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d4/d0f/namespacegram__schmidt.html
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35
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>del</b>() (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
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<tr bgcolor="#f0f0f0" class="odd"><td class="entry"><b>delfix</b>(node *) (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>disp</b>() (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0"><td class="entry"><b>display</b>(node *) (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0" class="odd"><td class="entry"><b>display</b>(node *) (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>insert</b>() (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0"><td class="entry"><b>insertfix</b>(node *) (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0" class="odd"><td class="entry"><b>insertfix</b>(node *) (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>leftrotate</b>(node *) (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0"><td class="entry"><b>q</b> (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
<tr bgcolor="#f0f0f0" class="odd"><td class="entry"><b>q</b> (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
<tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>RBtree</b>() (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
<tr bgcolor="#f0f0f0"><td class="entry"><b>rightrotate</b>(node *) (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0" class="odd"><td class="entry"><b>rightrotate</b>(node *) (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>root</b> (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
<tr bgcolor="#f0f0f0"><td class="entry"><b>search</b>() (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0" class="odd"><td class="entry"><b>search</b>() (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>successor</b>(node *) (defined in <a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a>)</td><td class="entry"><a class="el" href="../../d8/d72/class_r_btree.html">RBtree</a></td><td class="entry"></td></tr>
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<td id="projectalign" style="padding-left: 0.5em;">
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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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<p>This is the complete list of members for <a class="el" href="../../d2/d05/class_min_heap.html">MinHeap</a>, including all inherited members.</p>
<table class="directory">
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<tr bgcolor="#f0f0f0" class="odd"><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>
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<tr bgcolor="#f0f0f0"><td class="entry"><b>~MinHeap</b>() (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 bgcolor="#f0f0f0" class="odd"><td class="entry"><b>~MinHeap</b>() (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>
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<a href="#func-members">Functions</a> </div>
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<div class="title">least_common_multiple.cpp File Reference</div> </div>
<div class="headertitle"><div class="title">least_common_multiple.cpp File Reference</div></div>
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<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
@@ -105,7 +104,7 @@ Include dependency graph for least_common_multiple.cpp:</div>
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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>
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<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>
<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>
<a id="a8ba1fc66e4134ab25b2602b323150563" name="a8ba1fc66e4134ab25b2602b323150563"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8ba1fc66e4134ab25b2602b323150563">&#9670;&nbsp;</a></span>gcd()</h2>
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@@ -145,33 +144,39 @@ Functions</h2></td></tr>
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<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">unsigned</span> <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">unsigned</span> <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>
<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 id="l00016" name="l00016"></a><span class="lineno"> 16</span> {</div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> <span class="keywordflow">if</span> (x == 0) {</div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> }</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> <span class="keywordflow">if</span> (y == 0) {</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> <span class="keywordflow">return</span> x;</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> }</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keywordflow">if</span> (x == y) {</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="keywordflow">return</span> x;</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> }</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <span class="keywordflow">if</span> (x &gt; y) {</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// The following is valid because we have checked whether y == 0</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> temp = x / y;</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(y, x - temp * y);</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> }</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// Again the following is valid because we have checked whether x == 0</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> temp = y / x;</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y - temp * x);</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span>}</div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_a8ba1fc66e4134ab25b2602b323150563"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a></div><div class="ttdeci">unsigned int gcd(unsigned int x, unsigned int y)</div><div class="ttdef"><b>Definition:</b> least_common_multiple.cpp:16</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8d0e241db517813725e721a152e3a25">&#9670;&nbsp;</a></span>lcm()</h2>
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@@ -196,20 +201,20 @@ Functions</h2></td></tr>
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<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; {</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="keywordflow">return</span> x / <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y) * y;</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160;}</div>
<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 id="l00043" name="l00043"></a><span class="lineno"> 43</span> {</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">return</span> x / <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y) * y;</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span>}</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>
<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="../../d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</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>
<p >Main function </p>
<div class="fragment"><div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> {</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span>}</div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition:</b> least_common_multiple.cpp:50</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">&#9670;&nbsp;</a></span>tests()</h2>
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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>
<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">// First test on lcm(5,10) == 10</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;LCM of 5 and 10 is 10 but lcm function gives a different &quot;</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="stringliteral">&quot;result.\n&quot;</span>,</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10) == 10));</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;First assertion passes: LCM of 5 and 10 is &quot;</span> &lt;&lt; <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10)</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; </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="comment">// Second test on lcm(2,3) == 6 as 2 and 3 are coprime (prime in fact)</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;LCM of 2 and 3 is 6 but lcm function gives a different &quot;</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="stringliteral">&quot;result.\n&quot;</span>,</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(2, 3) == 6));</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;Second assertion passes: LCM of 2 and 3 is &quot;</span> &lt;&lt; <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(2, 3)</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</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="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">// Testing an integer overflow.</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="comment">// The algorithm should work as long as the result fits into integer.</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;LCM of 987654321 and 987654321 is 987654321 but lcm function&quot;</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="stringliteral">&quot; gives a different result.\n&quot;</span>,</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <a class="code" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(987654321, 987654321) == 987654321));</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; &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>
<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>
<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" target="_blank">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>
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<p>maximum number that can be computed - The result after 93 cannot be stored in a <code>uint64_t</code> data type. </p>
<p >maximum number that can be computed - The result after 93 cannot be stored in a <code>uint64_t</code> data type. </p>
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<h2 class="groupheader">Function Documentation</h2>
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<p>Algorithm </p>
<div class="fragment"><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; {</div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; &lt;&lt; <span class="stringliteral">&quot;Cannot compute for n&gt;93 due to limit of 64-bit integers\n&quot;</span>;</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; </div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160;}</div>
<p >Algorithm </p>
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<p>Main function </p>
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<p >Main function </p>
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<a href="#nested-classes">Classes</a> &#124;
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<div class="headertitle">
<div class="title">inorder_successor_of_bst.cpp File Reference</div> </div>
<div class="headertitle"><div class="title">inorder_successor_of_bst.cpp File Reference</div></div>
</div><!--header-->
<div class="contents">
<p>An implementation for finding the <a href="https://www.youtube.com/watch?v=5cPbNCrdotA">Inorder successor of a binary search tree</a> Inorder successor of a node is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inorder traversal.
<p>An implementation for finding the <a href="https://www.youtube.com/watch?v=5cPbNCrdotA" target="_blank">Inorder successor of a binary search tree</a> Inorder successor of a node is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inorder traversal.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
@@ -111,7 +110,7 @@ Include dependency graph for inorder_successor_of_bst.cpp:</div>
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<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">A <a class="el" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html" title="A Node structure representing a single node in BST.">Node</a> structure representing a single node in BST. <a href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html#details">More...</a><br /></td></tr>
@@ -120,38 +119,38 @@ Classes</h2></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">class encapsulating the necessary test cases <a href="../../d5/d58/class_test_cases.html#details">More...</a><br /></td></tr>
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<tr class="memdesc:da/d6d/namespaceoperations__on__datastructures"><td class="mdescLeft">&#160;</td><td class="mdescRight">for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> <br /></td></tr>
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<tr class="memdesc:dd/d74/namespaceinorder__successor__of__bst"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the <a href="https://www.youtube.com/watch?v=5cPbNCrdotA">Inorder successor of a binary search tree</a> implementation. <br /></td></tr>
<tr class="memitem:dd/d74/namespaceinorder__successor__of__bst"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d74/namespaceinorder__successor__of__bst.html">inorder_successor_of_bst</a></td></tr>
<tr class="memdesc:dd/d74/namespaceinorder__successor__of__bst"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the <a href="https://www.youtube.com/watch?v=5cPbNCrdotA" target="_blank">Inorder successor of a binary search tree</a> implementation. <br /></td></tr>
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<tr class="memdesc:a4852816cc9f28f7b9def0e5beb4e8545"><td class="mdescLeft">&#160;</td><td class="mdescRight">Allocates a new node in heap for given data and returns it's pointer. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a4852816cc9f28f7b9def0e5beb4e8545">More...</a><br /></td></tr>
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<tr class="memdesc:a2153df6265379da9bda259af3f46556a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Inserts the given data in BST while maintaining the properties of BST. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a2153df6265379da9bda259af3f46556a">More...</a><br /></td></tr>
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<tr class="memdesc:a744afaca22fa7bb91c92209a26f23e8f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Searches the given data in BST and returns the pointer to the node containing that data. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a744afaca22fa7bb91c92209a26f23e8f">More...</a><br /></td></tr>
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<tr class="memdesc:a25667588088eb647887d1c2bff0efa8c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Finds and return the minimum node in BST. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a25667588088eb647887d1c2bff0efa8c">More...</a><br /></td></tr>
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<tr class="memitem:a7f6f73a33beec448c27cc1d70b220702"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../db/d8b/struct_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7f6f73a33beec448c27cc1d70b220702">operations_on_datastructures::inorder_traversal_of_bst::makeNode</a> (int64_t <a class="el" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</td></tr>
<tr class="memdesc:a7f6f73a33beec448c27cc1d70b220702"><td class="mdescLeft">&#160;</td><td class="mdescRight">Allocates a new node in heap for given data and returns it's pointer. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7f6f73a33beec448c27cc1d70b220702">More...</a><br /></td></tr>
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<tr class="memitem:a3ae0bea4123fd2ce155108e88f2ef78c"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../db/d8b/struct_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a3ae0bea4123fd2ce155108e88f2ef78c">operations_on_datastructures::inorder_traversal_of_bst::Insert</a> (<a class="el" href="../../db/d8b/struct_node.html">Node</a> *root, int64_t <a class="el" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</td></tr>
<tr class="memdesc:a3ae0bea4123fd2ce155108e88f2ef78c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Inserts the given data in BST while maintaining the properties of BST. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a3ae0bea4123fd2ce155108e88f2ef78c">More...</a><br /></td></tr>
<tr class="separator:a3ae0bea4123fd2ce155108e88f2ef78c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a824cbf1814854824cf05f062eea07b95"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../db/d8b/struct_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a824cbf1814854824cf05f062eea07b95">operations_on_datastructures::inorder_traversal_of_bst::getNode</a> (<a class="el" href="../../db/d8b/struct_node.html">Node</a> *root, int64_t <a class="el" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</td></tr>
<tr class="memdesc:a824cbf1814854824cf05f062eea07b95"><td class="mdescLeft">&#160;</td><td class="mdescRight">Searches the given data in BST and returns the pointer to the node containing that data. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a824cbf1814854824cf05f062eea07b95">More...</a><br /></td></tr>
<tr class="separator:a824cbf1814854824cf05f062eea07b95"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a72483e3f6933e004a8d86371e8a990db"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../db/d8b/struct_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a72483e3f6933e004a8d86371e8a990db">operations_on_datastructures::inorder_traversal_of_bst::findMinNode</a> (<a class="el" href="../../db/d8b/struct_node.html">Node</a> *root)</td></tr>
<tr class="memdesc:a72483e3f6933e004a8d86371e8a990db"><td class="mdescLeft">&#160;</td><td class="mdescRight">Finds and return the minimum node in BST. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a72483e3f6933e004a8d86371e8a990db">More...</a><br /></td></tr>
<tr class="separator:a72483e3f6933e004a8d86371e8a990db"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5d7266b934ca50c4f53e4f1e725d89a4"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a> (<a class="el" href="../../db/d8b/struct_node.html">Node</a> *root)</td></tr>
<tr class="memdesc:a5d7266b934ca50c4f53e4f1e725d89a4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Prints the BST in inorder traversal using recursion. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">More...</a><br /></td></tr>
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<tr class="memitem:ad0ca93be4f9576bfb715a4864a30dbee"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../db/d8b/struct_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#ad0ca93be4f9576bfb715a4864a30dbee">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a> (<a class="el" href="../../db/d8b/struct_node.html">Node</a> *root, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int64_t &gt; &amp;<a class="el" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</td></tr>
<tr class="memdesc:ad0ca93be4f9576bfb715a4864a30dbee"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function is used in test cases to quickly create BST containing large data instead of hard coding it in code. For a given root, this will add all the nodes containing data passes in data vector. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#ad0ca93be4f9576bfb715a4864a30dbee">More...</a><br /></td></tr>
<tr class="separator:ad0ca93be4f9576bfb715a4864a30dbee"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9aa3fac9aa48a6568ecf89aaee190d43"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../db/d8b/struct_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a9aa3fac9aa48a6568ecf89aaee190d43">operations_on_datastructures::inorder_traversal_of_bst::getInorderSuccessor</a> (<a class="el" href="../../db/d8b/struct_node.html">Node</a> *root, int64_t <a class="el" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</td></tr>
<tr class="memdesc:a9aa3fac9aa48a6568ecf89aaee190d43"><td class="mdescLeft">&#160;</td><td class="mdescRight">Inorder successor of a node is the next node in inorder traversal of the Binary Tree. This function takes the root node and the data of the node for which we have to find the inorder successor, and returns the inorder successor node. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a9aa3fac9aa48a6568ecf89aaee190d43">More...</a><br /></td></tr>
<tr class="separator:a9aa3fac9aa48a6568ecf89aaee190d43"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a05fe8a029e155c43e4efa598d4d089d9"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../db/d8b/struct_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a> (<a class="el" href="../../db/d8b/struct_node.html">Node</a> *root, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int64_t &gt; &amp;<a class="el" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</td></tr>
<tr class="memdesc:a05fe8a029e155c43e4efa598d4d089d9"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function is used in test cases to quickly create BST containing large data instead of hard coding it in code. For a given root, this will add all the nodes containing data passes in data vector. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">More...</a><br /></td></tr>
<tr class="separator:a05fe8a029e155c43e4efa598d4d089d9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3923fb22b46e085376703cae0b44d690"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../db/d8b/struct_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a3923fb22b46e085376703cae0b44d690">operations_on_datastructures::inorder_traversal_of_bst::getInorderSuccessor</a> (<a class="el" href="../../db/d8b/struct_node.html">Node</a> *root, int64_t <a class="el" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</td></tr>
<tr class="memdesc:a3923fb22b46e085376703cae0b44d690"><td class="mdescLeft">&#160;</td><td class="mdescRight">Inorder successor of a node is the next node in inorder traversal of the Binary Tree. This function takes the root node and the data of the node for which we have to find the inorder successor, and returns the inorder successor node. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a3923fb22b46e085376703cae0b44d690">More...</a><br /></td></tr>
<tr class="separator:a3923fb22b46e085376703cae0b44d690"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7b20eb99272665c1777949e26ab59589"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">operations_on_datastructures::inorder_traversal_of_bst::deallocate</a> (<a class="el" href="../../db/d8b/struct_node.html">Node</a> *rootNode)</td></tr>
<tr class="memdesc:a7b20eb99272665c1777949e26ab59589"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function clears the memory allocated to entire tree recursively. Its just for clean up the memory and not relevant to the actual topic. <a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">More...</a><br /></td></tr>
<tr class="separator:a7b20eb99272665c1777949e26ab59589"><td class="memSeparator" colspan="2">&#160;</td></tr>
@@ -163,7 +162,7 @@ Functions</h2></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>An implementation for finding the <a href="https://www.youtube.com/watch?v=5cPbNCrdotA">Inorder successor of a binary search tree</a> Inorder successor of a node is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inorder traversal. </p>
<div class="textblock"><p >An implementation for finding the <a href="https://www.youtube.com/watch?v=5cPbNCrdotA" target="_blank">Inorder successor of a binary search tree</a> Inorder successor of a node is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inorder traversal. </p>
<h3><a class="anchor" id="autotoc_md77"></a>
Case 1: The given node has the right node/subtree</h3>
<pre class="fragment"> * In this case, the left-most deepest node in the right subtree will
@@ -184,9 +183,9 @@ Method 2: Search from the root node</h4>
<li>In case if there is no link from a child node to the parent node, we need to walk down the tree starting from the root node to the given node, by doing so, we are visiting every ancestor of the given node.</li>
<li>In order successor would be the deepest node in this path for which given node is in left subtree.</li>
</ul>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/foo290">Nitin Sharma</a> </dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/foo290" target="_blank">Nitin Sharma</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a7b20eb99272665c1777949e26ab59589"></a>
<a id="a7b20eb99272665c1777949e26ab59589" name="a7b20eb99272665c1777949e26ab59589"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7b20eb99272665c1777949e26ab59589">&#9670;&nbsp;</a></span>deallocate()</h2>
<div class="memitem">
@@ -210,14 +209,14 @@ Method 2: Search from the root node</h4>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<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; <span class="keywordflow">if</span> (rootNode == <span class="keyword">nullptr</span>) {</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>&#160; <span class="keywordflow">return</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; <a class="code" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">deallocate</a>(rootNode-&gt;left);</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>&#160; <a class="code" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">deallocate</a>(rootNode-&gt;right);</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>&#160; <span class="keyword">delete</span> (rootNode);</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> {</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="keywordflow">if</span> (rootNode == <span class="keyword">nullptr</span>) {</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> }</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">deallocate</a>(rootNode-&gt;left);</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">deallocate</a>(rootNode-&gt;right);</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keyword">delete</span> (rootNode);</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span>}</div>
<div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a7b20eb99272665c1777949e26ab59589"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">operations_on_datastructures::inorder_traversal_of_bst::deallocate</a></div><div class="ttdeci">void deallocate(Node *rootNode)</div><div class="ttdoc">This function clears the memory allocated to entire tree recursively. Its just for clean up the memor...</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:210</div></div>
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Here is the call graph for this function:</div>
@@ -228,14 +227,14 @@ Here is the call graph for this function:</div>
</div>
</div>
<a id="a25667588088eb647887d1c2bff0efa8c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a25667588088eb647887d1c2bff0efa8c">&#9670;&nbsp;</a></span>findMinNode()</h2>
<a id="a72483e3f6933e004a8d86371e8a990db" name="a72483e3f6933e004a8d86371e8a990db"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a72483e3f6933e004a8d86371e8a990db">&#9670;&nbsp;</a></span>findMinNode()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="../../db/d8b/struct_node.html">Node</a>* operations_on_datastructures::inorder_traversal_of_bst::findMinNode </td>
<td class="memname"><a class="el" href="../../db/d8b/struct_node.html">Node</a> * operations_on_datastructures::inorder_traversal_of_bst::findMinNode </td>
<td>(</td>
<td class="paramtype"><a class="el" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">Node</a> *&#160;</td>
<td class="paramname"><em>root</em></td><td>)</td>
@@ -252,32 +251,32 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>Node* Pointer to the found node </dd></dl>
<div class="fragment"><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; <span class="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; <span class="keywordflow">return</span> root;</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">while</span> (root-&gt;left != <span class="keyword">nullptr</span>) {</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; root = root-&gt;left;</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">return</span> root;</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> {</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordflow">return</span> root;</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> }</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">while</span> (root-&gt;left != <span class="keyword">nullptr</span>) {</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> root = root-&gt;left;</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> }</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keywordflow">return</span> root;</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span>}</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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<h2 class="memtitle"><span class="permalink"><a href="#a9aa3fac9aa48a6568ecf89aaee190d43">&#9670;&nbsp;</a></span>getInorderSuccessor()</h2>
<a id="a3923fb22b46e085376703cae0b44d690" name="a3923fb22b46e085376703cae0b44d690"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3923fb22b46e085376703cae0b44d690">&#9670;&nbsp;</a></span>getInorderSuccessor()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="../../db/d8b/struct_node.html">Node</a>* operations_on_datastructures::inorder_traversal_of_bst::getInorderSuccessor </td>
<td class="memname"><a class="el" href="../../db/d8b/struct_node.html">Node</a> * operations_on_datastructures::inorder_traversal_of_bst::getInorderSuccessor </td>
<td>(</td>
<td class="paramtype"><a class="el" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">Node</a> *&#160;</td>
<td class="paramname"><em>root</em>, </td>
@@ -297,7 +296,7 @@ Here is the call graph for this function:</div>
</div><div class="memdoc">
<p>Inorder successor of a node is the next node in inorder traversal of the Binary Tree. This function takes the root node and the data of the node for which we have to find the inorder successor, and returns the inorder successor node. </p>
<p>Search from the root node as we need to walk the tree starting from the root node to the given node, by doing so, we are visiting every ancestor of the given node. In order successor would be the deepest node in this path for which given node is in left subtree. Time complexity O(h) </p><dl class="params"><dt>Parameters</dt><dd>
<p >Search from the root node as we need to walk the tree starting from the root node to the given node, by doing so, we are visiting every ancestor of the given node. In order successor would be the deepest node in this path for which given node is in left subtree. Time complexity O(h) </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">root</td><td>A pointer to the root node of the BST </td></tr>
<tr><td class="paramname">data</td><td>The data (or the data of node) for which we have to find inorder successor. </td></tr>
@@ -305,54 +304,54 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><a class="el" href="../../db/d8b/struct_node.html">Node</a> pointer to the inorder successor node. </dd></dl>
<div class="fragment"><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; <a class="code" href="../../db/d8b/struct_node.html">Node</a> *current = <a class="code" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a744afaca22fa7bb91c92209a26f23e8f">getNode</a>(root, <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160; <span class="keywordflow">if</span> (current == <span class="keyword">nullptr</span>) {</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; <span class="keywordflow">return</span> <span class="keyword">nullptr</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; </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160; <span class="comment">// Case - 1</span></div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160; <span class="keywordflow">if</span> (current-&gt;right != <span class="keyword">nullptr</span>) {</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a25667588088eb647887d1c2bff0efa8c">findMinNode</a>(current-&gt;right);</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="comment">// case - 2</span></div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160; <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160; <a class="code" href="../../db/d8b/struct_node.html">Node</a> *successor = <span class="keyword">nullptr</span>;</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160; <a class="code" href="../../db/d8b/struct_node.html">Node</a> *ancestor = root;</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="keywordflow">while</span> (ancestor != current &amp;&amp; ancestor != <span class="keyword">nullptr</span>) {</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160; <span class="comment">// This means my current node is in left of the root node</span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>&#160; <span class="keywordflow">if</span> (current-&gt;data &lt; ancestor-&gt;data) {</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>&#160; successor = ancestor;</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160; ancestor = ancestor-&gt;left; <span class="comment">// keep going left</span></div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160; ancestor = ancestor-&gt;right;</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> successor; <span class="comment">// Nodes with maximum vales will not have a successor</span></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;}</div>
<div class="fragment"><div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> {</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *current = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a824cbf1814854824cf05f062eea07b95">getNode</a>(root, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="keywordflow">if</span> (current == <span class="keyword">nullptr</span>) {</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> }</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> </div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// Case - 1</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="keywordflow">if</span> (current-&gt;right != <span class="keyword">nullptr</span>) {</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a72483e3f6933e004a8d86371e8a990db">findMinNode</a>(current-&gt;right);</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> }</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="comment">// case - 2</span></div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *successor = <span class="keyword">nullptr</span>;</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *ancestor = root;</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> </div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="keywordflow">while</span> (ancestor != current &amp;&amp; ancestor != <span class="keyword">nullptr</span>) {</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="comment">// This means my current node is in left of the root node</span></div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keywordflow">if</span> (current-&gt;data &lt; ancestor-&gt;data) {</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> successor = ancestor;</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> ancestor = ancestor-&gt;left; <span class="comment">// keep going left</span></div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> ancestor = ancestor-&gt;right;</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> }</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> }</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="keywordflow">return</span> successor; <span class="comment">// Nodes with maximum vales will not have a successor</span></div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> }</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span>}</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="ainorder__successor__of__bst_8cpp_html_a25667588088eb647887d1c2bff0efa8c"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a25667588088eb647887d1c2bff0efa8c">operations_on_datastructures::inorder_traversal_of_bst::findMinNode</a></div><div class="ttdeci">Node * findMinNode(Node *root)</div><div class="ttdoc">Finds and return the minimum node in BST.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:121</div></div>
<div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a744afaca22fa7bb91c92209a26f23e8f"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a744afaca22fa7bb91c92209a26f23e8f">operations_on_datastructures::inorder_traversal_of_bst::getNode</a></div><div class="ttdeci">Node * getNode(Node *root, int64_t data)</div><div class="ttdoc">Searches the given data in BST and returns the pointer to the node containing that data.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:100</div></div>
<div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a72483e3f6933e004a8d86371e8a990db"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a72483e3f6933e004a8d86371e8a990db">operations_on_datastructures::inorder_traversal_of_bst::findMinNode</a></div><div class="ttdeci">Node * findMinNode(Node *root)</div><div class="ttdoc">Finds and return the minimum node in BST.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:121</div></div>
<div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a824cbf1814854824cf05f062eea07b95"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a824cbf1814854824cf05f062eea07b95">operations_on_datastructures::inorder_traversal_of_bst::getNode</a></div><div class="ttdeci">Node * getNode(Node *root, int64_t data)</div><div class="ttdoc">Searches the given data in BST and returns the pointer to the node containing that data.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:100</div></div>
<div class="ttc" id="astruct_node_html"><div class="ttname"><a href="../../db/d8b/struct_node.html">Node</a></div><div class="ttdef"><b>Definition:</b> linkedlist_implentation_usingarray.cpp:14</div></div>
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Here is the call graph for this function:</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a744afaca22fa7bb91c92209a26f23e8f">&#9670;&nbsp;</a></span>getNode()</h2>
<a id="a824cbf1814854824cf05f062eea07b95" name="a824cbf1814854824cf05f062eea07b95"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a824cbf1814854824cf05f062eea07b95">&#9670;&nbsp;</a></span>getNode()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="../../db/d8b/struct_node.html">Node</a>* operations_on_datastructures::inorder_traversal_of_bst::getNode </td>
<td class="memname"><a class="el" href="../../db/d8b/struct_node.html">Node</a> * operations_on_datastructures::inorder_traversal_of_bst::getNode </td>
<td>(</td>
<td class="paramtype"><a class="el" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">Node</a> *&#160;</td>
<td class="paramname"><em>root</em>, </td>
@@ -380,42 +379,41 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>Node* pointer to the found node </dd></dl>
<p><a class="el" href="../../db/d8b/struct_node.html">Node</a> found!</p>
<p>Traverse right subtree recursively as the given data is greater than the data in root node, data must be present in right subtree.</p>
<p>Traverse left subtree recursively as the given data is less than the data in root node, data must be present in left subtree.</p>
<div class="fragment"><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">if</span> (root == <span class="keyword">nullptr</span>) {</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</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;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a> == <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <span class="keywordflow">return</span> root; <span class="comment">/// Node found!</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> &gt; root-&gt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>) {<span class="comment"></span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160;<span class="comment"> /// Traverse right subtree recursively as the given data is greater than</span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160;<span class="comment"> /// the data in root node, data must be present in right subtree.</span></div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160;<span class="comment"></span> <span class="keywordflow">return</span> <a class="code" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a744afaca22fa7bb91c92209a26f23e8f">getNode</a>(root-&gt;right, <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; } <span class="keywordflow">else</span> {<span class="comment"></span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160;<span class="comment"> /// Traverse left subtree recursively as the given data is less than the</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160;<span class="comment"> /// data in root node, data must be present in left subtree.</span></div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160;<span class="comment"></span> <span class="keywordflow">return</span> <a class="code" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a744afaca22fa7bb91c92209a26f23e8f">getNode</a>(root-&gt;left, <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</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="ttc" id="adata_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/data.html">std::vector::data</a></div><div class="ttdeci">T data(T... args)</div></div>
<p ><a class="el" href="../../db/d8b/struct_node.html">Node</a> found!</p>
<p >Traverse right subtree recursively as the given data is greater than the data in root node, data must be present in right subtree.</p>
<p >Traverse left subtree recursively as the given data is less than the data in root node, data must be present in left subtree.</p>
<div class="fragment"><div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> {</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (root-&gt;data == <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordflow">return</span> root; <span class="comment">/// Node found!</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a> &gt; root-&gt;data) {<span class="comment"></span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span><span class="comment"> /// Traverse right subtree recursively as the given data is greater than</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="comment"> /// the data in root node, data must be present in right subtree.</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="comment"></span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a824cbf1814854824cf05f062eea07b95">getNode</a>(root-&gt;right, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> } <span class="keywordflow">else</span> {<span class="comment"></span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span><span class="comment"> /// Traverse left subtree recursively as the given data is less than the</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span><span class="comment"> /// data in root node, data must be present in left subtree.</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span><span class="comment"></span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a824cbf1814854824cf05f062eea07b95">getNode</a>(root-&gt;left, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> }</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span>}</div>
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Here is the call graph for this function:</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a2153df6265379da9bda259af3f46556a">&#9670;&nbsp;</a></span>Insert()</h2>
<a id="a3ae0bea4123fd2ce155108e88f2ef78c" name="a3ae0bea4123fd2ce155108e88f2ef78c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3ae0bea4123fd2ce155108e88f2ef78c">&#9670;&nbsp;</a></span>Insert()</h2>
<div class="memitem">
<div class="memproto">
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<tr>
<td class="memname"><a class="el" href="../../db/d8b/struct_node.html">Node</a>* operations_on_datastructures::inorder_traversal_of_bst::Insert </td>
<td class="memname"><a class="el" href="../../db/d8b/struct_node.html">Node</a> * operations_on_datastructures::inorder_traversal_of_bst::Insert </td>
<td>(</td>
<td class="paramtype"><a class="el" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">Node</a> *&#160;</td>
<td class="paramname"><em>root</em>, </td>
@@ -443,21 +441,21 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>Node* Pointer to the root node. </dd></dl>
<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="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; root = <a class="code" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a4852816cc9f28f7b9def0e5beb4e8545">makeNode</a>(<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (data &lt;= root-&gt;<a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; root-&gt;left = Insert(root-&gt;left, <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; root-&gt;right = Insert(root-&gt;right, <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</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; <span class="keywordflow">return</span> root;</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160;}</div>
<div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a4852816cc9f28f7b9def0e5beb4e8545"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a4852816cc9f28f7b9def0e5beb4e8545">operations_on_datastructures::inorder_traversal_of_bst::makeNode</a></div><div class="ttdeci">Node * makeNode(int64_t data)</div><div class="ttdoc">Allocates a new node in heap for given data and returns it's pointer.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:68</div></div>
<div class="fragment"><div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> {</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">if</span> (root == <span class="keyword">nullptr</span>) {</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> root = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7f6f73a33beec448c27cc1d70b220702">makeNode</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (data &lt;= root-&gt;<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> root-&gt;left = Insert(root-&gt;left, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> root-&gt;right = Insert(root-&gt;right, <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>);</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordflow">return</span> root;</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span>}</div>
<div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a7f6f73a33beec448c27cc1d70b220702"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7f6f73a33beec448c27cc1d70b220702">operations_on_datastructures::inorder_traversal_of_bst::makeNode</a></div><div class="ttdeci">Node * makeNode(int64_t data)</div><div class="ttdoc">Allocates a new node in heap for given data and returns it's pointer.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:68</div></div>
</div><!-- fragment -->
</div>
</div>
<a id="a0ddf1224851353fc92bfbff6f499fa97"></a>
<a id="a0ddf1224851353fc92bfbff6f499fa97" name="a0ddf1224851353fc92bfbff6f499fa97"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&nbsp;</a></span>main()</h2>
<div class="memitem">
@@ -492,51 +490,51 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p>&lt; root node of the bst</p>
<p>&lt; Data to add nodes in BST</p>
<p>&lt; An element to find inorder successor for.</p>
<p>&lt; Making BST</p>
<p>memory cleanup!</p>
<div class="fragment"><div class="line"><a name="l00398"></a><span class="lineno"> 398</span>&#160; {</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>&#160; <a class="code" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>&#160; </div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>&#160; <a class="code" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a> *root =</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>&#160; <span class="keyword">nullptr</span>; <span class="comment">///&lt; root node of the bst</span></div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_data{3, 4, 5,</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>&#160; 89, 1, 2}; <span class="comment">///&lt; Data to add nodes in BST</span></div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>&#160; </div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>&#160; int64_t targetElement = 4; <span class="comment">///&lt; An element to find inorder successor for.</span></div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>&#160; root = <a class="code" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#ad0ca93be4f9576bfb715a4864a30dbee">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a>(</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>&#160; root, node_data); <span class="comment">///&lt; Making BST</span></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; <a class="code" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>&#160; *inorderSuccessor = operations_on_datastructures::</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>&#160; inorder_traversal_of_bst::getInorderSuccessor(root, targetElement);</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>&#160; </div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</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;In-order sequence is : &quot;</span>;</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>&#160; <a class="code" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a>(root);</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</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="l00417"></a><span class="lineno"> 417</span>&#160; </div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>&#160; <span class="keywordflow">if</span> (inorderSuccessor == <span class="keyword">nullptr</span>) {</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</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;Inorder successor for last node is NULL&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="l00420"></a><span class="lineno"> 420</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</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;Target element is : &quot;</span> &lt;&lt; targetElement &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="l00422"></a><span class="lineno"> 422</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;Inorder successor for target element is : &quot;</span></div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>&#160; &lt;&lt; inorderSuccessor-&gt;<a class="code" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html#ae161f3e5ef33ade73429cab9291612e2">data</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="l00424"></a><span class="lineno"> 424</span>&#160; }</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>&#160; </div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>&#160; <a class="code" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">deallocate</a>(root); <span class="comment">/// memory cleanup!</span></div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>&#160; </div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>&#160;}</div>
<p >&lt; root node of the bst</p>
<p >&lt; Data to add nodes in BST</p>
<p >&lt; An element to find inorder successor for.</p>
<p >&lt; Making BST</p>
<p >memory cleanup!</p>
<div class="fragment"><div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> {</div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> </div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a> *root =</div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> <span class="keyword">nullptr</span>; <span class="comment">///&lt; root node of the bst</span></div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> node_data{3, 4, 5,</div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> 89, 1, 2}; <span class="comment">///&lt; Data to add nodes in BST</span></div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> </div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> int64_t targetElement = 4; <span class="comment">///&lt; An element to find inorder successor for.</span></div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> root = <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a>(</div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> root, node_data); <span class="comment">///&lt; Making BST</span></div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> </div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> <a class="code hl_class" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> *inorderSuccessor = operations_on_datastructures::</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> inorder_traversal_of_bst::getInorderSuccessor(root, targetElement);</div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> </div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;In-order sequence is : &quot;</span>;</div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a>(root);</div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> </div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> <span class="keywordflow">if</span> (inorderSuccessor == <span class="keyword">nullptr</span>) {</div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inorder successor for last node is NULL&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Target element is : &quot;</span> &lt;&lt; targetElement &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Inorder successor for target element is : &quot;</span></div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> &lt;&lt; inorderSuccessor-&gt;<a class="code hl_variable" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html#ae161f3e5ef33ade73429cab9291612e2">data</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> }</div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> </div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> <a class="code hl_function" href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a7b20eb99272665c1777949e26ab59589">deallocate</a>(root); <span class="comment">/// memory cleanup!</span></div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> </div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span>}</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="aclassoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node_html"><div class="ttname"><a href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">operations_on_datastructures::inorder_traversal_of_bst::Node</a></div><div class="ttdoc">A Node structure representing a single node in BST.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:56</div></div>
<div class="ttc" id="aclassoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node_html_ae161f3e5ef33ade73429cab9291612e2"><div class="ttname"><a href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html#ae161f3e5ef33ade73429cab9291612e2">operations_on_datastructures::inorder_traversal_of_bst::Node::data</a></div><div class="ttdeci">int64_t data</div><div class="ttdoc">The key/value of the node.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:58</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="ainorder__successor__of__bst_8cpp_html_a05fe8a029e155c43e4efa598d4d089d9"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a05fe8a029e155c43e4efa598d4d089d9">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a></div><div class="ttdeci">Node * makeBST(Node *root, const std::vector&lt; int64_t &gt; &amp;data)</div><div class="ttdoc">This function is used in test cases to quickly create BST containing large data instead of hard codin...</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:155</div></div>
<div class="ttc" id="ainorder__successor__of__bst_8cpp_html_a5d7266b934ca50c4f53e4f1e725d89a4"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#a5d7266b934ca50c4f53e4f1e725d89a4">operations_on_datastructures::inorder_traversal_of_bst::printInorder</a></div><div class="ttdeci">void printInorder(Node *root)</div><div class="ttdoc">Prints the BST in inorder traversal using recursion.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:136</div></div>
<div class="ttc" id="ainorder__successor__of__bst_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:387</div></div>
<div class="ttc" id="ainorder__successor__of__bst_8cpp_html_ad0ca93be4f9576bfb715a4864a30dbee"><div class="ttname"><a href="../../d4/d32/inorder__successor__of__bst_8cpp.html#ad0ca93be4f9576bfb715a4864a30dbee">operations_on_datastructures::inorder_traversal_of_bst::makeBST</a></div><div class="ttdeci">Node * makeBST(Node *root, const std::vector&lt; int64_t &gt; &amp;data)</div><div class="ttdoc">This function is used in test cases to quickly create BST containing large data instead of hard codin...</div><div class="ttdef"><b>Definition:</b> inorder_successor_of_bst.cpp:155</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; int64_t &gt;</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>
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<h2 class="memtitle"><span class="permalink"><a href="#ad0ca93be4f9576bfb715a4864a30dbee">&#9670;&nbsp;</a></span>makeBST()</h2>
<a id="a05fe8a029e155c43e4efa598d4d089d9" name="a05fe8a029e155c43e4efa598d4d089d9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a05fe8a029e155c43e4efa598d4d089d9">&#9670;&nbsp;</a></span>makeBST()</h2>
<div class="memitem">
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<table class="memname">
<tr>
<td class="memname"><a class="el" href="../../db/d8b/struct_node.html">Node</a>* operations_on_datastructures::inorder_traversal_of_bst::makeBST </td>
<td class="memname"><a class="el" href="../../db/d8b/struct_node.html">Node</a> * operations_on_datastructures::inorder_traversal_of_bst::makeBST </td>
<td>(</td>
<td class="paramtype"><a class="el" href="../../d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html">Node</a> *&#160;</td>
<td class="paramname"><em>root</em>, </td>
@@ -581,29 +579,29 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><a class="el" href="../../db/d8b/struct_node.html">Node</a> pointer to the root node. </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="keywordflow">for</span> (int64_t values : <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160; root = Insert(root, values);</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">return</span> root;</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> {</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordflow">for</span> (int64_t values : <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> root = Insert(root, values);</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> }</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keywordflow">return</span> root;</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a4852816cc9f28f7b9def0e5beb4e8545">&#9670;&nbsp;</a></span>makeNode()</h2>
<a id="a7f6f73a33beec448c27cc1d70b220702" name="a7f6f73a33beec448c27cc1d70b220702"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7f6f73a33beec448c27cc1d70b220702">&#9670;&nbsp;</a></span>makeNode()</h2>
<div class="memitem">
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<table class="memname">
<tr>
<td class="memname"><a class="el" href="../../db/d8b/struct_node.html">Node</a>* operations_on_datastructures::inorder_traversal_of_bst::makeNode </td>
<td class="memname"><a class="el" href="../../db/d8b/struct_node.html">Node</a> * operations_on_datastructures::inorder_traversal_of_bst::makeNode </td>
<td>(</td>
<td class="paramtype">int64_t&#160;</td>
<td class="paramname"><em>data</em></td><td>)</td>
@@ -620,28 +618,28 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A pointer to the newly allocated <a class="el" href="../../db/d8b/struct_node.html">Node</a>. </dd></dl>
<p>&lt; setting data for node</p>
<p>&lt; setting left child as null</p>
<p>&lt; setting right child as null</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="code" href="../../db/d8b/struct_node.html">Node</a> *<a class="code" href="../../d5/da1/structnode.html">node</a> = <span class="keyword">new</span> <a class="code" href="../../db/d8b/struct_node.html">Node</a>();</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <a class="code" href="../../d5/da1/structnode.html">node</a>-&gt;data = <a class="code" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>; <span class="comment">///&lt; setting data for node</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <a class="code" href="../../d5/da1/structnode.html">node</a>-&gt;left = <span class="keyword">nullptr</span>; <span class="comment">///&lt; setting left child as null</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <a class="code" href="../../d5/da1/structnode.html">node</a>-&gt;right = <span class="keyword">nullptr</span>; <span class="comment">///&lt; setting right child as null</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160;}</div>
<p >&lt; setting data for node</p>
<p >&lt; setting left child as null</p>
<p >&lt; setting right child as null</p>
<div class="fragment"><div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> {</div>
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<tr class="memitem:a89ab7d6c3e3ee72a8cbaa85127986185"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a89ab7d6c3e3ee72a8cbaa85127986185">math::power_of_two</a> (int n)</td></tr>
<tr class="memdesc:a89ab7d6c3e3ee72a8cbaa85127986185"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to test above algorithm. <a href="../../dd/d47/namespacemath.html#a89ab7d6c3e3ee72a8cbaa85127986185">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation to check whether a number is a power of 2 or not. </p>
<p>This algorithm uses bit manipulation to check if a number is a power of 2 or not.</p>
<div class="textblock"><p >Implementation to check whether a number is a power of 2 or not. </p>
<p >This algorithm uses bit manipulation to check if a number is a power of 2 or not.</p>
<h3><a class="anchor" id="autotoc_md75"></a>
Algorithm</h3>
<p>Let the input number be n, then the bitwise and between n and n-1 will let us know whether the number is power of 2 or not</p>
<p>For Example, If N= 32 then N-1 is 31, if we perform bitwise and of these two numbers then the result will be zero, which indicates that it is the power of 2 If N=23 then N-1 is 22, if we perform bitwise and of these two numbers then the result will not be zero , which indicates that it is not the power of 2 </p><dl class="section note"><dt>Note</dt><dd>This implementation is better than naive recursive or iterative approach.</dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/neha-hasija17">Neha Hasija</a> </dd></dl>
<p >Let the input number be n, then the bitwise and between n and n-1 will let us know whether the number is power of 2 or not</p>
<p >For Example, If N= 32 then N-1 is 31, if we perform bitwise and of these two numbers then the result will be zero, which indicates that it is the power of 2 If N=23 then N-1 is 22, if we perform bitwise and of these two numbers then the result will not be zero , which indicates that it is not the power of 2 </p><dl class="section note"><dt>Note</dt><dd>This implementation is better than naive recursive or iterative approach.</dd></dl>
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<div class="title">n_queens.cpp File Reference</div> </div>
<div class="headertitle"><div class="title">n_queens.cpp File Reference</div></div>
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<div class="contents">
<p><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle">Eight Queens</a> puzzle
<p><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;array&gt;</code><br />
@@ -109,16 +108,16 @@ Include dependency graph for n_queens.cpp:</div>
</div>
</div>
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<tr class="memitem:db/dc0/namespacebacktracking"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html">backtracking</a></td></tr>
<tr class="memitem:db/dc0/namespacebacktracking"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html">backtracking</a></td></tr>
<tr class="memdesc:db/dc0/namespacebacktracking"><td class="mdescLeft">&#160;</td><td class="mdescRight">Backtracking algorithms. <br /></td></tr>
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<tr class="memitem:d3/da1/namespacen__queens"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/da1/namespacen__queens.html">n_queens</a></td></tr>
<tr class="memdesc:d3/da1/namespacen__queens"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle">Eight Queens</a> puzzle. <br /></td></tr>
<tr class="memitem:d3/da1/namespacen__queens"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/da1/namespacen__queens.html">n_queens</a></td></tr>
<tr class="memdesc:d3/da1/namespacen__queens"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a40ae0c7fd04eb20e7f3bff13fc6a5808"><td class="memTemplParams" colspan="2">template&lt;size_t n&gt; </td></tr>
<tr class="memitem:a40ae0c7fd04eb20e7f3bff13fc6a5808"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d3e/n__queens_8cpp.html#a40ae0c7fd04eb20e7f3bff13fc6a5808">backtracking::n_queens::printSolution</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt;, n &gt; &amp;board)</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/Eight_queens_puzzle">Eight Queens</a> puzzle </p>
<p>The <b>eight queens puzzle</b> is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. The eight queens puzzle is an example of the more general <b>n queens problem</b> of placing n non-attacking queens on an n×n chessboard, for which solutions exist for all natural numbers n with the exception of n = 2 and n = 3.</p>
<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle </p>
<p >The <b>eight queens puzzle</b> is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. The eight queens puzzle is an example of the more general <b>n queens problem</b> of placing n non-attacking queens on an n×n chessboard, for which solutions exist for all natural numbers n with the exception of n = 2 and n = 3.</p>
<dl class="section author"><dt>Author</dt><dd>Unknown author </dd>
<dd>
<a href="https://github.com/Panquesito7">David Leal</a> </dd></dl>
<a href="https://github.com/Panquesito7" target="_blank">David Leal</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a5730b6683f6adcf5c5ef75cf53dc7160"></a>
<a id="a5730b6683f6adcf5c5ef75cf53dc7160" name="a5730b6683f6adcf5c5ef75cf53dc7160"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a5730b6683f6adcf5c5ef75cf53dc7160">&#9670;&nbsp;</a></span>isSafe()</h2>
<div class="memitem">
@@ -172,7 +171,7 @@ template&lt;size_t n&gt; </div>
</tr>
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<p>Check if a queen can be placed on matrix </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<p >Check if a queen can be placed on matrix </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">n</td><td>number of matrix size </td></tr>
</table>
@@ -189,34 +188,34 @@ template&lt;size_t n&gt; </div>
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if queen can be placed on matrix </dd>
<dd>
<code>false</code> if queen can't be placed on matrix </dd></dl>
<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="keywordtype">int</span> i = 0, j = 0;</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">// Check this row on left side</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="keywordflow">for</span> (i = 0; i &lt; col; i++) {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordflow">if</span> (board[row][i]) {</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</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="comment">// Check upper diagonal on left side</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keywordflow">for</span> (i = row, j = col; i &gt;= 0 &amp;&amp; j &gt;= 0; i--, j--) {</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <span class="keywordflow">if</span> (board[i][j]) {</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</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 class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="comment">// Check lower diagonal on left side</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordflow">for</span> (i = row, j = col; j &gt;= 0 &amp;&amp; i &lt; n; i++, j--) {</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</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; }</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; }</div>
<div class="fragment"><div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> {</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordtype">int</span> i = 0, j = 0;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// Check this row on left side</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">for</span> (i = 0; i &lt; col; i++) {</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">if</span> (board[row][i]) {</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> }</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> }</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// Check upper diagonal on left side</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">for</span> (i = row, j = col; i &gt;= 0 &amp;&amp; j &gt;= 0; i--, j--) {</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">if</span> (board[i][j]) {</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> }</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> }</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// Check lower diagonal on left side</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordflow">if</span> (board[i][j]) {</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</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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<p>Main function </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="keyword">const</span> <span class="keywordtype">int</span> n = 4;</div>
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<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/container/array.html">std::array&lt;int, n&gt;</a>({0, 0, 0, 0}),</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/container/array.html">std::array&lt;int, n&gt;</a>({0, 0, 0, 0}),</div>
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<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; backtracking::n_queens::solveNQ&lt;n&gt;(board, 0);</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160;}</div>
<p >Main function </p>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> </div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> backtracking::n_queens::solveNQ&lt;n&gt;(board, 0);</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a40ae0c7fd04eb20e7f3bff13fc6a5808">&#9670;&nbsp;</a></span>printSolution()</h2>
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<p>Utility function to print matrix </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<p >Utility function to print matrix </p><dl class="tparams"><dt>Template Parameters</dt><dd>
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<div class="fragment"><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; {</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_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;&quot;</span> &lt;&lt; board[i][j] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0dbd7af47d87f0b956609fe9e3288ecb">&#9670;&nbsp;</a></span>solveNQ()</h2>
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<p>Solve n queens problem </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<p >Solve n queens problem </p><dl class="tparams"><dt>Template Parameters</dt><dd>
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<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> (col &gt;= n) {</div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keywordflow">return</span>;</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; </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <span class="comment">// Consider this column and try placing</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="comment">// this queen in all rows one by one</span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; <span class="comment">// Check if queen can be placed</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; <span class="comment">// on board[i][col]</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="keywordflow">if</span> (isSafe&lt;n&gt;(board, i, col)) {</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; <span class="comment">// Place this queen in matrix</span></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; board[i][col] = 1;</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; <span class="comment">// Recursive to place rest of the queens</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; solveNQ&lt;n&gt;(board, col + 1);</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; board[i][col] = 0; <span class="comment">// backtrack</span></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; }</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// Consider this column and try placing</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="comment">// Check if queen can be placed</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">if</span> (isSafe&lt;n&gt;(board, i, col)) {</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// Place this queen in matrix</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="comment">// Recursive to place rest of the queens</span></div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> }</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> }</div>
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<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>Compute the greatest common denominator of two integers using <em>recursive form</em> of <a href="https://en.wikipedia.org/wiki/Euclidean_algorithm" target="_blank">Euclidean 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">
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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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<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>
<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" target="_blank">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>
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<h2 class="memtitle"><span class="permalink"><a href="#ae48807fa2b7000afae599e67f327545e">&#9670;&nbsp;</a></span>gcd()</h2>
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<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>
<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="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>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(num1 - num2, num2);</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(num1, num2 - num1);</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160;}</div>
<p >algorithm </p>
<div class="fragment"><div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> {</div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> <span class="keywordflow">if</span> (num1 &lt;= 0 | num2 &lt;= 0) {</div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" 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 id="l00017" name="l00017"></a><span class="lineno"> 17</span> }</div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> <span class="keywordflow">if</span> (num1 == num2) {</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> <span class="keywordflow">return</span> num1;</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> }</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="comment">// Everything divides 0</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="keywordflow">if</span> (num1 == 0)</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <span class="keywordflow">return</span> num2;</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <span class="keywordflow">if</span> (num2 == 0)</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="keywordflow">return</span> num1;</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// base case</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordflow">if</span> (num1 == num2)</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keywordflow">return</span> num1;</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// a is greater</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">if</span> (num1 &gt; num2)</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(num1 - num2, num2);</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(num1, num2 - num1);</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span>}</div>
<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>
<div class="ttc" id="agcd__recursive__euclidean_8cpp_html_ae48807fa2b7000afae599e67f327545e"><div class="ttname"><a href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a></div><div class="ttdeci">int gcd(int num1, int num2)</div><div class="ttdef"><b>Definition:</b> gcd_recursive_euclidean.cpp:14</div></div>
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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">
@@ -188,24 +193,24 @@ Functions</h2></td></tr>
</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; <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 120,7 is &quot;</span> &lt;&lt; (<a class="code" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(120, 7)) &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">try</span> {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</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 -120,10 is &quot;</span> &lt;&lt; <a class="code" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(-120, 10) &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="l00046"></a><span class="lineno"> 46</span>&#160; } <span class="keywordflow">catch</span> (<span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/domain_error.html">std::domain_error</a> &amp;e) {</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; <span class="stringliteral">&quot;Error handling was successful&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="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; <span class="stringliteral">&quot;gcd of 312,221 is &quot;</span> &lt;&lt; (<a class="code" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(312, 221)) &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; <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/d45/gcd__recursive__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>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;}</div>
<p >Main function </p>
<div class="fragment"><div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> {</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;gcd of 120,7 is &quot;</span> &lt;&lt; (<a class="code hl_function" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(120, 7)) &lt;&lt; <a class="code hl_functionRef" 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 id="l00045" name="l00045"></a><span class="lineno"> 45</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;gcd of -120,10 is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(-120, 10) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> } <span class="keywordflow">catch</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/domain_error.html">std::domain_error</a> &amp;e) {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Error handling was successful&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> }</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;gcd of 312,221 is &quot;</span> &lt;&lt; (<a class="code hl_function" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(312, 221)) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <a class="code hl_classRef" 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 hl_function" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>(289, 204)) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span>}</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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<div class="title">hamming_distance.cpp File Reference</div> </div>
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<p>Returns the <a href="https://en.wikipedia.org/wiki/Hamming_distance">Hamming distance</a> between two integers.
<p>Returns the <a href="https://en.wikipedia.org/wiki/Hamming_distance" target="_blank">Hamming distance</a> between two integers.
<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="memdesc:d7/d81/namespacebit__manipulation"><td class="mdescLeft">&#160;</td><td class="mdescRight">for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> <br /></td></tr>
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<tr class="memdesc:d4/d1c/namespacehamming__distance"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Hamming_distance">Hamming distance</a> implementation. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a65d845df3fecff7087a2126c7b72030b"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d48/hamming__distance_8cpp.html#a65d845df3fecff7087a2126c7b72030b">bit_manipulation::hamming_distance::bitCount</a> (uint64_t value)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Returns the <a href="https://en.wikipedia.org/wiki/Hamming_distance">Hamming distance</a> between two integers. </p>
<p>To find hamming distance between two integers, we take their xor, which will have a set bit iff those bits differ in the two numbers. Hence, we return the number of such set bits.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/ravibitsgoa">Ravishankar Joshi</a> </dd></dl>
<div class="textblock"><p >Returns the <a href="https://en.wikipedia.org/wiki/Hamming_distance" target="_blank">Hamming distance</a> between two integers. </p>
<p >To find hamming distance between two integers, we take their xor, which will have a set bit iff those bits differ in the two numbers. Hence, we return the number of such set bits.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/ravibitsgoa" target="_blank">Ravishankar Joshi</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<p>This function returns the number of set bits in the given number. </p><dl class="params"><dt>Parameters</dt><dd>
<p >This function returns the number of set bits in the given number. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">value</td><td>the number of which we want to count the number of set bits. </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>the number of set bits in the given number. </dd></dl>
<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; uint64_t count = 0;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">while</span> (value) { <span class="comment">// until all bits are zero</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordflow">if</span> (value &amp; 1) { <span class="comment">// check lower bit</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; value &gt;&gt;= 1; <span class="comment">// shift bits, removing lower bit</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">if</span> (value &amp; 1) { <span class="comment">// check lower bit</span></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a40ba9fe8b5df5c268f0c7d677ff2fe80">&#9670;&nbsp;</a></span>hamming_distance() <span class="overload">[1/2]</span></h2>
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<p>This function returns the hamming distance between two strings. </p><dl class="params"><dt>Parameters</dt><dd>
<p >This function returns the hamming distance between two strings. </p><dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>the number of characters differing between the two strings. </dd></dl>
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<p>This function returns the hamming distance between two integers. </p><dl class="params"><dt>Parameters</dt><dd>
<p >This function returns the hamming distance between two integers. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the first number </td></tr>
<tr><td class="paramname">b</td><td>the second number </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>the number of bits differing between the two integers. </dd></dl>
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<p>Main function. </p>
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<div class="fragment"><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; {</div>
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<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/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hamming distance between &quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot; and &quot;</span> &lt;&lt; b &lt;&lt; <span class="stringliteral">&quot; is &quot;</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; &lt;&lt; <a class="code" href="../../d4/d48/hamming__distance_8cpp.html#abfe6fbb2f3460a2623c96f283178a07a">bit_manipulation::hamming_distance::hamming_distance</a>(a, b)</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</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="l00107"></a><span class="lineno"> 107</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> {</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <a class="code hl_function" href="../../d4/d48/hamming__distance_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> uint64_t a = 11; <span class="comment">// 1011 in binary</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> uint64_t b = 2; <span class="comment">// 0010 in binary</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> </div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hamming distance between &quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot; and &quot;</span> &lt;&lt; b &lt;&lt; <span class="stringliteral">&quot; is &quot;</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> &lt;&lt; <a class="code hl_function" href="../../d4/d48/hamming__distance_8cpp.html#abfe6fbb2f3460a2623c96f283178a07a">bit_manipulation::hamming_distance::hamming_distance</a>(a, b)</div>
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<div class="ttc" id="ahamming__distance_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d4/d48/hamming__distance_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function to the test hamming distance.</div><div class="ttdef"><b>Definition:</b> hamming_distance.cpp:75</div></div>
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</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&nbsp;</a></span>test()</h2>
<div class="memitem">
@@ -340,25 +339,25 @@ Here is the call graph for this function:</div>
<p>Function to the test hamming distance. </p>
<dl class="section return"><dt>Returns</dt><dd>void </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; assert(bit_manipulation::hamming_distance::hamming_distance(11, 2) == 2);</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; assert(bit_manipulation::hamming_distance::hamming_distance(2, 0) == 1);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; assert(bit_manipulation::hamming_distance::hamming_distance(11, 0) == 3);</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; assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;1101&quot;</span>,</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <span class="stringliteral">&quot;1111&quot;</span>) == 1);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;1111&quot;</span>,</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <span class="stringliteral">&quot;1111&quot;</span>) == 0);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;0000&quot;</span>,</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="stringliteral">&quot;1111&quot;</span>) == 4);</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; assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;alpha&quot;</span>,</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <span class="stringliteral">&quot;alphb&quot;</span>) == 1);</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;abcd&quot;</span>,</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; <span class="stringliteral">&quot;abcd&quot;</span>) == 0);</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;dcba&quot;</span>,</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <span class="stringliteral">&quot;abcd&quot;</span>) == 4);</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> assert(bit_manipulation::hamming_distance::hamming_distance(11, 2) == 2);</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> assert(bit_manipulation::hamming_distance::hamming_distance(2, 0) == 1);</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> assert(bit_manipulation::hamming_distance::hamming_distance(11, 0) == 3);</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;1101&quot;</span>,</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="stringliteral">&quot;1111&quot;</span>) == 1);</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;1111&quot;</span>,</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="stringliteral">&quot;1111&quot;</span>) == 0);</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;0000&quot;</span>,</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="stringliteral">&quot;1111&quot;</span>) == 4);</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;alpha&quot;</span>,</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="stringliteral">&quot;alphb&quot;</span>) == 1);</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;abcd&quot;</span>,</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="stringliteral">&quot;abcd&quot;</span>) == 0);</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> assert(bit_manipulation::hamming_distance::hamming_distance(<span class="stringliteral">&quot;dcba&quot;</span>,</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="stringliteral">&quot;abcd&quot;</span>) == 4);</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span>}</div>
</div><!-- fragment -->
</div>
</div>
@@ -368,7 +367,7 @@ Here is the call graph for this function:</div>
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<a href="#func-members">Functions</a> </div>
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<div class="title">armstrong_number.cpp File Reference</div> </div>
<div class="headertitle"><div class="title">armstrong_number.cpp File Reference</div></div>
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<p>Program to check if a number is an <a href="https://en.wikipedia.org/wiki/Narcissistic_number">Armstrong/Narcissistic number</a> in decimal system.
<p>Program to check if a number is an <a href="https://en.wikipedia.org/wiki/Narcissistic_number" target="_blank">Armstrong/Narcissistic number</a> in decimal system.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
@@ -109,7 +108,7 @@ Include dependency graph for armstrong_number.cpp:</div>
</div>
</div>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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Functions</h2></td></tr>
<tr class="memitem:aab733299b170fa5a752503f95f090fcd"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d5d/math_2armstrong__number_8cpp.html#aab733299b170fa5a752503f95f090fcd">number_of_digits</a> (int num)</td></tr>
<tr class="separator:aab733299b170fa5a752503f95f090fcd"><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>Program to check if a number is an <a href="https://en.wikipedia.org/wiki/Narcissistic_number">Armstrong/Narcissistic number</a> in decimal system. </p>
<p>Armstrong number or <a href="https://en.wikipedia.org/wiki/Narcissistic_number">Narcissistic number</a> is a number that is the sum of its own digits raised to the power of the number of digits. </p><dl class="section author"><dt>Author</dt><dd>iamnambiar </dd></dl>
<div class="textblock"><p >Program to check if a number is an <a href="https://en.wikipedia.org/wiki/Narcissistic_number" target="_blank">Armstrong/Narcissistic number</a> in decimal system. </p>
<p >Armstrong number or <a href="https://en.wikipedia.org/wiki/Narcissistic_number" target="_blank">Narcissistic number</a> is a number that is the sum of its own digits raised to the power of the number of digits. </p><dl class="section author"><dt>Author</dt><dd>iamnambiar </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a9cebd92bc70890c3cfa261d68a5016e7"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a9cebd92bc70890c3cfa261d68a5016e7">&#9670;&nbsp;</a></span>is_armstrong()</h2>
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<p>Function to check whether the number is armstrong number or not. </p><dl class="params"><dt>Parameters</dt><dd>
<p >Function to check whether the number is armstrong number or not. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">num</td><td>Number </td></tr>
</table>
@@ -148,26 +147,26 @@ Functions</h2></td></tr>
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if the number is armstrong. </dd>
<dd>
<code>false</code> if the number is not armstrong. </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="comment">// If the number is less than 0, then it is not a armstrong number.</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <span class="keywordflow">if</span> (number &lt; 0) {</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</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="keywordtype">int</span> <a class="code" href="../../d8/d77/namespacemachine__learning.html#a5305cc18d11943d3dc0d66e70d7e9c44">sum</a> = 0;</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordtype">int</span> temp = number;</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="comment">// Finding the total number of digits in the number</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="keywordtype">int</span> total_digits = <a class="code" href="../../d4/d5d/math_2armstrong__number_8cpp.html#aab733299b170fa5a752503f95f090fcd">number_of_digits</a>(number);</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">while</span> (temp &gt; 0) {</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="keywordtype">int</span> rem = temp % 10;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="comment">// Finding each digit raised to the power total digit and add it to the</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="comment">// total sum</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <a class="code" href="../../d8/d77/namespacemachine__learning.html#a5305cc18d11943d3dc0d66e70d7e9c44">sum</a> = <a class="code" href="../../d8/d77/namespacemachine__learning.html#a5305cc18d11943d3dc0d66e70d7e9c44">sum</a> + <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(rem, total_digits);</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; temp = temp / 10;</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="keywordflow">return</span> number == <a class="code" href="../../d8/d77/namespacemachine__learning.html#a5305cc18d11943d3dc0d66e70d7e9c44">sum</a>;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> {</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// If the number is less than 0, then it is not a armstrong number.</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">if</span> (number &lt; 0) {</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> }</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> = 0;</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordtype">int</span> temp = number;</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// Finding the total number of digits in the number</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordtype">int</span> total_digits = <a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#aab733299b170fa5a752503f95f090fcd">number_of_digits</a>(number);</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">while</span> (temp &gt; 0) {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordtype">int</span> rem = temp % 10;</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// Finding each digit raised to the power total digit and add it to the</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// total sum</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> = <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(rem, total_digits);</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> temp = temp / 10;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> }</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">return</span> number == <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span>}</div>
<div class="ttc" id="amath_2armstrong__number_8cpp_html_aab733299b170fa5a752503f95f090fcd"><div class="ttname"><a href="../../d4/d5d/math_2armstrong__number_8cpp.html#aab733299b170fa5a752503f95f090fcd">number_of_digits</a></div><div class="ttdeci">int number_of_digits(int num)</div><div class="ttdef"><b>Definition:</b> armstrong_number.cpp:21</div></div>
<div class="ttc" id="anamespacemachine__learning_html_a5305cc18d11943d3dc0d66e70d7e9c44"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a5305cc18d11943d3dc0d66e70d7e9c44">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector&lt; std::valarray&lt; T &gt;&gt; &amp;A)</div><div class="ttdef"><b>Definition:</b> vector_ops.hpp:232</div></div>
<div class="ttc" id="anamespacemachine__learning_html_a6f1c98c016ad34ff3d9f39372161bd35"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector&lt; std::valarray&lt; T &gt; &gt; &amp;A)</div><div class="ttdef"><b>Definition:</b> vector_ops.hpp:232</div></div>
<div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
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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>
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<p>Main Function </p>
<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="../../d4/d5d/math_2armstrong__number_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160;}</div>
<p >Main Function </p>
<div class="fragment"><div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> {</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span>}</div>
<div class="ttc" id="amath_2armstrong__number_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d4/d5d/math_2armstrong__number_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition:</b> armstrong_number.cpp:59</div></div>
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<a id="aab733299b170fa5a752503f95f090fcd"></a>
<a id="aab733299b170fa5a752503f95f090fcd" name="aab733299b170fa5a752503f95f090fcd"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aab733299b170fa5a752503f95f090fcd">&#9670;&nbsp;</a></span>number_of_digits()</h2>
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</tr>
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<p>Function to calculate the total number of digits in the number. </p><dl class="params"><dt>Parameters</dt><dd>
<p >Function to calculate the total number of digits in the number. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">num</td><td>Number </td></tr>
</table>
</dd>
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<dl class="section return"><dt>Returns</dt><dd>Total number of digits. </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">int</span> total_digits = 0;</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; <span class="keywordflow">while</span> (num &gt; 0) {</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; num = num / 10;</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; ++total_digits;</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="keywordflow">return</span> total_digits;</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> {</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> <span class="keywordtype">int</span> total_digits = 0;</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keywordflow">while</span> (num &gt; 0) {</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> num = num / 10;</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> ++total_digits;</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> }</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="keywordflow">return</span> total_digits;</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span>}</div>
</div><!-- fragment -->
</div>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae1a3968e7947464bee7714f6d43b7002">&#9670;&nbsp;</a></span>test()</h2>
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<p>Function for testing the <a class="el" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong()</a> function with all the test cases. </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="comment">// is_armstrong(370) returns true.</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; assert(<a class="code" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(370) == <span class="keyword">true</span>);</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="comment">// is_armstrong(225) returns false.</span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; assert(<a class="code" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(225) == <span class="keyword">false</span>);</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="comment">// is_armstrong(-23) returns false.</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; assert(<a class="code" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(-23) == <span class="keyword">false</span>);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="comment">// is_armstrong(153) returns true.</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; assert(<a class="code" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(153) == <span class="keyword">true</span>);</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="comment">// is_armstrong(0) returns true.</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; assert(<a class="code" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(0) == <span class="keyword">true</span>);</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <span class="comment">// is_armstrong(12) returns false.</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; assert(<a class="code" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(12) == <span class="keyword">false</span>);</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160;}</div>
<p >Function for testing the <a class="el" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong()</a> function with all the test cases. </p>
<div class="fragment"><div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// is_armstrong(370) returns true.</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> assert(<a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(370) == <span class="keyword">true</span>);</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// is_armstrong(225) returns false.</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> assert(<a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(225) == <span class="keyword">false</span>);</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// is_armstrong(-23) returns false.</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> assert(<a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(-23) == <span class="keyword">false</span>);</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// is_armstrong(153) returns true.</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> assert(<a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(153) == <span class="keyword">true</span>);</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// is_armstrong(0) returns true.</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> assert(<a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(0) == <span class="keyword">true</span>);</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// is_armstrong(12) returns false.</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> assert(<a class="code hl_function" href="../../d4/d5d/math_2armstrong__number_8cpp.html#a9cebd92bc70890c3cfa261d68a5016e7">is_armstrong</a>(12) == <span class="keyword">false</span>);</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span>}</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.
<p>Library functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> of a given matrix.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;cstdlib&gt;</code><br />
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<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>
<div class="textblock"><p >Library functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> of a given matrix. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
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<div class="title">qr_decompose.h</div> </div>
<div class="headertitle"><div class="title">qr_decompose.h</div></div>
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<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>
<div class="line"><a name="l00033"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a7c63c78d6839b8ad73b77c161210b514"> 33</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,</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/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>
<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.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(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 class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160;<span class="comment"></span> </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"> * 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>
<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.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(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 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">/**</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, <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 * 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) {</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, 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,</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, 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; <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>
<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> k = 0; k &lt; ROWS; k++) {</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160; col_vector2[k] = Q[0][k][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> k = i; k &lt; COLUMNS; k++) {</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][k];</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][k] = (col_vector * col_vector2).<a class="code" href="../../d8/d77/namespacemachine__learning.html#a5305cc18d11943d3dc0d66e70d7e9c44">sum</a>();</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 class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160;} <span class="comment">// namespace qr_algorithm</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="preprocessor">#endif </span><span class="comment">// NUMERICAL_METHODS_QR_DECOMPOSE_H_</span></div>
<a href="../../d4/d68/qr__decompose_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">/**</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment"> * @file</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> * \brief Library functions to compute [QR</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> * decomposition](https://en.wikipedia.org/wiki/QR_decomposition) of a given</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"> * matrix.</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> * \author [Krishna Vedala](https://github.com/kvedala)</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> */</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span> </div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="preprocessor">#ifndef NUMERICAL_METHODS_QR_DECOMPOSE_H_</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="preprocessor">#define NUMERICAL_METHODS_QR_DECOMPOSE_H_</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include &lt;cstdlib&gt;</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &lt;iomanip&gt;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;limits&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;numeric&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;valarray&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include &lt;omp.h&gt;</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment"></span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html"> 23</a></span><span class="comment">/** \namespace qr_algorithm</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment"> * \brief Functions to compute [QR</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment"> * decomposition](https://en.wikipedia.org/wiki/QR_decomposition) of any</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment"> * rectangular matrix</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment"> */</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d2/d3b/namespaceqr__algorithm.html">qr_algorithm</a> {<span class="comment"></span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">/**</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment"> * operator to print a matrix</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment"> */</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#adfbdf47277c8cfee229b05b72f1f7834"> 33</a></span><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;<a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#adfbdf47277c8cfee229b05b72f1f7834">operator&lt;&lt;</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;out,</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;<a class="code hl_classRef" 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 id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keyword">const</span> <span class="keywordtype">int</span> width = 12;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> out.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(4);</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++) {</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; v[row].size(); col++)</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> out &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::right</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> &lt;&lt; v[row][col];</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> out &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> }</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordflow">return</span> out;</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span>}</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment"></span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">/**</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment"> * operator to print a vector</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment"> */</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a257425cb2365359da51c6fe6741834d8"> 53</a></span><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;<a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#adfbdf47277c8cfee229b05b72f1f7834">operator&lt;&lt;</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;out, <a class="code hl_classRef" 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 id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> out.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(4);</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++) {</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> out &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::right</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> &lt;&lt; v[row];</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> }</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">return</span> out;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span>}</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="comment"></span> </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">/**</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment"> * Compute dot product of two vectors of equal lengths</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="comment"> *</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><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 id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="comment"> * \f$\vec{b}=\left[b_0,b_1,b_1,...,b_L\right]\f$ then</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><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 id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="comment"> *</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="comment"> * \returns \f$\vec{a}\cdot\vec{b}\f$</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="comment"> */</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec"> 76</a></span><span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;a, <span class="keyword">const</span> <a class="code hl_classRef" 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 id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">return</span> (a * b).sum();</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// could also use following</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// return std::inner_product(std::begin(a), std::end(a), std::begin(b),</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// 0.f);</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span>}</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="comment"></span> </div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="comment">/**</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span><span class="comment"> * Compute magnitude of vector.</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="comment"> *</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span><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 id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="comment"> * \f$\left|\vec{a}\right|=\sqrt{\displaystyle\sum_{i=0}^L a_i^2}\f$</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="comment"> *</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="comment"> * \returns \f$\left|\vec{a}\right|\f$</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span><span class="comment"> */</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f"> 92</a></span><span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">vector_mag</a>(<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;a) {</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordtype">double</span> dot = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(a, a);</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(dot);</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span>}</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="comment"></span> </div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">/**</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment"> * Compute projection of vector \f$\vec{a}\f$ on \f$\vec{b}\f$ defined as</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><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 id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="comment"> *</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="comment"> * \returns NULL if error, otherwise pointer to output</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span><span class="comment"> */</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a6d3c7dce1f142141f509d09f6c0e25dc"> 104</a></span><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a6d3c7dce1f142141f509d09f6c0e25dc">vector_proj</a>(<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;a,</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keyword">const</span> <a class="code hl_classRef" 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 id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keywordtype">double</span> num = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(a, b);</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keywordtype">double</span> deno = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(b, b);</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="comment"></span> </div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span><span class="comment"> /*! check for division by zero using machine epsilon */</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordflow">if</span> (deno &lt;= <a class="code hl_classRef" 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 id="l00111" name="l00111"></a><span class="lineno"> 111</span> <a class="code hl_classRef" 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 id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordflow">return</span> a; <span class="comment">// return vector a back</span></div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> }</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordtype">double</span> scalar = num / deno;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> </div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">return</span> b * scalar;</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span>}</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="comment"></span> </div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="comment">/**</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="comment"> * Decompose matrix \f$A\f$ using [Gram-Schmidt</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span><span class="comment"> *process](https://en.wikipedia.org/wiki/QR_decomposition).</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span><span class="comment"> *</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span><span class="comment"> * \f{eqnarray*}{</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span><span class="comment"> * \text{given that}\quad A &amp;=&amp;</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span><span class="comment"> *\left[\mathbf{a}_1,\mathbf{a}_2,\ldots,\mathbf{a}_{N-1},\right]\\</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span><span class="comment"> * \text{where}\quad\mathbf{a}_i &amp;=&amp;</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span><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 id="l00129" name="l00129"></a><span class="lineno"> 129</span><span class="comment"> * vectors)}\\</span></div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span><span class="comment"> * \text{then}\quad\mathbf{u}_i &amp;=&amp; \mathbf{a}_i</span></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span><span class="comment"> *-\sum_{j=0}^{i-1}\text{proj}_{\mathbf{u}_j}\mathbf{a}_i\\</span></div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span><span class="comment"> * \mathbf{e}_i &amp;=&amp;\frac{\mathbf{u}_i}{\left|\mathbf{u}_i\right|}\\</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span><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 id="l00134" name="l00134"></a><span class="lineno"> 134</span><span class="comment"> * \mathbf{e}_{N-1}\end{bmatrix}\\</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span><span class="comment"> * R &amp;=&amp; \begin{bmatrix}\langle\mathbf{e}_0\,,\mathbf{a}_0\rangle &amp;</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span><span class="comment"> * \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &amp;</span></div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span><span class="comment"> * \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp; \dots \\</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span><span class="comment"> * 0 &amp; \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &amp;</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span><span class="comment"> * \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp; \dots\\</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span><span class="comment"> * 0 &amp; 0 &amp; \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp;</span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span><span class="comment"> * \dots\\ \vdots &amp; \vdots &amp; \vdots &amp; \ddots</span></div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span><span class="comment"> * \end{bmatrix}\\</span></div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="comment"> * \f}</span></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span><span class="comment"> */</span></div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a73ce637634fc49e1d10d190eb388ebf1"> 146</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a73ce637634fc49e1d10d190eb388ebf1">qr_decompose</a>(</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;<a class="code hl_classRef" 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 id="l00148" name="l00148"></a><span class="lineno"> 148</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;<a class="code hl_classRef" 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 id="l00149" name="l00149"></a><span class="lineno"> 149</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;<a class="code hl_classRef" 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 id="l00150" name="l00150"></a><span class="lineno"> 150</span>) {</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <a class="code hl_classRef" 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 id="l00152" name="l00152"></a><span class="lineno"> 152</span> <a class="code hl_classRef" 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 id="l00153" name="l00153"></a><span class="lineno"> 153</span> <a class="code hl_classRef" 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 id="l00154" name="l00154"></a><span class="lineno"> 154</span> <a class="code hl_classRef" 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 id="l00155" name="l00155"></a><span class="lineno"> 155</span> <a class="code hl_classRef" 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 id="l00156" name="l00156"></a><span class="lineno"> 156</span> </div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; COLUMNS; i++) {</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="comment">/* for each column =&gt; R is a square matrix of NxN */</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keywordtype">int</span> j;</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> R[0][i] = 0.; <span class="comment">/* make R upper triangular */</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> </div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="comment">/* get corresponding Q vector */</span></div>
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<div class="ttc" id="anamespaceqr__algorithm_html_a7c63c78d6839b8ad73b77c161210b514"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a7c63c78d6839b8ad73b77c161210b514">qr_algorithm::operator&lt;&lt;</a></div><div class="ttdeci">std::ostream &amp; operator&lt;&lt;(std::ostream &amp;out, std::valarray&lt; std::valarray&lt; T &gt;&gt; const &amp;v)</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:33</div></div>
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<p><a href="https://en.wikipedia.org/wiki/Shell_sort">Shell sort</a> algorithm
<p><a href="https://en.wikipedia.org/wiki/Shell_sort" target="_blank">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 />
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<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>
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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/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 class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Shell_sort" target="_blank">Shell sort</a> algorithm </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a7eb77daed2cf1513f6d68c47a1c2db1c">&#9670;&nbsp;</a></span>compare()</h2>
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<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);</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>
<p >function to compare sorting using cstdlib's qsort </p>
<div class="fragment"><div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> {</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> T arg1 = *<span class="keyword">static_cast&lt;</span><span class="keyword">const </span>T *<span class="keyword">&gt;</span>(a);</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> 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 id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">if</span> (arg1 &lt; arg2)</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">if</span> (arg1 &gt; arg2)</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">return</span> 1;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// return (arg1 &gt; arg2) - (arg1 &lt; arg2); // possible shortcut</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// return arg1 - arg2; // erroneous shortcut (fails if INT_MIN is present)</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&nbsp;</a></span>main()</h2>
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<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.f / 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>
<p >Main function </p>
<div class="fragment"><div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> {</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="comment">// initialize random number generator - once per program</span></div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(NULL));</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> </div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <a class="code hl_function" 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 id="l00188" name="l00188"></a><span class="lineno"> 188</span> <a class="code hl_classRef" 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 id="l00189" name="l00189"></a><span class="lineno"> 189</span> <a class="code hl_function" 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 id="l00190" name="l00190"></a><span class="lineno"> 190</span> <a class="code hl_classRef" 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 id="l00191" name="l00191"></a><span class="lineno"> 191</span> <a class="code hl_function" 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 id="l00192" name="l00192"></a><span class="lineno"> 192</span> <a class="code hl_classRef" 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 id="l00193" name="l00193"></a><span class="lineno"> 193</span> </div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <a class="code hl_function" 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 id="l00195" name="l00195"></a><span class="lineno"> 195</span> <a class="code hl_classRef" 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 id="l00196" name="l00196"></a><span class="lineno"> 196</span> <a class="code hl_function" 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 id="l00197" name="l00197"></a><span class="lineno"> 197</span> <a class="code hl_classRef" 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 id="l00198" name="l00198"></a><span class="lineno"> 198</span> <a class="code hl_function" 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 id="l00199" name="l00199"></a><span class="lineno"> 199</span> <a class="code hl_classRef" 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 id="l00200" name="l00200"></a><span class="lineno"> 200</span> </div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="keywordtype">int</span> i, NUM_DATA;</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> </div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <span class="keywordflow">if</span> (argc == 2)</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> NUM_DATA = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> NUM_DATA = 200;</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> </div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="comment">// int array = new int[NUM_DATA];</span></div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="keywordtype">int</span> *<a class="code hl_variable" 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 id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="comment">// int array2 = new int[NUM_DATA];</span></div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="keywordtype">int</span> range = 1800;</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> </div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a>(NULL));</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <span class="keywordflow">for</span> (i = 0; i &lt; NUM_DATA; i++) {</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="comment">// allocate random numbers in the given range</span></div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = (<a class="code hl_functionRef" 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 id="l00217" name="l00217"></a><span class="lineno"> 217</span> }</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> </div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <a class="code hl_classRef" 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="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA); <span class="comment">// perform sorting</span></div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> &lt;&lt; <span class="stringliteral">&quot;Data Sorted using custom implementation: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> </div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keywordtype">double</span> elapsed_time = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) * 1.f / CLOCKS_PER_SEC;</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <a class="code hl_classRef" 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="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> </div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="keyword">delete</span>[] <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span>}</div>
<div class="ttc" id="aatoi_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a></div><div class="ttdeci">T atoi(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="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>pretty print array </p><dl class="params"><dt>Parameters</dt><dd>
<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 class="fragment"><div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> {</div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> <span class="keywordtype">size_t</span> i;</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> <span class="keywordflow">for</span> (i = 0; i &lt; LEN; i++) {</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> <a class="code hl_classRef" 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 id="l00023" name="l00023"></a><span class="lineno"> 23</span> }</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span>}</div>
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<p>pretty print array </p><dl class="params"><dt>Parameters</dt><dd>
<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 class="fragment"><div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> {</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <a class="code hl_function" href="../../d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">show_data</a>(arr, N);</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a22ea0d1f7943ebb4371d31e44b465b6d">&#9670;&nbsp;</a></span>test_f()</h2>
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<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>
<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 id="l00145" name="l00145"></a><span class="lineno"> 145</span> {</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="comment">// int array = new int[NUM_DATA];</span></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordtype">float</span> *<a class="code hl_variable" 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 id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="keywordtype">float</span> *data2 = <span class="keyword">new</span> <span class="keywordtype">float</span>[NUM_DATA];</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="comment">// int array2 = new int[NUM_DATA];</span></div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordtype">int</span> range = 1000;</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> </div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++) {</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = data2[i] = ((<a class="code hl_functionRef" 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 id="l00154" name="l00154"></a><span class="lineno"> 154</span> }</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> </div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="comment">/* sort using our implementation */</span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <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="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <a class="code hl_classRef" 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 id="l00162" name="l00162"></a><span class="lineno"> 162</span> &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> </div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="comment">/* sort using std::qsort */</span></div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <a class="code hl_functionRef" 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 hl_struct" href="../../d1/db3/structcompare.html">compare&lt;float&gt;</a>);</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> </div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <a class="code hl_classRef" 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 id="l00171" name="l00171"></a><span class="lineno"> 171</span> &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> </div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++) {</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> assert(<a class="code hl_variable" 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 id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="comment">// the standard results</span></div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> }</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> </div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="keyword">delete</span>[] <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>;</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="keyword">delete</span>[] data2;</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span>}</div>
<div class="ttc" id="aqsort_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/qsort.html">std::qsort</a></div><div class="ttdeci">T qsort(T... args)</div></div>
<div class="ttc" id="astructcompare_html"><div class="ttname"><a href="../../d1/db3/structcompare.html">compare</a></div><div class="ttdef"><b>Definition:</b> huffman.cpp:28</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a895b313cb2671e8f712040460325573e">&#9670;&nbsp;</a></span>test_int()</h2>
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<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>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</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="l00125"></a><span class="lineno"> 125</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;int&gt;</a>);</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</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="l00127"></a><span class="lineno"> 127</span>&#160; </div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</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="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;Time spent sorting using std::qsort: &quot;</span> &lt;&lt; elapsed_time</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; &lt;&lt; <span class="stringliteral">&quot;s\n&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; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++) {</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</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="l00134"></a><span class="lineno"> 134</span>&#160; <span class="comment">// the standard results</span></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; </div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</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="l00138"></a><span class="lineno"> 138</span>&#160; <span class="keyword">delete</span>[] data2;</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160;}</div>
<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 id="l00105" name="l00105"></a><span class="lineno"> 105</span> {</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="comment">// int array = new int[NUM_DATA];</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keywordtype">int</span> *<a class="code hl_variable" 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 id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keywordtype">int</span> *data2 = <span class="keyword">new</span> <span class="keywordtype">int</span>[NUM_DATA];</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// int array2 = new int[NUM_DATA];</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordtype">int</span> range = 1800;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> </div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NUM_DATA; i++)</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>[i] = data2[i] = (<a class="code hl_functionRef" 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 id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">/* sort using our implementation */</span></div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#af2c5b92cbfe73f63f6074c61b0a45331">shell_sort</a>(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>, NUM_DATA);</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <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="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <a class="code hl_classRef" 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 id="l00121" name="l00121"></a><span class="lineno"> 121</span> &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="comment">/* sort using std::qsort */</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <a class="code hl_functionRef" 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 hl_struct" href="../../d1/db3/structcompare.html">compare&lt;int&gt;</a>);</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> </div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> elapsed_time = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - start) / CLOCKS_PER_SEC;</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <a class="code hl_classRef" 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 id="l00130" name="l00130"></a><span class="lineno"> 130</span> &lt;&lt; <span class="stringliteral">&quot;s\n&quot;</span>;</div>
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<div class="title">sum_of_digits.cpp File Reference</div> </div>
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Functions</h2></td></tr>
<tr class="memitem:a4619c78b6ad985713024f930f31c4395"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits</a> (int num)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>A C++ Program to find the Sum of Digits of input integer. </p>
<p>Copyright 2020 </p><dl class="section author"><dt>Author</dt><dd>iamnambiar </dd></dl>
<div class="textblock"><p >A C++ Program to find the Sum of Digits of input integer. </p>
<p >Copyright 2020 </p><dl class="section author"><dt>Author</dt><dd>iamnambiar </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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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>
<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="code" href="../../d4/d83/sum__of__digits_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</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/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Success.&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="l00071"></a><span class="lineno"> 71</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160;}</div>
<p >Main Function </p>
<div class="fragment"><div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> {</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <a class="code hl_function" href="../../d4/d83/sum__of__digits_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Success.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a4619c78b6ad985713024f930f31c4395">&#9670;&nbsp;</a></span>sum_of_digits()</h2>
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<p>Function to find the sum of the digits of an integer. </p><dl class="params"><dt>Parameters</dt><dd>
<p >Function to find the sum of the digits of an integer. </p><dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>Sum of the digits of the integer.</dd></dl>
<p>\detail First the algorithm check whether the num is negative or positive, if it is negative, then we neglect the negative sign. Next, the algorithm extract the last digit of num by dividing by 10 and extracting the remainder and this is added to the sum. The number is then divided by 10 to remove the last digit. This loop continues until num becomes 0. </p>
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<div class="fragment"><div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> {</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// If num is negative then negative sign is neglected.</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordflow">while</span> (num &gt; 0) {</div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> num = num / 10;</div>
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<p>Function for testing the <a class="el" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits()</a> with all the test cases. </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="comment">// First test.</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <a class="code" href="../../d4/d83/sum__of__digits_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="comment">// Second test.</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <a class="code" href="../../d4/d83/sum__of__digits_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160;}</div>
<p >Function for testing the <a class="el" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits()</a> with all the test cases. </p>
<div class="fragment"><div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> {</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// First test.</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <a class="code hl_function" href="../../d4/d83/sum__of__digits_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// Second test.</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <a class="code hl_function" href="../../d4/d83/sum__of__digits_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span>}</div>
<div class="ttc" id="asum__of__digits_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../d4/d83/sum__of__digits_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition:</b> sum_of_digits.cpp:49</div></div>
<div class="ttc" id="asum__of__digits_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../d4/d83/sum__of__digits_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition:</b> sum_of_digits.cpp:40</div></div>
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<p>Function for testing the <a class="el" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits()</a> function with a first test case of 119765 and assert statement. </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> test_case_1 = <a class="code" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits</a>(119765);</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; assert(test_case_1 == 29);</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160;}</div>
<p >Function for testing the <a class="el" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits()</a> function with a first test case of 119765 and assert statement. </p>
<div class="fragment"><div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> {</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordtype">int</span> test_case_1 = <a class="code hl_function" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits</a>(119765);</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> assert(test_case_1 == 29);</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0283886819c7c140a023582b7269e2d0">&#9670;&nbsp;</a></span>test2()</h2>
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<p>Function for testing the <a class="el" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits()</a> function with a second test case of -12256 and assert statement. </p>
<div class="fragment"><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; <span class="keywordtype">int</span> test_case_2 = <a class="code" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits</a>(-12256);</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; assert(test_case_2 == 16);</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;}</div>
<p >Function for testing the <a class="el" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits()</a> function with a second test case of -12256 and assert statement. </p>
<div class="fragment"><div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> {</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordtype">int</span> test_case_2 = <a class="code hl_function" href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits</a>(-12256);</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> assert(test_case_2 == 16);</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span>}</div>
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