From a0e8991686abf1fafd9894781e884145687b2458 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Thu, 9 Jun 2022 15:19:34 +0000
Subject: [PATCH] Documentation for 2a076c1b03273357bd1924c6b215af3c1ed22f39

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+\begin{eqnarray*}
+  \text{given that}\quad A &amp;=&amp;
+*\left[\mathbf{a}_1,\mathbf{a}_2,\ldots,\mathbf{a}_{N-1},\right]\\
+  \text{where}\quad\mathbf{a}_i &amp;=&amp;
+  \left[a_{0i},a_{1i},a_{2i},\ldots,a_{(M-1)i}\right]^T\quad\ldots\mbox{(column
+  vectors)}\\
+  \text{then}\quad\mathbf{u}_i &amp;=&amp; \mathbf{a}_i
+*-\sum_{j=0}^{i-1}\text{proj}_{\mathbf{u}_j}\mathbf{a}_i\\
+  \mathbf{e}_i &amp;=&amp;\frac{\mathbf{u}_i}{\left|\mathbf{u}_i\right|}\\
+  Q &amp;=&amp; \begin{bmatrix}\mathbf{e}_0 &amp; \mathbf{e}_1 &amp; \mathbf{e}_2 &amp; \dots &amp;
+  \mathbf{e}_{N-1}\end{bmatrix}\\
+  R &amp;=&amp; \begin{bmatrix}\langle\mathbf{e}_0\,,\mathbf{a}_0\rangle &amp;
+  \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &amp;
+  \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp; \dots \\
+                   0 &amp; \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &amp;
+  \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp; \dots\\
+                   0 &amp; 0 &amp; \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp;
+  \dots\\ \vdots &amp; \vdots &amp; \vdots &amp; \ddots
+       \end{bmatrix}\\
+  \end{eqnarray*}
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 <div class="textblock"><p >Solve a multivariable first order <a href="https://en.wikipedia.org/wiki/Ordinary_differential_equation" target="_blank">ordinary differential equation (ODEs)</a> using <a href="https://en.wikipedia.org/wiki/Semi-implicit_Euler_method" target="_blank">semi implicit Euler method</a> </p>
 <dl class="section author"><dt>Authors</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a></dd></dl>
 <p>The ODE being solved is: </p><p class="formulaDsp">
-\begin{eqnarray*} \dot{u} &amp;=&amp; v\\ \dot{v} &amp;=&amp; -\omega^2 u\\ \omega &amp;=&amp; 1\\ [x_0, u_0, v_0] &amp;=&amp; [0,1,0]\qquad\ldots\text{(initial values)} \end{eqnarray*}
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 <p> The computation results are stored to a text file <code>semi_implicit_euler.csv</code> and the exact soltuion results in <code>exact.csv</code> for comparison. <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/numerical_methods/ode_semi_implicit_euler.svg" alt="Implementation solution" style="pointer-events: none;" class="inline"/></p>
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+<tr class="separator:ae6b496dce691e04f7f95ba0f0d33a289"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:a0837468e1a653ed056e2cce3c914afa5"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d33/gram__schmidt_8cpp.html#a0837468e1a653ed056e2cce3c914afa5">numerical_methods::gram_schmidt::gram_schmidt</a> (int r, const int &amp;c, 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; double, 10 &gt;, 20 &gt; &amp;A, <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; double, 10 &gt;, 20 &gt; B)</td></tr>
+<tr class="separator:a0837468e1a653ed056e2cce3c914afa5"><td class="memSeparator" colspan="2">&#160;</td></tr>
 <tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d33/gram__schmidt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
 <tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2">&#160;</td></tr>
 <tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d33/gram__schmidt_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
@@ -139,21 +139,21 @@ Functions</h2></td></tr>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
 <div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process" target="_blank">Gram Schmidt Orthogonalisation Process</a> </p>
 <p >Takes the input of Linearly Independent Vectors, returns vectors orthogonal to each other.</p>
-<h3><a class="anchor" id="autotoc_md83"></a>
+<h3><a class="anchor" id="autotoc_md86"></a>
 Algorithm</h3>
 <p >Take the first vector of given LI vectors as first vector of Orthogonal vectors. Take projection of second input vector on the first vector of Orthogonal vector and subtract it from the 2nd LI vector. Take projection of third vector on the second vector of Othogonal vectors and subtract it from the 3rd LI vector. Keep repeating the above process until all the vectors in the given input array are exhausted.</p>
 <p >For Example: In R2, Input LI Vectors={(3,1),(2,2)} then Orthogonal Vectors= {(3, 1),(-0.4, 1.2)}</p>
 <p >Have defined maximum dimension of vectors to be 10 and number of vectors taken is 20. Please do not give linearly dependent vectors</p>
 <dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Akanksha-Gupta920" target="_blank">Akanksha Gupta</a> </dd></dl>
 </div><h2 class="groupheader">Function Documentation</h2>
-<a id="ab6b70f9680752e9fe2ac4e2cce158c40" name="ab6b70f9680752e9fe2ac4e2cce158c40"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#ab6b70f9680752e9fe2ac4e2cce158c40">&#9670;&nbsp;</a></span>display()</h2>
+<a id="ae6b496dce691e04f7f95ba0f0d33a289" name="ae6b496dce691e04f7f95ba0f0d33a289"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ae6b496dce691e04f7f95ba0f0d33a289">&#9670;&nbsp;</a></span>display()</h2>
 
 <div class="memitem">
 <div class="memproto">
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         <tr>
-          <td class="memname">void linear_algebra::gram_schmidt::display </td>
+          <td class="memname">void numerical_methods::gram_schmidt::display </td>
           <td>(</td>
           <td class="paramtype">const int &amp;&#160;</td>
           <td class="paramname"><em>r</em>, </td>
@@ -200,14 +200,14 @@ Algorithm</h3>
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-<h2 class="memtitle"><span class="permalink"><a href="#aed4d308f46ca1d91e348ca260ec1d2fb">&#9670;&nbsp;</a></span>dot_product()</h2>
+<a id="ac4a4504924ecc9f12a2ebd80788ec01d" name="ac4a4504924ecc9f12a2ebd80788ec01d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#ac4a4504924ecc9f12a2ebd80788ec01d">&#9670;&nbsp;</a></span>dot_product()</h2>
 
 <div class="memitem">
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-          <td class="memname">double linear_algebra::gram_schmidt::dot_product </td>
+          <td class="memname">double numerical_methods::gram_schmidt::dot_product </td>
           <td>(</td>
           <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; double, 10 &gt; &amp;&#160;</td>
           <td class="paramname"><em>x</em>, </td>
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+<div class="center"><iframe scrolling="no" frameborder="0" src="../../d5/d33/gram__schmidt_8cpp_ac4a4504924ecc9f12a2ebd80788ec01d_cgraph.svg" width="395" height="76"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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-<h2 class="memtitle"><span class="permalink"><a href="#aa31ca28f60c880802462335eedc5d91f">&#9670;&nbsp;</a></span>gram_schmidt()</h2>
+<a id="a0837468e1a653ed056e2cce3c914afa5" name="a0837468e1a653ed056e2cce3c914afa5"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#a0837468e1a653ed056e2cce3c914afa5">&#9670;&nbsp;</a></span>gram_schmidt()</h2>
 
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
-          <td class="memname">void linear_algebra::gram_schmidt::gram_schmidt </td>
+          <td class="memname">void numerical_methods::gram_schmidt::gram_schmidt </td>
           <td>(</td>
           <td class="paramtype">int&#160;</td>
           <td class="paramname"><em>r</em>, </td>
@@ -342,7 +342,7 @@ Here is the call graph for this function:</div>
 <div class="line"><span class="lineno">  149</span>                    temp{};           <span class="comment">/// to store previous projected array</span></div>
 <div class="line"><span class="lineno">  150</span>                <span class="keywordtype">double</span> factor = NAN;  <span class="comment">/// to store the factor by which the</span><span class="comment"></span></div>
 <div class="line"><span class="lineno">  151</span><span class="comment">                                      /// previous array will change</span></div>
-<div class="line"><span class="lineno">  152</span><span class="comment"></span>                factor = <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#a46e459aff5eafffb5ad9ceb129b4d274">projection</a>(A[k - 1], B[l - 1], c);</div>
+<div class="line"><span class="lineno">  152</span><span class="comment"></span>                factor = <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#a8eeaafdde8b56f459aadc6013cf078bc">projection</a>(A[k - 1], B[l - 1], c);</div>
 <div class="line"><span class="lineno">  153</span>                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; c; ++i) {</div>
 <div class="line"><span class="lineno">  154</span>                    temp[i] = B[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> - 1][i] * factor;  <span class="comment">/// projected array created</span></div>
 <div class="line"><span class="lineno">  155</span>                }</div>
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 <div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
 <div class="ttc" id="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:119</div></div>
-<div class="ttc" id="agram__schmidt_8cpp_html_a46e459aff5eafffb5ad9ceb129b4d274"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#a46e459aff5eafffb5ad9ceb129b4d274">linear_algebra::gram_schmidt::projection</a></div><div class="ttdeci">double projection(const std::array&lt; double, 10 &gt; &amp;x, const std::array&lt; double, 10 &gt; &amp;y, const int &amp;c)</div><div class="ttdef"><b>Definition:</b> gram_schmidt.cpp:79</div></div>
+<div class="ttc" id="agram__schmidt_8cpp_html_a8eeaafdde8b56f459aadc6013cf078bc"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#a8eeaafdde8b56f459aadc6013cf078bc">numerical_methods::gram_schmidt::projection</a></div><div class="ttdeci">double projection(const std::array&lt; double, 10 &gt; &amp;x, const std::array&lt; double, 10 &gt; &amp;y, const int &amp;c)</div><div class="ttdef"><b>Definition:</b> gram_schmidt.cpp:79</div></div>
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+<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d5/d33/gram__schmidt_8cpp_a0837468e1a653ed056e2cce3c914afa5_cgraph.svg" width="100%" height="300"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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 <div class="line"><span class="lineno">  268</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="charliteral">&#39;\n&#39;</span>;</div>
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-<div class="line"><span class="lineno">  271</span>    <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f">linear_algebra::gram_schmidt::gram_schmidt</a>(r, c, A, B);</div>
+<div class="line"><span class="lineno">  271</span>    <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#a0837468e1a653ed056e2cce3c914afa5">numerical_methods::gram_schmidt::gram_schmidt</a>(r, c, A, B);</div>
 <div class="line"><span class="lineno">  272</span> </div>
 <div class="line"><span class="lineno">  273</span>    <span class="keywordtype">double</span> dot = 0;</div>
 <div class="line"><span class="lineno">  274</span>    <span class="keywordtype">int</span> flag = 1;  <span class="comment">/// To check whether vectors are orthogonal or  not</span></div>
 <div class="line"><span class="lineno">  275</span>    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; r - 1; ++i) {</div>
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-<div class="line"><span class="lineno">  278</span>                <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(linear_algebra::gram_schmidt::dot_product(B[i], B[j], c));</div>
+<div class="line"><span class="lineno">  277</span>            dot = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">fabs</a>(</div>
+<div class="line"><span class="lineno">  278</span>                numerical_methods::gram_schmidt::dot_product(B[i], B[j], c));</div>
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 <div class="line"><span class="lineno">  280</span><span class="comment">                            /// bound for the dot product take 0.1</span></div>
 <div class="line"><span class="lineno">  281</span><span class="comment"></span>            {</div>
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 <div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
 <div class="ttc" id="afabs_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a></div><div class="ttdeci">T fabs(T... args)</div></div>
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+<div class="ttc" id="agram__schmidt_8cpp_html_a0837468e1a653ed056e2cce3c914afa5"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#a0837468e1a653ed056e2cce3c914afa5">numerical_methods::gram_schmidt::gram_schmidt</a></div><div class="ttdeci">void gram_schmidt(int r, const int &amp;c, const std::array&lt; std::array&lt; double, 10 &gt;, 20 &gt; &amp;A, std::array&lt; std::array&lt; double, 10 &gt;, 20 &gt; B)</div><div class="ttdef"><b>Definition:</b> gram_schmidt.cpp:121</div></div>
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-<h2 class="memtitle"><span class="permalink"><a href="#a46e459aff5eafffb5ad9ceb129b4d274">&#9670;&nbsp;</a></span>projection()</h2>
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+<h2 class="memtitle"><span class="permalink"><a href="#a8eeaafdde8b56f459aadc6013cf078bc">&#9670;&nbsp;</a></span>projection()</h2>
 
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
-          <td class="memname">double linear_algebra::gram_schmidt::projection </td>
+          <td class="memname">double numerical_methods::gram_schmidt::projection </td>
           <td>(</td>
           <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; double, 10 &gt; &amp;&#160;</td>
           <td class="paramname"><em>x</em>, </td>
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 <p >multiply that factor with every element in a 3rd vector, whose initial values are same as the 2nd vector.</p>
 <div class="fragment"><div class="line"><span class="lineno">   80</span>                                                               {</div>
 <div class="line"><span class="lineno">   81</span>    <span class="keywordtype">double</span> dot =</div>
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+<div class="line"><span class="lineno">   82</span>        <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#ac4a4504924ecc9f12a2ebd80788ec01d">dot_product</a>(x, y, c);  <span class="comment">/// The dot product of two vectors is taken</span></div>
 <div class="line"><span class="lineno">   83</span>    <span class="keywordtype">double</span> anorm =</div>
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+<div class="line"><span class="lineno">   84</span>        <a class="code hl_function" href="../../d5/d33/gram__schmidt_8cpp.html#ac4a4504924ecc9f12a2ebd80788ec01d">dot_product</a>(y, y, c);  <span class="comment">/// The norm of the second vector is taken.</span></div>
 <div class="line"><span class="lineno">   85</span>    <span class="keywordtype">double</span> factor =</div>
 <div class="line"><span class="lineno">   86</span>        dot /</div>
 <div class="line"><span class="lineno">   87</span>        anorm;  <span class="comment">/// multiply that factor with every element in a 3rd vector,</span><span class="comment"></span></div>
 <div class="line"><span class="lineno">   88</span><span class="comment">                /// whose initial values are same as the 2nd vector.</span></div>
 <div class="line"><span class="lineno">   89</span><span class="comment"></span>    <span class="keywordflow">return</span> factor;</div>
 <div class="line"><span class="lineno">   90</span>}</div>
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+<div class="ttc" id="agram__schmidt_8cpp_html_ac4a4504924ecc9f12a2ebd80788ec01d"><div class="ttname"><a href="../../d5/d33/gram__schmidt_8cpp.html#ac4a4504924ecc9f12a2ebd80788ec01d">numerical_methods::gram_schmidt::dot_product</a></div><div class="ttdeci">double dot_product(const std::array&lt; double, 10 &gt; &amp;x, const std::array&lt; double, 10 &gt; &amp;y, const int &amp;c)</div><div class="ttdef"><b>Definition:</b> gram_schmidt.cpp:59</div></div>
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-<p>An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\).  
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+<p >calculates the probability of a result within a range (inclusive, inclusive) </p><dl class="section return"><dt>Returns</dt><dd>\(\displaystyle \left.P(n,p)\right|_{x_0}^{x_1} =
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@@ -122,22 +122,30 @@ Functions</h2></td></tr>
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-\begin{eqnarray*} a \cdot x &amp;≡&amp; 1 \;\text{mod}\; m\\ x &amp;≡&amp; a^{-1} \;\text{mod}\; m \end{eqnarray*}
+\begin{eqnarray*}
+  a \cdot x &amp;≡&amp; 1 \;\text{mod}\; m\\
+  x &amp;≡&amp; a^{-1} \;\text{mod}\; m
+ \end{eqnarray*}
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 <p> Using Euler's theorem we can modify the equation. </p><p class="formulaDsp">
-\[ a^{ϕ(m)} ≡ 1 \;\text{mod}\; m \]
+\[
+ a^{ϕ(m)} ≡ 1 \;\text{mod}\; m
+ \]
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 <p> (Where '^' denotes the exponent operator)</p>
 <p >Here 'ϕ' is Euler's Totient Function. For modular inverse existence 'a' and 'm' must be relatively primes numbers. To apply Fermat's Little Theorem is necessary that 'm' must be a prime number. Generally in many competitive programming competitions 'm' is either 1000000007 (1e9+7) or 998244353.</p>
 <p >We considered m as large prime (1e9+7). \(a^{ϕ(m)} ≡ 1 \;\text{mod}\; m\) (Using Euler's Theorem) \(ϕ(m) = m-1\) using Fermat's Little Theorem. \(a^{m-1} ≡ 1 \;\text{mod}\; m\) Now multiplying both side by \(a^{-1}\). </p><p class="formulaDsp">
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+ a^{m-2} &amp;≡&amp;  a^{-1} \;\text{mod}\; m
+ \end{eqnarray*}
 </p>
 <p >We will find the exponent using binary exponentiation. Such that the algorithm works in \(O(\log m)\) time.</p>
 <p >Examples: -</p><ul>
 <li>a = 3 and m = 7</li>
 <li>\(a^{-1} \;\text{mod}\; m\) is equivalent to \(a^{m-2} \;\text{mod}\; m\)</li>
 <li>\(3^5 \;\text{mod}\; 7 = 243 \;\text{mod}\; 7 = 5\) <br  />
-Hence, \(3^{-1} \;\text{mod}\; 7 = 5\) or \(3 \times 5 \;\text{mod}\; 7 = 1 \;\text{mod}\; 7\) (as \(a\times a^{-1} = 1\)) </li>
+Hence, \(3^{-1} \;\text{mod}\; 7 = 5\) or \(3 \times 5  \;\text{mod}\; 7 = 1 \;\text{mod}\; 7\) (as \(a\times a^{-1} = 1\)) </li>
 </ul>
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 <p >Generate spirograph curve into arrays <code>x</code> and <code>y</code> such that the i^th point in 2D is represented by <code>(x[i],y[i])</code>. The generating function is given by: </p><p class="formulaDsp">
-\begin{eqnarray*} x &amp;=&amp; R\left[ (1-k) \cos (t) + l\cdot k\cdot\cos \left(\frac{1-k}{k}t\right) \right]\\ y &amp;=&amp; R\left[ (1-k) \sin (t) - l\cdot k\cdot\sin \left(\frac{1-k}{k}t\right) \right] \end{eqnarray*}
+\begin{eqnarray*}
+x &amp;=&amp; R\left[ (1-k) \cos (t) + l\cdot k\cdot\cos \left(\frac{1-k}{k}t\right)
+\right]\\
+y &amp;=&amp; R\left[ (1-k) \sin (t) - l\cdot k\cdot\sin \left(\frac{1-k}{k}t\right)
+\right] \end{eqnarray*}
 </p>
 <p> where</p><ul>
 <li>\(R\) is the scaling parameter that we will consider \(=1\)</li>
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index 1ed33d18a..93502e6ed 100644
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+++ b/df/d42/binary__search__tree2_8cpp_a1d42876440ac5346e2850a32497385c3_cgraph.svg
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index ebb079ebe..cc8166867 100644
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+++ b/df/d42/binary__search__tree2_8cpp_a8c882f43e1e52948a7841a8bfb091350_cgraph.map
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index 77b007ea3..6fb2468c6 100644
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index ebcac2fbe..3915782f7 100644
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index 758a0ecd4..7ddeb42c8 100644
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 <tr id="row_0_3_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d3e/n__queens_8cpp.html" target="_self">n_queens.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle </td></tr>
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-<tr id="row_20_4_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/d39/interpolation__search2_8cpp.html" target="_self">interpolation_search2.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Interpolation_search" target="_blank">Interpolation search</a> algorithm </td></tr>
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+<tr id="row_14_2_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d01/brent__method__extrema_8cpp.html" target="_self">brent_method_extrema.cpp</a></td><td class="desc">Find real extrema of a univariate real function in a given interval using <a href="https://en.wikipedia.org/wiki/Brent%27s_method" target="_blank">Brent's method</a> </td></tr>
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href="d8/dcc/binary__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">binary_insertion_sort.cpp</a>, <a class="el" href="d5/ddb/bogo__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">bogo_sort.cpp</a>, <a class="el" href="d2/d26/count__inversions_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">count_inversions.cpp</a>, <a class="el" href="de/d07/cycle__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">cycle_sort.cpp</a>, <a class="el" href="d6/d1a/dnf__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">dnf_sort.cpp</a>, <a class="el" href="d2/d21/gnome__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">gnome_sort.cpp</a>, <a class="el" href="d2/d52/heap__sort_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">heap_sort.cpp</a>, <a class="el" href="de/d7b/merge__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">merge_insertion_sort.cpp</a>, <a class="el" href="d3/d92/pancake__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">pancake_sort.cpp</a>, <a class="el" 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href="d9/d37/inverse__fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">inverse_fast_fourier_transform.cpp</a>, <a class="el" href="df/d11/midpoint__integral__method_8cpp.html#a2ae48a41e43dc6ab11b962742349646e">midpoint_integral_method.cpp</a>, <a class="el" href="d1/da6/rungekutta_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">rungekutta.cpp</a>, <a class="el" href="d9/d14/array__left__rotation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">array_left_rotation.cpp</a>, <a class="el" href="d6/d57/array__right__rotation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">array_right_rotation.cpp</a>, <a class="el" href="de/d33/circular__linked__list_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">circular_linked_list.cpp</a>, <a class="el" href="d4/d32/inorder__successor__of__bst_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">inorder_successor_of_bst.cpp</a>, <a class="el" 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 <tr id="row_12_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/dcd/namespacecircular__linked__list.html" target="_self">circular_linked_list</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/circular-linked-list/" target="_blank">Circular Linked List</a> implementation </td></tr>
 <tr id="row_13_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/d38/namespacecount__bits__flip.html" target="_self">count_bits_flip</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/count-set-bits-in-an-integer/" target="_blank">count bits flip</a> implementation </td></tr>
 <tr id="row_14_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/dae/namespacecount__of__set__bits.html" target="_self">count_of_set_bits</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/count-set-bits-in-an-integer/" target="_blank">count sets bits</a> implementation </td></tr>
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 <tr id="row_18_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/dfb/namespacecycle__sort.html" target="_self">cycle_sort</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Cycle_sort" target="_blank">Cycle sort</a> algorithm </td></tr>
 <tr id="row_19_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/db1/namespacedata__strcutres.html" target="_self">data_strcutres</a></td><td class="desc">Stack Data Structure Using the <a class="el" href="dc/db5/struct_queue.html">Queue</a> Data Structure </td></tr>
 <tr id="row_20_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_20_" class="arrow" onclick="toggleFolder('20_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d5/d3c/namespacedata__structures.html" target="_self">data_structures</a></td><td class="desc">Data Structures algorithms </td></tr>
-<tr id="row_20_0_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_20_0_" class="arrow" onclick="toggleFolder('20_0_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>linked_list</b></td><td class="desc"></td></tr>
-<tr id="row_20_0_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="de/d9d/classdata__structures_1_1linked__list_1_1link.html" target="_self">link</a></td><td class="desc"></td></tr>
-<tr id="row_20_0_1_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d1/def/classdata__structures_1_1linked__list_1_1list.html" target="_self">list</a></td><td class="desc"></td></tr>
-<tr id="row_20_0_2_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d4/d0e/classdata__structures_1_1linked__list_1_1_node.html" target="_self">Node</a></td><td class="desc"></td></tr>
-<tr id="row_20_1_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_20_1_" class="arrow" onclick="toggleFolder('20_1_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>list_array</b></td><td class="desc"></td></tr>
-<tr id="row_20_1_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d5/dab/structdata__structures_1_1list__array_1_1list.html" target="_self">list</a></td><td class="desc">Structure of List with supporting methods </td></tr>
-<tr id="row_20_2_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_20_2_" class="arrow" onclick="toggleFolder('20_2_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>queue_using_array</b></td><td class="desc"></td></tr>
-<tr id="row_20_2_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html" target="_self">Queue_Array</a></td><td class="desc"><a class="el" href="d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html" title="Queue_Array class containing the main data and also index of head and tail of the array.">Queue_Array</a> class containing the main data and also index of head and tail of the array </td></tr>
-<tr id="row_20_3_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_20_3_" class="arrow" onclick="toggleFolder('20_3_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>sparse_table</b></td><td class="desc"></td></tr>
-<tr id="row_20_3_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html" target="_self">Sparse_table</a></td><td class="desc"></td></tr>
-<tr id="row_20_4_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_20_4_" class="arrow" onclick="toggleFolder('20_4_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>stack_using_queue</b></td><td class="desc"></td></tr>
-<tr id="row_20_4_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="db/d5b/structdata__structures_1_1stack__using__queue_1_1_stack.html" target="_self">Stack</a></td><td class="desc"><a class="el" href="db/d5b/structdata__structures_1_1stack__using__queue_1_1_stack.html" title="Stack Class implementation for basic methods of Stack Data Structure.">Stack</a> Class implementation for basic methods of <a class="el" href="db/d5b/structdata__structures_1_1stack__using__queue_1_1_stack.html" title="Stack Class implementation for basic methods of Stack Data Structure.">Stack</a> Data Structure </td></tr>
-<tr id="row_20_5_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_20_5_" class="arrow" onclick="toggleFolder('20_5_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>tree_234</b></td><td class="desc"></td></tr>
-<tr id="row_20_5_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="dd/d40/classdata__structures_1_1tree__234_1_1_node.html" target="_self">Node</a></td><td class="desc">2-3-4 tree node class </td></tr>
-<tr id="row_20_5_1_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d3/d95/classdata__structures_1_1tree__234_1_1_tree234.html" target="_self">Tree234</a></td><td class="desc">2-3-4 tree class </td></tr>
-<tr id="row_20_6_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_20_6_" class="arrow" onclick="toggleFolder('20_6_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>trie_using_hashmap</b></td><td class="desc"></td></tr>
-<tr id="row_20_6_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span id="arr_20_6_0_" class="arrow" onclick="toggleFolder('20_6_0_')">&#9658;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html" target="_self">Trie</a></td><td class="desc"><a class="el" href="d3/d26/classdata__structures_1_1trie__using__hashmap_1_1_trie.html" title="Trie class, implementation of trie using hashmap in each trie node for all the characters of char16_t...">Trie</a> class, implementation of trie using hashmap in each trie node for all the characters of char16_t(UTF-16)type with methods to insert, delete, search, start with and to recommend words based on a given prefix </td></tr>
-<tr id="row_20_6_0_0_" style="display:none;"><td class="entry"><span style="width:64px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d5/d12/structdata__structures_1_1trie__using__hashmap_1_1_trie_1_1_node.html" target="_self">Node</a></td><td class="desc">Struct representing a trie node </td></tr>
-<tr id="row_20_7_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d9/d49/structdata__structures_1_1_node.html" target="_self">Node</a></td><td class="desc"></td></tr>
-<tr id="row_20_8_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d4/d90/classdata__structures_1_1_skip_list.html" target="_self">SkipList</a></td><td class="desc"></td></tr>
-<tr id="row_20_9_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d0/d3e/classdata__structures_1_1trie.html" target="_self">trie</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Trie" target="_blank">Trie</a> implementation for small-case English alphabets <code>a-z</code> </td></tr>
+<tr id="row_20_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d9/d49/structdata__structures_1_1_node.html" target="_self">Node</a></td><td class="desc"></td></tr>
+<tr id="row_20_1_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d4/d90/classdata__structures_1_1_skip_list.html" target="_self">SkipList</a></td><td class="desc"></td></tr>
+<tr id="row_20_2_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d0/d3e/classdata__structures_1_1trie.html" target="_self">trie</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Trie" target="_blank">Trie</a> implementation for small-case English alphabets <code>a-z</code> </td></tr>
 <tr id="row_21_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/da7/namespacedepth__first__search.html" target="_self">depth_first_search</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Depth-first_search" target="_blank">Depth First Search</a> algorithm </td></tr>
 <tr id="row_22_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/db4/namespacedisjoint__union.html" target="_self">disjoint_union</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Disjoint_union" target="_blank">Disjoint union</a> implementation </td></tr>
 <tr id="row_23_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/dba/namespacedivide__and__conquer.html" target="_self">divide_and_conquer</a></td><td class="desc">For <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> </td></tr>
@@ -155,25 +131,16 @@ $(document).ready(function(){initNavTree('namespaces.html',''); initResizable();
 <tr id="row_26_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d88/namespacedp.html" target="_self">dp</a></td><td class="desc">For <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> </td></tr>
 <tr id="row_27_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d24/namespacedynamic__programming.html" target="_self">dynamic_programming</a></td><td class="desc">Dynamic Programming algorithms </td></tr>
 <tr id="row_28_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/dea/namespacefalse__position.html" target="_self">false_position</a></td><td class="desc">Functions for [False Position] (<a href="https://en.wikipedia.org/wiki/Regula_falsi">https://en.wikipedia.org/wiki/Regula_falsi</a>) method </td></tr>
-<tr id="row_29_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/dc9/namespacefibonacci__sum.html" target="_self">fibonacci_sum</a></td><td class="desc">Functions for the sum of the Fibonacci Sequence: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\) </td></tr>
+<tr id="row_29_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/dc9/namespacefibonacci__sum.html" target="_self">fibonacci_sum</a></td><td class="desc">Functions for the sum of the Fibonacci Sequence: \(\mathrm{F}(n) +
+\mathrm{F}(n+1) + .. + \mathrm{F}(m)\) </td></tr>
 <tr id="row_30_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d8a/namespacegeometric__dist.html" target="_self">geometric_dist</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Geometric_distribution" target="_blank">Geometric Distribution</a> algorithm implementation </td></tr>
 <tr id="row_31_"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_31_" class="arrow" onclick="toggleFolder('31_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d5/d5f/namespacegeometry.html" target="_self">geometry</a></td><td class="desc">For <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> </td></tr>
-<tr id="row_31_0_" class="even" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_31_0_" class="arrow" onclick="toggleFolder('31_0_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>grahamscan</b></td><td class="desc"></td></tr>
-<tr id="row_31_0_0_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d7/d48/structgeometry_1_1grahamscan_1_1_point.html" target="_self">Point</a></td><td class="desc"></td></tr>
-<tr id="row_31_1_" class="even" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_31_1_" class="arrow" onclick="toggleFolder('31_1_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>jarvis</b></td><td class="desc"></td></tr>
-<tr id="row_31_1_0_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d4/dde/classgeometry_1_1jarvis_1_1_convexhull.html" target="_self">Convexhull</a></td><td class="desc"></td></tr>
-<tr id="row_31_1_1_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d9/d5a/structgeometry_1_1jarvis_1_1_point.html" target="_self">Point</a></td><td class="desc"></td></tr>
 <tr id="row_32_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/d0f/namespacegram__schmidt.html" target="_self">gram_schmidt</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process" target="_blank">Gram Schmidt Orthogonalisation Process</a> </td></tr>
 <tr id="row_33_"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_33_" class="arrow" onclick="toggleFolder('33_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/dce/namespacegraph.html" target="_self">graph</a></td><td class="desc"><a class="el" href="dc/d61/classgraph_1_1_graph.html">Graph</a> Algorithms </td></tr>
-<tr id="row_33_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>bidirectional_dijkstra</b></td><td class="desc"></td></tr>
-<tr id="row_33_1_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>depth_first_search</b></td><td class="desc"></td></tr>
-<tr id="row_33_2_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>disjoint_union</b></td><td class="desc"></td></tr>
-<tr id="row_33_3_" class="even" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_33_3_" class="arrow" onclick="toggleFolder('33_3_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>is_graph_bipartite</b></td><td class="desc"></td></tr>
-<tr id="row_33_3_0_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html" target="_self">Graph</a></td><td class="desc">Class for representing graph as an adjacency list </td></tr>
-<tr id="row_33_4_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="dc/d61/classgraph_1_1_graph.html" target="_self">Graph</a></td><td class="desc"></td></tr>
-<tr id="row_33_5_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d8/d69/classgraph_1_1_h_k_graph.html" target="_self">HKGraph</a></td><td class="desc">Represents Bipartite graph for Hopcroft Karp implementation </td></tr>
-<tr id="row_33_6_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d9/d23/classgraph_1_1_lowest_common_ancestor.html" target="_self">LowestCommonAncestor</a></td><td class="desc"></td></tr>
-<tr id="row_33_7_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d0/d58/classgraph_1_1_rooted_tree.html" target="_self">RootedTree</a></td><td class="desc"></td></tr>
+<tr id="row_33_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="dc/d61/classgraph_1_1_graph.html" target="_self">Graph</a></td><td class="desc"></td></tr>
+<tr id="row_33_1_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d8/d69/classgraph_1_1_h_k_graph.html" target="_self">HKGraph</a></td><td class="desc">Represents Bipartite graph for Hopcroft Karp implementation </td></tr>
+<tr id="row_33_2_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d9/d23/classgraph_1_1_lowest_common_ancestor.html" target="_self">LowestCommonAncestor</a></td><td class="desc"></td></tr>
+<tr id="row_33_3_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d0/d58/classgraph_1_1_rooted_tree.html" target="_self">RootedTree</a></td><td class="desc"></td></tr>
 <tr id="row_34_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d08/namespacegraph__coloring.html" target="_self">graph_coloring</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Graph_coloring" target="_blank">Graph Coloring</a> algorithm, </td></tr>
 <tr id="row_35_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/d1c/namespacehamming__distance.html" target="_self">hamming_distance</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Hamming_distance" target="_blank">Hamming distance</a> implementation </td></tr>
 <tr id="row_36_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/d0c/namespacehashing.html" target="_self">hashing</a></td><td class="desc">Hashing algorithms </td></tr>
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-<tr id="row_57_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>lru_tests</b></td><td class="desc"></td></tr>
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-<tr id="row_58_1_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>activations</b></td><td class="desc"></td></tr>
-<tr id="row_58_1_1_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span id="arr_58_1_1_" class="arrow" onclick="toggleFolder('58_1_1_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>layers</b></td><td class="desc"></td></tr>
-<tr id="row_58_1_1_0_" style="display:none;"><td class="entry"><span style="width:64px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="dc/d93/classmachine__learning_1_1neural__network_1_1layers_1_1_dense_layer.html" target="_self">DenseLayer</a></td><td class="desc"></td></tr>
-<tr id="row_58_1_2_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>util_functions</b></td><td class="desc"></td></tr>
-<tr id="row_58_1_3_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d4/df4/classmachine__learning_1_1neural__network_1_1_neural_network.html" target="_self">NeuralNetwork</a></td><td class="desc"></td></tr>
-<tr id="row_58_2_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d6/d30/classmachine__learning_1_1adaline.html" target="_self">adaline</a></td><td class="desc"></td></tr>
-<tr id="row_59_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d93/namespacemagic__sequence.html" target="_self">magic_sequence</a></td><td class="desc">Functions for the <a href="https://www.csplib.org/Problems/prob019/" target="_blank">Magic sequence</a> implementation </td></tr>
-<tr id="row_60_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/dc6/namespacemanacher.html" target="_self">manacher</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Longest_palindromic_substring" target="_blank">Manacher's Algorithm</a> implementation </td></tr>
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-<tr id="row_61_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>binomial</b></td><td class="desc"></td></tr>
-<tr id="row_61_1_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>fibonacci_sum</b></td><td class="desc"></td></tr>
-<tr id="row_61_2_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>modular_division</b></td><td class="desc"></td></tr>
-<tr id="row_61_3_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>monte_carlo</b></td><td class="desc"></td></tr>
-<tr id="row_61_4_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>n_bonacci</b></td><td class="desc"></td></tr>
-<tr id="row_61_5_" class="even" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_61_5_" class="arrow" onclick="toggleFolder('61_5_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>ncr_modulo_p</b></td><td class="desc"></td></tr>
-<tr id="row_61_5_0_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html" target="_self">NCRModuloP</a></td><td class="desc">Class which contains all methods required for calculating nCr mod p </td></tr>
-<tr id="row_61_6_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>vector_cross</b></td><td class="desc"></td></tr>
-<tr id="row_61_7_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="de/d4f/structmath_1_1_point.html" target="_self">Point</a></td><td class="desc"></td></tr>
-<tr id="row_62_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d43/namespace_m_d5.html" target="_self">MD5</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/MD5" target="_blank">MD5</a> algorithm implementation </td></tr>
-<tr id="row_63_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/dd4/namespacemedian__search.html" target="_self">median_search</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Median_search" target="_blank">Median search</a> algorithm </td></tr>
-<tr id="row_64_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d0a/namespacemerge__insertion.html" target="_self">merge_insertion</a></td><td class="desc">Combined Intersion-Merge sorting algorithm </td></tr>
-<tr id="row_65_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/daa/namespacemidpoint__rule.html" target="_self">midpoint_rule</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Midpoint_method" target="_blank">Midpoint Integral</a> method implementation </td></tr>
-<tr id="row_66_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d5/db8/namespacemincoins__topdown.html" target="_self">mincoins_topdown</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/coin-change/" target="_blank">minimum coin exchange</a> problem </td></tr>
-<tr id="row_67_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/d12/namespace_minimum.html" target="_self">Minimum</a></td><td class="desc">Implementation of <a href="https://en.wikipedia.org/wiki/Edit_distance" target="_blank">Minimum Edit Distance</a> algorithm </td></tr>
-<tr id="row_68_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d1/d64/namespacemodular__division.html" target="_self">modular_division</a></td><td class="desc">Functions for <a href="https://www.geeksforgeeks.org/modular-division" target="_blank">Modular Division</a> implementation </td></tr>
-<tr id="row_69_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/da4/namespacemonte__carlo.html" target="_self">monte_carlo</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Monte_Carlo_integration" target="_blank">Monte Carlo Integration</a> implementation </td></tr>
-<tr id="row_70_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/d8d/namespacemorse.html" target="_self">morse</a></td><td class="desc">Functions for [Morse Code] (<a href="https://en.wikipedia.org/wiki/Morse_code">https://en.wikipedia.org/wiki/Morse_code</a>) </td></tr>
-<tr id="row_71_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d36/namespacen__bonacci.html" target="_self">n_bonacci</a></td><td class="desc">Functions for the <a href="http://oeis.org/wiki/N-bonacci_numbers" target="_blank">N-bonacci</a> implementation </td></tr>
-<tr id="row_72_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/da1/namespacen__queens.html" target="_self">n_queens</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle </td></tr>
-<tr id="row_73_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d44/namespacen__queens__all__solutions.html" target="_self">n_queens_all_solutions</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle with all solutions </td></tr>
-<tr id="row_74_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d14/namespacen__queens__optimized.html" target="_self">n_queens_optimized</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle optimized </td></tr>
-<tr id="row_75_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/db9/namespacencr__modulo__p.html" target="_self">ncr_modulo_p</a></td><td class="desc">Functions for <a href="https://cp-algorithms.com/combinatorics/binomial-coefficients.html" target="_blank">nCr modulo p</a> implementation </td></tr>
-<tr id="row_76_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/d2e/namespaceneural__network.html" target="_self">neural_network</a></td><td class="desc">Neural Network or Multilayer Perceptron </td></tr>
-<tr id="row_77_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d1/de0/namespacenumerical__methods.html" target="_self">numerical_methods</a></td><td class="desc">For assert </td></tr>
-<tr id="row_78_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_78_" class="arrow" onclick="toggleFolder('78_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/d6d/namespaceoperations__on__datastructures.html" target="_self">operations_on_datastructures</a></td><td class="desc">For <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> </td></tr>
-<tr id="row_78_0_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_78_0_" class="arrow" onclick="toggleFolder('78_0_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>circular_linked_list</b></td><td class="desc"></td></tr>
-<tr id="row_78_0_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d8/d7c/classoperations__on__datastructures_1_1circular__linked__list_1_1_circular_linked_list.html" target="_self">CircularLinkedList</a></td><td class="desc">A class that implements a Circular Linked List </td></tr>
-<tr id="row_78_0_1_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" target="_self">Node</a></td><td class="desc">A <a class="el" href="da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> struct that represents a single <a class="el" href="da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> in a Binary Tree </td></tr>
-<tr id="row_78_1_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_78_1_" class="arrow" onclick="toggleFolder('78_1_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>inorder_traversal_of_bst</b></td><td class="desc"></td></tr>
-<tr id="row_78_1_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d5/db5/classoperations__on__datastructures_1_1inorder__traversal__of__bst_1_1_node.html" target="_self">Node</a></td><td class="desc">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 </td></tr>
-<tr id="row_78_2_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_78_2_" class="arrow" onclick="toggleFolder('78_2_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>reverse_binary_tree</b></td><td class="desc"></td></tr>
-<tr id="row_78_2_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="de/dcf/classoperations__on__datastructures_1_1reverse__binary__tree_1_1_binary_tree.html" target="_self">BinaryTree</a></td><td class="desc">A Binary Tree class that implements a Binary Search Tree (BST) by default </td></tr>
-<tr id="row_78_2_1_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d8/dfd/structoperations__on__datastructures_1_1reverse__binary__tree_1_1_node.html" target="_self">Node</a></td><td class="desc">A <a class="el" href="d8/dfd/structoperations__on__datastructures_1_1reverse__binary__tree_1_1_node.html" title="A Node struct that represents a single node in a Binary Tree.">Node</a> struct that represents a single node in a Binary Tree </td></tr>
-<tr id="row_78_3_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_78_3_" class="arrow" onclick="toggleFolder('78_3_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>trie_operations</b></td><td class="desc"></td></tr>
-<tr id="row_78_3_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html" target="_self">Tnode</a></td><td class="desc">Class defining the structure of trie node and containing the methods to perform operations on them </td></tr>
-<tr id="row_79_"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_79_" class="arrow" onclick="toggleFolder('79_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/d6f/namespaceothers.html" target="_self">others</a></td><td class="desc">For <code>vector</code> </td></tr>
-<tr id="row_79_0_" class="even" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_79_0_" class="arrow" onclick="toggleFolder('79_0_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>iterative_tree_traversals</b></td><td class="desc"></td></tr>
-<tr id="row_79_0_0_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d9/d12/classothers_1_1iterative__tree__traversals_1_1_binary_tree.html" target="_self">BinaryTree</a></td><td class="desc">Defines the functions associated with the binary tree </td></tr>
-<tr id="row_79_0_1_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/d9a/structothers_1_1iterative__tree__traversals_1_1_node.html" target="_self">Node</a></td><td class="desc">Defines the structure of a node of the tree </td></tr>
-<tr id="row_79_1_" class="even" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_79_1_" class="arrow" onclick="toggleFolder('79_1_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>lru_cache</b></td><td class="desc"></td></tr>
-<tr id="row_79_1_0_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d6/dae/classothers_1_1lru__cache_1_1_l_r_u_cache.html" target="_self">LRUCache</a></td><td class="desc">LRU cache class </td></tr>
-<tr id="row_79_2_" class="even" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_79_2_" class="arrow" onclick="toggleFolder('79_2_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>postfix_expression</b></td><td class="desc"></td></tr>
-<tr id="row_79_2_0_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d5/d8a/classothers_1_1postfix__expression_1_1_stack.html" target="_self">Stack</a></td><td class="desc">Creates an array to be used as stack for storing values </td></tr>
-<tr id="row_79_3_" class="even" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_79_3_" class="arrow" onclick="toggleFolder('79_3_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>recursive_tree_traversals</b></td><td class="desc"></td></tr>
-<tr id="row_79_3_0_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html" target="_self">BT</a></td><td class="desc"><a class="el" href="dd/de1/classothers_1_1recursive__tree__traversals_1_1_b_t.html" title="BT used to make the entire structure of the binary tree and the functions associated with the binary ...">BT</a> used to make the entire structure of the binary tree and the functions associated with the binary tree </td></tr>
-<tr id="row_79_3_1_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d9/df7/structothers_1_1recursive__tree__traversals_1_1_node.html" target="_self">Node</a></td><td class="desc">The structure to hold Nodes of the tree </td></tr>
-<tr id="row_80_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d5/d89/namespacepalindrome__partitioning.html" target="_self">palindrome_partitioning</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/palindrome-partitioning-ii/" target="_blank">Palindrome Partitioning</a> algorithm </td></tr>
-<tr id="row_81_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d10/namespacepancake__sort.html" target="_self">pancake_sort</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Pancake_sorting" target="_blank">Pancake sort</a> algorithm </td></tr>
-<tr id="row_82_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/de6/namespacepostfix__expression.html" target="_self">postfix_expression</a></td><td class="desc">Functions for Postfix Expression algorithm </td></tr>
-<tr id="row_83_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d88/namespaceprefix__sum__array.html" target="_self">prefix_sum_array</a></td><td class="desc">Range sum queries using prefix-sum-array </td></tr>
-<tr id="row_84_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_84_" class="arrow" onclick="toggleFolder('84_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/ded/namespaceprobability.html" target="_self">probability</a></td><td class="desc">Probability algorithms </td></tr>
-<tr id="row_84_0_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_84_0_" class="arrow" onclick="toggleFolder('84_0_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>geometric_dist</b></td><td class="desc"></td></tr>
-<tr id="row_84_0_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html" target="_self">geometric_distribution</a></td><td class="desc">A class to model the geometric distribution </td></tr>
-<tr id="row_84_1_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_84_1_" class="arrow" onclick="toggleFolder('84_1_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>windowed_median</b></td><td class="desc"></td></tr>
-<tr id="row_84_1_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html" target="_self">WindowedMedian</a></td><td class="desc">A class to calculate the median of a leading sliding window at the back of a stream of integer values </td></tr>
-<tr id="row_85_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d2/d3b/namespaceqr__algorithm.html" target="_self">qr_algorithm</a></td><td class="desc">Functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> of any rectangular matrix </td></tr>
-<tr id="row_86_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_86_" class="arrow" onclick="toggleFolder('86_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/dd2/namespacequadratic__probing.html" target="_self">quadratic_probing</a></td><td class="desc">An implementation of hash table using <a href="https://en.wikipedia.org/wiki/Quadratic_probing" target="_blank">quadratic probing</a> algorithm </td></tr>
-<tr id="row_86_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="da/dd1/structquadratic__probing_1_1_entry.html" target="_self">Entry</a></td><td class="desc"></td></tr>
-<tr id="row_87_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d70/namespacequeue__using__array.html" target="_self">queue_using_array</a></td><td class="desc">Functions for [<a class="el" href="dc/db5/struct_queue.html">Queue</a> using Array] (<a href="https://www.geeksforgeeks.org/array-implementation-of-queue-simple/">https://www.geeksforgeeks.org/array-implementation-of-queue-simple/</a>) implementation </td></tr>
-<tr id="row_88_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/dda/namespaceradix__sort.html" target="_self">radix_sort</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Radix_sort" target="_blank">Radix sort</a> algorithm </td></tr>
-<tr id="row_89_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d6b/namespacerandom__pivot__quick__sort.html" target="_self">random_pivot_quick_sort</a></td><td class="desc">Functions for the <a href="https://www.sanfoundry.com/cpp-program-implement-quick-sort-using-randomisation" target="_blank">Random Pivot Quick Sort</a> implementation </td></tr>
-<tr id="row_90_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_90_" class="arrow" onclick="toggleFolder('90_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d69/namespacerange__queries.html" target="_self">range_queries</a></td><td class="desc">Algorithms and Data Structures that support range queries and updates </td></tr>
-<tr id="row_90_0_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_90_0_" class="arrow" onclick="toggleFolder('90_0_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>heavy_light_decomposition</b></td><td class="desc"></td></tr>
-<tr id="row_90_0_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html" target="_self">HLD</a></td><td class="desc">The Heavy-Light Decomposition class </td></tr>
-<tr id="row_90_0_1_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html" target="_self">SG</a></td><td class="desc">Segment <a class="el" href="d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html" title="A Basic Tree, which supports binary lifting.">Tree</a>, to store heavy chains </td></tr>
-<tr id="row_90_0_2_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html" target="_self">Tree</a></td><td class="desc">A Basic <a class="el" href="d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html" title="A Basic Tree, which supports binary lifting.">Tree</a>, which supports binary lifting </td></tr>
-<tr id="row_90_1_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>prefix_sum_array</b></td><td class="desc"></td></tr>
-<tr id="row_90_2_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>sparse_table</b></td><td class="desc"></td></tr>
-<tr id="row_90_3_" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_90_3_" class="arrow" onclick="toggleFolder('90_3_')">&#9658;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d8/d28/classrange__queries_1_1per_seg_tree.html" target="_self">perSegTree</a></td><td class="desc">Range query here is range sum, but the code can be modified to make different queries like range max or min </td></tr>
-<tr id="row_90_3_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d5/d66/classrange__queries_1_1per_seg_tree_1_1_node.html" target="_self">Node</a></td><td class="desc"></td></tr>
-<tr id="row_91_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d60/namespacerat__maze.html" target="_self">rat_maze</a></td><td class="desc">Functions for &lt;a href="https://www.codesdope.com/blog/article/backtracking-to-
-solve-a-rat-in-a-maze-c-java-pytho/" </td></tr>
-<tr id="row_92_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dc/dc5/namespacereverse__binary__tree.html" target="_self">reverse_binary_tree</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/reverse-tree-path/" target="_blank">Reverse a Binary Tree</a> implementation </td></tr>
-<tr id="row_93_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d2/de7/namespacerunge__kutta.html" target="_self">runge_kutta</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods" target="_blank">Runge Kutta fourth order</a> method </td></tr>
-<tr id="row_94_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/dda/namespacesaddleback.html" target="_self">saddleback</a></td><td class="desc">Function for implementing <a href="https://www.geeksforgeeks.org/saddleback-search-algorithm-in-a-2d-array" target="_blank">Saddleback Algorithm</a> </td></tr>
-<tr id="row_95_"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_95_" class="arrow" onclick="toggleFolder('95_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/dca/namespacesearch.html" target="_self">search</a></td><td class="desc">For <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> </td></tr>
-<tr id="row_95_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>cycle_detection</b></td><td class="desc"></td></tr>
-<tr id="row_95_1_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>median_search</b></td><td class="desc"></td></tr>
-<tr id="row_95_2_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>saddleback</b></td><td class="desc"></td></tr>
-<tr id="row_95_3_" class="even" style="display:none;"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_95_3_" class="arrow" onclick="toggleFolder('95_3_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><b>sublist_search</b></td><td class="desc"></td></tr>
-<tr id="row_95_3_0_" class="even" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="da/d61/structsearch_1_1sublist__search_1_1_node.html" target="_self">Node</a></td><td class="desc">A <a class="el" href="da/d61/structsearch_1_1sublist__search_1_1_node.html" title="A Node structure representing a single link Node in a linked list.">Node</a> structure representing a single link <a class="el" href="da/d61/structsearch_1_1sublist__search_1_1_node.html" title="A Node structure representing a single link Node in a linked list.">Node</a> in a linked list </td></tr>
-<tr id="row_96_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d4a/namespaceselection__sort__recursive.html" target="_self">selection_sort_recursive</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Selection_sort" target="_blank">Selection sort</a> implementation using recursion </td></tr>
-<tr id="row_97_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d88/namespaceset_kth_bit.html" target="_self">setKthBit</a></td><td class="desc">Functions for the [From the right, set the Kth bit in the binary representation of N] (<a href="https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/">https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/</a>) implementation </td></tr>
-<tr id="row_98_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/dd3/namespace_s_h_a.html" target="_self">SHA</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/SHA-1" target="_blank">SHA-1</a> algorithm implementation </td></tr>
-<tr id="row_99_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/deb/namespaceshortest__common__supersequence.html" target="_self">shortest_common_supersequence</a></td><td class="desc">Shortest Common Super Sequence algorithm </td></tr>
-<tr id="row_100_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d6d/namespacesimpson__method.html" target="_self">simpson_method</a></td><td class="desc">Contains the Simpson's method implementation </td></tr>
-<tr id="row_101_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d5/d91/namespacesorting.html" target="_self">sorting</a></td><td class="desc">For working with vectors </td></tr>
-<tr id="row_102_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d55/namespacesparse__table.html" target="_self">sparse_table</a></td><td class="desc">Functions for Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> </td></tr>
-<tr id="row_103_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/dd3/namespacespirograph.html" target="_self">spirograph</a></td><td class="desc"></td></tr>
-<tr id="row_104_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d1c/namespacestack__using__queue.html" target="_self">stack_using_queue</a></td><td class="desc">Functions for the <a href="https://www.studytonight.com/data-structures/stack-using-queue" target="_blank">Stack Using Queue</a> implementation </td></tr>
-<tr id="row_105_"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_105_" class="arrow" onclick="toggleFolder('105_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d2/dcf/namespacestatistics.html" target="_self">statistics</a></td><td class="desc">Statistical algorithms </td></tr>
-<tr id="row_105_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html" target="_self">stats_computer1</a></td><td class="desc"></td></tr>
-<tr id="row_105_1_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html" target="_self">stats_computer2</a></td><td class="desc"></td></tr>
-<tr id="row_106_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_106_" class="arrow" onclick="toggleFolder('106_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/dcc/namespacestd.html" target="_self">std</a></td><td class="desc">STL namespace </td></tr>
-<tr id="row_106_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>chrono</b></td><td class="desc"></td></tr>
-<tr id="row_106_1_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>experimental</b></td><td class="desc"></td></tr>
-<tr id="row_106_2_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>rel_ops</b></td><td class="desc"></td></tr>
-<tr id="row_106_3_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><b>this_thread</b></td><td class="desc"></td></tr>
-<tr id="row_106_4_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/dfc/structstd_1_1is__arithmetic_3_01uint128__t_01_4.html" target="_self">is_arithmetic&lt; uint128_t &gt;</a></td><td class="desc"></td></tr>
-<tr id="row_106_5_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="dc/d6d/structstd_1_1is__arithmetic_3_01uint256__t_01_4.html" target="_self">is_arithmetic&lt; uint256_t &gt;</a></td><td class="desc"></td></tr>
-<tr id="row_106_6_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/dd4/structstd_1_1is__integral_3_01uint128__t_01_4.html" target="_self">is_integral&lt; uint128_t &gt;</a></td><td class="desc"></td></tr>
-<tr id="row_106_7_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d7/d47/structstd_1_1is__integral_3_01uint256__t_01_4.html" target="_self">is_integral&lt; uint256_t &gt;</a></td><td class="desc"></td></tr>
-<tr id="row_106_8_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d5/d25/structstd_1_1is__unsigned_3_01uint128__t_01_4.html" target="_self">is_unsigned&lt; uint128_t &gt;</a></td><td class="desc"></td></tr>
-<tr id="row_106_9_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="df/d99/structstd_1_1is__unsigned_3_01uint256__t_01_4.html" target="_self">is_unsigned&lt; uint256_t &gt;</a></td><td class="desc"></td></tr>
-<tr id="row_107_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d1d/namespacestrand.html" target="_self">strand</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Strand_sort" target="_blank">Strand Sort</a> algorithm </td></tr>
-<tr id="row_108_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d03/namespacestring__search.html" target="_self">string_search</a></td><td class="desc">String search algorithms </td></tr>
-<tr id="row_109_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/dcb/namespacestrings.html" target="_self">strings</a></td><td class="desc">Algorithms with strings </td></tr>
-<tr id="row_110_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d74/namespacesubarray__sum.html" target="_self">subarray_sum</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset sum</a> implementation </td></tr>
-<tr id="row_111_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/def/namespacesublist__search.html" target="_self">sublist_search</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/sublist-search-search-a-linked-list-in-another-list" target="_blank">Sublist Search</a> implementation </td></tr>
-<tr id="row_112_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d95/namespace_subsets.html" target="_self">Subsets</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset Sum</a> problem </td></tr>
-<tr id="row_113_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d9f/namespacesudoku__solver.html" target="_self">sudoku_solver</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Sudoku" target="_blank">Sudoku Solver</a> implementation </td></tr>
-<tr id="row_114_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/df4/namespacetests.html" target="_self">tests</a></td><td class="desc">Testcases to check Union of Two Arrays </td></tr>
-<tr id="row_115_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/dab/namespacetree__234.html" target="_self">tree_234</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/2%E2%80%933%E2%80%934_tree" target="_blank">2–3–4 tree</a> </td></tr>
-<tr id="row_116_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d8e/namespacetrie__operations.html" target="_self">trie_operations</a></td><td class="desc">Functions for <a href="https://iq.opengenus.org/autocomplete-using-trie-data-structure/" target="_blank">Trie datastructure</a> implementation </td></tr>
-<tr id="row_117_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d0a/namespacetrie__using__hashmap.html" target="_self">trie_using_hashmap</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Trie" target="_blank">Trie</a> data structure using hashmap implementation </td></tr>
-<tr id="row_118_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d17/namespaceutil__functions.html" target="_self">util_functions</a></td><td class="desc">Various utility functions used in Neural network </td></tr>
-<tr id="row_119_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/d91/namespacevector__cross.html" target="_self">vector_cross</a></td><td class="desc">Functions for Vector Cross Product algorithms </td></tr>
-<tr id="row_120_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/da2/namespacevigenere.html" target="_self">vigenere</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher" target="_blank">vigenère cipher</a> algorithm </td></tr>
-<tr id="row_121_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d21/namespacewave__sort.html" target="_self">wave_sort</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/sort-array-wave-form-2/" target="_blank">Wave sort</a> implementation </td></tr>
-<tr id="row_122_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/d52/namespacewiggle__sort.html" target="_self">wiggle_sort</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/wiggle-sort-ii/" target="_blank">Wiggle Sort</a> algorithm </td></tr>
-<tr id="row_123_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="db/d03/namespacewildcard__matching.html" target="_self">wildcard_matching</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/wildcard-pattern-matching/" target="_blank">Wildcard Matching</a> problem </td></tr>
-<tr id="row_124_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d21/namespacewindowed__median.html" target="_self">windowed_median</a></td><td class="desc">Functions for the Windowed Median algorithm implementation </td></tr>
-<tr id="row_125_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/d53/namespaceword__break.html" target="_self">word_break</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/word-break/" target="_blank">Word Break</a> problem </td></tr>
-<tr id="row_126_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d47/namespace_x_o_r.html" target="_self">XOR</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/XOR_cipher" target="_blank">XOR cipher</a> algorithm </td></tr>
+<tr id="row_51_"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_51_" class="arrow" onclick="toggleFolder('51_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d89/namespacelinear__probing.html" target="_self">linear_probing</a></td><td class="desc">An implementation of hash table using <a href="https://en.wikipedia.org/wiki/Linear_probing" target="_blank">linear probing</a> algorithm </td></tr>
+<tr id="row_51_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="db/d19/structlinear__probing_1_1_entry.html" target="_self">Entry</a></td><td class="desc"></td></tr>
+<tr id="row_52_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/dd1/namespacelinear__recurrence__matrix.html" target="_self">linear_recurrence_matrix</a></td><td class="desc">Functions for <a href="https://www.hackerearth.com/practice/notes/matrix-exponentiation-1/" target="_blank">Linear Recurrence Matrix</a> implementation </td></tr>
+<tr id="row_53_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/db0/namespacelinked__list.html" target="_self">linked_list</a></td><td class="desc">Functions for singly linked list algorithm </td></tr>
+<tr id="row_54_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d27/namespacelist__array.html" target="_self">list_array</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Dynamic_array" target="_blank">Dynamic Array</a> algorithm </td></tr>
+<tr id="row_55_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/dcd/namespacelru__cache.html" target="_self">lru_cache</a></td><td class="desc">Implementation of the <a href="https://en.wikipedia.org/wiki/Cache_replacement_policies#Least_recently_used_(LRU)" target="_blank">LRU caching algorithm</a> </td></tr>
+<tr id="row_56_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_56_" class="arrow" onclick="toggleFolder('56_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d77/namespacemachine__learning.html" target="_self">machine_learning</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/A*_search_algorithm" target="_blank">A* search algorithm</a> </td></tr>
+<tr id="row_56_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d6/d30/classmachine__learning_1_1adaline.html" target="_self">adaline</a></td><td class="desc"></td></tr>
+<tr id="row_57_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d93/namespacemagic__sequence.html" target="_self">magic_sequence</a></td><td class="desc">Functions for the <a href="https://www.csplib.org/Problems/prob019/" target="_blank">Magic sequence</a> implementation </td></tr>
+<tr id="row_58_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/dc6/namespacemanacher.html" target="_self">manacher</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Longest_palindromic_substring" target="_blank">Manacher's Algorithm</a> implementation </td></tr>
+<tr id="row_59_"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_59_" class="arrow" onclick="toggleFolder('59_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d47/namespacemath.html" target="_self">math</a></td><td class="desc">For <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a> </td></tr>
+<tr id="row_59_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="de/d4f/structmath_1_1_point.html" target="_self">Point</a></td><td class="desc"></td></tr>
+<tr id="row_60_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d43/namespace_m_d5.html" target="_self">MD5</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/MD5" target="_blank">MD5</a> algorithm implementation </td></tr>
+<tr id="row_61_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/dd4/namespacemedian__search.html" target="_self">median_search</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Median_search" target="_blank">Median search</a> algorithm </td></tr>
+<tr id="row_62_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d0a/namespacemerge__insertion.html" target="_self">merge_insertion</a></td><td class="desc">Combined Intersion-Merge sorting algorithm </td></tr>
+<tr id="row_63_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/daa/namespacemidpoint__rule.html" target="_self">midpoint_rule</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Midpoint_method" target="_blank">Midpoint Integral</a> method implementation </td></tr>
+<tr id="row_64_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d5/db8/namespacemincoins__topdown.html" target="_self">mincoins_topdown</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/coin-change/" target="_blank">minimum coin exchange</a> problem </td></tr>
+<tr id="row_65_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/d12/namespace_minimum.html" target="_self">Minimum</a></td><td class="desc">Implementation of <a href="https://en.wikipedia.org/wiki/Edit_distance" target="_blank">Minimum Edit Distance</a> algorithm </td></tr>
+<tr id="row_66_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d1/d64/namespacemodular__division.html" target="_self">modular_division</a></td><td class="desc">Functions for <a href="https://www.geeksforgeeks.org/modular-division" target="_blank">Modular Division</a> implementation </td></tr>
+<tr id="row_67_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/da4/namespacemonte__carlo.html" target="_self">monte_carlo</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Monte_Carlo_integration" target="_blank">Monte Carlo Integration</a> implementation </td></tr>
+<tr id="row_68_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/d8d/namespacemorse.html" target="_self">morse</a></td><td class="desc">Functions for [Morse Code] (<a href="https://en.wikipedia.org/wiki/Morse_code">https://en.wikipedia.org/wiki/Morse_code</a>) </td></tr>
+<tr id="row_69_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d36/namespacen__bonacci.html" target="_self">n_bonacci</a></td><td class="desc">Functions for the <a href="http://oeis.org/wiki/N-bonacci_numbers" target="_blank">N-bonacci</a> implementation </td></tr>
+<tr id="row_70_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/da1/namespacen__queens.html" target="_self">n_queens</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle </td></tr>
+<tr id="row_71_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d44/namespacen__queens__all__solutions.html" target="_self">n_queens_all_solutions</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle with all solutions </td></tr>
+<tr id="row_72_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d14/namespacen__queens__optimized.html" target="_self">n_queens_optimized</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle optimized </td></tr>
+<tr id="row_73_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/db9/namespacencr__modulo__p.html" target="_self">ncr_modulo_p</a></td><td class="desc">Functions for <a href="https://cp-algorithms.com/combinatorics/binomial-coefficients.html" target="_blank">nCr modulo p</a> implementation </td></tr>
+<tr id="row_74_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/d2e/namespaceneural__network.html" target="_self">neural_network</a></td><td class="desc">Neural Network or Multilayer Perceptron </td></tr>
+<tr id="row_75_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d1/de0/namespacenumerical__methods.html" target="_self">numerical_methods</a></td><td class="desc">For assert </td></tr>
+<tr id="row_76_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_76_" class="arrow" onclick="toggleFolder('76_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/d6d/namespaceoperations__on__datastructures.html" target="_self">operations_on_datastructures</a></td><td class="desc">For <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> </td></tr>
+<tr id="row_77_"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_77_" class="arrow" onclick="toggleFolder('77_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/d6f/namespaceothers.html" target="_self">others</a></td><td class="desc">For <code>vector</code> </td></tr>
+<tr id="row_78_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d5/d89/namespacepalindrome__partitioning.html" target="_self">palindrome_partitioning</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/palindrome-partitioning-ii/" target="_blank">Palindrome Partitioning</a> algorithm </td></tr>
+<tr id="row_79_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d10/namespacepancake__sort.html" target="_self">pancake_sort</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Pancake_sorting" target="_blank">Pancake sort</a> algorithm </td></tr>
+<tr id="row_80_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/de6/namespacepostfix__expression.html" target="_self">postfix_expression</a></td><td class="desc">Functions for Postfix Expression algorithm </td></tr>
+<tr id="row_81_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d88/namespaceprefix__sum__array.html" target="_self">prefix_sum_array</a></td><td class="desc">Range sum queries using prefix-sum-array </td></tr>
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+<tr id="row_84_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="da/dd1/structquadratic__probing_1_1_entry.html" target="_self">Entry</a></td><td class="desc"></td></tr>
+<tr id="row_85_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d70/namespacequeue__using__array.html" target="_self">queue_using_array</a></td><td class="desc">Functions for [<a class="el" href="dc/db5/struct_queue.html">Queue</a> using Array] (<a href="https://www.geeksforgeeks.org/array-implementation-of-queue-simple/">https://www.geeksforgeeks.org/array-implementation-of-queue-simple/</a>) implementation </td></tr>
+<tr id="row_86_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/dda/namespaceradix__sort.html" target="_self">radix_sort</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Radix_sort" target="_blank">Radix sort</a> algorithm </td></tr>
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+<tr id="row_88_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_88_" class="arrow" onclick="toggleFolder('88_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d69/namespacerange__queries.html" target="_self">range_queries</a></td><td class="desc">Algorithms and Data Structures that support range queries and updates </td></tr>
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+<tr id="row_88_0_0_" style="display:none;"><td class="entry"><span style="width:48px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d5/d66/classrange__queries_1_1per_seg_tree_1_1_node.html" target="_self">Node</a></td><td class="desc"></td></tr>
+<tr id="row_89_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d60/namespacerat__maze.html" target="_self">rat_maze</a></td><td class="desc">Functions for <a href="https://www.codesdope.com/blog/article/backtracking-to-
+solve-a-rat-in-a-maze-c-java-pytho/" target="_blank">Rat in a Maze</a> algorithm </td></tr>
+<tr id="row_90_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dc/dc5/namespacereverse__binary__tree.html" target="_self">reverse_binary_tree</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/reverse-tree-path/" target="_blank">Reverse a Binary Tree</a> implementation </td></tr>
+<tr id="row_91_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d2/de7/namespacerunge__kutta.html" target="_self">runge_kutta</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods" target="_blank">Runge Kutta fourth order</a> method </td></tr>
+<tr id="row_92_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/dda/namespacesaddleback.html" target="_self">saddleback</a></td><td class="desc">Function for implementing <a href="https://www.geeksforgeeks.org/saddleback-search-algorithm-in-a-2d-array" target="_blank">Saddleback Algorithm</a> </td></tr>
+<tr id="row_93_"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_93_" class="arrow" onclick="toggleFolder('93_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/dca/namespacesearch.html" target="_self">search</a></td><td class="desc">For <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> </td></tr>
+<tr id="row_94_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d4a/namespaceselection__sort__recursive.html" target="_self">selection_sort_recursive</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Selection_sort" target="_blank">Selection sort</a> implementation using recursion </td></tr>
+<tr id="row_95_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d88/namespaceset_kth_bit.html" target="_self">setKthBit</a></td><td class="desc">Functions for the [From the right, set the Kth bit in the binary representation of N] (<a href="https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/">https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/</a>) implementation </td></tr>
+<tr id="row_96_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/dd3/namespace_s_h_a.html" target="_self">SHA</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/SHA-1" target="_blank">SHA-1</a> algorithm implementation </td></tr>
+<tr id="row_97_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/deb/namespaceshortest__common__supersequence.html" target="_self">shortest_common_supersequence</a></td><td class="desc">Shortest Common Super Sequence algorithm </td></tr>
+<tr id="row_98_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d6d/namespacesimpson__method.html" target="_self">simpson_method</a></td><td class="desc">Contains the Simpson's method implementation </td></tr>
+<tr id="row_99_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d5/d91/namespacesorting.html" target="_self">sorting</a></td><td class="desc">For working with vectors </td></tr>
+<tr id="row_100_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d55/namespacesparse__table.html" target="_self">sparse_table</a></td><td class="desc">Functions for Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> </td></tr>
+<tr id="row_101_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/dd3/namespacespirograph.html" target="_self">spirograph</a></td><td class="desc"></td></tr>
+<tr id="row_102_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d1c/namespacestack__using__queue.html" target="_self">stack_using_queue</a></td><td class="desc">Functions for the <a href="https://www.studytonight.com/data-structures/stack-using-queue" target="_blank">Stack Using Queue</a> implementation </td></tr>
+<tr id="row_103_"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_103_" class="arrow" onclick="toggleFolder('103_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d2/dcf/namespacestatistics.html" target="_self">statistics</a></td><td class="desc">Statistical algorithms </td></tr>
+<tr id="row_103_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d7/d7c/classstatistics_1_1stats__computer1.html" target="_self">stats_computer1</a></td><td class="desc"></td></tr>
+<tr id="row_103_1_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d8/dab/classstatistics_1_1stats__computer2.html" target="_self">stats_computer2</a></td><td class="desc"></td></tr>
+<tr id="row_104_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_104_" class="arrow" onclick="toggleFolder('104_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/dcc/namespacestd.html" target="_self">std</a></td><td class="desc">STL namespace </td></tr>
+<tr id="row_104_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/dfc/structstd_1_1is__arithmetic_3_01uint128__t_01_4.html" target="_self">is_arithmetic&lt; uint128_t &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_104_1_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="dc/d6d/structstd_1_1is__arithmetic_3_01uint256__t_01_4.html" target="_self">is_arithmetic&lt; uint256_t &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_104_2_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d2/dd4/structstd_1_1is__integral_3_01uint128__t_01_4.html" target="_self">is_integral&lt; uint128_t &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_104_3_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d7/d47/structstd_1_1is__integral_3_01uint256__t_01_4.html" target="_self">is_integral&lt; uint256_t &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_104_4_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="d5/d25/structstd_1_1is__unsigned_3_01uint128__t_01_4.html" target="_self">is_unsigned&lt; uint128_t &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_104_5_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="df/d99/structstd_1_1is__unsigned_3_01uint256__t_01_4.html" target="_self">is_unsigned&lt; uint256_t &gt;</a></td><td class="desc"></td></tr>
+<tr id="row_105_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d1d/namespacestrand.html" target="_self">strand</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Strand_sort" target="_blank">Strand Sort</a> algorithm </td></tr>
+<tr id="row_106_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d03/namespacestring__search.html" target="_self">string_search</a></td><td class="desc">String search algorithms </td></tr>
+<tr id="row_107_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/dcb/namespacestrings.html" target="_self">strings</a></td><td class="desc">Algorithms with strings </td></tr>
+<tr id="row_108_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d74/namespacesubarray__sum.html" target="_self">subarray_sum</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset sum</a> implementation </td></tr>
+<tr id="row_109_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/def/namespacesublist__search.html" target="_self">sublist_search</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/sublist-search-search-a-linked-list-in-another-list" target="_blank">Sublist Search</a> implementation </td></tr>
+<tr id="row_110_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d95/namespace_subsets.html" target="_self">Subsets</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset Sum</a> problem </td></tr>
+<tr id="row_111_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d9f/namespacesudoku__solver.html" target="_self">sudoku_solver</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Sudoku" target="_blank">Sudoku Solver</a> implementation </td></tr>
+<tr id="row_112_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/df4/namespacetests.html" target="_self">tests</a></td><td class="desc">Testcases to check Union of Two Arrays </td></tr>
+<tr id="row_113_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/dab/namespacetree__234.html" target="_self">tree_234</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/2%E2%80%933%E2%80%934_tree" target="_blank">2–3–4 tree</a> </td></tr>
+<tr id="row_114_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d8e/namespacetrie__operations.html" target="_self">trie_operations</a></td><td class="desc">Functions for <a href="https://iq.opengenus.org/autocomplete-using-trie-data-structure/" target="_blank">Trie datastructure</a> implementation </td></tr>
+<tr id="row_115_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d0a/namespacetrie__using__hashmap.html" target="_self">trie_using_hashmap</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Trie" target="_blank">Trie</a> data structure using hashmap implementation </td></tr>
+<tr id="row_116_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d17/namespaceutil__functions.html" target="_self">util_functions</a></td><td class="desc">Various utility functions used in Neural network </td></tr>
+<tr id="row_117_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/d91/namespacevector__cross.html" target="_self">vector_cross</a></td><td class="desc">Functions for Vector Cross Product algorithms </td></tr>
+<tr id="row_118_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/da2/namespacevigenere.html" target="_self">vigenere</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher" target="_blank">vigenère cipher</a> algorithm </td></tr>
+<tr id="row_119_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d21/namespacewave__sort.html" target="_self">wave_sort</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/sort-array-wave-form-2/" target="_blank">Wave sort</a> implementation </td></tr>
+<tr id="row_120_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/d52/namespacewiggle__sort.html" target="_self">wiggle_sort</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/wiggle-sort-ii/" target="_blank">Wiggle Sort</a> algorithm </td></tr>
+<tr id="row_121_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="db/d03/namespacewildcard__matching.html" target="_self">wildcard_matching</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/wildcard-pattern-matching/" target="_blank">Wildcard Matching</a> problem </td></tr>
+<tr id="row_122_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d21/namespacewindowed__median.html" target="_self">windowed_median</a></td><td class="desc">Functions for the Windowed Median algorithm implementation </td></tr>
+<tr id="row_123_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/d53/namespaceword__break.html" target="_self">word_break</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/word-break/" target="_blank">Word Break</a> problem </td></tr>
+<tr id="row_124_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d47/namespace_x_o_r.html" target="_self">XOR</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/XOR_cipher" target="_blank">XOR cipher</a> algorithm </td></tr>
 </table>
 </div><!-- directory -->
 </div><!-- contents -->
@@ -347,7 +254,7 @@ solve-a-rat-in-a-maze-c-java-pytho/" </td></tr>
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index c81eeb24d..8c9ecfff2 100644
--- a/namespaces_dup.js
+++ b/namespaces_dup.js
@@ -6,47 +6,6 @@ var namespaces_dup =
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     [ "aystar_search", "db/ddc/namespaceaystar__search.html", null ],
     [ "backtracking", "db/dc0/namespacebacktracking.html", [
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-        [ "isSafe", "df/d80/graph__coloringg_8cpp.html#a976efe049deb042bf1f02612e181ab1d", null ],
-        [ "printSolution", "df/d80/graph__coloringg_8cpp.html#a8c47fa37fb6eeeb781b2ec1b05af6b07", null ]
-      ] ],
-      [ "knight_tour", null, [
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-        [ "solve", "d1/d2a/knight__tour_8cpp.html#aaa47356d98676cf5315d978f741e29c9", null ]
-      ] ],
-      [ "n_queens", null, [
-        [ "isSafe", "d4/d3e/n__queens_8cpp.html#a5730b6683f6adcf5c5ef75cf53dc7160", null ],
-        [ "printSolution", "d4/d3e/n__queens_8cpp.html#a40ae0c7fd04eb20e7f3bff13fc6a5808", null ],
-        [ "solveNQ", "d4/d3e/n__queens_8cpp.html#a0dbd7af47d87f0b956609fe9e3288ecb", null ]
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