin: 0px;
+	padding: 0px;
+}
+
+#projectnumber
+{
+	font: 50% Tahoma, Arial,sans-serif;
+	margin: 0px;
+	padding: 0px;
+}
+
+#titlearea
+{
+	padding: 0px;
+	margin: 0px;
+	width: 100%;
+	border-bottom: 1px solid #5373B4;
+}
+
+.image
+{
+        text-align: center;
+}
+
+.dotgraph
+{
+        text-align: center;
+}
+
+.mscgraph
+{
+        text-align: center;
+}
+
+.plantumlgraph
+{
+        text-align: center;
+}
+
+.diagraph
+{
+        text-align: center;
+}
+
+.caption
+{
+	font-weight: bold;
+}
+
+div.zoom
+{
+	border: 1px solid #90A5CE;
+}
+
+dl.citelist {
+        margin-bottom:50px;
+}
+
+dl.citelist dt {
+        color:#334975;
+        float:left;
+        font-weight:bold;
+        margin-right:10px;
+        padding:5px;
+}
+
+dl.citelist dd {
+        margin:2px 0;
+        padding:5px 0;
+}
+
+div.toc {
+        padding: 14px 25px;
+        background-color: #F4F6FA;
+        border: 1px solid #D8DFEE;
+        border-radius: 7px 7px 7px 7px;
+        float: right;
+        height: auto;
+        margin: 0 8px 10px 10px;
+        width: 200px;
+}
+
+.PageDocRTL-title div.toc {
+  float: left !important;
+  text-align: right;
+}
+
+div.toc li {
+        background: url("bdwn.png") no-repeat scroll 0 5px transparent;
+        font: 10px/1.2 Verdana,DejaVu Sans,Geneva,sans-serif;
+        margin-top: 5px;
+        padding-left: 10px;
+        padding-top: 2px;
+}
+
+.PageDocRTL-title div.toc li {
+  background-position-x: right !important;
+  padding-left: 0 !important;
+  padding-right: 10px;
+}
+
+div.toc h3 {
+        font: bold 12px/1.2 Arial,FreeSans,sans-serif;
+	color: #4665A2;
+        border-bottom: 0 none;
+        margin: 0;
+}
+
+div.toc ul {
+        list-style: none outside none;
+        border: medium none;
+        padding: 0px;
+}       
+
+div.toc li.level1 {
+        margin-left: 0px;
+}
+
+div.toc li.level2 {
+        margin-left: 15px;
+}
+
+div.toc li.level3 {
+        margin-left: 30px;
+}
+
+div.toc li.level4 {
+        margin-left: 45px;
+}
+
+.PageDocRTL-title div.toc li.level1 {
+  margin-left: 0 !important;
+  margin-right: 0;
+}
+
+.PageDocRTL-title div.toc li.level2 {
+  margin-left: 0 !important;
+  margin-right: 15px;
+}
+
+.PageDocRTL-title div.toc li.level3 {
+  margin-left: 0 !important;
+  margin-right: 30px;
+}
+
+.PageDocRTL-title div.toc li.level4 {
+  margin-left: 0 !important;
+  margin-right: 45px;
+}
+
+.inherit_header {
+        font-weight: bold;
+        color: gray;
+        cursor: pointer;
+	-webkit-touch-callout: none;
+	-webkit-user-select: none;
+	-khtml-user-select: none;
+	-moz-user-select: none;
+	-ms-user-select: none;
+	user-select: none;
+}
+
+.inherit_header td {
+        padding: 6px 0px 2px 5px;
+}
+
+.inherit {
+        display: none;
+}
+
+tr.heading h2 {
+        margin-top: 12px;
+        margin-bottom: 4px;
+}
+
+/* tooltip related style info */
+
+.ttc {
+        position: absolute;
+        display: none;
+}
+
+#powerTip {
+	cursor: default;
+	white-space: nowrap;
+	background-color: white;
+	border: 1px solid gray;
+	border-radius: 4px 4px 4px 4px;
+	box-shadow: 1px 1px 7px gray;
+	display: none;
+	font-size: smaller;
+	max-width: 80%;
+	opacity: 0.9;
+	padding: 1ex 1em 1em;
+	position: absolute;
+	z-index: 2147483647;
+}
+
+#powerTip div.ttdoc {
+        color: grey;
+	font-style: italic;
+}
+
+#powerTip div.ttname a {
+        font-weight: bold;
+}
+
+#powerTip div.ttname {
+        font-weight: bold;
+}
+
+#powerTip div.ttdeci {
+        color: #006318;
+}
+
+#powerTip div {
+        margin: 0px;
+        padding: 0px;
+        font: 12px/16px Roboto,sans-serif;
+}
+
+#powerTip:before, #powerTip:after {
+	content: "";
+	position: absolute;
+	margin: 0px;
+}
+
+#powerTip.n:after,  #powerTip.n:before,
+#powerTip.s:after,  #powerTip.s:before,
+#powerTip.w:after,  #powerTip.w:before,
+#powerTip.e:after,  #powerTip.e:before,
+#powerTip.ne:after, #powerTip.ne:before,
+#powerTip.se:after, #powerTip.se:before,
+#powerTip.nw:after, #powerTip.nw:before,
+#powerTip.sw:after, #powerTip.sw:before {
+	border: solid transparent;
+	content: " ";
+	height: 0;
+	width: 0;
+	position: absolute;
+}
+
+#powerTip.n:after,  #powerTip.s:after,
+#powerTip.w:after,  #powerTip.e:after,
+#powerTip.nw:after, #powerTip.ne:after,
+#powerTip.sw:after, #powerTip.se:after {
+	border-color: rgba(255, 255, 255, 0);
+}
+
+#powerTip.n:before,  #powerTip.s:before,
+#powerTip.w:before,  #powerTip.e:before,
+#powerTip.nw:before, #powerTip.ne:before,
+#powerTip.sw:before, #powerTip.se:before {
+	border-color: rgba(128, 128, 128, 0);
+}
+
+#powerTip.n:after,  #powerTip.n:before,
+#powerTip.ne:after, #powerTip.ne:before,
+#powerTip.nw:after, #powerTip.nw:before {
+	top: 100%;
+}
+
+#powerTip.n:after, #powerTip.ne:after, #powerTip.nw:after {
+	border-top-color: #FFFFFF;
+	border-width: 10px;
+	margin: 0px -10px;
+}
+#powerTip.n:before {
+	border-top-color: #808080;
+	border-width: 11px;
+	margin: 0px -11px;
+}
+#powerTip.n:after, #powerTip.n:before {
+	left: 50%;
+}
+
+#powerTip.nw:after, #powerTip.nw:before {
+	right: 14px;
+}
+
+#powerTip.ne:after, #powerTip.ne:before {
+	left: 14px;
+}
+
+#powerTip.s:after,  #powerTip.s:before,
+#powerTip.se:after, #powerTip.se:before,
+#powerTip.sw:after, #powerTip.sw:before {
+	bottom: 100%;
+}
+
+#powerTip.s:after, #powerTip.se:after, #powerTip.sw:after {
+	border-bottom-color: #FFFFFF;
+	border-width: 10px;
+	margin: 0px -10px;
+}
+
+#powerTip.s:before, #powerTip.se:before, #powerTip.sw:before {
+	border-bottom-color: #808080;
+	border-width: 11px;
+	margin: 0px -11px;
+}
+
+#powerTip.s:after, #powerTip.s:before {
+	left: 50%;
+}
+
+#powerTip.sw:after, #powerTip.sw:before {
+	right: 14px;
+}
+
+#powerTip.se:after, #powerTip.se:before {
+	left: 14px;
+}
+
+#powerTip.e:after, #powerTip.e:before {
+	left: 100%;
+}
+#powerTip.e:after {
+	border-left-color: #FFFFFF;
+	border-width: 10px;
+	top: 50%;
+	margin-top: -10px;
+}
+#powerTip.e:before {
+	border-left-color: #808080;
+	border-width: 11px;
+	top: 50%;
+	margin-top: -11px;
+}
+
+#powerTip.w:after, #powerTip.w:before {
+	right: 100%;
+}
+#powerTip.w:after {
+	border-right-color: #FFFFFF;
+	border-width: 10px;
+	top: 50%;
+	margin-top: -10px;
+}
+#powerTip.w:before {
+	border-right-color: #808080;
+	border-width: 11px;
+	top: 50%;
+	margin-top: -11px;
+}
+
+@media print
+{
+  #top { display: none; }
+  #side-nav { display: none; }
+  #nav-path { display: none; }
+  body { overflow:visible; }
+  h1, h2, h3, h4, h5, h6 { page-break-after: avoid; }
+  .summary { display: none; }
+  .memitem { page-break-inside: avoid; }
+  #doc-content
+  {
+    margin-left:0 !important;
+    height:auto !important;
+    width:auto !important;
+    overflow:inherit;
+    display:inline;
+  }
+}
+
+/* @group Markdown */
+
+table.markdownTable {
+	border-collapse:collapse;
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+ The above copyright notice and this permission notice shall be included in all copies or
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+ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING
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+   <div id="projectname">Algorithms_in_C++
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+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+<div class="textblock">Here is a list of all documented files with brief descriptions:</div><div class="directory">
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+<div id="main-nav"></div>
+</div><!-- top -->
+<div id="side-nav" class="ui-resizable side-nav-resizable">
+  <div id="nav-tree">
+    <div id="nav-tree-contents">
+      <div id="nav-sync" class="sync"></div>
+    </div>
+  </div>
+  <div id="splitbar" style="-moz-user-select:none;" 
+       class="ui-resizable-handle">
+  </div>
+</div>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+$(document).ready(function(){initNavTree('functions.html',''); initResizable(); });
+/* @license-end */
+</script>
+<div id="doc-content">
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
+     onmouseout="return searchBox.OnSearchSelectHide()"
+     onkeydown="return searchBox.OnSearchSelectKey(event)">
+</div>
+
+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+<div class="textblock">Here is a list of all documented class members with links to the class documentation for each member:</div>
+
+<h3><a id="index__5F"></a>- _ -</h3><ul>
+<li>_digits
+: <a class="el" href="db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">large_number</a>
+</li>
+</ul>
+
+
+<h3><a id="index_a"></a>- a -</h3><ul>
+<li>accuracy
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">machine_learning::adaline</a>
+</li>
+<li>adaline()
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#a0acbe32aaab897e7939e5b0454035b8c">machine_learning::adaline</a>
+</li>
+<li>add_digit()
+: <a class="el" href="db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">large_number</a>
+</li>
+<li>addEdge()
+: <a class="el" href="da/d9a/class_graph.html#af765dda8f21280e1cecea19e129f1bc5">Graph</a>
+</li>
+<li>addVertices()
+: <a class="el" href="da/d9a/class_graph.html#ac5a4d9a4f894a179198936042c778413">Graph</a>
+</li>
+</ul>
+
+
+<h3><a id="index_c"></a>- c -</h3><ul>
+<li>capacity
+: <a class="el" href="d2/d05/class_min_heap.html#a88b4aa3e66392a3eabbf2517a9a79a02">MinHeap</a>
+</li>
+<li>check_size_match()
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#ac8a9c2aaaa63b0f27ea176857e1e7d56">machine_learning::adaline</a>
+</li>
+<li>clear()
+: <a class="el" href="d2/d36/structqueue.html#ab2019d91e28c06de325fb3076b93a930">queue&lt; Kind &gt;</a>
+, <a class="el" href="d1/dc2/classstack.html#a5cc5efbbd4ea14b3e378580f1388423b">stack&lt; Type &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_d"></a>- d -</h3><ul>
+<li>decreaseKey()
+: <a class="el" href="d2/d05/class_min_heap.html#aa7f726cc6327955d22871592227432f5">MinHeap</a>
+</li>
+<li>deleteKey()
+: <a class="el" href="d2/d05/class_min_heap.html#a37ac126eabb0c3ce04047172abccca29">MinHeap</a>
+</li>
+<li>deQueue()
+: <a class="el" href="d2/d36/structqueue.html#a089d4af5532e0a801f560070da6e1f86">queue&lt; Kind &gt;</a>
+</li>
+<li>digit_char()
+: <a class="el" href="db/d82/classlarge__number.html#af530d90830d385c76973658ff3214f98">large_number</a>
+</li>
+<li>direction()
+: <a class="el" href="d4/db4/struct_segment_intersection.html#a3beb2ac1b35d67354f1dbaf9a971e655">SegmentIntersection</a>
+</li>
+<li>display()
+: <a class="el" href="d2/d36/structqueue.html#a26f48801df462ade003b50739196fa4c">queue&lt; Kind &gt;</a>
+, <a class="el" href="d1/dc2/classstack.html#a67f65710c376f67d1ba3bde45a9cb628">stack&lt; Type &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_e"></a>- e -</h3><ul>
+<li>Edge()
+: <a class="el" href="d7/d77/class_edge.html#a415a5d002fe11c58711e48aabe975980">Edge</a>
+</li>
+<li>enQueue()
+: <a class="el" href="d2/d36/structqueue.html#a592c0580551ec0d3b4d43e8198d8a377">queue&lt; Kind &gt;</a>
+</li>
+<li>eta
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">machine_learning::adaline</a>
+</li>
+<li>extractMin()
+: <a class="el" href="d2/d05/class_min_heap.html#a4014f1edaed0bd7db0c0d2ca53228980">MinHeap</a>
+</li>
+</ul>
+
+
+<h3><a id="index_f"></a>- f -</h3><ul>
+<li>fit()
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#a74e3c6c037b67895014414c5d75465e5">machine_learning::adaline</a>
+</li>
+<li>front()
+: <a class="el" href="d2/d36/structqueue.html#a36d47fdbedc199609818385110d9f922">queue&lt; Kind &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_g"></a>- g -</h3><ul>
+<li>getAdjList()
+: <a class="el" href="da/d9a/class_graph.html#ae8959064e179573cc48f8cee99115c07">Graph</a>
+</li>
+<li>getMin()
+: <a class="el" href="d2/d05/class_min_heap.html#a336ac71f0d857269fe9a98058a3cd130">MinHeap</a>
+</li>
+<li>getVertices()
+: <a class="el" href="da/d9a/class_graph.html#a8aa88a88269773cc4dba255dec035898">Graph</a>
+</li>
+<li>Graph()
+: <a class="el" href="da/d9a/class_graph.html#ae30edce9b4e7c6347e67edc343f366d8">Graph</a>
+</li>
+</ul>
+
+
+<h3><a id="index_h"></a>- h -</h3><ul>
+<li>harr
+: <a class="el" href="d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">MinHeap</a>
+</li>
+<li>hasChildren()
+: <a class="el" href="dd/d2f/class_trie.html#a6d10eb1669453395d1900ebd401954fb">Trie</a>
+</li>
+<li>heap_size
+: <a class="el" href="d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">MinHeap</a>
+</li>
+</ul>
+
+
+<h3><a id="index_i"></a>- i -</h3><ul>
+<li>insert()
+: <a class="el" href="dd/d2f/class_trie.html#afd8b79959009b554e98ea7128b2886f2">Trie</a>
+</li>
+<li>insertKey()
+: <a class="el" href="d2/d05/class_min_heap.html#aef78f3384f5a0ae880ad0883d2d44b82">MinHeap</a>
+</li>
+<li>isCyclicBFS()
+: <a class="el" href="d3/dbb/class_cycle_check.html#a399292a33edf87499daa52b51315aca5">CycleCheck</a>
+</li>
+<li>isCyclicDFS()
+: <a class="el" href="d3/dbb/class_cycle_check.html#ad9a270ffba3a68539b92272c702e3474">CycleCheck</a>
+</li>
+<li>isCyclicDFSHelper()
+: <a class="el" href="d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">CycleCheck</a>
+</li>
+<li>isEmptyQueue()
+: <a class="el" href="d2/d36/structqueue.html#ac2fff88dce4d7d2eb7134af382bd1b31">queue&lt; Kind &gt;</a>
+</li>
+<li>isEmptyStack()
+: <a class="el" href="d1/dc2/classstack.html#a066e4505155b009913c47b2648b1067a">stack&lt; Type &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_k"></a>- k -</h3><ul>
+<li>key
+: <a class="el" href="d8/d10/structlist.html#aaab2e33bc1ca6f44e72239bfb58f100c">list</a>
+</li>
+</ul>
+
+
+<h3><a id="index_l"></a>- l -</h3><ul>
+<li>large_number()
+: <a class="el" href="db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>
+</li>
+<li>left()
+: <a class="el" href="d2/d05/class_min_heap.html#aa8c6c141e3de664819686aa637e1afca">MinHeap</a>
+</li>
+</ul>
+
+
+<h3><a id="index_m"></a>- m -</h3><ul>
+<li>mean()
+: <a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html#a390697dcee210b91823ceff04b25081b">statistics::stats_computer1&lt; T &gt;</a>
+, <a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html#a8290966ad468f2a8c266d008bc60720e">statistics::stats_computer2&lt; T &gt;</a>
+</li>
+<li>MinHeap()
+: <a class="el" href="d2/d05/class_min_heap.html#ad89ca80a217655a735d266618197965e">MinHeap</a>
+</li>
+<li>MinHeapify()
+: <a class="el" href="d2/d05/class_min_heap.html#aaef438c1056492cb62c4a4d9035b5cad">MinHeap</a>
+</li>
+<li>multiply()
+: <a class="el" href="db/d82/classlarge__number.html#a2f5571e66305cf68bb8283e4aeda58bc">large_number</a>
+</li>
+</ul>
+
+
+<h3><a id="index_n"></a>- n -</h3><ul>
+<li>new_val()
+: <a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html#aa13bf7c38de112f71921a5525d71a2f2">statistics::stats_computer1&lt; T &gt;</a>
+, <a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html#ade6de704deea24fdc88077b3d9a0d534">statistics::stats_computer2&lt; T &gt;</a>
+</li>
+<li>next
+: <a class="el" href="d8/d10/structlist.html#a1900fe79e875e2838625b2eb60837f8f">list</a>
+</li>
+<li>num_digits()
+: <a class="el" href="db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">large_number</a>
+</li>
+</ul>
+
+
+<h3><a id="index_o"></a>- o -</h3><ul>
+<li>on_segment()
+: <a class="el" href="d4/db4/struct_segment_intersection.html#a008941b2272866c64cdaf959afa939bf">SegmentIntersection</a>
+</li>
+<li>operator!=
+: <a class="el" href="db/d82/classlarge__number.html#a72ae1ef050c4c28c50952ecab22d4b94">large_number</a>
+</li>
+<li>operator*=()
+: <a class="el" href="db/d82/classlarge__number.html#ab1af3e0f425cdf7ea2039c9dcfe22f0b">large_number</a>
+</li>
+<li>operator+
+: <a class="el" href="db/d82/classlarge__number.html#a70d23d67535e67030db570e56c00e16d">large_number</a>
+</li>
+<li>operator++()
+: <a class="el" href="db/d82/classlarge__number.html#a622d84883180ff42f04955909adea5a9">large_number</a>
+</li>
+<li>operator+=()
+: <a class="el" href="db/d82/classlarge__number.html#ac27b399ed872731758ec33ebb102730e">large_number</a>
+</li>
+<li>operator&lt;&lt;
+: <a class="el" href="db/d82/classlarge__number.html#a778428c4761b6ea5e7770743f0eab5ab">large_number</a>
+, <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#a1d821a24e1503d468c95d4acedca58b3">machine_learning::adaline</a>
+</li>
+<li>operator=()
+: <a class="el" href="db/d82/classlarge__number.html#aeb22d2aae39d1b1e0bd39c7f47b333eb">large_number</a>
+, <a class="el" href="d1/dc2/classstack.html#a61370d5fbaf9ec6bca4a8c114c1058e1">stack&lt; Type &gt;</a>
+</li>
+<li>operator==
+: <a class="el" href="db/d82/classlarge__number.html#a7ba872b9a3ce1f3da6c06c5409663cca">large_number</a>
+</li>
+<li>operator&gt;&gt;
+: <a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html#ab5b4bfecdf391cae7edb1fe98548b846">statistics::stats_computer1&lt; T &gt;</a>
+, <a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html#a7e7a1a2b0a03df0a70cac40d193421d2">statistics::stats_computer2&lt; T &gt;</a>
+</li>
+<li>operator[]()
+: <a class="el" href="db/d82/classlarge__number.html#ace19126cf343a09efc0010735f6e3a8d">large_number</a>
+</li>
+</ul>
+
+
+<h3><a id="index_p"></a>- p -</h3><ul>
+<li>Point()
+: <a class="el" href="d8/dc8/struct_point.html#ae2d6fb1b3fd3a96169d963d62e37130a">Point</a>
+</li>
+<li>pop()
+: <a class="el" href="d1/dc2/classstack.html#a6cd4b95d5de00d41b2491392338384dc">stack&lt; Type &gt;</a>
+</li>
+<li>predict()
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#ab11242d9ad5b03a75911e29b04f78fd3">machine_learning::adaline</a>
+</li>
+<li>push()
+: <a class="el" href="d1/dc2/classstack.html#a5705c3926dcf5fd3f9c964467a50b81d">stack&lt; Type &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_q"></a>- q -</h3><ul>
+<li>queue()
+: <a class="el" href="d2/d36/structqueue.html#a21381ee7f95daae0332665914780e970">queue&lt; Kind &gt;</a>
+</li>
+<li>queueFront
+: <a class="el" href="d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queue&lt; Kind &gt;</a>
+</li>
+<li>queueRear
+: <a class="el" href="d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queue&lt; Kind &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_r"></a>- r -</h3><ul>
+<li>removeWordHelper()
+: <a class="el" href="dd/d2f/class_trie.html#a95216ffc56cb9f8cede982cecb872af4">Trie</a>
+</li>
+<li>right()
+: <a class="el" href="d2/d05/class_min_heap.html#ac760b85cf90265b8d674b942a43fb70e">MinHeap</a>
+</li>
+</ul>
+
+
+<h3><a id="index_s"></a>- s -</h3><ul>
+<li>search()
+: <a class="el" href="dd/d2f/class_trie.html#a411e77126930a0942dd7b65e96b15206">Trie</a>
+</li>
+<li>stack()
+: <a class="el" href="d1/dc2/classstack.html#a5b64337ec34b12e98458bb9b9d5f8f83">stack&lt; Type &gt;</a>
+</li>
+<li>stackTop
+: <a class="el" href="d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stack&lt; Type &gt;</a>
+</li>
+<li>std()
+: <a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html#af57e942d49f4fd70f059f224b4ac07e1">statistics::stats_computer1&lt; T &gt;</a>
+, <a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html#acf2e84df4fc386bb3295016ef8fd156e">statistics::stats_computer2&lt; T &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_t"></a>- t -</h3><ul>
+<li>test()
+: <a class="el" href="db/d82/classlarge__number.html#a959c5c1a982949bbf98e1ea0f9afe6a9">large_number</a>
+</li>
+<li>top()
+: <a class="el" href="d1/dc2/classstack.html#a21c0bb6ce7dcfe445cc12031977ea344">stack&lt; Type &gt;</a>
+, <a class="el" href="d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">tower</a>
+</li>
+<li>Trie()
+: <a class="el" href="dd/d2f/class_trie.html#a6af57e9f25d0d0a2d59eea5a4a802908">Trie</a>
+</li>
+</ul>
+
+
+<h3><a id="index_v"></a>- v -</h3><ul>
+<li>values
+: <a class="el" href="d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">tower</a>
+</li>
+<li>variance()
+: <a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html#a27f0a03e2fd2254f1c81fe668226bd92">statistics::stats_computer1&lt; T &gt;</a>
+, <a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">statistics::stats_computer2&lt; T &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_w"></a>- w -</h3><ul>
+<li>weights
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">machine_learning::adaline</a>
+</li>
+</ul>
+
+
+<h3><a id="index_x"></a>- x -</h3><ul>
+<li>x
+: <a class="el" href="d8/dc8/struct_point.html#ab99c56589bc8ad5fa5071387110a5bc7">Point</a>
+</li>
+</ul>
+
+
+<h3><a id="index_y"></a>- y -</h3><ul>
+<li>y
+: <a class="el" href="d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">Point</a>
+</li>
+</ul>
+
+
+<h3><a id="index__7E"></a>- ~ -</h3><ul>
+<li>~queue()
+: <a class="el" href="d2/d36/structqueue.html#ad215eee654953d25150bb25d5ac12b7c">queue&lt; Kind &gt;</a>
+</li>
+<li>~stack()
+: <a class="el" href="d1/dc2/classstack.html#a0ac1dba9c7019acdc825b31d06eb0b71">stack&lt; Type &gt;</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
diff --git a/functions_func.html b/functions_func.html
new file mode 100644
index 000000000..088a3d5a2
--- /dev/null
+++ b/functions_func.html
@@ -0,0 +1,364 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml">
+<head>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: Class Members - Functions</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
+<link href="navtree.css" rel="stylesheet" type="text/css"/>
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+<script type="text/javascript" src="search/searchdata.js"></script>
+<script type="text/javascript" src="search/search.js"></script>
+<script type="text/x-mathjax-config">
+  MathJax.Hub.Config({
+    extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
+    jax: ["input/TeX","output/HTML-CSS"],
+});
+</script>
+<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+var searchBox = new SearchBox("searchBox", "search",false,'Search');
+/* @license-end */
+</script>
+<script type="text/javascript" src="menudata.js"></script>
+<script type="text/javascript" src="menu.js"></script>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+$(function() {
+  initMenu('',true,false,'search.php','Search');
+  $(document).ready(function() { init_search(); });
+});
+/* @license-end */</script>
+<div id="main-nav"></div>
+</div><!-- top -->
+<div id="side-nav" class="ui-resizable side-nav-resizable">
+  <div id="nav-tree">
+    <div id="nav-tree-contents">
+      <div id="nav-sync" class="sync"></div>
+    </div>
+  </div>
+  <div id="splitbar" style="-moz-user-select:none;" 
+       class="ui-resizable-handle">
+  </div>
+</div>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+$(document).ready(function(){initNavTree('functions_func.html',''); initResizable(); });
+/* @license-end */
+</script>
+<div id="doc-content">
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
+     onmouseout="return searchBox.OnSearchSelectHide()"
+     onkeydown="return searchBox.OnSearchSelectKey(event)">
+</div>
+
+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+&#160;
+
+<h3><a id="index_a"></a>- a -</h3><ul>
+<li>adaline()
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#a0acbe32aaab897e7939e5b0454035b8c">machine_learning::adaline</a>
+</li>
+<li>add_digit()
+: <a class="el" href="db/d82/classlarge__number.html#a60c436d1a1c5e3795d6177d3815ad615">large_number</a>
+</li>
+<li>addEdge()
+: <a class="el" href="da/d9a/class_graph.html#ac85c63bcca4764a621f9f8609a8e5910">Graph</a>
+</li>
+<li>addVertices()
+: <a class="el" href="da/d9a/class_graph.html#ac5a4d9a4f894a179198936042c778413">Graph</a>
+</li>
+</ul>
+
+
+<h3><a id="index_c"></a>- c -</h3><ul>
+<li>check_size_match()
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#ac8a9c2aaaa63b0f27ea176857e1e7d56">machine_learning::adaline</a>
+</li>
+<li>clear()
+: <a class="el" href="d2/d36/structqueue.html#ab2019d91e28c06de325fb3076b93a930">queue&lt; Kind &gt;</a>
+, <a class="el" href="d1/dc2/classstack.html#a5cc5efbbd4ea14b3e378580f1388423b">stack&lt; Type &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_d"></a>- d -</h3><ul>
+<li>decreaseKey()
+: <a class="el" href="d2/d05/class_min_heap.html#aa7f726cc6327955d22871592227432f5">MinHeap</a>
+</li>
+<li>deleteKey()
+: <a class="el" href="d2/d05/class_min_heap.html#a37ac126eabb0c3ce04047172abccca29">MinHeap</a>
+</li>
+<li>deQueue()
+: <a class="el" href="d2/d36/structqueue.html#a089d4af5532e0a801f560070da6e1f86">queue&lt; Kind &gt;</a>
+</li>
+<li>digit_char()
+: <a class="el" href="db/d82/classlarge__number.html#af530d90830d385c76973658ff3214f98">large_number</a>
+</li>
+<li>direction()
+: <a class="el" href="d4/db4/struct_segment_intersection.html#a3beb2ac1b35d67354f1dbaf9a971e655">SegmentIntersection</a>
+</li>
+<li>display()
+: <a class="el" href="d2/d36/structqueue.html#a26f48801df462ade003b50739196fa4c">queue&lt; Kind &gt;</a>
+, <a class="el" href="d1/dc2/classstack.html#a67f65710c376f67d1ba3bde45a9cb628">stack&lt; Type &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_e"></a>- e -</h3><ul>
+<li>Edge()
+: <a class="el" href="d7/d77/class_edge.html#a415a5d002fe11c58711e48aabe975980">Edge</a>
+</li>
+<li>enQueue()
+: <a class="el" href="d2/d36/structqueue.html#a592c0580551ec0d3b4d43e8198d8a377">queue&lt; Kind &gt;</a>
+</li>
+<li>extractMin()
+: <a class="el" href="d2/d05/class_min_heap.html#a4014f1edaed0bd7db0c0d2ca53228980">MinHeap</a>
+</li>
+</ul>
+
+
+<h3><a id="index_f"></a>- f -</h3><ul>
+<li>fit()
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#a74e3c6c037b67895014414c5d75465e5">machine_learning::adaline</a>
+</li>
+<li>front()
+: <a class="el" href="d2/d36/structqueue.html#a36d47fdbedc199609818385110d9f922">queue&lt; Kind &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_g"></a>- g -</h3><ul>
+<li>getAdjList()
+: <a class="el" href="da/d9a/class_graph.html#ae8959064e179573cc48f8cee99115c07">Graph</a>
+</li>
+<li>getMin()
+: <a class="el" href="d2/d05/class_min_heap.html#a336ac71f0d857269fe9a98058a3cd130">MinHeap</a>
+</li>
+<li>getVertices()
+: <a class="el" href="da/d9a/class_graph.html#a8aa88a88269773cc4dba255dec035898">Graph</a>
+</li>
+<li>Graph()
+: <a class="el" href="da/d9a/class_graph.html#ae30edce9b4e7c6347e67edc343f366d8">Graph</a>
+</li>
+</ul>
+
+
+<h3><a id="index_h"></a>- h -</h3><ul>
+<li>hasChildren()
+: <a class="el" href="dd/d2f/class_trie.html#a6d10eb1669453395d1900ebd401954fb">Trie</a>
+</li>
+</ul>
+
+
+<h3><a id="index_i"></a>- i -</h3><ul>
+<li>insert()
+: <a class="el" href="dd/d2f/class_trie.html#afd8b79959009b554e98ea7128b2886f2">Trie</a>
+</li>
+<li>insertKey()
+: <a class="el" href="d2/d05/class_min_heap.html#aef78f3384f5a0ae880ad0883d2d44b82">MinHeap</a>
+</li>
+<li>isCyclicBFS()
+: <a class="el" href="d3/dbb/class_cycle_check.html#a399292a33edf87499daa52b51315aca5">CycleCheck</a>
+</li>
+<li>isCyclicDFS()
+: <a class="el" href="d3/dbb/class_cycle_check.html#ad9a270ffba3a68539b92272c702e3474">CycleCheck</a>
+</li>
+<li>isCyclicDFSHelper()
+: <a class="el" href="d3/dbb/class_cycle_check.html#a2f4485c08b45e7a21a2e86f9c3f01d8b">CycleCheck</a>
+</li>
+<li>isEmptyQueue()
+: <a class="el" href="d2/d36/structqueue.html#ac2fff88dce4d7d2eb7134af382bd1b31">queue&lt; Kind &gt;</a>
+</li>
+<li>isEmptyStack()
+: <a class="el" href="d1/dc2/classstack.html#a066e4505155b009913c47b2648b1067a">stack&lt; Type &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_l"></a>- l -</h3><ul>
+<li>large_number()
+: <a class="el" href="db/d82/classlarge__number.html#a10119a83839e65962621b73df46a5337">large_number</a>
+</li>
+<li>left()
+: <a class="el" href="d2/d05/class_min_heap.html#aa8c6c141e3de664819686aa637e1afca">MinHeap</a>
+</li>
+</ul>
+
+
+<h3><a id="index_m"></a>- m -</h3><ul>
+<li>mean()
+: <a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html#a390697dcee210b91823ceff04b25081b">statistics::stats_computer1&lt; T &gt;</a>
+, <a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html#a8290966ad468f2a8c266d008bc60720e">statistics::stats_computer2&lt; T &gt;</a>
+</li>
+<li>MinHeap()
+: <a class="el" href="d2/d05/class_min_heap.html#ad89ca80a217655a735d266618197965e">MinHeap</a>
+</li>
+<li>MinHeapify()
+: <a class="el" href="d2/d05/class_min_heap.html#aaef438c1056492cb62c4a4d9035b5cad">MinHeap</a>
+</li>
+<li>multiply()
+: <a class="el" href="db/d82/classlarge__number.html#a2f5571e66305cf68bb8283e4aeda58bc">large_number</a>
+</li>
+</ul>
+
+
+<h3><a id="index_n"></a>- n -</h3><ul>
+<li>new_val()
+: <a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html#aa13bf7c38de112f71921a5525d71a2f2">statistics::stats_computer1&lt; T &gt;</a>
+, <a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html#ade6de704deea24fdc88077b3d9a0d534">statistics::stats_computer2&lt; T &gt;</a>
+</li>
+<li>num_digits()
+: <a class="el" href="db/d82/classlarge__number.html#a2305a82e7b372617419337b2d2119c7d">large_number</a>
+</li>
+</ul>
+
+
+<h3><a id="index_o"></a>- o -</h3><ul>
+<li>on_segment()
+: <a class="el" href="d4/db4/struct_segment_intersection.html#a008941b2272866c64cdaf959afa939bf">SegmentIntersection</a>
+</li>
+<li>operator*=()
+: <a class="el" href="db/d82/classlarge__number.html#ab1af3e0f425cdf7ea2039c9dcfe22f0b">large_number</a>
+</li>
+<li>operator++()
+: <a class="el" href="db/d82/classlarge__number.html#ac4fafa6289295419d48d444f0ae4b706">large_number</a>
+</li>
+<li>operator+=()
+: <a class="el" href="db/d82/classlarge__number.html#ac27b399ed872731758ec33ebb102730e">large_number</a>
+</li>
+<li>operator=()
+: <a class="el" href="db/d82/classlarge__number.html#aeb22d2aae39d1b1e0bd39c7f47b333eb">large_number</a>
+, <a class="el" href="d1/dc2/classstack.html#a61370d5fbaf9ec6bca4a8c114c1058e1">stack&lt; Type &gt;</a>
+</li>
+<li>operator[]()
+: <a class="el" href="db/d82/classlarge__number.html#ace19126cf343a09efc0010735f6e3a8d">large_number</a>
+</li>
+</ul>
+
+
+<h3><a id="index_p"></a>- p -</h3><ul>
+<li>Point()
+: <a class="el" href="d8/dc8/struct_point.html#ae2d6fb1b3fd3a96169d963d62e37130a">Point</a>
+</li>
+<li>pop()
+: <a class="el" href="d1/dc2/classstack.html#a6cd4b95d5de00d41b2491392338384dc">stack&lt; Type &gt;</a>
+</li>
+<li>predict()
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#ab11242d9ad5b03a75911e29b04f78fd3">machine_learning::adaline</a>
+</li>
+<li>push()
+: <a class="el" href="d1/dc2/classstack.html#a5705c3926dcf5fd3f9c964467a50b81d">stack&lt; Type &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_q"></a>- q -</h3><ul>
+<li>queue()
+: <a class="el" href="d2/d36/structqueue.html#a21381ee7f95daae0332665914780e970">queue&lt; Kind &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_r"></a>- r -</h3><ul>
+<li>removeWordHelper()
+: <a class="el" href="dd/d2f/class_trie.html#a95216ffc56cb9f8cede982cecb872af4">Trie</a>
+</li>
+<li>right()
+: <a class="el" href="d2/d05/class_min_heap.html#ac760b85cf90265b8d674b942a43fb70e">MinHeap</a>
+</li>
+</ul>
+
+
+<h3><a id="index_s"></a>- s -</h3><ul>
+<li>search()
+: <a class="el" href="dd/d2f/class_trie.html#a411e77126930a0942dd7b65e96b15206">Trie</a>
+</li>
+<li>stack()
+: <a class="el" href="d1/dc2/classstack.html#a5b64337ec34b12e98458bb9b9d5f8f83">stack&lt; Type &gt;</a>
+</li>
+<li>std()
+: <a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html#af57e942d49f4fd70f059f224b4ac07e1">statistics::stats_computer1&lt; T &gt;</a>
+, <a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html#acf2e84df4fc386bb3295016ef8fd156e">statistics::stats_computer2&lt; T &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index_t"></a>- t -</h3><ul>
+<li>test()
+: <a class="el" href="db/d82/classlarge__number.html#a959c5c1a982949bbf98e1ea0f9afe6a9">large_number</a>
+</li>
+<li>top()
+: <a class="el" href="d1/dc2/classstack.html#a21c0bb6ce7dcfe445cc12031977ea344">stack&lt; Type &gt;</a>
+</li>
+<li>Trie()
+: <a class="el" href="dd/d2f/class_trie.html#a6af57e9f25d0d0a2d59eea5a4a802908">Trie</a>
+</li>
+</ul>
+
+
+<h3><a id="index_v"></a>- v -</h3><ul>
+<li>variance()
+: <a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html#a27f0a03e2fd2254f1c81fe668226bd92">statistics::stats_computer1&lt; T &gt;</a>
+, <a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">statistics::stats_computer2&lt; T &gt;</a>
+</li>
+</ul>
+
+
+<h3><a id="index__7E"></a>- ~ -</h3><ul>
+<li>~queue()
+: <a class="el" href="d2/d36/structqueue.html#ad215eee654953d25150bb25d5ac12b7c">queue&lt; Kind &gt;</a>
+</li>
+<li>~stack()
+: <a class="el" href="d1/dc2/classstack.html#a0ac1dba9c7019acdc825b31d06eb0b71">stack&lt; Type &gt;</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
diff --git a/functions_rela.html b/functions_rela.html
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+<html xmlns="http://www.w3.org/1999/xhtml">
+<head>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: Class Members - Related Functions</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
+<link href="navtree.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="resize.js"></script>
+<script type="text/javascript" src="navtreedata.js"></script>
+<script type="text/javascript" src="navtree.js"></script>
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+<script type="text/javascript" src="search/search.js"></script>
+<script type="text/x-mathjax-config">
+  MathJax.Hub.Config({
+    extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
+    jax: ["input/TeX","output/HTML-CSS"],
+});
+</script>
+<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+var searchBox = new SearchBox("searchBox", "search",false,'Search');
+/* @license-end */
+</script>
+<script type="text/javascript" src="menudata.js"></script>
+<script type="text/javascript" src="menu.js"></script>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+$(function() {
+  initMenu('',true,false,'search.php','Search');
+  $(document).ready(function() { init_search(); });
+});
+/* @license-end */</script>
+<div id="main-nav"></div>
+</div><!-- top -->
+<div id="side-nav" class="ui-resizable side-nav-resizable">
+  <div id="nav-tree">
+    <div id="nav-tree-contents">
+      <div id="nav-sync" class="sync"></div>
+    </div>
+  </div>
+  <div id="splitbar" style="-moz-user-select:none;" 
+       class="ui-resizable-handle">
+  </div>
+</div>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+$(document).ready(function(){initNavTree('functions_rela.html',''); initResizable(); });
+/* @license-end */
+</script>
+<div id="doc-content">
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
+     onmouseout="return searchBox.OnSearchSelectHide()"
+     onkeydown="return searchBox.OnSearchSelectKey(event)">
+</div>
+
+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+&#160;<ul>
+<li>operator!=
+: <a class="el" href="db/d82/classlarge__number.html#a72ae1ef050c4c28c50952ecab22d4b94">large_number</a>
+</li>
+<li>operator+
+: <a class="el" href="db/d82/classlarge__number.html#a70d23d67535e67030db570e56c00e16d">large_number</a>
+</li>
+<li>operator&lt;&lt;
+: <a class="el" href="db/d82/classlarge__number.html#a778428c4761b6ea5e7770743f0eab5ab">large_number</a>
+, <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#a1d821a24e1503d468c95d4acedca58b3">machine_learning::adaline</a>
+</li>
+<li>operator==
+: <a class="el" href="db/d82/classlarge__number.html#a7ba872b9a3ce1f3da6c06c5409663cca">large_number</a>
+</li>
+<li>operator&gt;&gt;
+: <a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html#ab5b4bfecdf391cae7edb1fe98548b846">statistics::stats_computer1&lt; T &gt;</a>
+, <a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html#a7e7a1a2b0a03df0a70cac40d193421d2">statistics::stats_computer2&lt; T &gt;</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
diff --git a/functions_vars.html b/functions_vars.html
new file mode 100644
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--- /dev/null
+++ b/functions_vars.html
@@ -0,0 +1,154 @@
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+<title>Algorithms_in_C++: Class Members - Variables</title>
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+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
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+   <div id="projectname">Algorithms_in_C++
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+  </td>
+ </tr>
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+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
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+<div id="doc-content">
+<!-- window showing the filter options -->
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+<iframe src="javascript:void(0)" frameborder="0" 
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+
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+&#160;<ul>
+<li>_digits
+: <a class="el" href="db/d82/classlarge__number.html#af2b3ec9c35842d3a46ac7326f268af57">large_number</a>
+</li>
+<li>accuracy
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#aa23d60262f917f35836ef4b1c1d9f7d3">machine_learning::adaline</a>
+</li>
+<li>capacity
+: <a class="el" href="d2/d05/class_min_heap.html#a88b4aa3e66392a3eabbf2517a9a79a02">MinHeap</a>
+</li>
+<li>eta
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#a28160d17e492597a2f112e0d38551cda">machine_learning::adaline</a>
+</li>
+<li>harr
+: <a class="el" href="d2/d05/class_min_heap.html#a34a93a87967308eb516328c0aca3c48e">MinHeap</a>
+</li>
+<li>heap_size
+: <a class="el" href="d2/d05/class_min_heap.html#ae4d358bf063bb196a1945b3fb99b4913">MinHeap</a>
+</li>
+<li>key
+: <a class="el" href="d8/d10/structlist.html#aaab2e33bc1ca6f44e72239bfb58f100c">list</a>
+</li>
+<li>next
+: <a class="el" href="d8/d10/structlist.html#a1900fe79e875e2838625b2eb60837f8f">list</a>
+</li>
+<li>queueFront
+: <a class="el" href="d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5">queue&lt; Kind &gt;</a>
+</li>
+<li>queueRear
+: <a class="el" href="d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5">queue&lt; Kind &gt;</a>
+</li>
+<li>stackTop
+: <a class="el" href="d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453">stack&lt; Type &gt;</a>
+</li>
+<li>top
+: <a class="el" href="d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">tower</a>
+</li>
+<li>values
+: <a class="el" href="d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">tower</a>
+</li>
+<li>weights
+: <a class="el" href="d6/d30/classmachine__learning_1_1adaline.html#a4cd8fe438032fedaa66f93bfd66f5492">machine_learning::adaline</a>
+</li>
+<li>x
+: <a class="el" href="d8/dc8/struct_point.html#ab99c56589bc8ad5fa5071387110a5bc7">Point</a>
+</li>
+<li>y
+: <a class="el" href="d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">Point</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
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+<title>Algorithms_in_C++: File Members</title>
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+   <div id="projectname">Algorithms_in_C++
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+  </td>
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+<div id="doc-content">
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+<div id="MSearchSelectWindow"
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+<div class="contents">
+<div class="textblock">Here is a list of all documented file members with links to the documentation:</div>
+
+<h3><a id="index__5F"></a>- _ -</h3><ul>
+<li>_random()
+: <a class="el" href="d9/d66/group__machine__learning.html#gaf5ce14f026d6d231bef29161bac2b485">kohonen_som_topology.cpp</a>
+</li>
+<li>_target
+: <a class="el" href="dc/dfe/ternary__search_8cpp.html#a23ad617bfce1e7cf4591059c85c1a027">ternary_search.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
diff --git a/globals_a.html b/globals_a.html
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+</head>
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+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
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+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">Algorithms_in_C++
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+<!-- end header part -->
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+<script type="text/javascript">
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+/* @license-end */</script>
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+<div id="side-nav" class="ui-resizable side-nav-resizable">
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+<div id="doc-content">
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+<div id="MSearchSelectWindow"
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+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
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+</div>
+
+<div class="contents">
+<div class="textblock">Here is a list of all documented file members with links to the documentation:</div>
+
+<h3><a id="index_a"></a>- a -</h3><ul>
+<li>a
+: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">matrix_exponentiation.cpp</a>
+</li>
+<li>ab()
+: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#a8bcf0bfddddfd7f6d0848703632d795d">matrix_exponentiation.cpp</a>
+</li>
+<li>absolutePrecision
+: <a class="el" href="dc/dfe/ternary__search_8cpp.html#ae01eda5098801bb6b5b778828fb4fddc">ternary_search.cpp</a>
+</li>
+<li>ACCURACY
+: <a class="el" href="da/df2/durand__kerner__roots_8cpp.html#af270a96662132d0385cb6b4637c5a689">durand_kerner_roots.cpp</a>
+</li>
+<li>add()
+: <a class="el" href="de/d47/string__fibonacci_8cpp.html#a28052eee05d43c2ebc5147c52bd50c35">string_fibonacci.cpp</a>
+</li>
+<li>addition_rule_dependent()
+: <a class="el" href="d6/d4a/addition__rule_8cpp.html#a565ffcbbdbe496ced37250bc8dc36bc0">addition_rule.cpp</a>
+</li>
+<li>addition_rule_independent()
+: <a class="el" href="d6/d4a/addition__rule_8cpp.html#a4adfd055c758546456d440ee9133555d">addition_rule.cpp</a>
+</li>
+<li>ans()
+: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">matrix_exponentiation.cpp</a>
+</li>
+<li>AvailArray
+: <a class="el" href="d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">linkedlist_implentation_usingarray.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
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+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
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+<div class="contents">
+&#160;<ul>
+<li>_target
+: <a class="el" href="dc/dfe/ternary__search_8cpp.html#a23ad617bfce1e7cf4591059c85c1a027">ternary_search.cpp</a>
+</li>
+<li>absolutePrecision
+: <a class="el" href="dc/dfe/ternary__search_8cpp.html#ae01eda5098801bb6b5b778828fb4fddc">ternary_search.cpp</a>
+</li>
+<li>ACCURACY
+: <a class="el" href="da/df2/durand__kerner__roots_8cpp.html#af270a96662132d0385cb6b4637c5a689">durand_kerner_roots.cpp</a>
+</li>
+<li>endl
+: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">matrix_exponentiation.cpp</a>
+</li>
+<li>HASHMAX
+: <a class="el" href="d1/df3/hash__search_8cpp.html#a77c722016053a1d484aa177ce205b367">hash_search.cpp</a>
+</li>
+<li>LIMS
+: <a class="el" href="de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">qr_eigen_values.cpp</a>
+</li>
+<li>ll
+: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">matrix_exponentiation.cpp</a>
+</li>
+<li>MAX
+: <a class="el" href="df/def/power__for__huge__numbers_8cpp.html#a392fb874e547e582e9c66a08a1f23326">power_for_huge_numbers.cpp</a>
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+, <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#a392fb874e547e582e9c66a08a1f23326">paranthesis_matching.cpp</a>
+</li>
+<li>MAX_ITERATIONS
+: <a class="el" href="d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">bisection_method.cpp</a>
+, <a class="el" href="de/dd3/newton__raphson__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">newton_raphson_method.cpp</a>
+, <a class="el" href="dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">false_position.cpp</a>
+</li>
+<li>MAX_NUM
+: <a class="el" href="d9/d69/median__search_8cpp.html#a55bfdcfe7613d75fb48ec99c7bf4dd5e">median_search.cpp</a>
+</li>
+<li>MIN_DISTANCE
+: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a549d41dcf9444ed7d6df1da3c73e7d16">kohonen_som_topology.cpp</a>
+</li>
+<li>pb
+: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#a276c5a0e984cf60015b27252fe04fe6b">matrix_exponentiation.cpp</a>
+</li>
+<li>PRIME
+: <a class="el" href="d6/dce/rabin__karp_8cpp.html#ac4add2a227a10511e0128d63952030e8">rabin_karp.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
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+<title>Algorithms_in_C++: File Members</title>
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+<script type="text/javascript" src="dynsections.js"></script>
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+<div id="titlearea">
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+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
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+<div class="contents">
+<div class="textblock">Here is a list of all documented file members with links to the documentation:</div>
+
+<h3><a id="index_e"></a>- e -</h3><ul>
+<li>endl
+: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">matrix_exponentiation.cpp</a>
+</li>
+<li>eq()
+: <a class="el" href="d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">bisection_method.cpp</a>
+, <a class="el" href="de/dd3/newton__raphson__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">newton_raphson_method.cpp</a>
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+, <a class="el" href="dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">false_position.cpp</a>
+</li>
+<li>eq_der()
+: <a class="el" href="de/dd3/newton__raphson__method_8cpp.html#a3d3f7f41977394680af6ebbed96f3386">newton_raphson_method.cpp</a>
+</li>
+<li>eqd()
+: <a class="el" href="df/dc8/successive__approximation_8cpp.html#ae89c36add7c55298c5195d0a83de1456">successive_approximation.cpp</a>
+</li>
+<li>exact_solution()
+: <a class="el" href="db/dd3/ode__forward__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">ode_forward_euler.cpp</a>
+, <a class="el" href="d3/d06/ode__semi__implicit__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">ode_semi_implicit_euler.cpp</a>
+, <a class="el" href="d6/dd3/ode__midpoint__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">ode_midpoint_euler.cpp</a>
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+<li>extendedEuclid()
+: <a class="el" href="d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d">extended_euclid_algorithm.cpp</a>
+</li>
+<li>extendedEuclid_1()
+: <a class="el" href="d9/d5d/extended__euclid__algorithm_8cpp.html#a1792ac7c33aaf26b860ab55f5652ab25">extended_euclid_algorithm.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
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+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: File Members</title>
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+<script type="text/javascript" src="dynsections.js"></script>
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+   <div id="projectname">Algorithms_in_C++
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+<div class="contents">
+<div class="textblock">Here is a list of all documented file members with links to the documentation:</div>
+
+<h3><a id="index_f"></a>- f -</h3><ul>
+<li>f
+: <a class="el" href="d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">fibonacci_fast.cpp</a>
+</li>
+<li>fact()
+: <a class="el" href="d9/d24/poisson__dist_8cpp.html#a63ffd347e75d5ed7a518cbcfbfeec71a">poisson_dist.cpp</a>
+</li>
+<li>factorial()
+: <a class="el" href="d9/d00/factorial_8cpp.html#ae9945c15826a9c1b5c141db314b7f8b4">factorial.cpp</a>
+</li>
+<li>factors
+: <a class="el" href="db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">prime_factorization.cpp</a>
+</li>
+<li>fast_power_linear()
+: <a class="el" href="d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power.cpp</a>
+</li>
+<li>fast_power_recursive()
+: <a class="el" href="d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power.cpp</a>
+</li>
+<li>fastinput()
+: <a class="el" href="d4/de8/fast__interger__input_8cpp.html#a4e097ac8509b717bdc8ab09ecd86ae82">fast_interger_input.cpp</a>
+</li>
+<li>fib()
+: <a class="el" href="d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fibonacci_fast.cpp</a>
+, <a class="el" href="de/de4/fibonacci__large_8cpp.html#adf3e906875ab257f7fab3bc1370aa2db">fibonacci_large.cpp</a>
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+<li>fib_Accurate()
+: <a class="el" href="de/d47/string__fibonacci_8cpp.html#ad8055ee368a5d5b24de01bdde6bf8fca">string_fibonacci.cpp</a>
+</li>
+<li>fibonacci()
+: <a class="el" href="d9/d89/fibonacci_8cpp.html#a4bc27e88a3da5cc590f1f78622019a7b">fibonacci.cpp</a>
+</li>
+<li>fill()
+: <a class="el" href="de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">decimal_to_roman_numeral.cpp</a>
+</li>
+<li>fit_OLS_regressor()
+: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a38ff1d954e9b7de93eb20e2dd101a045">ordinary_least_squares_regressor.cpp</a>
+</li>
+<li>forward_euler()
+: <a class="el" href="d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">ode_forward_euler.cpp</a>
+</li>
+<li>forward_euler_step()
+: <a class="el" href="d6/d60/group__ode.html#gaa197c6b7085ac9ea71abc4c063e6f52f">ode_forward_euler.cpp</a>
+</li>
+<li>freeNode()
+: <a class="el" href="d3/dce/linkedlist__implentation__usingarray_8cpp.html#a08ba214242a900e7251cec556b592f02">linkedlist_implentation_usingarray.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
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+: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a38ff1d954e9b7de93eb20e2dd101a045">ordinary_least_squares_regressor.cpp</a>
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+&#160;
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+<li>pascal_triangle()
+: <a class="el" href="dc/d1a/pascal__triangle_8cpp.html#afd3f52dd56ddedbf7af5d26a202a199e">pascal_triangle.cpp</a>
+</li>
+<li>phiFunction()
+: <a class="el" href="da/d23/eulers__totient__function_8cpp.html#a35e4874a3e1d67eb708dc57944c8aea0">eulers_totient_function.cpp</a>
+</li>
+<li>PointInCircle()
+: <a class="el" href="d0/d01/smallest__circle_8cpp.html#aee6d48762c1dfb9f14627927f0c16fad">smallest_circle.cpp</a>
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+</li>
+<li>poisson_x_successes()
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+</li>
+<li>poly_function()
+: <a class="el" href="da/df2/durand__kerner__roots_8cpp.html#a51637ff89e55ca749993d3e84b95d153">durand_kerner_roots.cpp</a>
+</li>
+<li>pop()
+: <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#a6d25c7dfbfeb52c3cb9d1b56ab49b664">paranthesis_matching.cpp</a>
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+: <a class="el" href="df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power_for_huge_numbers.cpp</a>
+, <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#a5769b745458157ef2679949155684f3b">matrix_exponentiation.cpp</a>
+</li>
+<li>predict_OLS_regressor()
+: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a4bcaaf41c66da4d3a471dacef133def7">ordinary_least_squares_regressor.cpp</a>
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+</li>
+<li>primes()
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+<li>print()
+: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#af50a5c87d27cfd3462745b37fb9b0f46">sieve_of_eratosthenes.cpp</a>
+</li>
+<li>problem()
+: <a class="el" href="d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">ode_semi_implicit_euler.cpp</a>
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+, <a class="el" href="db/dd3/ode__forward__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">ode_forward_euler.cpp</a>
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+<li>push()
+: <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#aae41c72130114bf31204cde6873b6095">paranthesis_matching.cpp</a>
+</li>
+</ul>
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+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
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+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+<h3><a id="index_s"></a>- s -</h3><ul>
+<li>save_2d_data()
+: <a class="el" href="d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336">kohonen_som_topology.cpp</a>
+</li>
+<li>save_exact_solution()
+: <a class="el" href="db/dd3/ode__forward__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">ode_forward_euler.cpp</a>
+, <a class="el" href="d3/d06/ode__semi__implicit__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">ode_semi_implicit_euler.cpp</a>
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+</li>
+<li>semi_implicit_euler()
+: <a class="el" href="d6/d60/group__ode.html#ga3874d294ab00fe9ce8731c5b7991a089">ode_semi_implicit_euler.cpp</a>
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+<li>semi_implicit_euler_step()
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+<li>sgn()
+: <a class="el" href="d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">bisection_method.cpp</a>
+, <a class="el" href="dd/d29/false__position_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">false_position.cpp</a>
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+<li>show()
+: <a class="el" href="db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">tower_of_hanoi.cpp</a>
+</li>
+<li>show_data()
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+<li>show_pascal()
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+</li>
+<li>Sieve()
+: <a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html#a031cada84819ed6426f58e4f7e81261c">primes_up_to_billion.cpp</a>
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+: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#abce89d8999986f085c368969590376b8">sieve_of_eratosthenes.cpp</a>
+</li>
+<li>SieveOfEratosthenes()
+: <a class="el" href="db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">prime_factorization.cpp</a>
+</li>
+<li>spiralPrint()
+: <a class="el" href="db/d07/spiral__print_8cpp.html#a850d3f55e1a8d227176cdcc67352c197">spiral_print.cpp</a>
+</li>
+<li>Sqrt()
+: <a class="el" href="da/d24/sqrt__double_8cpp.html#ae662282ad0740d2063ac404ca3bd74fc">sqrt_double.cpp</a>
+</li>
+<li>struzik_search()
+: <a class="el" href="d8/d8a/exponential__search_8cpp.html#a67e9c84b4e2eb30e3c5170eabfbb363d">exponential_search.cpp</a>
+</li>
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+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+&#160;
+
+<h3><a id="index_t"></a>- t -</h3><ul>
+<li>ternary_search()
+: <a class="el" href="dc/dfe/ternary__search_8cpp.html#aef655a27eb82efa299bf9d0becf6e9c8">ternary_search.cpp</a>
+</li>
+<li>test()
+: <a class="el" href="d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">smallest_circle.cpp</a>
+</li>
+<li>test1()
+: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">kohonen_som_topology.cpp</a>
+, <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">qr_eigen_values.cpp</a>
+, <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">kohonen_som_trace.cpp</a>
+, <a class="el" href="d5/db0/adaline__learning_8cpp.html#a52053d88ea1bcbbed9aca67ab4eeb499">adaline_learning.cpp</a>
+, <a class="el" href="d6/d9d/large__factorial_8cpp.html#a3f93b60e229b6683e24c4754a7106ee8">large_factorial.cpp</a>
+, <a class="el" href="da/df2/durand__kerner__roots_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">durand_kerner_roots.cpp</a>
+</li>
+<li>test2()
+: <a class="el" href="d5/db0/adaline__learning_8cpp.html#a379f7488a305f2571f2932b319931f82">adaline_learning.cpp</a>
+, <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a0283886819c7c140a023582b7269e2d0">kohonen_som_topology.cpp</a>
+, <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a0283886819c7c140a023582b7269e2d0">kohonen_som_trace.cpp</a>
+, <a class="el" href="d6/d9d/large__factorial_8cpp.html#a76aae4778fbe89a3d59fd61fbc050cfa">large_factorial.cpp</a>
+, <a class="el" href="da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">durand_kerner_roots.cpp</a>
+, <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">qr_eigen_values.cpp</a>
+, <a class="el" href="d0/d01/smallest__circle_8cpp.html#a0283886819c7c140a023582b7269e2d0">smallest_circle.cpp</a>
+</li>
+<li>test3()
+: <a class="el" href="d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">smallest_circle.cpp</a>
+, <a class="el" href="d5/db0/adaline__learning_8cpp.html#a992bdf1fdb0b9d414bcf7981d2d87aa9">adaline_learning.cpp</a>
+, <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_topology.cpp</a>
+, <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_trace.cpp</a>
+</li>
+<li>test_2d_classes()
+: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a6b5e744876fd980a3451cbb385d4e755">kohonen_som_topology.cpp</a>
+</li>
+<li>test_3d_classes()
+: <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a9ab8c79ffb674a63f151f282faeb723b">kohonen_som_trace.cpp</a>
+</li>
+<li>test_3d_classes1()
+: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#ab3081e021270ba21a9fd88646f6a6e26">kohonen_som_topology.cpp</a>
+</li>
+<li>test_3d_classes2()
+: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a0e7435446ed7c763f7de79a468add2e0">kohonen_som_topology.cpp</a>
+</li>
+<li>test_circle()
+: <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#ab47fb569e63648bd76e7edfdacc02dbd">kohonen_som_trace.cpp</a>
+</li>
+<li>test_f()
+: <a class="el" href="d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">shell_sort2.cpp</a>
+</li>
+<li>test_function()
+: <a class="el" href="d0/d08/realtime__stats_8cpp.html#aa54c915581fcc495489175a4386d59fd">realtime_stats.cpp</a>
+</li>
+<li>test_int()
+: <a class="el" href="d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">shell_sort2.cpp</a>
+</li>
+<li>test_lamniscate()
+: <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a412b7afa156306b1f8788643c91a1c60">kohonen_som_trace.cpp</a>
+</li>
+<li>tests()
+: <a class="el" href="d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">least_common_multiple.cpp</a>
+</li>
+<li>TH()
+: <a class="el" href="db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">tower_of_hanoi.cpp</a>
+</li>
+<li>tolowerRoman()
+: <a class="el" href="de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">decimal_to_roman_numeral.cpp</a>
+</li>
+<li>toupperRoman()
+: <a class="el" href="de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">decimal_to_roman_numeral.cpp</a>
+</li>
+<li>TriangleArea()
+: <a class="el" href="d0/d01/smallest__circle_8cpp.html#a94682a4a70d5906857ca09de5b9fb2cc">smallest_circle.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
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+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
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+<div id="doc-content">
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+</iframe>
+</div>
+
+<div class="contents">
+&#160;
+
+<h3><a id="index_u"></a>- u -</h3><ul>
+<li>update_step()
+: <a class="el" href="d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">extended_euclid_algorithm.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
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+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: File Members</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
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+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
+  </td>
+ </tr>
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+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
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+    </div>
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+  <div id="splitbar" style="-moz-user-select:none;" 
+       class="ui-resizable-handle">
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+</div>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+$(document).ready(function(){initNavTree('globals_g.html',''); initResizable(); });
+/* @license-end */
+</script>
+<div id="doc-content">
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
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+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+<div class="textblock">Here is a list of all documented file members with links to the documentation:</div>
+
+<h3><a id="index_g"></a>- g -</h3><ul>
+<li>gcd()
+: <a class="el" href="d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd_iterative_euclidean.cpp</a>
+, <a class="el" href="d1/d11/gcd__of__n__numbers_8cpp.html#a25034543c20f271da04fb24ad2b2747a">gcd_of_n_numbers.cpp</a>
+, <a class="el" href="d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">least_common_multiple.cpp</a>
+, <a class="el" href="d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd_recursive_euclidean.cpp</a>
+</li>
+<li>genArray()
+: <a class="el" href="db/d07/spiral__print_8cpp.html#acfff36db81326fb990a643ab198ee8a5">spiral_print.cpp</a>
+</li>
+<li>get_clock_diff()
+: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a2256c10b16edba377b64a44b6c656908">kohonen_som_topology.cpp</a>
+, <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a2256c10b16edba377b64a44b6c656908">kohonen_som_trace.cpp</a>
+</li>
+<li>get_input()
+: <a class="el" href="dc/dfe/ternary__search_8cpp.html#a7f7d866eccdabe51bb16818a792618b1">ternary_search.cpp</a>
+</li>
+<li>get_inverse()
+: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a98ab8f75d981088369b89b8be2182483">ordinary_least_squares_regressor.cpp</a>
+</li>
+<li>get_min_2d()
+: <a class="el" href="d9/d66/group__machine__learning.html#gab53c14440b2b2dd3172c66afc5c2f63f">kohonen_som_topology.cpp</a>
+</li>
+<li>get_transpose()
+: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a889f9de199fa793497c864d8e493af05">ordinary_least_squares_regressor.cpp</a>
+</li>
+<li>getBalance()
+: <a class="el" href="d8/dee/avltree_8cpp.html#aaa457ffec24c9643f2768e7a65e96546">avltree.cpp</a>
+</li>
+<li>getnode()
+: <a class="el" href="d3/dce/linkedlist__implentation__usingarray_8cpp.html#a73e11e0871f56342a30da93b6c93e8be">linkedlist_implentation_usingarray.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
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+, <a class="el" href="dc/d93/trie__modern_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">trie_modern.cpp</a>
+, <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">kohonen_som_topology.cpp</a>
+, <a class="el" href="d9/d5d/extended__euclid__algorithm_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">extended_euclid_algorithm.cpp</a>
+, <a class="el" href="df/def/power__for__huge__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">power_for_huge_numbers.cpp</a>
+, <a class="el" href="db/d0d/prime__factorization_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">prime_factorization.cpp</a>
+, <a class="el" href="de/d47/string__fibonacci_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">string_fibonacci.cpp</a>
+, <a class="el" href="da/d24/sqrt__double_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">sqrt_double.cpp</a>
+, <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">sieve_of_eratosthenes.cpp</a>
+, <a class="el" href="d0/d08/realtime__stats_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">realtime_stats.cpp</a>
+, <a class="el" href="d9/d00/factorial_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">factorial.cpp</a>
+, <a class="el" href="de/d9b/prime__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">prime_numbers.cpp</a>
+, <a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">primes_up_to_billion.cpp</a>
+, <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">kohonen_som_trace.cpp</a>
+, <a class="el" href="d2/d0b/fast__power_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">fast_power.cpp</a>
+, <a class="el" href="d9/d89/fibonacci_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">fibonacci.cpp</a>
+</li>
+<li>mat_mul()
+: <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a7558fd7779bf207157ced66f275951a0">qr_eigen_values.cpp</a>
+</li>
+<li>MAX
+: <a class="el" href="dc/dfe/ternary__search_8cpp.html#a392fb874e547e582e9c66a08a1f23326">ternary_search.cpp</a>
+, <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#a392fb874e547e582e9c66a08a1f23326">paranthesis_matching.cpp</a>
+, <a class="el" href="d4/d32/fibonacci__fast_8cpp.html#a692ac7187ee88621a9f78fca78ec498d">fibonacci_fast.cpp</a>
+, <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a392fb874e547e582e9c66a08a1f23326">sieve_of_eratosthenes.cpp</a>
+, <a class="el" href="df/def/power__for__huge__numbers_8cpp.html#a392fb874e547e582e9c66a08a1f23326">power_for_huge_numbers.cpp</a>
+, <a class="el" href="d1/df3/hash__search_8cpp.html#a392fb874e547e582e9c66a08a1f23326">hash_search.cpp</a>
+</li>
+<li>MAX_ITERATIONS
+: <a class="el" href="d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">bisection_method.cpp</a>
+, <a class="el" href="dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">false_position.cpp</a>
+, <a class="el" href="de/dd3/newton__raphson__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">newton_raphson_method.cpp</a>
+</li>
+<li>MAX_NUM
+: <a class="el" href="d9/d69/median__search_8cpp.html#a55bfdcfe7613d75fb48ec99c7bf4dd5e">median_search.cpp</a>
+</li>
+<li>method1()
+: <a class="el" href="df/d06/decimal__to__binary_8cpp.html#a9240f2e79074a2a248395258aebbfa11">decimal_to_binary.cpp</a>
+</li>
+<li>method2()
+: <a class="el" href="df/d06/decimal__to__binary_8cpp.html#a10df57491019f0ac39b492740fb388f7">decimal_to_binary.cpp</a>
+</li>
+<li>midpoint_euler()
+: <a class="el" href="d6/d60/group__ode.html#ga36ff0710861ca39d957046c0b09b2985">ode_midpoint_euler.cpp</a>
+</li>
+<li>midpoint_euler_step()
+: <a class="el" href="d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">ode_midpoint_euler.cpp</a>
+</li>
+<li>MIN_DISTANCE
+: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a549d41dcf9444ed7d6df1da3c73e7d16">kohonen_som_topology.cpp</a>
+</li>
+<li>minValue()
+: <a class="el" href="d8/dee/avltree_8cpp.html#adb8e952bf1c266bae84111b9d6a12015">avltree.cpp</a>
+</li>
+<li>mov()
+: <a class="el" href="db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">tower_of_hanoi.cpp</a>
+</li>
+<li>multiply()
+: <a class="el" href="df/def/power__for__huge__numbers_8cpp.html#aa141a7904f0c4668bac112d652a3acf9">power_for_huge_numbers.cpp</a>
+, <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#ac62a499b83c7895dd0aa69da1b64c904">matrix_exponentiation.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
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+<meta name="generator" content="Doxygen 1.8.18"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: File Members</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
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+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
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+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
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+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
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+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
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+</iframe>
+</div>
+
+<div class="contents">
+<div class="textblock">Here is a list of all documented file members with links to the documentation:</div>
+
+<h3><a id="index_n"></a>- n -</h3><ul>
+<li>nCr()
+: <a class="el" href="d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">binomial_dist.cpp</a>
+</li>
+<li>node
+: <a class="el" href="d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">hash_search.cpp</a>
+</li>
+<li>number_of_positive_divisors()
+: <a class="el" href="d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
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+<meta name="generator" content="Doxygen 1.8.18"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: File Members</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
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+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+  <div id="nav-tree">
+    <div id="nav-tree-contents">
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+  </div>
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+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+<div id="doc-content">
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+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+<div class="textblock">Here is a list of all documented file members with links to the documentation:</div>
+
+<h3><a id="index_o"></a>- o -</h3><ul>
+<li>opening()
+: <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#ade525d33459755a32ba21e1b6910ff21">paranthesis_matching.cpp</a>
+</li>
+<li>operator*()
+: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#ab6171f4db68a5e50ae0f3500a63acd26">ordinary_least_squares_regressor.cpp</a>
+</li>
+<li>operator+()
+: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a67249e31221231cf3aaf3cfd870372d0">ordinary_least_squares_regressor.cpp</a>
+</li>
+<li>operator-()
+: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a31be3fe36e76b87d5616ff8e7918cd24">ordinary_least_squares_regressor.cpp</a>
+</li>
+<li>operator/()
+: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a30acf52af3184bc22274234ef5a73536">ordinary_least_squares_regressor.cpp</a>
+</li>
+<li>operator&lt;&lt;()
+: <a class="el" href="dd/d65/lu__decompose_8cpp.html#a98eb5807f21b783c341cab402ced6732">lu_decompose.cpp</a>
+, <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#aa799b4cec1681219887d89d037cfab50">ordinary_least_squares_regressor.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
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+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+<div class="textblock">Here is a list of all documented file members with links to the documentation:</div>
+
+<h3><a id="index_p"></a>- p -</h3><ul>
+<li>pascal_triangle()
+: <a class="el" href="dc/d1a/pascal__triangle_8cpp.html#afd3f52dd56ddedbf7af5d26a202a199e">pascal_triangle.cpp</a>
+</li>
+<li>pb
+: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#a276c5a0e984cf60015b27252fe04fe6b">matrix_exponentiation.cpp</a>
+</li>
+<li>phiFunction()
+: <a class="el" href="da/d23/eulers__totient__function_8cpp.html#a35e4874a3e1d67eb708dc57944c8aea0">eulers_totient_function.cpp</a>
+</li>
+<li>PointInCircle()
+: <a class="el" href="d0/d01/smallest__circle_8cpp.html#aee6d48762c1dfb9f14627927f0c16fad">smallest_circle.cpp</a>
+</li>
+<li>poisson_expected()
+: <a class="el" href="d9/d24/poisson__dist_8cpp.html#ad0aa718023ce802dd5899f0e03a7ac71">poisson_dist.cpp</a>
+</li>
+<li>poisson_range_successes()
+: <a class="el" href="d9/d24/poisson__dist_8cpp.html#ad9c9e74079278ca10e3b97a8d5391c9a">poisson_dist.cpp</a>
+</li>
+<li>poisson_rate()
+: <a class="el" href="d9/d24/poisson__dist_8cpp.html#ac217ab9a06291f360d816700a6958ca8">poisson_dist.cpp</a>
+</li>
+<li>poisson_x_successes()
+: <a class="el" href="d9/d24/poisson__dist_8cpp.html#a69a136b32707bdc7950fb9057b5fa1e1">poisson_dist.cpp</a>
+</li>
+<li>poly_function()
+: <a class="el" href="da/df2/durand__kerner__roots_8cpp.html#a51637ff89e55ca749993d3e84b95d153">durand_kerner_roots.cpp</a>
+</li>
+<li>pop()
+: <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#a6d25c7dfbfeb52c3cb9d1b56ab49b664">paranthesis_matching.cpp</a>
+</li>
+<li>power()
+: <a class="el" href="df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power_for_huge_numbers.cpp</a>
+, <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#a5769b745458157ef2679949155684f3b">matrix_exponentiation.cpp</a>
+</li>
+<li>predict_OLS_regressor()
+: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a4bcaaf41c66da4d3a471dacef133def7">ordinary_least_squares_regressor.cpp</a>
+</li>
+<li>PRIME
+: <a class="el" href="d6/dce/rabin__karp_8cpp.html#ac4add2a227a10511e0128d63952030e8">rabin_karp.cpp</a>
+</li>
+<li>prime
+: <a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html#ac0f4b77b901ddb15dab4c4dee1ac6e95">primes_up_to_billion.cpp</a>
+</li>
+<li>prime_factorization()
+: <a class="el" href="db/d0d/prime__factorization_8cpp.html#a0ece0145fb29a5cf48378c23dde2da46">prime_factorization.cpp</a>
+</li>
+<li>prime_numbers
+: <a class="el" href="db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_factorization.cpp</a>
+</li>
+<li>primes()
+: <a class="el" href="de/d9b/prime__numbers_8cpp.html#a3b91f208e8365c95a295cfe3e67df5c3">prime_numbers.cpp</a>
+</li>
+<li>print()
+: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#af50a5c87d27cfd3462745b37fb9b0f46">sieve_of_eratosthenes.cpp</a>
+</li>
+<li>problem()
+: <a class="el" href="d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">ode_semi_implicit_euler.cpp</a>
+, <a class="el" href="db/dd3/ode__forward__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">ode_forward_euler.cpp</a>
+, <a class="el" href="d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">ode_midpoint_euler.cpp</a>
+</li>
+<li>push()
+: <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#aae41c72130114bf31204cde6873b6095">paranthesis_matching.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
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+<title>Algorithms_in_C++: File Members</title>
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+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
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+   <div id="projectname">Algorithms_in_C++
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+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+<div class="contents">
+<div class="textblock">Here is a list of all documented file members with links to the documentation:</div>
+
+<h3><a id="index_r"></a>- r -</h3><ul>
+<li>rec_ternary_search()
+: <a class="el" href="dc/dfe/ternary__search_8cpp.html#a93d0099db95022f1eb90ddfd68f73ead">ternary_search.cpp</a>
+</li>
+<li>rightRotate()
+: <a class="el" href="d8/dee/avltree_8cpp.html#a4d93589966920b2756b84f8b92c54d1c">avltree.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
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+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
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+</html>
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+<title>Algorithms_in_C++: File Members</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
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+<script type="text/javascript" src="dynsections.js"></script>
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+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+/* @license-end */
+</script>
+<div id="doc-content">
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
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+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+<div class="textblock">Here is a list of all documented file members with links to the documentation:</div>
+
+<h3><a id="index_s"></a>- s -</h3><ul>
+<li>save_2d_data()
+: <a class="el" href="d9/d66/group__machine__learning.html#ga6c606bc85a3e9fd9d010f874ad760336">kohonen_som_topology.cpp</a>
+</li>
+<li>save_exact_solution()
+: <a class="el" href="db/dd3/ode__forward__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">ode_forward_euler.cpp</a>
+, <a class="el" href="d3/d06/ode__semi__implicit__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">ode_semi_implicit_euler.cpp</a>
+, <a class="el" href="d6/dd3/ode__midpoint__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">ode_midpoint_euler.cpp</a>
+</li>
+<li>save_nd_data()
+: <a class="el" href="d9/d66/group__machine__learning.html#ga72699c805c19a6cc47a937a6f3378afa">kohonen_som_trace.cpp</a>
+</li>
+<li>semi_implicit_euler()
+: <a class="el" href="d6/d60/group__ode.html#ga3874d294ab00fe9ce8731c5b7991a089">ode_semi_implicit_euler.cpp</a>
+</li>
+<li>semi_implicit_euler_step()
+: <a class="el" href="d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">ode_semi_implicit_euler.cpp</a>
+</li>
+<li>sgn()
+: <a class="el" href="d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">bisection_method.cpp</a>
+, <a class="el" href="dd/d29/false__position_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">false_position.cpp</a>
+</li>
+<li>show()
+: <a class="el" href="db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">tower_of_hanoi.cpp</a>
+</li>
+<li>show_data()
+: <a class="el" href="d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">shell_sort2.cpp</a>
+</li>
+<li>show_pascal()
+: <a class="el" href="dc/d1a/pascal__triangle_8cpp.html#ad7a31d9cb2818d21b1ba12aead7f4c5c">pascal_triangle.cpp</a>
+</li>
+<li>sieve()
+: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#abce89d8999986f085c368969590376b8">sieve_of_eratosthenes.cpp</a>
+</li>
+<li>Sieve()
+: <a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html#a031cada84819ed6426f58e4f7e81261c">primes_up_to_billion.cpp</a>
+</li>
+<li>SieveOfEratosthenes()
+: <a class="el" href="db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">prime_factorization.cpp</a>
+</li>
+<li>spiralPrint()
+: <a class="el" href="db/d07/spiral__print_8cpp.html#a850d3f55e1a8d227176cdcc67352c197">spiral_print.cpp</a>
+</li>
+<li>Sqrt()
+: <a class="el" href="da/d24/sqrt__double_8cpp.html#ae662282ad0740d2063ac404ca3bd74fc">sqrt_double.cpp</a>
+</li>
+<li>stack
+: <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#aa37d24a036d239b3b528f13b9de880c7">paranthesis_matching.cpp</a>
+</li>
+<li>struzik_search()
+: <a class="el" href="d8/d8a/exponential__search_8cpp.html#a67e9c84b4e2eb30e3c5170eabfbb363d">exponential_search.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
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+</html>
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+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+var searchBox = new SearchBox("searchBox", "search",false,'Search');
+/* @license-end */
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+<script type="text/javascript" src="menu.js"></script>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+  initMenu('',true,false,'search.php','Search');
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+/* @license-end */</script>
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+</div><!-- top -->
+<div id="side-nav" class="ui-resizable side-nav-resizable">
+  <div id="nav-tree">
+    <div id="nav-tree-contents">
+      <div id="nav-sync" class="sync"></div>
+    </div>
+  </div>
+  <div id="splitbar" style="-moz-user-select:none;" 
+       class="ui-resizable-handle">
+  </div>
+</div>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+$(document).ready(function(){initNavTree('globals_t.html',''); initResizable(); });
+/* @license-end */
+</script>
+<div id="doc-content">
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
+     onmouseout="return searchBox.OnSearchSelectHide()"
+     onkeydown="return searchBox.OnSearchSelectKey(event)">
+</div>
+
+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+<div class="textblock">Here is a list of all documented file members with links to the documentation:</div>
+
+<h3><a id="index_t"></a>- t -</h3><ul>
+<li>ternary_search()
+: <a class="el" href="dc/dfe/ternary__search_8cpp.html#aef655a27eb82efa299bf9d0becf6e9c8">ternary_search.cpp</a>
+</li>
+<li>test()
+: <a class="el" href="d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">smallest_circle.cpp</a>
+</li>
+<li>test1()
+: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">kohonen_som_topology.cpp</a>
+, <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">qr_eigen_values.cpp</a>
+, <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">kohonen_som_trace.cpp</a>
+, <a class="el" href="d5/db0/adaline__learning_8cpp.html#a52053d88ea1bcbbed9aca67ab4eeb499">adaline_learning.cpp</a>
+, <a class="el" href="d6/d9d/large__factorial_8cpp.html#a3f93b60e229b6683e24c4754a7106ee8">large_factorial.cpp</a>
+, <a class="el" href="da/df2/durand__kerner__roots_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">durand_kerner_roots.cpp</a>
+</li>
+<li>test2()
+: <a class="el" href="d5/db0/adaline__learning_8cpp.html#a379f7488a305f2571f2932b319931f82">adaline_learning.cpp</a>
+, <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a0283886819c7c140a023582b7269e2d0">kohonen_som_topology.cpp</a>
+, <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a0283886819c7c140a023582b7269e2d0">kohonen_som_trace.cpp</a>
+, <a class="el" href="d6/d9d/large__factorial_8cpp.html#a76aae4778fbe89a3d59fd61fbc050cfa">large_factorial.cpp</a>
+, <a class="el" href="da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">durand_kerner_roots.cpp</a>
+, <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">qr_eigen_values.cpp</a>
+, <a class="el" href="d0/d01/smallest__circle_8cpp.html#a0283886819c7c140a023582b7269e2d0">smallest_circle.cpp</a>
+</li>
+<li>test3()
+: <a class="el" href="d5/db0/adaline__learning_8cpp.html#a992bdf1fdb0b9d414bcf7981d2d87aa9">adaline_learning.cpp</a>
+, <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_topology.cpp</a>
+, <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_trace.cpp</a>
+, <a class="el" href="d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">smallest_circle.cpp</a>
+</li>
+<li>test_2d_classes()
+: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a6b5e744876fd980a3451cbb385d4e755">kohonen_som_topology.cpp</a>
+</li>
+<li>test_3d_classes()
+: <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a9ab8c79ffb674a63f151f282faeb723b">kohonen_som_trace.cpp</a>
+</li>
+<li>test_3d_classes1()
+: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#ab3081e021270ba21a9fd88646f6a6e26">kohonen_som_topology.cpp</a>
+</li>
+<li>test_3d_classes2()
+: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a0e7435446ed7c763f7de79a468add2e0">kohonen_som_topology.cpp</a>
+</li>
+<li>test_circle()
+: <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#ab47fb569e63648bd76e7edfdacc02dbd">kohonen_som_trace.cpp</a>
+</li>
+<li>test_f()
+: <a class="el" href="d4/d7a/shell__sort2_8cpp.html#a22ea0d1f7943ebb4371d31e44b465b6d">shell_sort2.cpp</a>
+</li>
+<li>test_function()
+: <a class="el" href="d0/d08/realtime__stats_8cpp.html#aa54c915581fcc495489175a4386d59fd">realtime_stats.cpp</a>
+</li>
+<li>test_int()
+: <a class="el" href="d4/d7a/shell__sort2_8cpp.html#a895b313cb2671e8f712040460325573e">shell_sort2.cpp</a>
+</li>
+<li>test_lamniscate()
+: <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a412b7afa156306b1f8788643c91a1c60">kohonen_som_trace.cpp</a>
+</li>
+<li>test_set
+: <a class="el" href="d3/d7d/brute__force__string__searching_8cpp.html#ae2abaa9caa13fff35e45edca00bee123">brute_force_string_searching.cpp</a>
+</li>
+<li>tests()
+: <a class="el" href="d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">least_common_multiple.cpp</a>
+</li>
+<li>TH()
+: <a class="el" href="db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">tower_of_hanoi.cpp</a>
+</li>
+<li>tolowerRoman()
+: <a class="el" href="de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">decimal_to_roman_numeral.cpp</a>
+</li>
+<li>top
+: <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#af93f4f37fc2ad9c37af4a715423b110c">paranthesis_matching.cpp</a>
+</li>
+<li>toupperRoman()
+: <a class="el" href="de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">decimal_to_roman_numeral.cpp</a>
+</li>
+<li>TriangleArea()
+: <a class="el" href="d0/d01/smallest__circle_8cpp.html#a94682a4a70d5906857ca09de5b9fb2cc">smallest_circle.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
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+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
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+<meta name="generator" content="Doxygen 1.8.18"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: File Members</title>
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+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
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+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
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+   <div id="projectname">Algorithms_in_C++
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+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+/* @license-end */
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+<div id="doc-content">
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
+     onmouseout="return searchBox.OnSearchSelectHide()"
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+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+&#160;<ul>
+<li>link
+: <a class="el" href="d1/df3/hash__search_8cpp.html#ad6fcd983304f85afa199d97a9b0ca9f6">hash_search.cpp</a>
+</li>
+<li>node
+: <a class="el" href="d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">hash_search.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
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+<html xmlns="http://www.w3.org/1999/xhtml">
+<head>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: File Members</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
+<link href="navtree.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="resize.js"></script>
+<script type="text/javascript" src="navtreedata.js"></script>
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+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+  $(document).ready(function() { init_search(); });
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+/* @license-end */</script>
+<div id="main-nav"></div>
+</div><!-- top -->
+<div id="side-nav" class="ui-resizable side-nav-resizable">
+  <div id="nav-tree">
+    <div id="nav-tree-contents">
+      <div id="nav-sync" class="sync"></div>
+    </div>
+  </div>
+  <div id="splitbar" style="-moz-user-select:none;" 
+       class="ui-resizable-handle">
+  </div>
+</div>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+$(document).ready(function(){initNavTree('globals_u.html',''); initResizable(); });
+/* @license-end */
+</script>
+<div id="doc-content">
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
+     onmouseout="return searchBox.OnSearchSelectHide()"
+     onkeydown="return searchBox.OnSearchSelectKey(event)">
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+
+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+<div class="textblock">Here is a list of all documented file members with links to the documentation:</div>
+
+<h3><a id="index_u"></a>- u -</h3><ul>
+<li>update_step()
+: <a class="el" href="d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">extended_euclid_algorithm.cpp</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
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+++ b/globals_vars.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml">
+<head>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: File Members</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
+<link href="navtree.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="resize.js"></script>
+<script type="text/javascript" src="navtreedata.js"></script>
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+  MathJax.Hub.Config({
+    extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
+    jax: ["input/TeX","output/HTML-CSS"],
+});
+</script>
+<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
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+<table cellspacing="0" cellpadding="0">
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+&#160;<ul>
+<li>a
+: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">matrix_exponentiation.cpp</a>
+</li>
+<li>AvailArray
+: <a class="el" href="d3/dce/linkedlist__implentation__usingarray_8cpp.html#aed19b403f559fc5d5a4bce724f9e263c">linkedlist_implentation_usingarray.cpp</a>
+</li>
+<li>data
+: <a class="el" href="d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">hash_search.cpp</a>
+</li>
+<li>f
+: <a class="el" href="d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">fibonacci_fast.cpp</a>
+</li>
+<li>factors
+: <a class="el" href="db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">prime_factorization.cpp</a>
+</li>
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+: <a class="el" href="d1/df3/hash__search_8cpp.html#af413b1740073db54796642b0ab814d6d">hash_search.cpp</a>
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+<li>isprime
+: <a class="el" href="db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">prime_factorization.cpp</a>
+, <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a0560e21edb54d5ad8d80b2d80348ce22">sieve_of_eratosthenes.cpp</a>
+</li>
+<li>k
+: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">matrix_exponentiation.cpp</a>
+</li>
+<li>MAX
+: <a class="el" href="d4/d32/fibonacci__fast_8cpp.html#a692ac7187ee88621a9f78fca78ec498d">fibonacci_fast.cpp</a>
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+</li>
+<li>stack
+: <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#aa37d24a036d239b3b528f13b9de880c7">paranthesis_matching.cpp</a>
+</li>
+<li>test_set
+: <a class="el" href="d3/d7d/brute__force__string__searching_8cpp.html#ae2abaa9caa13fff35e45edca00bee123">brute_force_string_searching.cpp</a>
+</li>
+<li>top
+: <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#af93f4f37fc2ad9c37af4a715423b110c">paranthesis_matching.cpp</a>
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+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
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+<div class="textblock"><p><a class="anchor" id="mainpage"></a><a href="https://gitpod.io/#https://github.com/TheAlgorithms/C-Plus-Plus"><img src="https://img.shields.io/badge/Gitpod-Ready--to--Code-blue?logo=gitpod" alt="Gitpod Ready-to-Code" class="inline"/></a> <a href="https://gitter.im/TheAlgorithms"><img src="https://img.shields.io/badge/Chat-Gitter-ff69b4.svg?label=Chat&amp;logo=gitter&amp;style=flat-square" alt="Gitter chat" style="pointer-events: none;" class="inline"/></a> <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/CONTRIBUTING.md"><img src="https://img.shields.io/static/v1.svg?label=Contributions&amp;message=Welcome&amp;color=0059b3&amp;style=flat-square" alt="contributions welcome" style="pointer-events: none;" class="inline"/></a> <img src="https://img.shields.io/github/repo-size/TheAlgorithms/C-Plus-Plus?color=red&amp;style=flat-square" alt="GitHub repo size" class="inline"/> <img src="https://img.shields.io/github/issues-pr-closed/TheAlgorithms/C-Plus-Plus?color=green&amp;style=flat-square" alt="GitHub closed pull requests" class="inline"/> <a href="https://TheAlgorithms.github.io/C-Plus-Plus"><img src="https://github.com/TheAlgorithms/C-Plus-Plus/workflows/Doxygen%20CI/badge.svg" alt="Doxygen CI" style="pointer-events: none;" class="inline"/></a> <a href="https://github.com/TheAlgorithms/C-Plus-Plus/actions?query=workflow%3A%22Awesome+CI+Workflow%22"><img src="https://github.com/TheAlgorithms/C-Plus-Plus/workflows/Awesome%20CI%20Workflow/badge.svg" alt="Awesome CI" style="pointer-events: none;" class="inline"/></a></p>
+<p><a href="https://TheAlgorithms.github.io/C-Plus-Plus">Online Documentation</a>.</p>
+<p>Click on <a href="https://TheAlgorithms.github.io/C-Plus-Plus/files.html">Files menu</a> to see the list of all the files documented with the code.</p>
+<h2><a class="anchor" id="autotoc_md33"></a>
+Algorithms implemented in C++ (for education)</h2>
+<p>The implementations are for learning purpose. They may be less efficient than the implementation in the standard library.</p>
+<h2><a class="anchor" id="autotoc_md34"></a>
+Contribute Guidelines</h2>
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n=C.setTimeout(e,r);t.stop=function(){C.clearTimeout(n)}})},ot=E.createElement("input"),at=E.createElement("select").appendChild(E.createElement("option")),ot.type="checkbox",y.checkOn=""!==ot.value,y.optSelected=at.selected,(ot=E.createElement("input")).value="t",ot.type="radio",y.radioValue="t"===ot.value;var ht,gt=k.expr.attrHandle;k.fn.extend({attr:function(e,t){return _(this,k.attr,e,t,1<arguments.length)},removeAttr:function(e){return this.each(function(){k.removeAttr(this,e)})}}),k.extend({attr:function(e,t,n){var r,i,o=e.nodeType;if(3!==o&&8!==o&&2!==o)return"undefined"==typeof e.getAttribute?k.prop(e,t,n):(1===o&&k.isXMLDoc(e)||(i=k.attrHooks[t.toLowerCase()]||(k.expr.match.bool.test(t)?ht:void 0)),void 0!==n?null===n?void k.removeAttr(e,t):i&&"set"in i&&void 0!==(r=i.set(e,n,t))?r:(e.setAttribute(t,n+""),n):i&&"get"in i&&null!==(r=i.get(e,t))?r:null==(r=k.find.attr(e,t))?void 0:r)},attrHooks:{type:{set:function(e,t){if(!y.radioValue&&"radio"===t&&A(e,"input")){var 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i,o,a,s,u,l,c,f,p=[n||E],d=v.call(e,"type")?e.type:e,h=v.call(e,"namespace")?e.namespace.split("."):[];if(o=f=a=n=n||E,3!==n.nodeType&&8!==n.nodeType&&!Tt.test(d+k.event.triggered)&&(-1<d.indexOf(".")&&(d=(h=d.split(".")).shift(),h.sort()),u=d.indexOf(":")<0&&"on"+d,(e=e[k.expando]?e:new k.Event(d,"object"==typeof e&&e)).isTrigger=r?2:3,e.namespace=h.join("."),e.rnamespace=e.namespace?new RegExp("(^|\\.)"+h.join("\\.(?:.*\\.|)")+"(\\.|$)"):null,e.result=void 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+* Copyright jQuery Foundation and other contributors; Licensed MIT */
+
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s=t(this).resizable("instance"),n=s.options,o=s.originalSize,a=s.originalPosition,r={height:s.size.height-o.height||0,width:s.size.width-o.width||0,top:s.position.top-a.top||0,left:s.position.left-a.left||0};t(n.alsoResize).each(function(){var e=t(this),s=t(this).data("ui-resizable-alsoresize"),n={},o=e.parents(i.originalElement[0]).length?["width","height"]:["width","height","top","left"];t.each(o,function(t,e){var i=(s[e]||0)+(r[e]||0);i&&i>=0&&(n[e]=i||null)}),e.css(n)})},stop:function(){t(this).removeData("ui-resizable-alsoresize")}}),t.ui.plugin.add("resizable","ghost",{start:function(){var e=t(this).resizable("instance"),i=e.size;e.ghost=e.originalElement.clone(),e.ghost.css({opacity:.25,display:"block",position:"relative",height:i.height,width:i.width,margin:0,left:0,top:0}),e._addClass(e.ghost,"ui-resizable-ghost"),t.uiBackCompat!==!1&&"string"==typeof e.options.ghost&&e.ghost.addClass(this.options.ghost),e.ghost.appendTo(e.helper)},resize:function(){var 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+ * Copyright (c) 2007 Ariel Flesler - aflesler ○ gmail • com | https://github.com/flesler
+ * Licensed under MIT
+ * @author Ariel Flesler
+ * @version 2.1.2
+ */
+;(function(f){"use strict";"function"===typeof define&&define.amd?define(["jquery"],f):"undefined"!==typeof module&&module.exports?module.exports=f(require("jquery")):f(jQuery)})(function($){"use strict";function n(a){return!a.nodeName||-1!==$.inArray(a.nodeName.toLowerCase(),["iframe","#document","html","body"])}function h(a){return $.isFunction(a)||$.isPlainObject(a)?a:{top:a,left:a}}var p=$.scrollTo=function(a,d,b){return $(window).scrollTo(a,d,b)};p.defaults={axis:"xy",duration:0,limit:!0};$.fn.scrollTo=function(a,d,b){"object"=== typeof d&&(b=d,d=0);"function"===typeof b&&(b={onAfter:b});"max"===a&&(a=9E9);b=$.extend({},p.defaults,b);d=d||b.duration;var u=b.queue&&1<b.axis.length;u&&(d/=2);b.offset=h(b.offset);b.over=h(b.over);return this.each(function(){function k(a){var k=$.extend({},b,{queue:!0,duration:d,complete:a&&function(){a.call(q,e,b)}});r.animate(f,k)}if(null!==a){var l=n(this),q=l?this.contentWindow||window:this,r=$(q),e=a,f={},t;switch(typeof e){case "number":case "string":if(/^([+-]=?)?\d+(\.\d+)?(px|%)?$/.test(e)){e= h(e);break}e=l?$(e):$(e,q);case "object":if(e.length===0)return;if(e.is||e.style)t=(e=$(e)).offset()}var v=$.isFunction(b.offset)&&b.offset(q,e)||b.offset;$.each(b.axis.split(""),function(a,c){var d="x"===c?"Left":"Top",m=d.toLowerCase(),g="scroll"+d,h=r[g](),n=p.max(q,c);t?(f[g]=t[m]+(l?0:h-r.offset()[m]),b.margin&&(f[g]-=parseInt(e.css("margin"+d),10)||0,f[g]-=parseInt(e.css("border"+d+"Width"),10)||0),f[g]+=v[m]||0,b.over[m]&&(f[g]+=e["x"===c?"width":"height"]()*b.over[m])):(d=e[m],f[g]=d.slice&& "%"===d.slice(-1)?parseFloat(d)/100*n:d);b.limit&&/^\d+$/.test(f[g])&&(f[g]=0>=f[g]?0:Math.min(f[g],n));!a&&1<b.axis.length&&(h===f[g]?f={}:u&&(k(b.onAfterFirst),f={}))});k(b.onAfter)}})};p.max=function(a,d){var b="x"===d?"Width":"Height",h="scroll"+b;if(!n(a))return a[h]-$(a)[b.toLowerCase()]();var b="client"+b,k=a.ownerDocument||a.document,l=k.documentElement,k=k.body;return Math.max(l[h],k[h])-Math.min(l[b],k[b])};$.Tween.propHooks.scrollLeft=$.Tween.propHooks.scrollTop={get:function(a){return $(a.elem)[a.prop]()}, set:function(a){var d=this.get(a);if(a.options.interrupt&&a._last&&a._last!==d)return $(a.elem).stop();var b=Math.round(a.now);d!==b&&($(a.elem)[a.prop](b),a._last=this.get(a))}};return p});
+/*!
+ PowerTip v1.3.1 (2018-04-15)
+ https://stevenbenner.github.io/jquery-powertip/
+ Copyright (c) 2018 Steven Benner (http://stevenbenner.com/).
+ Released under MIT license.
+ https://raw.github.com/stevenbenner/jquery-powertip/master/LICENSE.txt
+*/
+(function(root,factory){if(typeof define==="function"&&define.amd){define(["jquery"],factory)}else if(typeof module==="object"&&module.exports){module.exports=factory(require("jquery"))}else{factory(root.jQuery)}})(this,function($){var $document=$(document),$window=$(window),$body=$("body");var DATA_DISPLAYCONTROLLER="displayController",DATA_HASACTIVEHOVER="hasActiveHover",DATA_FORCEDOPEN="forcedOpen",DATA_HASMOUSEMOVE="hasMouseMove",DATA_MOUSEONTOTIP="mouseOnToPopup",DATA_ORIGINALTITLE="originalTitle",DATA_POWERTIP="powertip",DATA_POWERTIPJQ="powertipjq",DATA_POWERTIPTARGET="powertiptarget",EVENT_NAMESPACE=".powertip",RAD2DEG=180/Math.PI,MOUSE_EVENTS=["click","dblclick","mousedown","mouseup","mousemove","mouseover","mouseout","mouseenter","mouseleave","contextmenu"];var 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+ * jQuery UI Touch Punch 0.2.3
+ *
+ * Copyright 2011–2014, Dave Furfero
+ * Dual licensed under the MIT or GPL Version 2 licenses.
+ *
+ * Depends:
+ *  jquery.ui.widget.js
+ *  jquery.ui.mouse.js
+ */
+!function(a){function f(a,b){if(!(a.originalEvent.touches.length>1)){a.preventDefault();var c=a.originalEvent.changedTouches[0],d=document.createEvent("MouseEvents");d.initMouseEvent(b,!0,!0,window,1,c.screenX,c.screenY,c.clientX,c.clientY,!1,!1,!1,!1,0,null),a.target.dispatchEvent(d)}}if(a.support.touch="ontouchend"in document,a.support.touch){var e,b=a.ui.mouse.prototype,c=b._mouseInit,d=b._mouseDestroy;b._touchStart=function(a){var b=this;!e&&b._mouseCapture(a.originalEvent.changedTouches[0])&&(e=!0,b._touchMoved=!1,f(a,"mouseover"),f(a,"mousemove"),f(a,"mousedown"))},b._touchMove=function(a){e&&(this._touchMoved=!0,f(a,"mousemove"))},b._touchEnd=function(a){e&&(f(a,"mouseup"),f(a,"mouseout"),this._touchMoved||f(a,"click"),e=!1)},b._mouseInit=function(){var b=this;b.element.bind({touchstart:a.proxy(b,"_touchStart"),touchmove:a.proxy(b,"_touchMove"),touchend:a.proxy(b,"_touchEnd")}),c.call(b)},b._mouseDestroy=function(){var b=this;b.element.unbind({touchstart:a.proxy(b,"_touchStart"),touchmove:a.proxy(b,"_touchMove"),touchend:a.proxy(b,"_touchEnd")}),d.call(b)}}}(jQuery);/*! SmartMenus jQuery Plugin - v1.1.0 - September 17, 2017
+ * http://www.smartmenus.org/
+ * Copyright Vasil Dinkov, Vadikom Web Ltd. http://vadikom.com; Licensed MIT */(function(t){"function"==typeof define&&define.amd?define(["jquery"],t):"object"==typeof module&&"object"==typeof module.exports?module.exports=t(require("jquery")):t(jQuery)})(function($){function initMouseDetection(t){var e=".smartmenus_mouse";if(mouseDetectionEnabled||t)mouseDetectionEnabled&&t&&($(document).off(e),mouseDetectionEnabled=!1);else{var i=!0,s=null,o={mousemove:function(t){var e={x:t.pageX,y:t.pageY,timeStamp:(new Date).getTime()};if(s){var o=Math.abs(s.x-e.x),a=Math.abs(s.y-e.y);if((o>0||a>0)&&2>=o&&2>=a&&300>=e.timeStamp-s.timeStamp&&(mouse=!0,i)){var n=$(t.target).closest("a");n.is("a")&&$.each(menuTrees,function(){return $.contains(this.$root[0],n[0])?(this.itemEnter({currentTarget:n[0]}),!1):void 0}),i=!1}}s=e}};o[touchEvents?"touchstart":"pointerover pointermove pointerout MSPointerOver MSPointerMove 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r=t.dataSM("level");if(this.activatedItems[r-1]&&this.activatedItems[r-1].dataSM("sub")&&this.activatedItems[r-1].dataSM("sub").is(":visible")&&this.menuHideSubMenus(r-1),o.y=o.up&&o.y>=n||!o.up&&n>=o.y?o.y:Math.abs(n-o.y)>s?o.y+(o.up?s:-s):n,t.css(this.cssTransforms3d?{"-webkit-transform":"translate3d(0, "+o.y+"px, 0)",transform:"translate3d(0, "+o.y+"px, 0)"}:{marginTop:o.y}),mouse&&(o.up&&o.y>o.downEnd||!o.up&&o.y<o.upEnd)&&a.eq(o.up?1:0).show(),o.y==n)mouse&&a.eq(o.up?0:1).hide(),this.menuScrollStop(t);else if(!e){this.opts.scrollAccelerate&&o.step<this.opts.scrollStep&&(o.step+=.2);var h=this;this.scrollTimeout=requestAnimationFrame(function(){h.menuScroll(t)})}},menuScrollMousewheel:function(t,e){if(this.getClosestMenu(e.target)==t[0]){e=e.originalEvent;var i=(e.wheelDelta||-e.detail)>0;t.dataSM("scroll-arrows").eq(i?0:1).is(":visible")&&(t.dataSM("scroll").up=i,this.menuScroll(t,!0))}e.preventDefault()},menuScrollOut:function(t,e){mouse&&(/^scroll-(up|down)/.test((e.relatedTarget||"").className)||(t[0]==e.relatedTarget||$.contains(t[0],e.relatedTarget))&&this.getClosestMenu(e.relatedTarget)==t[0]||t.dataSM("scroll-arrows").css("visibility","hidden"))},menuScrollOver:function(t,e){if(mouse&&!/^scroll-(up|down)/.test(e.target.className)&&this.getClosestMenu(e.target)==t[0]){this.menuScrollRefreshData(t);var i=t.dataSM("scroll"),s=$(window).scrollTop()-t.dataSM("parent-a").offset().top-i.itemH;t.dataSM("scroll-arrows").eq(0).css("margin-top",s).end().eq(1).css("margin-top",s+this.getViewportHeight()-i.arrowDownH).end().css("visibility","visible")}},menuScrollRefreshData:function(t){var e=t.dataSM("scroll"),i=$(window).scrollTop()-t.dataSM("parent-a").offset().top-e.itemH;this.cssTransforms3d&&(i=-(parseFloat(t.css("margin-top"))-i)),$.extend(e,{upEnd:i,downEnd:i+this.getViewportHeight()-e.subH})},menuScrollStop:function(t){return this.scrollTimeout?(cancelAnimationFrame(this.scrollTimeout),this.scrollTimeout=0,t.dataSM("scroll").step=1,!0):void 0},menuScrollTouch:function(t,e){if(e=e.originalEvent,isTouchEvent(e)){var i=this.getTouchPoint(e);if(this.getClosestMenu(i.target)==t[0]){var s=t.dataSM("scroll");if(/(start|down)$/i.test(e.type))this.menuScrollStop(t)?(e.preventDefault(),this.$touchScrollingSub=t):this.$touchScrollingSub=null,this.menuScrollRefreshData(t),$.extend(s,{touchStartY:i.pageY,touchStartTime:e.timeStamp});else if(/move$/i.test(e.type)){var o=void 0!==s.touchY?s.touchY:s.touchStartY;if(void 0!==o&&o!=i.pageY){this.$touchScrollingSub=t;var a=i.pageY>o;void 0!==s.up&&s.up!=a&&$.extend(s,{touchStartY:i.pageY,touchStartTime:e.timeStamp}),$.extend(s,{up:a,touchY:i.pageY}),this.menuScroll(t,!0,Math.abs(i.pageY-o))}e.preventDefault()}else void 0!==s.touchY&&((s.momentum=15*Math.pow(Math.abs(i.pageY-s.touchStartY)/(e.timeStamp-s.touchStartTime),2))&&(this.menuScrollStop(t),this.menuScroll(t),e.preventDefault()),delete s.touchY)}}},menuShow:function(t){if((t.dataSM("beforefirstshowfired")||(t.dataSM("beforefirstshowfired",!0),this.$root.triggerHandler("beforefirstshow.smapi",t[0])!==!1))&&this.$root.triggerHandler("beforeshow.smapi",t[0])!==!1&&(t.dataSM("shown-before",!0),canAnimate&&t.stop(!0,!0),!t.is(":visible"))){var e=t.dataSM("parent-a"),i=this.isCollapsible();if((this.opts.keepHighlighted||i)&&e.addClass("highlighted"),i)t.removeClass("sm-nowrap").css({zIndex:"",width:"auto",minWidth:"",maxWidth:"",top:"",left:"",marginLeft:"",marginTop:""});else{if(t.css("z-index",this.zIndexInc=(this.zIndexInc||this.getStartZIndex())+1),(this.opts.subMenusMinWidth||this.opts.subMenusMaxWidth)&&(t.css({width:"auto",minWidth:"",maxWidth:""}).addClass("sm-nowrap"),this.opts.subMenusMinWidth&&t.css("min-width",this.opts.subMenusMinWidth),this.opts.subMenusMaxWidth)){var s=this.getWidth(t);t.css("max-width",this.opts.subMenusMaxWidth),s>this.getWidth(t)&&t.removeClass("sm-nowrap").css("width",this.opts.subMenusMaxWidth)}this.menuPosition(t)}var o=function(){t.css("overflow","")};i?canAnimate&&this.opts.collapsibleShowFunction?this.opts.collapsibleShowFunction.call(this,t,o):t.show(this.opts.collapsibleShowDuration,o):canAnimate&&this.opts.showFunction?this.opts.showFunction.call(this,t,o):t.show(this.opts.showDuration,o),e.attr("aria-expanded","true"),t.attr({"aria-expanded":"true","aria-hidden":"false"}),this.visibleSubMenus.push(t),this.$root.triggerHandler("show.smapi",t[0])}},popupHide:function(t){this.hideTimeout&&(clearTimeout(this.hideTimeout),this.hideTimeout=0);var e=this;this.hideTimeout=setTimeout(function(){e.menuHideAll()},t?1:this.opts.hideTimeout)},popupShow:function(t,e){if(!this.opts.isPopup)return alert('SmartMenus jQuery Error:\n\nIf you want to show this menu via the "popupShow" method, set the isPopup:true option.'),void 0;if(this.hideTimeout&&(clearTimeout(this.hideTimeout),this.hideTimeout=0),this.$root.dataSM("shown-before",!0),canAnimate&&this.$root.stop(!0,!0),!this.$root.is(":visible")){this.$root.css({left:t,top:e});var i=this,s=function(){i.$root.css("overflow","")};canAnimate&&this.opts.showFunction?this.opts.showFunction.call(this,this.$root,s):this.$root.show(this.opts.showDuration,s),this.visibleSubMenus[0]=this.$root}},refresh:function(){this.destroy(!0),this.init(!0)},rootKeyDown:function(t){if(this.handleEvents())switch(t.keyCode){case 27:var e=this.activatedItems[0];if(e){this.menuHideAll(),e[0].focus();var i=e.dataSM("sub");i&&this.menuHide(i)}break;case 32:var s=$(t.target);if(s.is("a")&&this.handleItemEvents(s)){var i=s.dataSM("sub");i&&!i.is(":visible")&&(this.itemClick({currentTarget:t.target}),t.preventDefault())}}},rootOut:function(t){if(this.handleEvents()&&!this.isTouchMode()&&t.target!=this.$root[0]&&(this.hideTimeout&&(clearTimeout(this.hideTimeout),this.hideTimeout=0),!this.opts.showOnClick||!this.opts.hideOnClick)){var e=this;this.hideTimeout=setTimeout(function(){e.menuHideAll()},this.opts.hideTimeout)}},rootOver:function(t){this.handleEvents()&&!this.isTouchMode()&&t.target!=this.$root[0]&&this.hideTimeout&&(clearTimeout(this.hideTimeout),this.hideTimeout=0)},winResize:function(t){if(this.handleEvents()){if(!("onorientationchange"in window)||"orientationchange"==t.type){var e=this.isCollapsible();this.wasCollapsible&&e||(this.activatedItems.length&&this.activatedItems[this.activatedItems.length-1][0].blur(),this.menuHideAll()),this.wasCollapsible=e}}else if(this.$disableOverlay){var i=this.$root.offset();this.$disableOverlay.css({top:i.top,left:i.left,width:this.$root.outerWidth(),height:this.$root.outerHeight()})}}}}),$.fn.dataSM=function(t,e){return e?this.data(t+"_smartmenus",e):this.data(t+"_smartmenus")},$.fn.removeDataSM=function(t){return this.removeData(t+"_smartmenus")},$.fn.smartmenus=function(options){if("string"==typeof options){var args=arguments,method=options;return Array.prototype.shift.call(args),this.each(function(){var t=$(this).data("smartmenus");t&&t[method]&&t[method].apply(t,args)})}return this.each(function(){var dataOpts=$(this).data("sm-options")||null;if(dataOpts)try{dataOpts=eval("("+dataOpts+")")}catch(e){dataOpts=null,alert('ERROR\n\nSmartMenus jQuery init:\nInvalid "data-sm-options" attribute value syntax.')}new $.SmartMenus(this,$.extend({},$.fn.smartmenus.defaults,options,dataOpts))})},$.fn.smartmenus.defaults={isPopup:!1,mainMenuSubOffsetX:0,mainMenuSubOffsetY:0,subMenusSubOffsetX:0,subMenusSubOffsetY:0,subMenusMinWidth:"10em",subMenusMaxWidth:"20em",subIndicators:!0,subIndicatorsPos:"append",subIndicatorsText:"",scrollStep:30,scrollAccelerate:!0,showTimeout:250,hideTimeout:500,showDuration:0,showFunction:null,hideDuration:0,hideFunction:function(t,e){t.fadeOut(200,e)},collapsibleShowDuration:0,collapsibleShowFunction:function(t,e){t.slideDown(200,e)},collapsibleHideDuration:0,collapsibleHideFunction:function(t,e){t.slideUp(200,e)},showOnClick:!1,hideOnClick:!0,noMouseOver:!1,keepInViewport:!0,keepHighlighted:!0,markCurrentItem:!1,markCurrentTree:!0,rightToLeftSubMenus:!1,bottomToTopSubMenus:!1,collapsibleBehavior:"default"},$});
\ No newline at end of file
diff --git a/menu.js b/menu.js
new file mode 100644
index 000000000..d18a2fe2a
--- /dev/null
+++ b/menu.js
@@ -0,0 +1,51 @@
+/*
+ @licstart  The following is the entire license notice for the JavaScript code in this file.
+
+ The MIT License (MIT)
+
+ Copyright (C) 1997-2020 by Dimitri van Heesch
+
+ Permission is hereby granted, free of charge, to any person obtaining a copy of this software
+ and associated documentation files (the "Software"), to deal in the Software without restriction,
+ including without limitation the rights to use, copy, modify, merge, publish, distribute,
+ sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is
+ furnished to do so, subject to the following conditions:
+
+ The above copyright notice and this permission notice shall be included in all copies or
+ substantial portions of the Software.
+
+ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING
+ BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+ DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+ @licend  The above is the entire license notice for the JavaScript code in this file
+ */
+function initMenu(relPath,searchEnabled,serverSide,searchPage,search) {
+  function makeTree(data,relPath) {
+    var result='';
+    if ('children' in data) {
+      result+='<ul>';
+      for (var i in data.children) {
+        result+='<li><a href="'+relPath+data.children[i].url+'">'+
+                                data.children[i].text+'</a>'+
+                                makeTree(data.children[i],relPath)+'</li>';
+      }
+      result+='</ul>';
+    }
+    return result;
+  }
+
+  $('#main-nav').append(makeTree(menudata,relPath));
+  $('#main-nav').children(':first').addClass('sm sm-dox').attr('id','main-menu');
+  if (searchEnabled) {
+    if (serverSide) {
+      $('#main-menu').append('<li style="float:right"><div id="MSearchBox" class="MSearchBoxInactive"><div class="left"><form id="FSearchBox" action="'+relPath+searchPage+'" method="get"><img id="MSearchSelect" src="'+relPath+'search/mag.png" alt=""/><input type="text" id="MSearchField" name="query" value="'+search+'" size="20" accesskey="S" onfocus="searchBox.OnSearchFieldFocus(true)" onblur="searchBox.OnSearchFieldFocus(false)"></form></div><div class="right"></div></div></li>');
+    } else {
+      $('#main-menu').append('<li style="float:right"><div id="MSearchBox" class="MSearchBoxInactive"><span class="left"><img id="MSearchSelect" src="'+relPath+'search/mag_sel.png" onmouseover="return searchBox.OnSearchSelectShow()" onmouseout="return searchBox.OnSearchSelectHide()" alt=""/><input type="text" id="MSearchField" value="'+search+'" accesskey="S" onfocus="searchBox.OnSearchFieldFocus(true)" onblur="searchBox.OnSearchFieldFocus(false)" onkeyup="searchBox.OnSearchFieldChange(event)"/></span><span class="right"><a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="'+relPath+'search/close.png" alt=""/></a></span></div></li>');
+    }
+  }
+  $('#main-menu').smartmenus();
+}
+/* @license-end */
diff --git a/menudata.js b/menudata.js
new file mode 100644
index 000000000..67de24047
--- /dev/null
+++ b/menudata.js
@@ -0,0 +1,133 @@
+/*
+ @licstart  The following is the entire license notice for the JavaScript code in this file.
+
+ The MIT License (MIT)
+
+ Copyright (C) 1997-2020 by Dimitri van Heesch
+
+ Permission is hereby granted, free of charge, to any person obtaining a copy of this software
+ and associated documentation files (the "Software"), to deal in the Software without restriction,
+ including without limitation the rights to use, copy, modify, merge, publish, distribute,
+ sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is
+ furnished to do so, subject to the following conditions:
+
+ The above copyright notice and this permission notice shall be included in all copies or
+ substantial portions of the Software.
+
+ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING
+ BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+ DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+ @licend  The above is the entire license notice for the JavaScript code in this file
+*/
+var menudata={children:[
+{text:"Main Page",url:"index.html"},
+{text:"Related Pages",url:"pages.html"},
+{text:"Modules",url:"modules.html"},
+{text:"Namespaces",url:"namespaces.html",children:[
+{text:"Namespace List",url:"namespaces.html"},
+{text:"Namespace Members",url:"namespacemembers.html",children:[
+{text:"All",url:"namespacemembers.html"},
+{text:"Functions",url:"namespacemembers_func.html"}]}]},
+{text:"Classes",url:"annotated.html",children:[
+{text:"Class List",url:"annotated.html"},
+{text:"Class Index",url:"classes.html"},
+{text:"Class Members",url:"functions.html",children:[
+{text:"All",url:"functions.html",children:[
+{text:"_",url:"functions.html#index__5F"},
+{text:"a",url:"functions.html#index_a"},
+{text:"c",url:"functions.html#index_c"},
+{text:"d",url:"functions.html#index_d"},
+{text:"e",url:"functions.html#index_e"},
+{text:"f",url:"functions.html#index_f"},
+{text:"g",url:"functions.html#index_g"},
+{text:"h",url:"functions.html#index_h"},
+{text:"i",url:"functions.html#index_i"},
+{text:"k",url:"functions.html#index_k"},
+{text:"l",url:"functions.html#index_l"},
+{text:"m",url:"functions.html#index_m"},
+{text:"n",url:"functions.html#index_n"},
+{text:"o",url:"functions.html#index_o"},
+{text:"p",url:"functions.html#index_p"},
+{text:"q",url:"functions.html#index_q"},
+{text:"r",url:"functions.html#index_r"},
+{text:"s",url:"functions.html#index_s"},
+{text:"t",url:"functions.html#index_t"},
+{text:"v",url:"functions.html#index_v"},
+{text:"w",url:"functions.html#index_w"},
+{text:"x",url:"functions.html#index_x"},
+{text:"y",url:"functions.html#index_y"},
+{text:"~",url:"functions.html#index__7E"}]},
+{text:"Functions",url:"functions_func.html",children:[
+{text:"a",url:"functions_func.html#index_a"},
+{text:"c",url:"functions_func.html#index_c"},
+{text:"d",url:"functions_func.html#index_d"},
+{text:"e",url:"functions_func.html#index_e"},
+{text:"f",url:"functions_func.html#index_f"},
+{text:"g",url:"functions_func.html#index_g"},
+{text:"h",url:"functions_func.html#index_h"},
+{text:"i",url:"functions_func.html#index_i"},
+{text:"l",url:"functions_func.html#index_l"},
+{text:"m",url:"functions_func.html#index_m"},
+{text:"n",url:"functions_func.html#index_n"},
+{text:"o",url:"functions_func.html#index_o"},
+{text:"p",url:"functions_func.html#index_p"},
+{text:"q",url:"functions_func.html#index_q"},
+{text:"r",url:"functions_func.html#index_r"},
+{text:"s",url:"functions_func.html#index_s"},
+{text:"t",url:"functions_func.html#index_t"},
+{text:"v",url:"functions_func.html#index_v"},
+{text:"~",url:"functions_func.html#index__7E"}]},
+{text:"Variables",url:"functions_vars.html"},
+{text:"Related Functions",url:"functions_rela.html"}]}]},
+{text:"Files",url:"files.html",children:[
+{text:"File List",url:"files.html"},
+{text:"File Members",url:"globals.html",children:[
+{text:"All",url:"globals.html",children:[
+{text:"_",url:"globals.html#index__5F"},
+{text:"a",url:"globals_a.html#index_a"},
+{text:"b",url:"globals_b.html#index_b"},
+{text:"c",url:"globals_c.html#index_c"},
+{text:"d",url:"globals_d.html#index_d"},
+{text:"e",url:"globals_e.html#index_e"},
+{text:"f",url:"globals_f.html#index_f"},
+{text:"g",url:"globals_g.html#index_g"},
+{text:"h",url:"globals_h.html#index_h"},
+{text:"i",url:"globals_i.html#index_i"},
+{text:"j",url:"globals_j.html#index_j"},
+{text:"k",url:"globals_k.html#index_k"},
+{text:"l",url:"globals_l.html#index_l"},
+{text:"m",url:"globals_m.html#index_m"},
+{text:"n",url:"globals_n.html#index_n"},
+{text:"o",url:"globals_o.html#index_o"},
+{text:"p",url:"globals_p.html#index_p"},
+{text:"r",url:"globals_r.html#index_r"},
+{text:"s",url:"globals_s.html#index_s"},
+{text:"t",url:"globals_t.html#index_t"},
+{text:"u",url:"globals_u.html#index_u"}]},
+{text:"Functions",url:"globals_func.html",children:[
+{text:"_",url:"globals_func.html#index__5F"},
+{text:"a",url:"globals_func_a.html#index_a"},
+{text:"b",url:"globals_func_b.html#index_b"},
+{text:"c",url:"globals_func_c.html#index_c"},
+{text:"d",url:"globals_func_d.html#index_d"},
+{text:"e",url:"globals_func_e.html#index_e"},
+{text:"f",url:"globals_func_f.html#index_f"},
+{text:"g",url:"globals_func_g.html#index_g"},
+{text:"h",url:"globals_func_h.html#index_h"},
+{text:"i",url:"globals_func_i.html#index_i"},
+{text:"j",url:"globals_func_j.html#index_j"},
+{text:"l",url:"globals_func_l.html#index_l"},
+{text:"m",url:"globals_func_m.html#index_m"},
+{text:"n",url:"globals_func_n.html#index_n"},
+{text:"o",url:"globals_func_o.html#index_o"},
+{text:"p",url:"globals_func_p.html#index_p"},
+{text:"r",url:"globals_func_r.html#index_r"},
+{text:"s",url:"globals_func_s.html#index_s"},
+{text:"t",url:"globals_func_t.html#index_t"},
+{text:"u",url:"globals_func_u.html#index_u"}]},
+{text:"Variables",url:"globals_vars.html"},
+{text:"Typedefs",url:"globals_type.html"},
+{text:"Macros",url:"globals_defs.html"}]}]}]}
diff --git a/modules.html b/modules.html
new file mode 100644
index 000000000..55ee5bfae
--- /dev/null
+++ b/modules.html
@@ -0,0 +1,114 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml">
+<head>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: Modules</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
+<link href="navtree.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="resize.js"></script>
+<script type="text/javascript" src="navtreedata.js"></script>
+<script type="text/javascript" src="navtree.js"></script>
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+<div id="titlearea">
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+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+/* @license-end */
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+        name="MSearchResults" id="MSearchResults">
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+  <div class="headertitle">
+<div class="title">Modules</div>  </div>
+</div><!--header-->
+<div class="contents">
+<div class="textblock">Here is a list of all modules:</div><div class="directory">
+<table class="directory">
+<tr id="row_0_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><a class="el" href="d9/d66/group__machine__learning.html" target="_self">Machine Learning Algorithms</a></td><td class="desc"></td></tr>
+<tr id="row_1_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><a class="el" href="d6/d60/group__ode.html" target="_self">Ordinary Differential Equations</a></td><td class="desc"></td></tr>
+</table>
+</div><!-- directory -->
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
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+<html xmlns="http://www.w3.org/1999/xhtml">
+<head>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: Namespace Members</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
+<link href="navtree.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="resize.js"></script>
+<script type="text/javascript" src="navtreedata.js"></script>
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+<script type="text/javascript" src="search/searchdata.js"></script>
+<script type="text/javascript" src="search/search.js"></script>
+<script type="text/x-mathjax-config">
+  MathJax.Hub.Config({
+    extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
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+});
+</script>
+<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+var searchBox = new SearchBox("searchBox", "search",false,'Search');
+/* @license-end */
+</script>
+<script type="text/javascript" src="menudata.js"></script>
+<script type="text/javascript" src="menu.js"></script>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+  initMenu('',true,false,'search.php','Search');
+  $(document).ready(function() { init_search(); });
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+<div id="side-nav" class="ui-resizable side-nav-resizable">
+  <div id="nav-tree">
+    <div id="nav-tree-contents">
+      <div id="nav-sync" class="sync"></div>
+    </div>
+  </div>
+  <div id="splitbar" style="-moz-user-select:none;" 
+       class="ui-resizable-handle">
+  </div>
+</div>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+$(document).ready(function(){initNavTree('namespacemembers.html',''); initResizable(); });
+/* @license-end */
+</script>
+<div id="doc-content">
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
+     onmouseout="return searchBox.OnSearchSelectHide()"
+     onkeydown="return searchBox.OnSearchSelectKey(event)">
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+
+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+<div class="textblock">Here is a list of all documented namespace members with links to the namespaces they belong to:</div><ul>
+<li>brute_force()
+: <a class="el" href="d9/d03/namespacestring__search.html#aeb2cd81064717aedd62bfb096b1a73d8">string_search</a>
+</li>
+<li>check_if_equal()
+: <a class="el" href="d9/d03/namespacestring__search.html#aebe07cea289a13142503d98be7df11fd">string_search</a>
+</li>
+<li>create_hash()
+: <a class="el" href="d9/d03/namespacestring__search.html#a8fb0bc932ba8b582c9f4c71338d050f8">string_search</a>
+</li>
+<li>eigen_values()
+: <a class="el" href="d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm</a>
+</li>
+<li>getFailureArray()
+: <a class="el" href="d9/d03/namespacestring__search.html#aa422aab133d4ed5e5d6022a7f701271f">string_search</a>
+</li>
+<li>kmp()
+: <a class="el" href="d9/d03/namespacestring__search.html#a26a58225ce7d3fa9d4c2f5349a65ed93">string_search</a>
+</li>
+<li>kohonen_som()
+: <a class="el" href="d8/d77/namespacemachine__learning.html#adc731720947b4bc2ab047c141e7d0299">machine_learning</a>
+</li>
+<li>kohonen_som_tracer()
+: <a class="el" href="d8/d77/namespacemachine__learning.html#acc6a28f40512dbda75ab1a3969248898">machine_learning</a>
+</li>
+<li>merge()
+: <a class="el" href="d5/d91/namespacesorting.html#aa26de383227859210f14dcf12201a079">sorting</a>
+</li>
+<li>non_recursive_merge_sort()
+: <a class="el" href="d5/d91/namespacesorting.html#a140d913e42fb94176a0b2c8b29a80420">sorting</a>
+</li>
+<li>operator&lt;&lt;()
+: <a class="el" href="d2/d3b/namespaceqr__algorithm.html#a7c63c78d6839b8ad73b77c161210b514">qr_algorithm</a>
+</li>
+<li>partition()
+: <a class="el" href="d5/d91/namespacesorting.html#a7e7f25f31c50523990437abf2ac3907e">sorting</a>
+</li>
+<li>qr_decompose()
+: <a class="el" href="d2/d3b/namespaceqr__algorithm.html#ab1ac74497ffb2101040cc1efe3546de8">qr_algorithm</a>
+</li>
+<li>quickSort()
+: <a class="el" href="d5/d91/namespacesorting.html#a50b66a1c652291b9a346ec7342967178">sorting</a>
+</li>
+<li>rabin_karp()
+: <a class="el" href="d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">string_search</a>
+</li>
+<li>recalculate_hash()
+: <a class="el" href="d9/d03/namespacestring__search.html#aed769d565b705a9b3e0eb1ec74088893">string_search</a>
+</li>
+<li>save_u_matrix()
+: <a class="el" href="d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">machine_learning</a>
+</li>
+<li>shell_sort()
+: <a class="el" href="d5/d91/namespacesorting.html#a5669396c6a6b1e14b97589b6e37980aa">sorting</a>
+</li>
+<li>update_weights()
+: <a class="el" href="d8/d77/namespacemachine__learning.html#ac4010fe3a52a74e8b5b1aaadfe38b46f">machine_learning</a>
+</li>
+<li>vector_dot()
+: <a class="el" href="d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">qr_algorithm</a>
+</li>
+<li>vector_mag()
+: <a class="el" href="d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">qr_algorithm</a>
+</li>
+<li>vector_proj()
+: <a class="el" href="d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">qr_algorithm</a>
+</li>
+</ul>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+  <ul>
+    <li class="footer">Generated on Fri Jun 19 2020 16:06:45 for Algorithms_in_C++ by
+    <a href="http://www.doxygen.org/index.html">
+    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
+  </ul>
+</div>
+</body>
+</html>
diff --git a/namespacemembers_func.html b/namespacemembers_func.html
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+<head>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<title>Algorithms_in_C++: Namespace Members</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
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+<script type="text/javascript" src="search/search.js"></script>
+<script type="text/x-mathjax-config">
+  MathJax.Hub.Config({
+    extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
+    jax: ["input/TeX","output/HTML-CSS"],
+});
+</script>
+<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
+<link href="doxygen.css" rel="stylesheet" type="text/css" />
+</head>
+<body>
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+  <td id="projectalign" style="padding-left: 0.5em;">
+   <div id="projectname">Algorithms_in_C++
+   &#160;<span id="projectnumber">1.0.0</span>
+   </div>
+   <div id="projectbrief">Set of algorithms implemented in C++.</div>
+  </td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.18 -->
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+<script type="text/javascript" src="menudata.js"></script>
+<script type="text/javascript" src="menu.js"></script>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
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+  $(document).ready(function() { init_search(); });
+});
+/* @license-end */</script>
+<div id="main-nav"></div>
+</div><!-- top -->
+<div id="side-nav" class="ui-resizable side-nav-resizable">
+  <div id="nav-tree">
+    <div id="nav-tree-contents">
+      <div id="nav-sync" class="sync"></div>
+    </div>
+  </div>
+  <div id="splitbar" style="-moz-user-select:none;" 
+       class="ui-resizable-handle">
+  </div>
+</div>
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+$(document).ready(function(){initNavTree('namespacemembers_func.html',''); initResizable(); });
+/* @license-end */
+</script>
+<div id="doc-content">
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+     onmouseover="return searchBox.OnSearchSelectShow()"
+     onmouseout="return searchBox.OnSearchSelectHide()"
+     onkeydown="return searchBox.OnSearchSelectKey(event)">
+</div>
+
+<!-- iframe showing the search results (closed by default) -->
+<div id="MSearchResultsWindow">
+<iframe src="javascript:void(0)" frameborder="0" 
+        name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="contents">
+&#160;<ul>
+<li>brute_force()
+: <a class="el" href="d9/d03/namespacestring__search.html#aeb2cd81064717aedd62bfb096b1a73d8">string_search</a>
+</li>
+<li>check_if_equal()
+: <a class="el" href="d9/d03/namespacestring__search.html#aebe07cea289a13142503d98be7df11fd">string_search</a>
+</li>
+<li>create_hash()
+: <a class="el" href="d9/d03/namespacestring__search.html#a8fb0bc932ba8b582c9f4c71338d050f8">string_search</a>
+</li>
+<li>eigen_values()
+: <a class="el" href="d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm</a>
+</li>
+<li>getFailureArray()
+: <a class="el" href="d9/d03/namespacestring__search.html#aa422aab133d4ed5e5d6022a7f701271f">string_search</a>
+</li>
+<li>kmp()
+: <a class="el" href="d9/d03/namespacestring__search.html#a26a58225ce7d3fa9d4c2f5349a65ed93">string_search</a>
+</li>
+<li>kohonen_som()
+: <a class="el" href="d8/d77/namespacemachine__learning.html#adc731720947b4bc2ab047c141e7d0299">machine_learning</a>
+</li>
+<li>kohonen_som_tracer()
+: <a class="el" href="d8/d77/namespacemachine__learning.html#acc6a28f40512dbda75ab1a3969248898">machine_learning</a>
+</li>
+<li>merge()
+: <a class="el" href="d5/d91/namespacesorting.html#aa26de383227859210f14dcf12201a079">sorting</a>
+</li>
+<li>non_recursive_merge_sort()
+: <a class="el" href="d5/d91/namespacesorting.html#a140d913e42fb94176a0b2c8b29a80420">sorting</a>
+</li>
+<li>operator&lt;&lt;()
+: <a class="el" href="d2/d3b/namespaceqr__algorithm.html#a7c63c78d6839b8ad73b77c161210b514">qr_algorithm</a>
+</li>
+<li>partition()
+: <a class="el" href="d5/d91/namespacesorting.html#a7e7f25f31c50523990437abf2ac3907e">sorting</a>
+</li>
+<li>qr_decompose()
+: <a class="el" href="d2/d3b/namespaceqr__algorithm.html#ab1ac74497ffb2101040cc1efe3546de8">qr_algorithm</a>
+</li>
+<li>quickSort()
+: <a class="el" href="d5/d91/namespacesorting.html#a50b66a1c652291b9a346ec7342967178">sorting</a>
+</li>
+<li>rabin_karp()
+: <a class="el" href="d9/d03/namespacestring__search.html#a21c673d56cbf67b1d2ee4d869185b7d9">string_search</a>
+</li>
+<li>recalculate_hash()
+: <a class="el" href="d9/d03/namespacestring__search.html#aed769d565b705a9b3e0eb1ec74088893">string_search</a>
+</li>
+<li>save_u_matrix()
+: <a class="el" href="d8/d77/namespacemachine__learning.html#a1d577f5d95b774ae97eb6838852d0df5">machine_learning</a>
+</li>
+<li>shell_sort()
+: <a class="el" href="d5/d91/namespacesorting.html#a5669396c6a6b1e14b97589b6e37980aa">sorting</a>
+</li>
+<li>update_weights()
+: <a class="el" href="d8/d77/namespacemachine__learning.html#ac4010fe3a52a74e8b5b1aaadfe38b46f">machine_learning</a>
+</li>
+<li>vector_dot()
+: <a class="el" href="d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">qr_algorithm</a>
+</li>
+<li>vector_mag()
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+    var rows = $('.memberdecls tr[class$="'+hashValue()+'"]');
+    glowEffect(rows.children(),300); // member without details
+  } else if (anchor.parent().attr('class')=='fieldname'){
+    glowEffect(anchor.parent().parent(),1000); // enum value
+  } else if (anchor.parent().attr('class')=='fieldtype'){
+    glowEffect(anchor.parent().parent(),1000); // struct field
+  } else if (anchor.parent().is(":header")) {
+    glowEffect(anchor.parent(),1000); // section header
+  } else {
+    glowEffect(anchor.next(),1000); // normal member
+  }
+}
+
+function selectAndHighlight(hash,n)
+{
+  var a;
+  if (hash) {
+    var link=stripPath(pathName())+':'+hash.substring(1);
+    a=$('.item a[class$="'+link+'"]');
+  }
+  if (a && a.length) {
+    a.parent().parent().addClass('selected');
+    a.parent().parent().attr('id','selected');
+    highlightAnchor();
+  } else if (n) {
+    $(n.itemDiv).addClass('selected');
+    $(n.itemDiv).attr('id','selected');
+  }
+  if ($('#nav-tree-contents .item:first').hasClass('selected')) {
+    $('#nav-sync').css('top','30px');
+  } else {
+    $('#nav-sync').css('top','5px');
+  }
+  showRoot();
+}
+
+function showNode(o, node, index, hash)
+{
+  if (node && node.childrenData) {
+    if (typeof(node.childrenData)==='string') {
+      var varName    = node.childrenData;
+      getScript(node.relpath+varName,function(){
+        node.childrenData = getData(varName);
+        showNode(o,node,index,hash);
+      },true);
+    } else {
+      if (!node.childrenVisited) {
+        getNode(o, node);
+      }
+      $(node.getChildrenUL()).css({'display':'block'});
+      node.plus_img.innerHTML = arrowDown;
+      node.expanded = true;
+      var n = node.children[o.breadcrumbs[index]];
+      if (index+1<o.breadcrumbs.length) {
+        showNode(o,n,index+1,hash);
+      } else {
+        if (typeof(n.childrenData)==='string') {
+          var varName = n.childrenData;
+          getScript(n.relpath+varName,function(){
+            n.childrenData = getData(varName);
+            node.expanded=false;
+            showNode(o,node,index,hash); // retry with child node expanded
+          },true);
+        } else {
+          var rootBase = stripPath(o.toroot.replace(/\..+$/, ''));
+          if (rootBase=="index" || rootBase=="pages" || rootBase=="search") {
+            expandNode(o, n, true, true);
+          }
+          selectAndHighlight(hash,n);
+        }
+      }
+    }
+  } else {
+    selectAndHighlight(hash);
+  }
+}
+
+function removeToInsertLater(element) {
+  var parentNode = element.parentNode;
+  var nextSibling = element.nextSibling;
+  parentNode.removeChild(element);
+  return function() {
+    if (nextSibling) {
+      parentNode.insertBefore(element, nextSibling);
+    } else {
+      parentNode.appendChild(element);
+    }
+  };
+}
+
+function getNode(o, po)
+{
+  var insertFunction = removeToInsertLater(po.li);
+  po.childrenVisited = true;
+  var l = po.childrenData.length-1;
+  for (var i in po.childrenData) {
+    var nodeData = po.childrenData[i];
+    po.children[i] = newNode(o, po, nodeData[0], nodeData[1], nodeData[2],
+      i==l);
+  }
+  insertFunction();
+}
+
+function gotoNode(o,subIndex,root,hash,relpath)
+{
+  var nti = navTreeSubIndices[subIndex][root+hash];
+  o.breadcrumbs = $.extend(true, [], nti ? nti : navTreeSubIndices[subIndex][root]);
+  if (!o.breadcrumbs && root!=NAVTREE[0][1]) { // fallback: show index
+    navTo(o,NAVTREE[0][1],"",relpath);
+    $('.item').removeClass('selected');
+    $('.item').removeAttr('id');
+  }
+  if (o.breadcrumbs) {
+    o.breadcrumbs.unshift(0); // add 0 for root node
+    showNode(o, o.node, 0, hash);
+  }
+}
+
+function navTo(o,root,hash,relpath)
+{
+  var link = cachedLink();
+  if (link) {
+    var parts = link.split('#');
+    root = parts[0];
+    if (parts.length>1) hash = '#'+parts[1].replace(/[^\w\-]/g,'');
+    else hash='';
+  }
+  if (hash.match(/^#l\d+$/)) {
+    var anchor=$('a[name='+hash.substring(1)+']');
+    glowEffect(anchor.parent(),1000); // line number
+    hash=''; // strip line number anchors
+  }
+  var url=root+hash;
+  var i=-1;
+  while (NAVTREEINDEX[i+1]<=url) i++;
+  if (i==-1) { i=0; root=NAVTREE[0][1]; } // fallback: show index
+  if (navTreeSubIndices[i]) {
+    gotoNode(o,i,root,hash,relpath)
+  } else {
+    getScript(relpath+'navtreeindex'+i,function(){
+      navTreeSubIndices[i] = eval('NAVTREEINDEX'+i);
+      if (navTreeSubIndices[i]) {
+        gotoNode(o,i,root,hash,relpath);
+      }
+    },true);
+  }
+}
+
+function showSyncOff(n,relpath)
+{
+    n.html('<img src="'+relpath+'sync_off.png" title="'+SYNCOFFMSG+'"/>');
+}
+
+function showSyncOn(n,relpath)
+{
+    n.html('<img src="'+relpath+'sync_on.png" title="'+SYNCONMSG+'"/>');
+}
+
+function toggleSyncButton(relpath)
+{
+  var navSync = $('#nav-sync');
+  if (navSync.hasClass('sync')) {
+    navSync.removeClass('sync');
+    showSyncOff(navSync,relpath);
+    storeLink(stripPath2(pathName())+hashUrl());
+  } else {
+    navSync.addClass('sync');
+    showSyncOn(navSync,relpath);
+    deleteLink();
+  }
+}
+
+var loadTriggered = false;
+var readyTriggered = false;
+var loadObject,loadToRoot,loadUrl,loadRelPath;
+
+$(window).on('load',function(){
+  if (readyTriggered) { // ready first
+    navTo(loadObject,loadToRoot,loadUrl,loadRelPath);
+    showRoot();
+  }
+  loadTriggered=true;
+});
+
+function initNavTree(toroot,relpath)
+{
+  var o = new Object();
+  o.toroot = toroot;
+  o.node = new Object();
+  o.node.li = document.getElementById("nav-tree-contents");
+  o.node.childrenData = NAVTREE;
+  o.node.children = new Array();
+  o.node.childrenUL = document.createElement("ul");
+  o.node.getChildrenUL = function() { return o.node.childrenUL; };
+  o.node.li.appendChild(o.node.childrenUL);
+  o.node.depth = 0;
+  o.node.relpath = relpath;
+  o.node.expanded = false;
+  o.node.isLast = true;
+  o.node.plus_img = document.createElement("span");
+  o.node.plus_img.className = 'arrow';
+  o.node.plus_img.innerHTML = arrowRight;
+
+  if (localStorageSupported()) {
+    var navSync = $('#nav-sync');
+    if (cachedLink()) {
+      showSyncOff(navSync,relpath);
+      navSync.removeClass('sync');
+    } else {
+      showSyncOn(navSync,relpath);
+    }
+    navSync.click(function(){ toggleSyncButton(relpath); });
+  }
+
+  if (loadTriggered) { // load before ready
+    navTo(o,toroot,hashUrl(),relpath);
+    showRoot();
+  } else { // ready before load
+    loadObject  = o;
+    loadToRoot  = toroot;
+    loadUrl     = hashUrl();
+    loadRelPath = relpath;
+    readyTriggered=true;
+  }
+
+  $(window).bind('hashchange', function(){
+     if (window.location.hash && window.location.hash.length>1){
+       var a;
+       if ($(location).attr('hash')){
+         var clslink=stripPath(pathName())+':'+hashValue();
+         a=$('.item a[class$="'+clslink.replace(/</g,'\\3c ')+'"]');
+       }
+       if (a==null || !$(a).parent().parent().hasClass('selected')){
+         $('.item').removeClass('selected');
+         $('.item').removeAttr('id');
+       }
+       var link=stripPath2(pathName());
+       navTo(o,link,hashUrl(),relpath);
+     } else if (!animationInProgress) {
+       $('#doc-content').scrollTop(0);
+       $('.item').removeClass('selected');
+       $('.item').removeAttr('id');
+       navTo(o,toroot,hashUrl(),relpath);
+     }
+  })
+}
+/* @license-end */
diff --git a/navtreedata.js b/navtreedata.js
new file mode 100644
index 000000000..2d8f92078
--- /dev/null
+++ b/navtreedata.js
@@ -0,0 +1,109 @@
+/*
+ @licstart  The following is the entire license notice for the JavaScript code in this file.
+
+ The MIT License (MIT)
+
+ Copyright (C) 1997-2020 by Dimitri van Heesch
+
+ Permission is hereby granted, free of charge, to any person obtaining a copy of this software
+ and associated documentation files (the "Software"), to deal in the Software without restriction,
+ including without limitation the rights to use, copy, modify, merge, publish, distribute,
+ sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is
+ furnished to do so, subject to the following conditions:
+
+ The above copyright notice and this permission notice shall be included in all copies or
+ substantial portions of the Software.
+
+ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING
+ BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+ DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+ @licend  The above is the entire license notice for the JavaScript code in this file
+*/
+var NAVTREE =
+[
+  [ "Algorithms_in_C++", "index.html", [
+    [ "The Algorithms - C++", "index.html", null ],
+    [ "CONTRIBUTION GUIDELINES", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html", [
+      [ "Before contributing", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html#autotoc_md1", null ],
+      [ "Contributing", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html#autotoc_md2", [
+        [ "Algorithms implemented in C++ (for education)", "index.html#autotoc_md33", null ],
+        [ "Contribute Guidelines", "index.html#autotoc_md34", null ],
+        [ "Contributor", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html#autotoc_md3", null ],
+        [ "Making Changes", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html#autotoc_md4", [
+          [ "Code", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html#autotoc_md5", null ],
+          [ "New File Name guidelines", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html#autotoc_md6", null ],
+          [ "New Directory guidelines", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html#autotoc_md7", null ],
+          [ "Commit Guidelines", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html#autotoc_md8", null ],
+          [ "Documentation", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html#autotoc_md9", null ],
+          [ "Test", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html#autotoc_md10", null ]
+        ] ],
+        [ "Pull Requests", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html#autotoc_md11", [
+          [ "cpplint", "d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html#autotoc_md12", null ]
+        ] ]
+      ] ]
+    ] ],
+    [ "List of all files", "d5/d88/md__d_i_r_e_c_t_o_r_y.html", [
+      [ "Backtracking", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md14", null ],
+      [ "Data Structures", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md15", null ],
+      [ "Dynamic Programming", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md16", null ],
+      [ "Geometry", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md17", null ],
+      [ "Graph", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md18", null ],
+      [ "Greedy Algorithms", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md19", null ],
+      [ "Hashing", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md20", null ],
+      [ "Machine Learning", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md21", null ],
+      [ "Math", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md22", null ],
+      [ "Numerical Methods", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md23", null ],
+      [ "Operations On Datastructures", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md24", null ],
+      [ "Others", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md25", null ],
+      [ "Probability", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md26", null ],
+      [ "Range Queries", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md27", null ],
+      [ "Search", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md28", null ],
+      [ "Sorting", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md29", null ],
+      [ "Strings", "d5/d88/md__d_i_r_e_c_t_o_r_y.html#autotoc_md30", null ]
+    ] ],
+    [ "Prime factorization", "d7/d7f/section.html", null ],
+    [ "Todo List", "dd/da0/todo.html", null ],
+    [ "Modules", "modules.html", "modules" ],
+    [ "Namespaces", "namespaces.html", [
+      [ "Namespace List", "namespaces.html", "namespaces_dup" ],
+      [ "Namespace Members", "namespacemembers.html", [
+        [ "All", "namespacemembers.html", null ],
+        [ "Functions", "namespacemembers_func.html", null ]
+      ] ]
+    ] ],
+    [ "Classes", "annotated.html", [
+      [ "Class List", "annotated.html", "annotated_dup" ],
+      [ "Class Index", "classes.html", null ],
+      [ "Class Members", "functions.html", [
+        [ "All", "functions.html", null ],
+        [ "Functions", "functions_func.html", null ],
+        [ "Variables", "functions_vars.html", null ],
+        [ "Related Functions", "functions_rela.html", null ]
+      ] ]
+    ] ],
+    [ "Files", "files.html", [
+      [ "File List", "files.html", "files_dup" ],
+      [ "File Members", "globals.html", [
+        [ "All", "globals.html", "globals_dup" ],
+        [ "Functions", "globals_func.html", "globals_func" ],
+        [ "Variables", "globals_vars.html", null ],
+        [ "Typedefs", "globals_type.html", null ],
+        [ "Macros", "globals_defs.html", null ]
+      ] ]
+    ] ]
+  ] ]
+];
+
+var NAVTREEINDEX =
+[
+"annotated.html",
+"d5/d15/classcll.html#a852ab0b4ec38b8462df3f32ee6f11290",
+"d9/d49/kohonen__som__trace_8cpp.html",
+"dd/d4f/class_solution.html#ae8ca86dfb0d034665027aa99af3c88c6"
+];
+
+var SYNCONMSG = 'click to disable panel synchronisation';
+var SYNCOFFMSG = 'click to enable panel synchronisation';
\ No newline at end of file
diff --git a/navtreeindex0.js b/navtreeindex0.js
new file mode 100644
index 000000000..b2efa4619
--- /dev/null
+++ b/navtreeindex0.js
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+  ['std_2386',['std',['../d8/dcc/namespacestd.html',1,'']]],
+  ['string_5fsearch_2387',['string_search',['../d9/d03/namespacestring__search.html',1,'']]],
+  ['this_5fthread_2388',['this_thread',['http://en.cppreference.com/w/d7/dbf/namespacestd_1_1this__thread.html',0,'std']]]
+];
diff --git a/search/nomatches.html b/search/nomatches.html
new file mode 100644
index 000000000..437732089
--- /dev/null
+++ b/search/nomatches.html
@@ -0,0 +1,12 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html><head><title></title>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<link rel="stylesheet" type="text/css" href="search.css"/>
+<script type="text/javascript" src="search.js"></script>
+</head>
+<body class="SRPage">
+<div id="SRIndex">
+<div class="SRStatus" id="NoMatches">No Matches</div>
+</div>
+</body>
+</html>
diff --git a/search/pages_0.html b/search/pages_0.html
new file mode 100644
index 000000000..ca7755f40
--- /dev/null
+++ b/search/pages_0.html
@@ -0,0 +1,36 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html><head><title></title>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<link rel="stylesheet" type="text/css" href="search.css"/>
+<script type="text/javascript" src="pages_0.js"></script>
+<script type="text/javascript" src="search.js"></script>
+</head>
+<body class="SRPage">
+<div id="SRIndex">
+<div class="SRStatus" id="Loading">Loading...</div>
+<div id="SRResults"></div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+createResults();
+/* @license-end */
+--></script>
+<div class="SRStatus" id="Searching">Searching...</div>
+<div class="SRStatus" id="NoMatches">No Matches</div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+document.getElementById("Loading").style.display="none";
+document.getElementById("NoMatches").style.display="none";
+var searchResults = new SearchResults("searchResults");
+searchResults.Search();
+window.addEventListener("message", function(event) {
+  if (event.data == "take_focus") {
+    var elem = searchResults.NavNext(0);
+    if (elem) elem.focus();
+  }
+});
+/* @license-end */
+--></script>
+</div>
+</body>
+</html>
diff --git a/search/pages_0.js b/search/pages_0.js
new file mode 100644
index 000000000..a401d3060
--- /dev/null
+++ b/search/pages_0.js
@@ -0,0 +1,4 @@
+var searchData=
+[
+  ['contribution_20guidelines_3937',['CONTRIBUTION GUIDELINES',['../d6/dcd/md__c_o_n_t_r_i_b_u_t_i_n_g.html',1,'']]]
+];
diff --git a/search/pages_1.html b/search/pages_1.html
new file mode 100644
index 000000000..4e469b4ad
--- /dev/null
+++ b/search/pages_1.html
@@ -0,0 +1,36 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html><head><title></title>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<link rel="stylesheet" type="text/css" href="search.css"/>
+<script type="text/javascript" src="pages_1.js"></script>
+<script type="text/javascript" src="search.js"></script>
+</head>
+<body class="SRPage">
+<div id="SRIndex">
+<div class="SRStatus" id="Loading">Loading...</div>
+<div id="SRResults"></div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+createResults();
+/* @license-end */
+--></script>
+<div class="SRStatus" id="Searching">Searching...</div>
+<div class="SRStatus" id="NoMatches">No Matches</div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+document.getElementById("Loading").style.display="none";
+document.getElementById("NoMatches").style.display="none";
+var searchResults = new SearchResults("searchResults");
+searchResults.Search();
+window.addEventListener("message", function(event) {
+  if (event.data == "take_focus") {
+    var elem = searchResults.NavNext(0);
+    if (elem) elem.focus();
+  }
+});
+/* @license-end */
+--></script>
+</div>
+</body>
+</html>
diff --git a/search/pages_1.js b/search/pages_1.js
new file mode 100644
index 000000000..22ae15391
--- /dev/null
+++ b/search/pages_1.js
@@ -0,0 +1,4 @@
+var searchData=
+[
+  ['list_20of_20all_20files_3938',['List of all files',['../d5/d88/md__d_i_r_e_c_t_o_r_y.html',1,'']]]
+];
diff --git a/search/pages_2.html b/search/pages_2.html
new file mode 100644
index 000000000..702915305
--- /dev/null
+++ b/search/pages_2.html
@@ -0,0 +1,36 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html><head><title></title>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<link rel="stylesheet" type="text/css" href="search.css"/>
+<script type="text/javascript" src="pages_2.js"></script>
+<script type="text/javascript" src="search.js"></script>
+</head>
+<body class="SRPage">
+<div id="SRIndex">
+<div class="SRStatus" id="Loading">Loading...</div>
+<div id="SRResults"></div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+createResults();
+/* @license-end */
+--></script>
+<div class="SRStatus" id="Searching">Searching...</div>
+<div class="SRStatus" id="NoMatches">No Matches</div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+document.getElementById("Loading").style.display="none";
+document.getElementById("NoMatches").style.display="none";
+var searchResults = new SearchResults("searchResults");
+searchResults.Search();
+window.addEventListener("message", function(event) {
+  if (event.data == "take_focus") {
+    var elem = searchResults.NavNext(0);
+    if (elem) elem.focus();
+  }
+});
+/* @license-end */
+--></script>
+</div>
+</body>
+</html>
diff --git a/search/pages_2.js b/search/pages_2.js
new file mode 100644
index 000000000..b9290b09e
--- /dev/null
+++ b/search/pages_2.js
@@ -0,0 +1,4 @@
+var searchData=
+[
+  ['prime_20factorization_3939',['Prime factorization',['../d7/d7f/section.html',1,'']]]
+];
diff --git a/search/pages_3.html b/search/pages_3.html
new file mode 100644
index 000000000..fce1ba40c
--- /dev/null
+++ b/search/pages_3.html
@@ -0,0 +1,36 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html><head><title></title>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<link rel="stylesheet" type="text/css" href="search.css"/>
+<script type="text/javascript" src="pages_3.js"></script>
+<script type="text/javascript" src="search.js"></script>
+</head>
+<body class="SRPage">
+<div id="SRIndex">
+<div class="SRStatus" id="Loading">Loading...</div>
+<div id="SRResults"></div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+createResults();
+/* @license-end */
+--></script>
+<div class="SRStatus" id="Searching">Searching...</div>
+<div class="SRStatus" id="NoMatches">No Matches</div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+document.getElementById("Loading").style.display="none";
+document.getElementById("NoMatches").style.display="none";
+var searchResults = new SearchResults("searchResults");
+searchResults.Search();
+window.addEventListener("message", function(event) {
+  if (event.data == "take_focus") {
+    var elem = searchResults.NavNext(0);
+    if (elem) elem.focus();
+  }
+});
+/* @license-end */
+--></script>
+</div>
+</body>
+</html>
diff --git a/search/pages_3.js b/search/pages_3.js
new file mode 100644
index 000000000..03f109400
--- /dev/null
+++ b/search/pages_3.js
@@ -0,0 +1,5 @@
+var searchData=
+[
+  ['the_20algorithms_20_2d_20c_2b_2b_3940',['The Algorithms - C++',['../index.html',1,'']]],
+  ['todo_20list_3941',['Todo List',['../dd/da0/todo.html',1,'']]]
+];
diff --git a/search/related_0.html b/search/related_0.html
new file mode 100644
index 000000000..1b314088e
--- /dev/null
+++ b/search/related_0.html
@@ -0,0 +1,36 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html><head><title></title>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<link rel="stylesheet" type="text/css" href="search.css"/>
+<script type="text/javascript" src="related_0.js"></script>
+<script type="text/javascript" src="search.js"></script>
+</head>
+<body class="SRPage">
+<div id="SRIndex">
+<div class="SRStatus" id="Loading">Loading...</div>
+<div id="SRResults"></div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+createResults();
+/* @license-end */
+--></script>
+<div class="SRStatus" id="Searching">Searching...</div>
+<div class="SRStatus" id="NoMatches">No Matches</div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+document.getElementById("Loading").style.display="none";
+document.getElementById("NoMatches").style.display="none";
+var searchResults = new SearchResults("searchResults");
+searchResults.Search();
+window.addEventListener("message", function(event) {
+  if (event.data == "take_focus") {
+    var elem = searchResults.NavNext(0);
+    if (elem) elem.focus();
+  }
+});
+/* @license-end */
+--></script>
+</div>
+</body>
+</html>
diff --git a/search/related_0.js b/search/related_0.js
new file mode 100644
index 000000000..c78c6d934
--- /dev/null
+++ b/search/related_0.js
@@ -0,0 +1,8 @@
+var searchData=
+[
+  ['operator_21_3d_3917',['operator!=',['../db/d82/classlarge__number.html#a72ae1ef050c4c28c50952ecab22d4b94',1,'large_number']]],
+  ['operator_2b_3918',['operator+',['../db/d82/classlarge__number.html#a70d23d67535e67030db570e56c00e16d',1,'large_number']]],
+  ['operator_3c_3c_3919',['operator&lt;&lt;',['../d6/d30/classmachine__learning_1_1adaline.html#a1d821a24e1503d468c95d4acedca58b3',1,'machine_learning::adaline::operator&lt;&lt;()'],['../db/d82/classlarge__number.html#a778428c4761b6ea5e7770743f0eab5ab',1,'large_number::operator&lt;&lt;()']]],
+  ['operator_3d_3d_3920',['operator==',['../db/d82/classlarge__number.html#a7ba872b9a3ce1f3da6c06c5409663cca',1,'large_number']]],
+  ['operator_3e_3e_3921',['operator&gt;&gt;',['../d7/d7c/classstatistics_1_1stats__computer1.html#ab5b4bfecdf391cae7edb1fe98548b846',1,'statistics::stats_computer1::operator&gt;&gt;()'],['../d8/dab/classstatistics_1_1stats__computer2.html#a7e7a1a2b0a03df0a70cac40d193421d2',1,'statistics::stats_computer2::operator&gt;&gt;()']]]
+];
diff --git a/search/search.css b/search/search.css
new file mode 100644
index 000000000..3cf9df94a
--- /dev/null
+++ b/search/search.css
@@ -0,0 +1,271 @@
+/*---------------- Search Box */
+
+#FSearchBox {
+    float: left;
+}
+
+#MSearchBox {
+    white-space : nowrap;
+    float: none;
+    margin-top: 8px;
+    right: 0px;
+    width: 170px;
+    height: 24px;
+    z-index: 102;
+}
+
+#MSearchBox .left
+{
+    display:block;
+    position:absolute;
+    left:10px;
+    width:20px;
+    height:19px;
+    background:url('search_l.png') no-repeat;
+    background-position:right;
+}
+
+#MSearchSelect {
+    display:block;
+    position:absolute;
+    width:20px;
+    height:19px;
+}
+
+.left #MSearchSelect {
+    left:4px;
+}
+
+.right #MSearchSelect {
+    right:5px;
+}
+
+#MSearchField {
+    display:block;
+    position:absolute;
+    height:19px;
+    background:url('search_m.png') repeat-x;
+    border:none;
+    width:115px;
+    margin-left:20px;
+    padding-left:4px;
+    color: #909090;
+    outline: none;
+    font: 9pt Arial, Verdana, sans-serif;
+    -webkit-border-radius: 0px;
+}
+
+#FSearchBox #MSearchField {
+    margin-left:15px;
+}
+
+#MSearchBox .right {
+    display:block;
+    position:absolute;
+    right:10px;
+    top:8px;
+    width:20px;
+    height:19px;
+    background:url('search_r.png') no-repeat;
+    background-position:left;
+}
+
+#MSearchClose {
+    display: none;
+    position: absolute;
+    top: 4px;
+    background : none;
+    border: none;
+    margin: 0px 4px 0px 0px;
+    padding: 0px 0px;
+    outline: none;
+}
+
+.left #MSearchClose {
+    left: 6px;
+}
+
+.right #MSearchClose {
+    right: 2px;
+}
+
+.MSearchBoxActive #MSearchField {
+    color: #000000;
+}
+
+/*---------------- Search filter selection */
+
+#MSearchSelectWindow {
+    display: none;
+    position: absolute;
+    left: 0; top: 0;
+    border: 1px solid #90A5CE;
+    background-color: #F9FAFC;
+    z-index: 10001;
+    padding-top: 4px;
+    padding-bottom: 4px;
+    -moz-border-radius: 4px;
+    -webkit-border-top-left-radius: 4px;
+    -webkit-border-top-right-radius: 4px;
+    -webkit-border-bottom-left-radius: 4px;
+    -webkit-border-bottom-right-radius: 4px;
+    -webkit-box-shadow: 5px 5px 5px rgba(0, 0, 0, 0.15);
+}
+
+.SelectItem {
+    font: 8pt Arial, Verdana, sans-serif;
+    padding-left:  2px;
+    padding-right: 12px;
+    border: 0px;
+}
+
+span.SelectionMark {
+    margin-right: 4px;
+    font-family: monospace;
+    outline-style: none;
+    text-decoration: none;
+}
+
+a.SelectItem {
+    display: block;
+    outline-style: none;
+    color: #000000; 
+    text-decoration: none;
+    padding-left:   6px;
+    padding-right: 12px;
+}
+
+a.SelectItem:focus,
+a.SelectItem:active {
+    color: #000000; 
+    outline-style: none;
+    text-decoration: none;
+}
+
+a.SelectItem:hover {
+    color: #FFFFFF;
+    background-color: #3D578C;
+    outline-style: none;
+    text-decoration: none;
+    cursor: pointer;
+    display: block;
+}
+
+/*---------------- Search results window */
+
+iframe#MSearchResults {
+    width: 60ex;
+    height: 15em;
+}
+
+#MSearchResultsWindow {
+    display: none;
+    position: absolute;
+    left: 0; top: 0;
+    border: 1px solid #000;
+    background-color: #EEF1F7;
+    z-index:10000;
+}
+
+/* ----------------------------------- */
+
+
+#SRIndex {
+    clear:both; 
+    padding-bottom: 15px;
+}
+
+.SREntry {
+    font-size: 10pt;
+    padding-left: 1ex;
+}
+
+.SRPage .SREntry {
+    font-size: 8pt;
+    padding: 1px 5px;
+}
+
+body.SRPage {
+    margin: 5px 2px;
+}
+
+.SRChildren {
+    padding-left: 3ex; padding-bottom: .5em 
+}
+
+.SRPage .SRChildren {
+    display: none;
+}
+
+.SRSymbol {
+    font-weight: bold; 
+    color: #425E97;
+    font-family: Arial, Verdana, sans-serif;
+    text-decoration: none;
+    outline: none;
+}
+
+a.SRScope {
+    display: block;
+    color: #425E97; 
+    font-family: Arial, Verdana, sans-serif;
+    text-decoration: none;
+    outline: none;
+}
+
+a.SRSymbol:focus, a.SRSymbol:active,
+a.SRScope:focus, a.SRScope:active {
+    text-decoration: underline;
+}
+
+span.SRScope {
+    padding-left: 4px;
+}
+
+.SRPage .SRStatus {
+    padding: 2px 5px;
+    font-size: 8pt;
+    font-style: italic;
+}
+
+.SRResult {
+    display: none;
+}
+
+DIV.searchresults {
+    margin-left: 10px;
+    margin-right: 10px;
+}
+
+/*---------------- External search page results */
+
+.searchresult {
+    background-color: #F0F3F8;
+}
+
+.pages b {
+   color: white;
+   padding: 5px 5px 3px 5px;
+   background-image: url("../tab_a.png");
+   background-repeat: repeat-x;
+   text-shadow: 0 1px 1px #000000;
+}
+
+.pages {
+    line-height: 17px;
+    margin-left: 4px;
+    text-decoration: none;
+}
+
+.hl {
+    font-weight: bold;
+}
+
+#searchresults {
+    margin-bottom: 20px;
+}
+
+.searchpages {
+    margin-top: 10px;
+}
+
diff --git a/search/search.js b/search/search.js
new file mode 100644
index 000000000..ff2b8c81b
--- /dev/null
+++ b/search/search.js
@@ -0,0 +1,814 @@
+/*
+ @licstart  The following is the entire license notice for the JavaScript code in this file.
+
+ The MIT License (MIT)
+
+ Copyright (C) 1997-2020 by Dimitri van Heesch
+
+ Permission is hereby granted, free of charge, to any person obtaining a copy of this software
+ and associated documentation files (the "Software"), to deal in the Software without restriction,
+ including without limitation the rights to use, copy, modify, merge, publish, distribute,
+ sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is
+ furnished to do so, subject to the following conditions:
+
+ The above copyright notice and this permission notice shall be included in all copies or
+ substantial portions of the Software.
+
+ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING
+ BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+ DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+ @licend  The above is the entire license notice for the JavaScript code in this file
+ */
+function convertToId(search)
+{
+  var result = '';
+  for (i=0;i<search.length;i++)
+  {
+    var c = search.charAt(i);
+    var cn = c.charCodeAt(0);
+    if (c.match(/[a-z0-9\u0080-\uFFFF]/))
+    {
+      result+=c;
+    }
+    else if (cn<16)
+    {
+      result+="_0"+cn.toString(16);
+    }
+    else
+    {
+      result+="_"+cn.toString(16);
+    }
+  }
+  return result;
+}
+
+function getXPos(item)
+{
+  var x = 0;
+  if (item.offsetWidth)
+  {
+    while (item && item!=document.body)
+    {
+      x   += item.offsetLeft;
+      item = item.offsetParent;
+    }
+  }
+  return x;
+}
+
+function getYPos(item)
+{
+  var y = 0;
+  if (item.offsetWidth)
+  {
+     while (item && item!=document.body)
+     {
+       y   += item.offsetTop;
+       item = item.offsetParent;
+     }
+  }
+  return y;
+}
+
+/* A class handling everything associated with the search panel.
+
+   Parameters:
+   name - The name of the global variable that will be
+          storing this instance.  Is needed to be able to set timeouts.
+   resultPath - path to use for external files
+*/
+function SearchBox(name, resultsPath, inFrame, label)
+{
+  if (!name || !resultsPath) {  alert("Missing parameters to SearchBox."); }
+
+  // ---------- Instance variables
+  this.name                  = name;
+  this.resultsPath           = resultsPath;
+  this.keyTimeout            = 0;
+  this.keyTimeoutLength      = 500;
+  this.closeSelectionTimeout = 300;
+  this.lastSearchValue       = "";
+  this.lastResultsPage       = "";
+  this.hideTimeout           = 0;
+  this.searchIndex           = 0;
+  this.searchActive          = false;
+  this.insideFrame           = inFrame;
+  this.searchLabel           = label;
+
+  // ----------- DOM Elements
+
+  this.DOMSearchField = function()
+  {  return document.getElementById("MSearchField");  }
+
+  this.DOMSearchSelect = function()
+  {  return document.getElementById("MSearchSelect");  }
+
+  this.DOMSearchSelectWindow = function()
+  {  return document.getElementById("MSearchSelectWindow");  }
+
+  this.DOMPopupSearchResults = function()
+  {  return document.getElementById("MSearchResults");  }
+
+  this.DOMPopupSearchResultsWindow = function()
+  {  return document.getElementById("MSearchResultsWindow");  }
+
+  this.DOMSearchClose = function()
+  {  return document.getElementById("MSearchClose"); }
+
+  this.DOMSearchBox = function()
+  {  return document.getElementById("MSearchBox");  }
+
+  // ------------ Event Handlers
+
+  // Called when focus is added or removed from the search field.
+  this.OnSearchFieldFocus = function(isActive)
+  {
+    this.Activate(isActive);
+  }
+
+  this.OnSearchSelectShow = function()
+  {
+    var searchSelectWindow = this.DOMSearchSelectWindow();
+    var searchField        = this.DOMSearchSelect();
+
+    if (this.insideFrame)
+    {
+      var left = getXPos(searchField);
+      var top  = getYPos(searchField);
+      left += searchField.offsetWidth + 6;
+      top += searchField.offsetHeight;
+
+      // show search selection popup
+      searchSelectWindow.style.display='block';
+      left -= searchSelectWindow.offsetWidth;
+      searchSelectWindow.style.left =  left + 'px';
+      searchSelectWindow.style.top  =  top  + 'px';
+    }
+    else
+    {
+      var left = getXPos(searchField);
+      var top  = getYPos(searchField);
+      top += searchField.offsetHeight;
+
+      // show search selection popup
+      searchSelectWindow.style.display='block';
+      searchSelectWindow.style.left =  left + 'px';
+      searchSelectWindow.style.top  =  top  + 'px';
+    }
+
+    // stop selection hide timer
+    if (this.hideTimeout)
+    {
+      clearTimeout(this.hideTimeout);
+      this.hideTimeout=0;
+    }
+    return false; // to avoid "image drag" default event
+  }
+
+  this.OnSearchSelectHide = function()
+  {
+    this.hideTimeout = setTimeout(this.name +".CloseSelectionWindow()",
+                                  this.closeSelectionTimeout);
+  }
+
+  // Called when the content of the search field is changed.
+  this.OnSearchFieldChange = function(evt)
+  {
+    if (this.keyTimeout) // kill running timer
+    {
+      clearTimeout(this.keyTimeout);
+      this.keyTimeout = 0;
+    }
+
+    var e  = (evt) ? evt : window.event; // for IE
+    if (e.keyCode==40 || e.keyCode==13)
+    {
+      if (e.shiftKey==1)
+      {
+        this.OnSearchSelectShow();
+        var win=this.DOMSearchSelectWindow();
+        for (i=0;i<win.childNodes.length;i++)
+        {
+          var child = win.childNodes[i]; // get span within a
+          if (child.className=='SelectItem')
+          {
+            child.focus();
+            return;
+          }
+        }
+        return;
+      }
+      else
+      {
+        window.frames.MSearchResults.postMessage("take_focus", "*");
+      }
+    }
+    else if (e.keyCode==27) // Escape out of the search field
+    {
+      this.DOMSearchField().blur();
+      this.DOMPopupSearchResultsWindow().style.display = 'none';
+      this.DOMSearchClose().style.display = 'none';
+      this.lastSearchValue = '';
+      this.Activate(false);
+      return;
+    }
+
+    // strip whitespaces
+    var searchValue = this.DOMSearchField().value.replace(/ +/g, "");
+
+    if (searchValue != this.lastSearchValue) // search value has changed
+    {
+      if (searchValue != "") // non-empty search
+      {
+        // set timer for search update
+        this.keyTimeout = setTimeout(this.name + '.Search()',
+                                     this.keyTimeoutLength);
+      }
+      else // empty search field
+      {
+        this.DOMPopupSearchResultsWindow().style.display = 'none';
+        this.DOMSearchClose().style.display = 'none';
+        this.lastSearchValue = '';
+      }
+    }
+  }
+
+  this.SelectItemCount = function(id)
+  {
+    var count=0;
+    var win=this.DOMSearchSelectWindow();
+    for (i=0;i<win.childNodes.length;i++)
+    {
+      var child = win.childNodes[i]; // get span within a
+      if (child.className=='SelectItem')
+      {
+        count++;
+      }
+    }
+    return count;
+  }
+
+  this.SelectItemSet = function(id)
+  {
+    var i,j=0;
+    var win=this.DOMSearchSelectWindow();
+    for (i=0;i<win.childNodes.length;i++)
+    {
+      var child = win.childNodes[i]; // get span within a
+      if (child.className=='SelectItem')
+      {
+        var node = child.firstChild;
+        if (j==id)
+        {
+          node.innerHTML='&#8226;';
+        }
+        else
+        {
+          node.innerHTML='&#160;';
+        }
+        j++;
+      }
+    }
+  }
+
+  // Called when an search filter selection is made.
+  // set item with index id as the active item
+  this.OnSelectItem = function(id)
+  {
+    this.searchIndex = id;
+    this.SelectItemSet(id);
+    var searchValue = this.DOMSearchField().value.replace(/ +/g, "");
+    if (searchValue!="" && this.searchActive) // something was found -> do a search
+    {
+      this.Search();
+    }
+  }
+
+  this.OnSearchSelectKey = function(evt)
+  {
+    var e = (evt) ? evt : window.event; // for IE
+    if (e.keyCode==40 && this.searchIndex<this.SelectItemCount()) // Down
+    {
+      this.searchIndex++;
+      this.OnSelectItem(this.searchIndex);
+    }
+    else if (e.keyCode==38 && this.searchIndex>0) // Up
+    {
+      this.searchIndex--;
+      this.OnSelectItem(this.searchIndex);
+    }
+    else if (e.keyCode==13 || e.keyCode==27)
+    {
+      this.OnSelectItem(this.searchIndex);
+      this.CloseSelectionWindow();
+      this.DOMSearchField().focus();
+    }
+    return false;
+  }
+
+  // --------- Actions
+
+  // Closes the results window.
+  this.CloseResultsWindow = function()
+  {
+    this.DOMPopupSearchResultsWindow().style.display = 'none';
+    this.DOMSearchClose().style.display = 'none';
+    this.Activate(false);
+  }
+
+  this.CloseSelectionWindow = function()
+  {
+    this.DOMSearchSelectWindow().style.display = 'none';
+  }
+
+  // Performs a search.
+  this.Search = function()
+  {
+    this.keyTimeout = 0;
+
+    // strip leading whitespace
+    var searchValue = this.DOMSearchField().value.replace(/^ +/, "");
+
+    var code = searchValue.toLowerCase().charCodeAt(0);
+    var idxChar = searchValue.substr(0, 1).toLowerCase();
+    if ( 0xD800 <= code && code <= 0xDBFF && searchValue > 1) // surrogate pair
+    {
+      idxChar = searchValue.substr(0, 2);
+    }
+
+    var resultsPage;
+    var resultsPageWithSearch;
+    var hasResultsPage;
+
+    var idx = indexSectionsWithContent[this.searchIndex].indexOf(idxChar);
+    if (idx!=-1)
+    {
+       var hexCode=idx.toString(16);
+       resultsPage = this.resultsPath + '/' + indexSectionNames[this.searchIndex] + '_' + hexCode + '.html';
+       resultsPageWithSearch = resultsPage+'?'+escape(searchValue);
+       hasResultsPage = true;
+    }
+    else // nothing available for this search term
+    {
+       resultsPage = this.resultsPath + '/nomatches.html';
+       resultsPageWithSearch = resultsPage;
+       hasResultsPage = false;
+    }
+
+    window.frames.MSearchResults.location = resultsPageWithSearch;
+    var domPopupSearchResultsWindow = this.DOMPopupSearchResultsWindow();
+
+    if (domPopupSearchResultsWindow.style.display!='block')
+    {
+       var domSearchBox = this.DOMSearchBox();
+       this.DOMSearchClose().style.display = 'inline';
+       if (this.insideFrame)
+       {
+         var domPopupSearchResults = this.DOMPopupSearchResults();
+         domPopupSearchResultsWindow.style.position = 'relative';
+         domPopupSearchResultsWindow.style.display  = 'block';
+         var width = document.body.clientWidth - 8; // the -8 is for IE :-(
+         domPopupSearchResultsWindow.style.width    = width + 'px';
+         domPopupSearchResults.style.width          = width + 'px';
+       }
+       else
+       {
+         var domPopupSearchResults = this.DOMPopupSearchResults();
+         var left = getXPos(domSearchBox) + 150; // domSearchBox.offsetWidth;
+         var top  = getYPos(domSearchBox) + 20;  // domSearchBox.offsetHeight + 1;
+         domPopupSearchResultsWindow.style.display = 'block';
+         left -= domPopupSearchResults.offsetWidth;
+         domPopupSearchResultsWindow.style.top     = top  + 'px';
+         domPopupSearchResultsWindow.style.left    = left + 'px';
+       }
+    }
+
+    this.lastSearchValue = searchValue;
+    this.lastResultsPage = resultsPage;
+  }
+
+  // -------- Activation Functions
+
+  // Activates or deactivates the search panel, resetting things to
+  // their default values if necessary.
+  this.Activate = function(isActive)
+  {
+    if (isActive || // open it
+        this.DOMPopupSearchResultsWindow().style.display == 'block'
+       )
+    {
+      this.DOMSearchBox().className = 'MSearchBoxActive';
+
+      var searchField = this.DOMSearchField();
+
+      if (searchField.value == this.searchLabel) // clear "Search" term upon entry
+      {
+        searchField.value = '';
+        this.searchActive = true;
+      }
+    }
+    else if (!isActive) // directly remove the panel
+    {
+      this.DOMSearchBox().className = 'MSearchBoxInactive';
+      this.DOMSearchField().value   = this.searchLabel;
+      this.searchActive             = false;
+      this.lastSearchValue          = ''
+      this.lastResultsPage          = '';
+    }
+  }
+}
+
+// -----------------------------------------------------------------------
+
+// The class that handles everything on the search results page.
+function SearchResults(name)
+{
+    // The number of matches from the last run of <Search()>.
+    this.lastMatchCount = 0;
+    this.lastKey = 0;
+    this.repeatOn = false;
+
+    // Toggles the visibility of the passed element ID.
+    this.FindChildElement = function(id)
+    {
+      var parentElement = document.getElementById(id);
+      var element = parentElement.firstChild;
+
+      while (element && element!=parentElement)
+      {
+        if (element.nodeName == 'DIV' && element.className == 'SRChildren')
+        {
+          return element;
+        }
+
+        if (element.nodeName == 'DIV' && element.hasChildNodes())
+        {
+           element = element.firstChild;
+        }
+        else if (element.nextSibling)
+        {
+           element = element.nextSibling;
+        }
+        else
+        {
+          do
+          {
+            element = element.parentNode;
+          }
+          while (element && element!=parentElement && !element.nextSibling);
+
+          if (element && element!=parentElement)
+          {
+            element = element.nextSibling;
+          }
+        }
+      }
+    }
+
+    this.Toggle = function(id)
+    {
+      var element = this.FindChildElement(id);
+      if (element)
+      {
+        if (element.style.display == 'block')
+        {
+          element.style.display = 'none';
+        }
+        else
+        {
+          element.style.display = 'block';
+        }
+      }
+    }
+
+    // Searches for the passed string.  If there is no parameter,
+    // it takes it from the URL query.
+    //
+    // Always returns true, since other documents may try to call it
+    // and that may or may not be possible.
+    this.Search = function(search)
+    {
+      if (!search) // get search word from URL
+      {
+        search = window.location.search;
+        search = search.substring(1);  // Remove the leading '?'
+        search = unescape(search);
+      }
+
+      search = search.replace(/^ +/, ""); // strip leading spaces
+      search = search.replace(/ +$/, ""); // strip trailing spaces
+      search = search.toLowerCase();
+      search = convertToId(search);
+
+      var resultRows = document.getElementsByTagName("div");
+      var matches = 0;
+
+      var i = 0;
+      while (i < resultRows.length)
+      {
+        var row = resultRows.item(i);
+        if (row.className == "SRResult")
+        {
+          var rowMatchName = row.id.toLowerCase();
+          rowMatchName = rowMatchName.replace(/^sr\d*_/, ''); // strip 'sr123_'
+
+          if (search.length<=rowMatchName.length &&
+             rowMatchName.substr(0, search.length)==search)
+          {
+            row.style.display = 'block';
+            matches++;
+          }
+          else
+          {
+            row.style.display = 'none';
+          }
+        }
+        i++;
+      }
+      document.getElementById("Searching").style.display='none';
+      if (matches == 0) // no results
+      {
+        document.getElementById("NoMatches").style.display='block';
+      }
+      else // at least one result
+      {
+        document.getElementById("NoMatches").style.display='none';
+      }
+      this.lastMatchCount = matches;
+      return true;
+    }
+
+    // return the first item with index index or higher that is visible
+    this.NavNext = function(index)
+    {
+      var focusItem;
+      while (1)
+      {
+        var focusName = 'Item'+index;
+        focusItem = document.getElementById(focusName);
+        if (focusItem && focusItem.parentNode.parentNode.style.display=='block')
+        {
+          break;
+        }
+        else if (!focusItem) // last element
+        {
+          break;
+        }
+        focusItem=null;
+        index++;
+      }
+      return focusItem;
+    }
+
+    this.NavPrev = function(index)
+    {
+      var focusItem;
+      while (1)
+      {
+        var focusName = 'Item'+index;
+        focusItem = document.getElementById(focusName);
+        if (focusItem && focusItem.parentNode.parentNode.style.display=='block')
+        {
+          break;
+        }
+        else if (!focusItem) // last element
+        {
+          break;
+        }
+        focusItem=null;
+        index--;
+      }
+      return focusItem;
+    }
+
+    this.ProcessKeys = function(e)
+    {
+      if (e.type == "keydown")
+      {
+        this.repeatOn = false;
+        this.lastKey = e.keyCode;
+      }
+      else if (e.type == "keypress")
+      {
+        if (!this.repeatOn)
+        {
+          if (this.lastKey) this.repeatOn = true;
+          return false; // ignore first keypress after keydown
+        }
+      }
+      else if (e.type == "keyup")
+      {
+        this.lastKey = 0;
+        this.repeatOn = false;
+      }
+      return this.lastKey!=0;
+    }
+
+    this.Nav = function(evt,itemIndex)
+    {
+      var e  = (evt) ? evt : window.event; // for IE
+      if (e.keyCode==13) return true;
+      if (!this.ProcessKeys(e)) return false;
+
+      if (this.lastKey==38) // Up
+      {
+        var newIndex = itemIndex-1;
+        var focusItem = this.NavPrev(newIndex);
+        if (focusItem)
+        {
+          var child = this.FindChildElement(focusItem.parentNode.parentNode.id);
+          if (child && child.style.display == 'block') // children visible
+          {
+            var n=0;
+            var tmpElem;
+            while (1) // search for last child
+            {
+              tmpElem = document.getElementById('Item'+newIndex+'_c'+n);
+              if (tmpElem)
+              {
+                focusItem = tmpElem;
+              }
+              else // found it!
+              {
+                break;
+              }
+              n++;
+            }
+          }
+        }
+        if (focusItem)
+        {
+          focusItem.focus();
+        }
+        else // return focus to search field
+        {
+           parent.document.getElementById("MSearchField").focus();
+        }
+      }
+      else if (this.lastKey==40) // Down
+      {
+        var newIndex = itemIndex+1;
+        var focusItem;
+        var item = document.getElementById('Item'+itemIndex);
+        var elem = this.FindChildElement(item.parentNode.parentNode.id);
+        if (elem && elem.style.display == 'block') // children visible
+        {
+          focusItem = document.getElementById('Item'+itemIndex+'_c0');
+        }
+        if (!focusItem) focusItem = this.NavNext(newIndex);
+        if (focusItem)  focusItem.focus();
+      }
+      else if (this.lastKey==39) // Right
+      {
+        var item = document.getElementById('Item'+itemIndex);
+        var elem = this.FindChildElement(item.parentNode.parentNode.id);
+        if (elem) elem.style.display = 'block';
+      }
+      else if (this.lastKey==37) // Left
+      {
+        var item = document.getElementById('Item'+itemIndex);
+        var elem = this.FindChildElement(item.parentNode.parentNode.id);
+        if (elem) elem.style.display = 'none';
+      }
+      else if (this.lastKey==27) // Escape
+      {
+        parent.searchBox.CloseResultsWindow();
+        parent.document.getElementById("MSearchField").focus();
+      }
+      else if (this.lastKey==13) // Enter
+      {
+        return true;
+      }
+      return false;
+    }
+
+    this.NavChild = function(evt,itemIndex,childIndex)
+    {
+      var e  = (evt) ? evt : window.event; // for IE
+      if (e.keyCode==13) return true;
+      if (!this.ProcessKeys(e)) return false;
+
+      if (this.lastKey==38) // Up
+      {
+        if (childIndex>0)
+        {
+          var newIndex = childIndex-1;
+          document.getElementById('Item'+itemIndex+'_c'+newIndex).focus();
+        }
+        else // already at first child, jump to parent
+        {
+          document.getElementById('Item'+itemIndex).focus();
+        }
+      }
+      else if (this.lastKey==40) // Down
+      {
+        var newIndex = childIndex+1;
+        var elem = document.getElementById('Item'+itemIndex+'_c'+newIndex);
+        if (!elem) // last child, jump to parent next parent
+        {
+          elem = this.NavNext(itemIndex+1);
+        }
+        if (elem)
+        {
+          elem.focus();
+        }
+      }
+      else if (this.lastKey==27) // Escape
+      {
+        parent.searchBox.CloseResultsWindow();
+        parent.document.getElementById("MSearchField").focus();
+      }
+      else if (this.lastKey==13) // Enter
+      {
+        return true;
+      }
+      return false;
+    }
+}
+
+function setKeyActions(elem,action)
+{
+  elem.setAttribute('onkeydown',action);
+  elem.setAttribute('onkeypress',action);
+  elem.setAttribute('onkeyup',action);
+}
+
+function setClassAttr(elem,attr)
+{
+  elem.setAttribute('class',attr);
+  elem.setAttribute('className',attr);
+}
+
+function createResults()
+{
+  var results = document.getElementById("SRResults");
+  for (var e=0; e<searchData.length; e++)
+  {
+    var id = searchData[e][0];
+    var srResult = document.createElement('div');
+    srResult.setAttribute('id','SR_'+id);
+    setClassAttr(srResult,'SRResult');
+    var srEntry = document.createElement('div');
+    setClassAttr(srEntry,'SREntry');
+    var srLink = document.createElement('a');
+    srLink.setAttribute('id','Item'+e);
+    setKeyActions(srLink,'return searchResults.Nav(event,'+e+')');
+    setClassAttr(srLink,'SRSymbol');
+    srLink.innerHTML = searchData[e][1][0];
+    srEntry.appendChild(srLink);
+    if (searchData[e][1].length==2) // single result
+    {
+      srLink.setAttribute('href',searchData[e][1][1][0]);
+      if (searchData[e][1][1][1])
+      {
+       srLink.setAttribute('target','_parent');
+      }
+      var srScope = document.createElement('span');
+      setClassAttr(srScope,'SRScope');
+      srScope.innerHTML = searchData[e][1][1][2];
+      srEntry.appendChild(srScope);
+    }
+    else // multiple results
+    {
+      srLink.setAttribute('href','javascript:searchResults.Toggle("SR_'+id+'")');
+      var srChildren = document.createElement('div');
+      setClassAttr(srChildren,'SRChildren');
+      for (var c=0; c<searchData[e][1].length-1; c++)
+      {
+        var srChild = document.createElement('a');
+        srChild.setAttribute('id','Item'+e+'_c'+c);
+        setKeyActions(srChild,'return searchResults.NavChild(event,'+e+','+c+')');
+        setClassAttr(srChild,'SRScope');
+        srChild.setAttribute('href',searchData[e][1][c+1][0]);
+        if (searchData[e][1][c+1][1])
+        {
+         srChild.setAttribute('target','_parent');
+        }
+        srChild.innerHTML = searchData[e][1][c+1][2];
+        srChildren.appendChild(srChild);
+      }
+      srEntry.appendChild(srChildren);
+    }
+    srResult.appendChild(srEntry);
+    results.appendChild(srResult);
+  }
+}
+
+function init_search()
+{
+  var results = document.getElementById("MSearchSelectWindow");
+  for (var key in indexSectionLabels)
+  {
+    var link = document.createElement('a');
+    link.setAttribute('class','SelectItem');
+    link.setAttribute('onclick','searchBox.OnSelectItem('+key+')');
+    link.href='javascript:void(0)';
+    link.innerHTML='<span class="SelectionMark">&#160;</span>'+indexSectionLabels[key];
+    results.appendChild(link);
+  }
+  searchBox.OnSelectItem(0);
+}
+/* @license-end */
diff --git a/search/search_l.png b/search/search_l.png
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+--></script>
+</div>
+</body>
+</html>
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new file mode 100644
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+++ b/search/variables_c.js
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+var searchData=
+[
+  ['queuefront_3905',['queueFront',['../d2/d36/structqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5',1,'queue']]],
+  ['queuerear_3906',['queueRear',['../d2/d36/structqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5',1,'queue']]]
+];
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+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html><head><title></title>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<link rel="stylesheet" type="text/css" href="search.css"/>
+<script type="text/javascript" src="variables_d.js"></script>
+<script type="text/javascript" src="search.js"></script>
+</head>
+<body class="SRPage">
+<div id="SRIndex">
+<div class="SRStatus" id="Loading">Loading...</div>
+<div id="SRResults"></div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+createResults();
+/* @license-end */
+--></script>
+<div class="SRStatus" id="Searching">Searching...</div>
+<div class="SRStatus" id="NoMatches">No Matches</div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+document.getElementById("Loading").style.display="none";
+document.getElementById("NoMatches").style.display="none";
+var searchResults = new SearchResults("searchResults");
+searchResults.Search();
+window.addEventListener("message", function(event) {
+  if (event.data == "take_focus") {
+    var elem = searchResults.NavNext(0);
+    if (elem) elem.focus();
+  }
+});
+/* @license-end */
+--></script>
+</div>
+</body>
+</html>
diff --git a/search/variables_d.js b/search/variables_d.js
new file mode 100644
index 000000000..40b0a9ce1
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+++ b/search/variables_d.js
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+var searchData=
+[
+  ['stack_3907',['stack',['../dc/dc5/paranthesis__matching_8cpp.html#aa37d24a036d239b3b528f13b9de880c7',1,'paranthesis_matching.cpp']]],
+  ['stacktop_3908',['stackTop',['../d1/dc2/classstack.html#a7289037c059aaad492b4d68e6bd54453',1,'stack']]]
+];
diff --git a/search/variables_e.html b/search/variables_e.html
new file mode 100644
index 000000000..8f22eb94c
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+++ b/search/variables_e.html
@@ -0,0 +1,36 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html><head><title></title>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<link rel="stylesheet" type="text/css" href="search.css"/>
+<script type="text/javascript" src="variables_e.js"></script>
+<script type="text/javascript" src="search.js"></script>
+</head>
+<body class="SRPage">
+<div id="SRIndex">
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+<div id="SRResults"></div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+createResults();
+/* @license-end */
+--></script>
+<div class="SRStatus" id="Searching">Searching...</div>
+<div class="SRStatus" id="NoMatches">No Matches</div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+document.getElementById("Loading").style.display="none";
+document.getElementById("NoMatches").style.display="none";
+var searchResults = new SearchResults("searchResults");
+searchResults.Search();
+window.addEventListener("message", function(event) {
+  if (event.data == "take_focus") {
+    var elem = searchResults.NavNext(0);
+    if (elem) elem.focus();
+  }
+});
+/* @license-end */
+--></script>
+</div>
+</body>
+</html>
diff --git a/search/variables_e.js b/search/variables_e.js
new file mode 100644
index 000000000..b43be978c
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+++ b/search/variables_e.js
@@ -0,0 +1,5 @@
+var searchData=
+[
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+  ['top_3910',['top',['../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d',1,'tower::top()'],['../dc/dc5/paranthesis__matching_8cpp.html#af93f4f37fc2ad9c37af4a715423b110c',1,'top():&#160;paranthesis_matching.cpp']]]
+];
diff --git a/search/variables_f.html b/search/variables_f.html
new file mode 100644
index 000000000..5dc917951
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+++ b/search/variables_f.html
@@ -0,0 +1,36 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html><head><title></title>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta name="generator" content="Doxygen 1.8.18"/>
+<link rel="stylesheet" type="text/css" href="search.css"/>
+<script type="text/javascript" src="variables_f.js"></script>
+<script type="text/javascript" src="search.js"></script>
+</head>
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+<div id="SRIndex">
+<div class="SRStatus" id="Loading">Loading...</div>
+<div id="SRResults"></div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+createResults();
+/* @license-end */
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+<div class="SRStatus" id="Searching">Searching...</div>
+<div class="SRStatus" id="NoMatches">No Matches</div>
+<script type="text/javascript"><!--
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
+document.getElementById("Loading").style.display="none";
+document.getElementById("NoMatches").style.display="none";
+var searchResults = new SearchResults("searchResults");
+searchResults.Search();
+window.addEventListener("message", function(event) {
+  if (event.data == "take_focus") {
+    var elem = searchResults.NavNext(0);
+    if (elem) elem.focus();
+  }
+});
+/* @license-end */
+--></script>
+</div>
+</body>
+</html>
diff --git a/search/variables_f.js b/search/variables_f.js
new file mode 100644
index 000000000..59c5586fc
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+++ b/search/variables_f.js
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+var searchData=
+[
+  ['values_3911',['values',['../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9',1,'tower']]]
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diff --git a/svgpan.js b/svgpan.js
new file mode 100644
index 000000000..2678d3846
--- /dev/null
+++ b/svgpan.js
@@ -0,0 +1,323 @@
+/*
+ @licstart  The following is the entire license notice for the JavaScript code in this file.
+ The code below is based on SVGPan Library 1.2 and was modified for doxygen
+ to support both zooming and panning via the mouse and via embedded buttons.
+
+ This code is licensed under the following BSD license:
+
+ Copyright 2009-2010 Andrea Leofreddi <a.leofreddi@itcharm.com>. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification, are
+ permitted provided that the following conditions are met:
+
+    1. Redistributions of source code must retain the above copyright notice, this list of
+       conditions and the following disclaimer.
+
+    2. Redistributions in binary form must reproduce the above copyright notice, this list
+       of conditions and the following disclaimer in the documentation and/or other materials
+       provided with the distribution.
+
+ THIS SOFTWARE IS PROVIDED BY Andrea Leofreddi ``AS IS'' AND ANY EXPRESS OR IMPLIED
+ WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL Andrea Leofreddi OR
+ CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+ SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
+ ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ The views and conclusions contained in the software and documentation are those of the
+ authors and should not be interpreted as representing official policies, either expressed
+ or implied, of Andrea Leofreddi.
+
+ @licend  The above is the entire license notice for the JavaScript code in this file
+ */
+
+var root = document.documentElement;
+var state = 'none';
+var stateOrigin;
+var stateTf = root.createSVGMatrix();
+var cursorGrab = ' url("data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAOCAMAAAAolt3jAAAAGXRFWHRTb2Z0d2FyZQBBZG9iZSBJbWFnZVJlYWR5ccllPAAAAAlQTFRFAAAA////////c3ilYwAAAAN0Uk5T//8A18oNQQAAAD1JREFUeNp0zlEKACAIA9Bt9z90bZBZkQj29qFBEuBOzQHSnWTTyckEfqUuZgFvslH4ch3qLCO/Kr8cAgwATw4Ax6XRCcoAAAAASUVORK5CYII="), move';
+var zoomSteps = 10;
+var zoomInFactor;
+var zoomOutFactor;
+var windowWidth;
+var windowHeight;
+var svgDoc;
+var minZoom;
+var maxZoom;
+if (!window) window=this;
+
+/**
+ * Show the graph in the middle of the view, scaled to fit
+ */
+function show()
+{
+  if (window.innerHeight) // Firefox
+  {
+    windowWidth = window.innerWidth;
+    windowHeight = window.innerHeight;
+  }
+  else if (document.documentElement.clientWidth) // Chrome/Safari
+  {
+    windowWidth = document.documentElement.clientWidth
+    windowHeight = document.documentElement.clientHeight
+  }
+  if (!windowWidth || !windowHeight) // failsafe
+  {
+    windowWidth = 800;
+    windowHeight = 600;
+  }
+  minZoom = Math.min(Math.min(viewHeight,windowHeight)/viewHeight,Math.min(viewWidth,windowWidth)/viewWidth);
+  maxZoom = minZoom+1.5;
+  zoomInFactor = Math.pow(maxZoom/minZoom,1.0/zoomSteps);
+  zoomOutFactor = 1.0/zoomInFactor;
+
+  var g = svgDoc.getElementById('viewport');
+  try
+  {
+    var bb = g.getBBox(); // this can throw an exception if css { display: none }
+    var tx = (windowWidth-viewWidth*minZoom+8)/(2*minZoom);
+    var ty = viewHeight+(windowHeight-viewHeight*minZoom)/(2*minZoom);
+    var a = 'scale('+minZoom+') rotate(0) translate('+tx+' '+ty+')';
+    g.setAttribute('transform',a);
+  }
+  catch(e) {}
+}
+
+/**
+ * Register handlers
+ */
+function init(evt)
+{
+  svgDoc = evt.target.ownerDocument;
+  try {
+    if (top.window && top.window.registerShow) { // register show function in html doc for dynamic sections
+      top.window.registerShow(sectionId,show);
+    }
+  } catch(e) {
+    // ugh, we are not allowed to talk to the parent; can happen with Chrome when viewing pages
+    // locally, since they treat every local page as having a different origin
+  }
+  show();
+
+  setAttributes(root, {
+     "onmousedown" : "handleMouseDown(evt)",
+     "onmousemove" : "handleMouseMove(evt)",
+     "onmouseup"   : "handleMouseUp(evt)"
+  });
+
+  if (window.addEventListener)
+  {
+    if (navigator.userAgent.toLowerCase().indexOf('webkit') >= 0 ||
+        navigator.userAgent.toLowerCase().indexOf("opera") >= 0 ||
+        navigator.appVersion.indexOf("MSIE") != -1)
+    {
+      window.addEventListener('mousewheel', handleMouseWheel, false); // Chrome/Safari/IE9
+    }
+    else
+    {
+      window.addEventListener('DOMMouseScroll', handleMouseWheel, false); // Others
+    }
+  }
+}
+
+window.onresize=function()
+{
+  if (svgDoc) { show(); }
+}
+
+/**
+ * Instance an SVGPoint object with given event coordinates.
+ */
+function getEventPoint(evt)
+{
+  var p = root.createSVGPoint();
+  p.x = evt.clientX;
+  p.y = evt.clientY;
+  return p;
+}
+
+/**
+ * Sets the current transform matrix of an element.
+ */
+function setCTM(element, matrix)
+{
+  var s = "matrix(" + matrix.a + "," + matrix.b + "," + matrix.c + "," + matrix.d + "," + matrix.e + "," + matrix.f + ")";
+  element.setAttribute("transform", s);
+}
+
+/**
+ * Sets attributes of an element.
+ */
+function setAttributes(element, attributes)
+{
+  for (i in attributes)
+    element.setAttributeNS(null, i, attributes[i]);
+}
+
+function doZoom(g,point,zoomFactor)
+{
+  var p = point.matrixTransform(g.getCTM().inverse());
+  var k = root.createSVGMatrix().translate(p.x, p.y).scale(zoomFactor).translate(-p.x, -p.y);
+  var n = g.getCTM().multiply(k);
+  var s = Math.max(n.a,n.d);
+  if      (s>maxZoom) n=n.translate(p.x,p.y).scale(maxZoom/s).translate(-p.x,-p.y);
+  else if (s<minZoom) n=n.translate(p.x,p.y).scale(minZoom/s).translate(-p.x,-p.y);
+  setCTM(g, n);
+  stateTf = stateTf.multiply(n.inverse());
+}
+
+/**
+ * Handle mouse move event.
+ */
+function handleMouseWheel(evt)
+{
+  if (!evt) evt = window.evt;
+  if (!evt.shiftKey) return; // only zoom when shift is pressed
+  if (evt.preventDefault) evt.preventDefault();
+  evt.returnValue = false;
+
+  if (state!='pan')
+  {
+    var delta;
+    if (evt.wheelDelta)
+    {
+      delta = evt.wheelDelta / 7200; // Opera/Chrome/IE9/Safari
+    }
+    else
+    {
+      delta = evt.detail / -180; // Mozilla
+    }
+    var svgDoc = evt.target.ownerDocument;
+    var g = svgDoc.getElementById("viewport");
+    var p = getEventPoint(evt);
+    doZoom(g,p,1+delta);
+  }
+}
+
+/**
+ * Handle mouse move event.
+ */
+function handleMouseMove(evt)
+{
+  if(evt.preventDefault)
+    evt.preventDefault();
+
+  evt.returnValue = false;
+
+  var g = svgDoc.getElementById("viewport");
+
+  if (state == 'pan')
+  {
+    // Pan mode
+    var p = getEventPoint(evt).matrixTransform(stateTf);
+    setCTM(g,stateTf.inverse().translate(p.x - stateOrigin.x, p.y - stateOrigin.y));
+  }
+}
+
+/**
+ * Handle click event.
+ */
+function handleMouseDown(evt)
+{
+  if(evt.preventDefault)
+    evt.preventDefault();
+  evt.returnValue = false;
+  var g = svgDoc.getElementById("viewport");
+  state = 'pan';
+  stateTf = g.getCTM().inverse();
+  stateOrigin = getEventPoint(evt).matrixTransform(stateTf);
+  g.style.cursor = cursorGrab;
+}
+
+/**
+ * Handle mouse button release event.
+ */
+function handleMouseUp(evt)
+{
+  if (evt.preventDefault) evt.preventDefault();
+  evt.returnValue = false;
+  var g = svgDoc.getElementById("viewport");
+  g.style.cursor = "default";
+  // Quit pan mode
+  state = '';
+}
+
+/**
+ * Dumps a matrix to a string (useful for debug).
+ */
+function dumpMatrix(matrix)
+{
+  var s = "[ " + matrix.a + ", " + matrix.c + ", " + matrix.e + "\n  " + matrix.b + ", " + matrix.d + ", " + matrix.f + "\n  0, 0, 1 ]";
+  return s;
+}
+
+/**
+ * Handler for pan buttons
+ */
+function handlePan(x,y)
+{
+  var g = svgDoc.getElementById("viewport");
+  setCTM(g,g.getCTM().translate(x*20/minZoom,y*20/minZoom));
+}
+
+/**
+ * Handle reset button
+ */
+function handleReset()
+{
+  show();
+}
+
+/**
+ * Handler for zoom buttons
+ */
+function handleZoom(evt,direction)
+{
+  var g = svgDoc.getElementById("viewport");
+  var factor = direction=='in' ? zoomInFactor : zoomOutFactor;
+  var m = g.getCTM();
+  var p = root.createSVGPoint();
+  p.x = windowWidth/2;
+  p.y = windowHeight/2;
+  doZoom(g,p,factor);
+}
+
+function serializeXmlNode(xmlNode)
+{
+  if (typeof window.XMLSerializer != "undefined") {
+    return (new window.XMLSerializer()).serializeToString(xmlNode);
+  } else if (typeof xmlNode.xml != "undefined") {
+    return xmlNode.xml;
+  }
+  return "";
+}
+
+/**
+ * Handler for print function
+ */
+function handlePrint(evt)
+{
+  evt.returnValue = false;
+  var g = svgDoc.getElementById("graph");
+  var xs = serializeXmlNode(g);
+  try {
+    var w = window.open('about:blank','_blank','width='+windowWidth+',height='+windowHeight+
+                        ',toolbar=0,status=0,menubar=0,scrollbars=0,resizable=0,location=0,directories=0');
+    var d = w.document;
+    d.write('<html xmlns="http://www.w3.org/1999/xhtml" '+
+            'xmlns:svg="http://www.w3.org/2000/svg" '+
+            'xmlns:xlink="http://www.w3.org/1999/xlink">');
+    d.write('<head><title>Print SVG</title></head>');
+    d.write('<body style="margin: 0px; padding: 0px;" onload="window.print();">');
+    d.write('<div id="svg" style="width:'+windowWidth+'px; height:'+windowHeight+'px;">'+xs+'</div>');
+    d.write('</body>');
+    d.write('</html>');
+    d.close();
+  } catch(e) {
+    alert('Failed to open popup window needed for printing!\n'+e.message);
+  }
+}
+/* @license-end */
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