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2020-06-21 19:44:25 +00:00
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18
annotated.html
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d0/d01/smallest__circle_8cpp.html
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@@ -563,7 +563,7 @@ Here is the call graph for this function:</div>
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<li class="navelem"><a class="el" href="../../dir_9510827d0b234b3cc54b29892f217477.html">others</a></li><li class="navelem"><a class="el" href="../../d0/d01/smallest__circle_8cpp.html">smallest_circle.cpp</a></li>
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2
d0/d08/realtime__stats_8cpp.html
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@@ -304,7 +304,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d0/d08/realtime__stats_8cpp.html">realtime_stats.cpp</a></li>
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d0/d0d/structmst-members.html
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d0/d55/classcll-members.html
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@@ -113,7 +113,7 @@ $(document).ready(function(){initNavTree('d5/d15/classcll.html','../../'); initR
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d0/d78/classstatistics_1_1stats__computer1-members.html
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@@ -111,7 +111,7 @@ $(document).ready(function(){initNavTree('d7/d7c/classstatistics_1_1stats__compu
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2
d0/da2/number__of__positive__divisors_8cpp.html
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@@ -232,7 +232,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp.html">number_of_positive_divisors.cpp</a></li>
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2
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@@ -144,7 +144,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>main</b> (int argc, ch
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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2
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@@ -107,7 +107,7 @@ $(document).ready(function(){initNavTree('d8/dc8/struct_point.html','../../'); i
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2
d0/dd2/class_queue___array.html
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@@ -139,7 +139,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>size</b></td></tr>
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d0/de2/gaussian__elimination_8cpp.html
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@@ -217,7 +217,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../d0/de2/gaussian__elimination_8cpp.html">gaussian_elimination.cpp</a></li>
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@@ -122,7 +122,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>data</b></td></tr>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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2
d1/d07/class_solution-members.html
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@@ -110,7 +110,7 @@ $(document).ready(function(){initNavTree('dd/d4f/class_solution.html','../../');
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2
d1/d11/gcd__of__n__numbers_8cpp.html
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@@ -214,7 +214,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp.html">gcd_of_n_numbers.cpp</a></li>
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@@ -144,7 +144,7 @@ $(document).ready(function(){initNavTree('da/d9a/class_graph.html','../../'); in
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2
d1/d21/quick__sort_8cpp.html
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@@ -191,7 +191,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_bb1b521853a9c46347182a9d10420771.html">sorting</a></li><li class="navelem"><a class="el" href="../../d1/d21/quick__sort_8cpp.html">quick_sort.cpp</a></li>
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2
d1/d76/buzz__number_8cpp.html
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@@ -160,7 +160,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_9510827d0b234b3cc54b29892f217477.html">others</a></li><li class="navelem"><a class="el" href="../../d1/d76/buzz__number_8cpp.html">buzz_number.cpp</a></li>
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2
d1/d77/structmst.html
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@@ -119,7 +119,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>near</b></td></tr>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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2
d1/db3/structcompare.html
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@@ -113,7 +113,7 @@ bool&#160;</td><td class="memItemRight" valign="bottom"><b>operator()</b> (<a cl
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d1/dc2/classstack.html
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@@ -511,7 +511,7 @@ template&lt;class Type &gt; </div>
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2
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@@ -118,7 +118,7 @@ $(document).ready(function(){initNavTree('d5/da1/structnode.html','../../'); ini
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2
d1/df3/hash__search_8cpp.html
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@@ -397,7 +397,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_19b2bf9199a15c634a08b1ede1dd896a.html">search</a></li><li class="navelem"><a class="el" href="../../d1/df3/hash__search_8cpp.html">hash_search.cpp</a></li>
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2
d2/d05/class_min_heap.html
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@@ -469,7 +469,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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1
d2/d07/class_bit__coll__graph.md5
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@@ -1 +0,0 @@
427190570e081c982a2b8e65b94a704c

2
d2/d0b/fast__power_8cpp.html
View File

@@ -292,7 +292,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d2/d0b/fast__power_8cpp.html">fast_power.cpp</a></li>
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2
d2/d22/jump__search_8cpp.html
View File

@@ -200,7 +200,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_19b2bf9199a15c634a08b1ede1dd896a.html">search</a></li><li class="navelem"><a class="el" href="../../d2/d22/jump__search_8cpp.html">jump_search.cpp</a></li>
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2
d2/d2c/structtower.html
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@@ -120,7 +120,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../..
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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2
d2/d36/structqueue.html
View File

@@ -508,7 +508,7 @@ template&lt;class Kind &gt; </div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../d2/d36/structqueue.html">queue</a></li>
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2
d2/d3b/namespaceqr__algorithm.html
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@@ -625,7 +625,7 @@ template&lt;typename T &gt; </div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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2
d2/d52/heap__sort_8cpp.html
View File

@@ -256,7 +256,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_bb1b521853a9c46347182a9d10420771.html">sorting</a></li><li class="navelem"><a class="el" href="../../d2/d52/heap__sort_8cpp.html">heap_sort.cpp</a></li>
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2
d2/dc4/classstack__linked_list.html
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@@ -135,7 +135,7 @@ Public Attributes</h2></td></tr>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
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2
d2/dcf/namespacestatistics.html
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@@ -115,7 +115,7 @@ Classes</h2></td></tr>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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@@ -323,7 +323,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
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<div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
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<div class="ttc" id="aclose_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">std::ofstream::close</a></div><div class="ttdeci">T close(T... args)</div></div>
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<div class="ttc" id="aperror_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a></div><div class="ttdeci">T perror(T... args)</div></div>
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<div class="ttc" id="asubstr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">std::string::substr</a></div><div class="ttdeci">T substr(T... args)</div></div>
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<div class="ttc" id="amiller__rabin_8cpp_html_a6f9c31c1047aa3191676d64571d4c506"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a6f9c31c1047aa3191676d64571d4c506">miller_test</a></div><div class="ttdeci">bool miller_test(T d, T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:73</div></div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> least_common_multiple.cpp:67</div></div>
<div class="ttc" id="aode__forward__euler_8cpp_html_abaeae8f62a018d197f0187a1c80a90fe"><div class="ttname"><a href="../../db/dd3/ode__forward__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a></div><div class="ttdeci">void problem(const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Problem statement for a system with first-order differential equations. Updates the system differenti...</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:54</div></div>
<div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</div></div>
@@ -424,7 +424,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="ttc" id="agroup__ode_html_ga36ff0710861ca39d957046c0b09b2985"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga36ff0710861ca39d957046c0b09b2985">midpoint_euler</a></div><div class="ttdeci">double midpoint_euler(double dx, double x0, double x_max, std::valarray&lt; double &gt; *y, bool save_to_file=false)</div><div class="ttdoc">Compute approximation using the midpoint-Euler method in the given limits.</div><div class="ttdef"><b>Definition:</b> ode_midpoint_euler.cpp:107</div></div>
<div class="ttc" id="anumber__of__positive__divisors_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d0/da2/number__of__positive__divisors_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> number_of_positive_divisors.cpp:62</div></div>
<div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/begin.html">std::vector::cbegin</a></div><div class="ttdeci">T cbegin(T... args)</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:180</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:183</div></div>
<div class="ttc" id="astrtof_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/strtof.html">std::strtod</a></div><div class="ttdeci">T strtod(T... args)</div></div>
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<div class="ttc" id="aprime__factorization_8cpp_html_a0ece0145fb29a5cf48378c23dde2da46"><div class="ttname"><a href="../../db/d0d/prime__factorization_8cpp.html#a0ece0145fb29a5cf48378c23dde2da46">prime_factorization</a></div><div class="ttdeci">void prime_factorization(int num)</div><div class="ttdef"><b>Definition:</b> prime_factorization.cpp:40</div></div>
@@ -466,7 +466,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="ttc" id="apower__for__huge__numbers_8cpp_html_a392fb874e547e582e9c66a08a1f23326"><div class="ttname"><a href="../../df/def/power__for__huge__numbers_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a></div><div class="ttdeci">#define MAX</div><div class="ttdef"><b>Definition:</b> power_for_huge_numbers.cpp:10</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer1_html_ab5b4bfecdf391cae7edb1fe98548b846"><div class="ttname"><a href="../../d7/d7c/classstatistics_1_1stats__computer1.html#ab5b4bfecdf391cae7edb1fe98548b846">statistics::stats_computer1::operator&gt;&gt;</a></div><div class="ttdeci">friend std::istream &amp; operator&gt;&gt;(std::istream &amp;input, stats_computer1 &amp;stat)</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:53</div></div>
<div class="ttc" id="aode__midpoint__euler_8cpp_html_a0ddf1224851353fc92bfbff6f499fa97"><div class="ttname"><a href="../../d6/dd3/ode__midpoint__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a></div><div class="ttdeci">int main(int argc, char *argv[])</div><div class="ttdef"><b>Definition:</b> ode_midpoint_euler.cpp:192</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:154</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:157</div></div>
<div class="ttc" id="aprimes__up__to__billion_8cpp_html_ac0f4b77b901ddb15dab4c4dee1ac6e95"><div class="ttname"><a href="../../d4/d9c/primes__up__to__billion_8cpp.html#ac0f4b77b901ddb15dab4c4dee1ac6e95">prime</a></div><div class="ttdeci">char prime[100000000]</div><div class="ttdef"><b>Definition:</b> primes_up_to_billion.cpp:10</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>
<div class="ttc" id="aprime__factorization_8cpp_html_a7fe38b570a51e448430d6a0f072c2f23"><div class="ttname"><a href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a></div><div class="ttdeci">bool isprime[1000006]</div><div class="ttdef"><b>Definition:</b> prime_factorization.cpp:13</div></div>
@@ -475,7 +475,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
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@@ -513,7 +513,7 @@ Here is the call graph for this function:</div>
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<ul>
<li class="navelem"><a class="el" href="../../dir_bb1b521853a9c46347182a9d10420771.html">sorting</a></li><li class="navelem"><a class="el" href="../../d4/d7a/shell__sort2_8cpp.html">shell_sort2.cpp</a></li>
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@@ -135,7 +135,7 @@ Classes</h2></td></tr>
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<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d4/d86/large__number_8h.html">large_number.h</a></li>
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@@ -646,7 +646,7 @@ $(document).ready(function(){initNavTree('d4/d86/large__number_8h_source.html','
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@@ -217,7 +217,7 @@ Here is the call graph for this function:</div>
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<ul>
<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d4/d9c/primes__up__to__billion_8cpp.html">primes_up_to_billion.cpp</a></li>
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@@ -222,7 +222,7 @@ Here is the call graph for this function:</div>
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<ul>
<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html">gcd_iterative_euclidean.cpp</a></li>
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@@ -138,7 +138,7 @@ Private Attributes</h2></td></tr>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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@@ -231,7 +231,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
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@@ -107,7 +107,7 @@ $(document).ready(function(){initNavTree('d5/d29/struct_min_heap_node.html','../
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@@ -122,7 +122,7 @@ bool&#160;</td><td class="memItemRight" valign="bottom"><b>isEndofWord</b></td><
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@@ -202,7 +202,7 @@ Here is the call graph for this function:</div>
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2
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@@ -684,7 +684,7 @@ Here is the call graph for this function:</div>
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<li class="navelem"><a class="el" href="../../dir_3343723ae086de42ee4ca9774da3a13f.html">machine_learning</a></li><li class="navelem"><a class="el" href="../../d4/def/kohonen__som__topology_8cpp.html">kohonen_som_topology.cpp</a></li>
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@@ -148,7 +148,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><b>total</b></td></tr>
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@@ -135,7 +135,7 @@ unsigned&#160;</td><td class="memItemRight" valign="bottom"><b>freq</b></td></tr
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@@ -240,7 +240,7 @@ Here is the call graph for this function:</div>
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@@ -230,6 +230,7 @@ Math</h1>
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<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/least_common_multiple.cpp">Least Common Multiple</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/miller_rabin.cpp">Miller Rabin</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_inverse_fermat_little_theorem.cpp">Modular Inverse Fermat Little Theorem</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/number_of_positive_divisors.cpp">Number Of Positive Divisors</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/power_for_huge_numbers.cpp">Power For Huge Numbers</a></li>
@@ -304,8 +305,7 @@ Probability</h1>
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<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/fenwicktree.cpp">Fenwicktree</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/fenwick_tree.cpp">Fenwick Tree</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/mo.cpp">Mo</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/segtree.cpp">Segtree</a></li>
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@@ -597,7 +597,7 @@ Here is the call graph for this function:</div>
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<p>Fenwick tree.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d2e/fenwick__tree_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Fenwick tree. </p>
<p>A Fenwick tree or binary indexed tree is a data structure that can efficiently update elements and calculate prefix sums in a table of numbers. </p>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> arr = {1, 2, 3, 4, 5};</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; </div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; assert(fenwick_tree.sum_range(0, 1) == 3);</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; assert(fenwick_tree.sum_range(0, 2) == 6);</div>
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@@ -145,10 +145,10 @@ Functions</h2></td></tr>
</table>
</div><div class="memdoc">
<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160; {</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160;}</div>
<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; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160;}</div>
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<div class="dyncontent">
@@ -196,33 +196,33 @@ template&lt;typename T &gt; </div>
<dd>
'true' if num is (probably) prime</dd></dl>
<p>\detail First we check whether the num input is less than 4, if so we can determine whether this is a prime or composite by checking for 2 and 3. Next we check whether this num is odd (as all primes greater than 2 are odd). Next we write our num in the following format \(num = 2^r \cdot d + 1\). After finding r and d for our input num, we use for loop repeat number of times inside which we check the miller conditions using the function miller_test. If miller_test returns false then the number is composite After the loop finishes completely without issuing a false return call, we can conclude that this number is probably prime. </p>
<div class="fragment"><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="keywordflow">if</span> (num &lt;= 4) {</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; <span class="comment">// If num == 2 or num == 3 then prime</span></div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; <span class="keywordflow">if</span> (num == 2 || num == 3) {</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; }</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; }</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160; <span class="comment">// If num is even then not prime</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; <span class="keywordflow">if</span> (num % 2 == 0) {</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; }</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160; <span class="comment">// Finding d and r in num = 2^r * d + 1</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160; T d = num - 1, r = 0;</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160; <span class="keywordflow">while</span> (d % 2 == 0) {</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160; d = d / 2;</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160; r++;</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160; }</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160; </div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160; <span class="keywordflow">for</span> (T i = 0; i &lt; repeats; ++i) {</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160; <span class="keywordflow">if</span> (!<a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a6f9c31c1047aa3191676d64571d4c506">miller_test</a>(d, num)) {</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160; }</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160; }</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160;}</div>
<div class="fragment"><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; {</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; <span class="keywordflow">if</span> (num &lt;= 4) {</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; <span class="comment">// If num == 2 or num == 3 then prime</span></div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <span class="keywordflow">if</span> (num == 2 || num == 3) {</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; }</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; }</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; <span class="comment">// If num is even then not prime</span></div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160; <span class="keywordflow">if</span> (num % 2 == 0) {</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160; }</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160; <span class="comment">// Finding d and r in num = 2^r * d + 1</span></div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160; T d = num - 1, r = 0;</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160; <span class="keywordflow">while</span> (d % 2 == 0) {</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160; d = d / 2;</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160; r++;</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160; }</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160; </div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160; <span class="keywordflow">for</span> (T i = 0; i &lt; repeats; ++i) {</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160; <span class="keywordflow">if</span> (!<a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a6f9c31c1047aa3191676d64571d4c506">miller_test</a>(d, num)) {</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160; }</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160; }</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160;}</div>
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@@ -269,36 +269,36 @@ template&lt;typename T &gt; </div>
<dl class="section return"><dt>Returns</dt><dd>'false' if n is composite </dd>
<dd>
'true' if n is (probably) prime. </dd></dl>
<div class="fragment"><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; {</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="comment">// random number seed</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/random_device.html">std::random_device</a> rd_seed;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="comment">// random number generator</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/mersenne_twister_engine.html">std::mt19937</a> gen(rd_seed());</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="comment">// Uniformly distributed range [2, num - 2] for random numbers</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/uniform_int_distribution.html">std::uniform_int_distribution&lt;&gt;</a> distribution(2, num - 2);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="comment">// Random number generated in the range [2, num -2].</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; T random = distribution(gen);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="comment">// vector for reverse binary of the power</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a> = <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a798398d5bfd375a3c0ce68100842f6f5">reverse_binary</a>(d);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="comment">// x = random ^ d % num</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; T x = <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#ad6c2c67ea416d0e80003a88623f98b29">modular_exponentiation</a>(random, <a class="code" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a>, num);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="comment">// miller conditions</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="keywordflow">if</span> (x == 1 || x == num - 1) {</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; }</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; </div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <span class="keywordflow">while</span> (d != num - 1) {</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; x = (x * x) % num;</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; d *= 2;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <span class="keywordflow">if</span> (x == 1) {</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</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; <span class="keywordflow">if</span> (x == num - 1) {</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; }</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; }</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160;}</div>
<div class="fragment"><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">// random number seed</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/random_device.html">std::random_device</a> rd_seed;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="comment">// random number generator</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/mersenne_twister_engine.html">std::mt19937</a> gen(rd_seed());</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="comment">// Uniformly distributed range [2, num - 2] for random numbers</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/uniform_int_distribution.html">std::uniform_int_distribution&lt;&gt;</a> distribution(2, num - 2);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="comment">// Random number generated in the range [2, num -2].</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; T random = distribution(gen);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="comment">// vector for reverse binary of the power</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a> = <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a798398d5bfd375a3c0ce68100842f6f5">reverse_binary</a>(d);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="comment">// x = random ^ d % num</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; T x = <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#ad6c2c67ea416d0e80003a88623f98b29">modular_exponentiation</a>(random, <a class="code" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a>, num);</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="comment">// miller conditions</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; <span class="keywordflow">if</span> (x == 1 || x == num - 1) {</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</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; </div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <span class="keywordflow">while</span> (d != num - 1) {</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; x = (x * x) % num;</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; d *= 2;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="keywordflow">if</span> (x == 1) {</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; }</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="keywordflow">if</span> (x == num - 1) {</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; }</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; }</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;}</div>
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@@ -350,25 +350,25 @@ template&lt;typename T &gt; </div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>r the modular exponentiation of \(a^{n} \equiv r \mod{m}\) where \(n\) is the base 10 representation of rev_binary_exponent and \(m = mod \) parameter. </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">if</span> (mod == 1)</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; T b = 1;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="keywordflow">if</span> (rev_binary_exponent.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0)</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordflow">return</span> b;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; T A = base;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="keywordflow">if</span> (rev_binary_exponent[0] == 1)</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; b = base;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">typename</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;::const_iterator</a> it =</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; rev_binary_exponent.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">cbegin</a>() + 1;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; it != rev_binary_exponent.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">cend</a>(); ++it) {</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; A = A * A % mod;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordflow">if</span> (*it == 1)</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; b = A * b % mod;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; }</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordflow">return</span> b;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160;}</div>
<div class="fragment"><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">if</span> (mod == 1)</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; T b = 1;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordflow">if</span> (rev_binary_exponent.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0)</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="keywordflow">return</span> b;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; T A = base;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="keywordflow">if</span> (rev_binary_exponent[0] == 1)</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; b = base;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">typename</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;::const_iterator</a> it =</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; rev_binary_exponent.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">cbegin</a>() + 1;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; it != rev_binary_exponent.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">cend</a>(); ++it) {</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; A = A * A % mod;</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordflow">if</span> (*it == 1)</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; b = A * b % mod;</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="keywordflow">return</span> b;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160;}</div>
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@@ -396,15 +396,15 @@ template&lt;typename T &gt; </div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>result vector of the number input in reverse binary </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; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> result;</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160; T temp = num;</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160; <span class="keywordflow">while</span> (temp &gt; 0) {</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160; result.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(temp % 2);</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; temp = temp / 2;</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; }</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160;}</div>
<div class="fragment"><div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160; {</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> result;</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160; T temp = num;</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160; <span class="keywordflow">while</span> (temp &gt; 0) {</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; result.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(temp % 2);</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; temp = temp / 2;</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">return</span> result;</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160;}</div>
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@@ -429,28 +429,28 @@ Here is the call graph for this function:</div>
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<p>Functions for testing the <a class="el" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test()</a> function with some assert statements. </p>
<div class="fragment"><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>&#160; {</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160; <span class="comment">// First test on 2</span></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;2 is prime but function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(2, 1) == <span class="keyword">true</span>));</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;First test passes.&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="l00159"></a><span class="lineno"> 159</span>&#160; <span class="comment">// Second test on 5</span></div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;5 should be prime but the function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(5, 3) == <span class="keyword">true</span>));</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Second test passes.&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="l00163"></a><span class="lineno"> 163</span>&#160; <span class="comment">// Third test on 23</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;23 should be prime but the function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(23, 3) == <span class="keyword">true</span>));</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/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Third test passes.&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="l00167"></a><span class="lineno"> 167</span>&#160; <span class="comment">// Fourth test on 16</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;16 is not a prime but the function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(16, 3) == <span class="keyword">false</span>));</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;Fourth test passes.&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="l00171"></a><span class="lineno"> 171</span>&#160; <span class="comment">// Fifth test on 27</span></div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;27 is not a prime but the function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(27, 3) == <span class="keyword">false</span>));</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Fifth test passes.&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="l00175"></a><span class="lineno"> 175</span>&#160;}</div>
<div class="fragment"><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160; {</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160; <span class="comment">// First test on 2</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;2 is prime but function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(2, 1) == <span class="keyword">true</span>));</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;First test passes.&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="l00162"></a><span class="lineno"> 162</span>&#160; <span class="comment">// Second test on 5</span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;5 should be prime but the function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(5, 3) == <span class="keyword">true</span>));</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Second test passes.&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="l00166"></a><span class="lineno"> 166</span>&#160; <span class="comment">// Third test on 23</span></div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;23 should be prime but the function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(23, 3) == <span class="keyword">true</span>));</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</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;Third test passes.&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="l00170"></a><span class="lineno"> 170</span>&#160; <span class="comment">// Fourth test on 16</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;16 is not a prime but the function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(16, 3) == <span class="keyword">false</span>));</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</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;Fourth test passes.&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="l00174"></a><span class="lineno"> 174</span>&#160; <span class="comment">// Fifth test on 27</span></div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;27 is not a prime but the function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(27, 3) == <span class="keyword">false</span>));</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</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;Fifth test passes.&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="l00178"></a><span class="lineno"> 178</span>&#160;}</div>
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@@ -463,26 +463,26 @@ Here is the call graph for this function:</div>
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</div><!-- doc-content -->
<div class="ttc" id="auniform_int_distribution_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/uniform_int_distribution.html">std::uniform_int_distribution</a></div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a901288288ef5ebe8e97414cc30797cce"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a></div><div class="ttdeci">bool miller_rabin_primality_test(T num, T repeats)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:122</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a901288288ef5ebe8e97414cc30797cce"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a></div><div class="ttdeci">bool miller_rabin_primality_test(T num, T repeats)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:125</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div><div class="ttdoc">STL class.</div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a798398d5bfd375a3c0ce68100842f6f5"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a798398d5bfd375a3c0ce68100842f6f5">reverse_binary</a></div><div class="ttdeci">std::vector&lt; T &gt; reverse_binary(T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:18</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a798398d5bfd375a3c0ce68100842f6f5"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a798398d5bfd375a3c0ce68100842f6f5">reverse_binary</a></div><div class="ttdeci">std::vector&lt; T &gt; reverse_binary(T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:19</div></div>
<div class="ttc" id="apower__for__huge__numbers_8cpp_html_ae249a2af508aa94266023ce8aa81426f"><div class="ttname"><a href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a></div><div class="ttdeci">void power(int x, int n)</div><div class="ttdef"><b>Definition:</b> power_for_huge_numbers.cpp:56</div></div>
<div class="ttc" id="amersenne_twister_engine_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/mersenne_twister_engine.html">std::mt19937</a></div></div>
<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
<div class="ttc" id="arandom_device_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/random_device.html">std::random_device</a></div></div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_ad6c2c67ea416d0e80003a88623f98b29"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#ad6c2c67ea416d0e80003a88623f98b29">modular_exponentiation</a></div><div class="ttdeci">T modular_exponentiation(T base, const std::vector&lt; T &gt; &amp;rev_binary_exponent, T mod)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:42</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a6f9c31c1047aa3191676d64571d4c506"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a6f9c31c1047aa3191676d64571d4c506">miller_test</a></div><div class="ttdeci">bool miller_test(T d, T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:71</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_ad6c2c67ea416d0e80003a88623f98b29"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#ad6c2c67ea416d0e80003a88623f98b29">modular_exponentiation</a></div><div class="ttdeci">T modular_exponentiation(T base, const std::vector&lt; T &gt; &amp;rev_binary_exponent, T mod)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:43</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a6f9c31c1047aa3191676d64571d4c506"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a6f9c31c1047aa3191676d64571d4c506">miller_test</a></div><div class="ttdeci">bool miller_test(T d, T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:73</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="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/begin.html">std::vector::cbegin</a></div><div class="ttdeci">T cbegin(T... args)</div></div>
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