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@@ -129,9 +129,9 @@ Functions</h2></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >The implementation of <a href="https://en.wikipedia.org/wiki/Hamiltonian_path" target="_blank">Hamilton's cycle</a> dynamic solution for vertices number less than 20. </p>
<p >I use \(2^n\times n\) matrix and for every \([i, j]\) ( \(i &lt; 2^n\) and \(j &lt; n\)) in the matrix I store <code>true</code> if it is possible to get to all vertices on which position in <code>i</code>'s binary representation is <code>1</code> so as \(j\) would be the last one.</p>
<p >In the the end if any cell in \((2^n - 1)^{\mbox{th}}\) row is <code>true</code> there exists hamiltonian cycle.</p>
<div class="textblock"><p>The implementation of <a href="https://en.wikipedia.org/wiki/Hamiltonian_path" target="_blank">Hamilton's cycle</a> dynamic solution for vertices number less than 20. </p>
<p>I use \(2^n\times n\) matrix and for every \([i, j]\) ( \(i &lt; 2^n\) and \(j &lt; n\)) in the matrix I store <code>true</code> if it is possible to get to all vertices on which position in <code>i</code>'s binary representation is <code>1</code> so as \(j\) would be the last one.</p>
<p>In the the end if any cell in \((2^n - 1)^{\mbox{th}}\) row is <code>true</code> there exists hamiltonian cycle.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/vakhokoto" target="_blank">vakhokoto</a> </dd>
<dd>
<a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
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<p >The function determines if there is a hamilton's cycle in the graph</p>
<p>The function determines if there is a hamilton's cycle in the graph</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">routes</td><td>nxn boolean matrix of \([i, j]\) where \([i, j]\) is <code>true</code> if there is a road from \(i\) to \(j\) </td></tr>
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<p >Main function</p>
<p>Main function</p>
<dl class="params"><dt>Parameters</dt><dd>
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<p >this test is testing if <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp.html#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <code>true</code> for graph: <code>1 -&gt; 2 -&gt; 3 -&gt; 4</code> </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
<p>this test is testing if <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp.html#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <code>true</code> for graph: <code>1 -&gt; 2 -&gt; 3 -&gt; 4</code> </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
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<div class="line"><span class="lineno"> 82</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;bool&gt;</a>&gt; arr{</div>
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<p >this test is testing if <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp.html#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <code>false</code> for <br />
<p>this test is testing if <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp.html#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <code>false</code> for <br />
graph:</p><pre>
1 -&gt; 2 -&gt; 3
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<p >this test is testing if <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp.html#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <code>true</code> for clique with 4 vertices </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
<p>this test is testing if <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp.html#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <code>true</code> for clique with 4 vertices </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
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<tr class="memitem:a78cb2f3b97b6db2c062b2a1df05c9ea9"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a> (T *arr, int n)</td></tr>
<tr class="memdesc:a78cb2f3b97b6db2c062b2a1df05c9ea9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insertion Sort Function. <a href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">More...</a><br /></td></tr>
<tr class="memdesc:a78cb2f3b97b6db2c062b2a1df05c9ea9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insertion Sort Function. <br /></td></tr>
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<tr class="memitem:a8fe6bac9e03f58abcc2ce26ef3de1b5f"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#a8fe6bac9e03f58abcc2ce26ef3de1b5f">sorting::insertionSort</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; *arr)</td></tr>
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<tr class="memitem:a59914553f24088342c139645a02a8a49"><td class="memTemplItemLeft" align="right" valign="top">static void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d0d/insertion__sort_8cpp.html#a59914553f24088342c139645a02a8a49">create_random_array</a> (T *arr, int N)</td></tr>
<tr class="memdesc:a59914553f24088342c139645a02a8a49"><td class="mdescLeft">&#160;</td><td class="mdescRight">Create a random array objecthelper function to create a random array. <a href="../../dd/d0d/insertion__sort_8cpp.html#a59914553f24088342c139645a02a8a49">More...</a><br /></td></tr>
<tr class="memdesc:a59914553f24088342c139645a02a8a49"><td class="mdescLeft">&#160;</td><td class="mdescRight">Create a random array objecthelper function to create a random array. <br /></td></tr>
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<tr class="memitem:a88ec9ad42717780d6caaff9d3d6977f9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d0d/insertion__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Insertion_sort" target="_blank">Insertion Sort Algorithm (Insertion Sort)</a> </p>
<p >Insertion sort is a simple sorting algorithm that builds the final sorted array one at a time. It is much less efficient compared to other sorting algorithms like heap sort, merge sort or quick sort. However it has several advantages such as</p><ol type="1">
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Insertion_sort" target="_blank">Insertion Sort Algorithm (Insertion Sort)</a> </p>
<p>Insertion sort is a simple sorting algorithm that builds the final sorted array one at a time. It is much less efficient compared to other sorting algorithms like heap sort, merge sort or quick sort. However it has several advantages such as</p><ol type="1">
<li>Easy to implement</li>
<li>For small set of data it is quite efficient</li>
<li>More efficient that other Quadratic complexity algorithms like Selection sort or bubble sort.</li>
<li>It's stable that is it does not change the relative order of elements with equal keys</li>
<li>Works on hand means it can sort the array or list as it receives.</li>
</ol>
<p >It is based on the same idea that people use to sort the playing cards in their hands. the algorithms goes in the manner that we start iterating over the array of elements as soon as we find a unsorted element that is a misplaced element we place it at a sorted position.</p>
<p >Example execution steps:</p><ol type="1">
<p>It is based on the same idea that people use to sort the playing cards in their hands. the algorithms goes in the manner that we start iterating over the array of elements as soon as we find a unsorted element that is a misplaced element we place it at a sorted position.</p>
<p>Example execution steps:</p><ol type="1">
<li>Suppose initially we have <p class="formulaDsp">
\begin{bmatrix}4 &amp;3 &amp;2 &amp;5 &amp;1\end{bmatrix}
</p>
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<p >Main Function </p>
<p >Running predefined tests to test algorithm</p>
<p >For user insteraction</p>
<p>Main Function </p>
<p>Running predefined tests to test algorithm</p>
<p>For user insteraction</p>
<div class="fragment"><div class="line"><span class="lineno"> 150</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 151</span><span class="comment"> /// Running predefined tests to test algorithm</span></div>
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<p >Test Cases to test algorithm </p>
<p>Test Cases to test algorithm </p>
<div class="fragment"><div class="line"><span class="lineno"> 109</span> {</div>
<div class="line"><span class="lineno"> 110</span> <span class="keywordtype">int</span> arr1[10] = {78, 34, 35, 6, 34, 56, 3, 56, 2, 4};</div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implementation of <a href="https://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher" target="_blank">Vigenère cipher</a> algorithm. </p>
<p >The Vigenère cipher is a method of encrypting alphabetic text by using a series of interwoven vigenere ciphers, based on the letters of a keyword. It employs a form of polyalphabetic substitution.</p>
<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher" target="_blank">Vigenère cipher</a> algorithm. </p>
<p>The Vigenère cipher is a method of encrypting alphabetic text by using a series of interwoven vigenere ciphers, based on the letters of a keyword. It employs a form of polyalphabetic substitution.</p>
<h3><a class="anchor" id="autotoc_md2"></a>
Algorithm</h3>
<p >The encryption can also be represented using modular arithmetic by first transforming the letters into numbers, according to the scheme, A → 0, B → 1, ..., Z → 25. Encryption of \(i^{th}\) character in Message M by key K can be described mathematically as,</p>
<p>The encryption can also be represented using modular arithmetic by first transforming the letters into numbers, according to the scheme, A → 0, B → 1, ..., Z → 25. Encryption of \(i^{th}\) character in Message M by key K can be described mathematically as,</p>
<p class="formulaDsp">
\[ E_{K}(M_{i}) = (M_{i} + K_{i})\;\mbox{mod}\; 26\]
</p>
<p >while decryption of \(i^{th}\) character in Cipher C by key K can be described mathematically as,</p>
<p>while decryption of \(i^{th}\) character in Cipher C by key K can be described mathematically as,</p>
<p class="formulaDsp">
\[ D_{k}(C_{i}) = (C_{i} - K_{i} + 26)\;\mbox{mod}\; 26\]
</p>
<p >Where \(K_{i}\) denotes corresponding character in key. If \(|key| &lt; |text|\) than same key is repeated untill their lengths are equal.</p>
<p >For Example, If M = "ATTACKATDAWN" and K = "LEMON" than K becomes "LEMONLEMONLE".</p>
<p>Where \(K_{i}\) denotes corresponding character in key. If \(|key| &lt; |text|\) than same key is repeated untill their lengths are equal.</p>
<p>For Example, If M = "ATTACKATDAWN" and K = "LEMON" than K becomes "LEMONLEMONLE".</p>
<dl class="section note"><dt>Note</dt><dd>Rather than creating new key of equal length this program does this by using modular index for key (i.e. \((j + 1) \;\mbox{mod}\; |\mbox{key}|\))</dd>
<dd>
This program implements Vigenère cipher for only uppercase English alphabet characters (i.e. A-Z).</dd></dl>
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<p >Decrypt given text using vigenere cipher. </p><dl class="params"><dt>Parameters</dt><dd>
<p>Decrypt given text using vigenere cipher. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
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<tr><td class="paramname">key</td><td>key to be used for decryption </td></tr>
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<p >Encrypt given text using vigenere cipher. </p><dl class="params"><dt>Parameters</dt><dd>
<p>Encrypt given text using vigenere cipher. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
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<p >Driver Code </p>
<p>Driver Code </p>
<div class="fragment"><div class="line"><span class="lineno"> 131</span> {</div>
<div class="line"><span class="lineno"> 132</span> <span class="comment">// Testing</span></div>
<div class="line"><span class="lineno"> 133</span> <a class="code hl_function" href="../../dd/d12/vigenere__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
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<p >Function to test above algorithm </p>
<p>Function to test above algorithm </p>
<div class="fragment"><div class="line"><span class="lineno"> 111</span> {</div>
<div class="line"><span class="lineno"> 112</span> <span class="comment">// Test 1</span></div>
<div class="line"><span class="lineno"> 113</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text1 = <span class="stringliteral">&quot;NIKOLATESLA&quot;</span>;</div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
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<tr class="memdesc:a80c8b902a15b4fd062ed727ecf8f3595"><td class="mdescLeft">&#160;</td><td class="mdescRight">Construct a new chain object. <a href="../../dd/d1c/classhash__chain.html#a80c8b902a15b4fd062ed727ecf8f3595">More...</a><br /></td></tr>
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<tr class="memdesc:a6b4b4de1a8c96f98a63a77f650a9dcff"><td class="mdescLeft">&#160;</td><td class="mdescRight">create and add a new node with a give value and at a given height <a href="../../dd/d1c/classhash__chain.html#a6b4b4de1a8c96f98a63a77f650a9dcff">More...</a><br /></td></tr>
<tr class="memdesc:a6b4b4de1a8c96f98a63a77f650a9dcff"><td class="mdescLeft">&#160;</td><td class="mdescRight">create and add a new node with a give value and at a given height <br /></td></tr>
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<tr class="memitem:a706964ad13587fc9a8b3fe8381d410ed"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1c/classhash__chain.html#a706964ad13587fc9a8b3fe8381d410ed">display</a> ()</td></tr>
<tr class="memdesc:a706964ad13587fc9a8b3fe8381d410ed"><td class="mdescLeft">&#160;</td><td class="mdescRight">Display the chain. <a href="../../dd/d1c/classhash__chain.html#a706964ad13587fc9a8b3fe8381d410ed">More...</a><br /></td></tr>
<tr class="memdesc:a706964ad13587fc9a8b3fe8381d410ed"><td class="mdescLeft">&#160;</td><td class="mdescRight">Display the chain. <br /></td></tr>
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<tr class="memitem:a846a2f921f8fb7ea572e03901b671d64"><td class="memItemLeft" align="right" valign="top">virtual int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1c/classhash__chain.html#a846a2f921f8fb7ea572e03901b671d64">hash</a> (int x) const</td></tr>
<tr class="memdesc:a846a2f921f8fb7ea572e03901b671d64"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute the hash of a value for current chain. <a href="../../dd/d1c/classhash__chain.html#a846a2f921f8fb7ea572e03901b671d64">More...</a><br /></td></tr>
<tr class="memdesc:a846a2f921f8fb7ea572e03901b671d64"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute the hash of a value for current chain. <br /></td></tr>
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<tr class="memdesc:a55aa5c6753cb8853152d469c375d946a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Find if a value and corresponding hash exist. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Chain class with a given modulus. </p>
<div class="textblock"><p>Chain class with a given modulus. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a126e3002a464e53cd54b07ba56482a72"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#a126e3002a464e53cd54b07ba56482a72">dsu</a> (uint64_t n)</td></tr>
<tr class="memdesc:a126e3002a464e53cd54b07ba56482a72"><td class="mdescLeft">&#160;</td><td class="mdescRight">contructor for initialising all data members. <a href="../../dd/d1f/classdsu.html#a126e3002a464e53cd54b07ba56482a72">More...</a><br /></td></tr>
<tr class="memdesc:a126e3002a464e53cd54b07ba56482a72"><td class="mdescLeft">&#160;</td><td class="mdescRight">contructor for initialising all data members. <br /></td></tr>
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<tr class="memitem:a16851f78fe390fc1430905c83d6a2f1c"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a> (uint64_t i)</td></tr>
<tr class="memdesc:a16851f78fe390fc1430905c83d6a2f1c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Method to find the representative of the set to which i belongs to, T(n) = O(1) <a href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">More...</a><br /></td></tr>
<tr class="memdesc:a16851f78fe390fc1430905c83d6a2f1c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Method to find the representative of the set to which i belongs to, T(n) = O(1) <br /></td></tr>
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<tr class="memitem:a6ac30c07abca2aaa3b291504c25c3559"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#a6ac30c07abca2aaa3b291504c25c3559">UnionSet</a> (uint64_t i, uint64_t j)</td></tr>
<tr class="memdesc:a6ac30c07abca2aaa3b291504c25c3559"><td class="mdescLeft">&#160;</td><td class="mdescRight">Method that combines two disjoint sets to which i and j belongs to and make a single set having a common representative. <a href="../../dd/d1f/classdsu.html#a6ac30c07abca2aaa3b291504c25c3559">More...</a><br /></td></tr>
<tr class="memdesc:a6ac30c07abca2aaa3b291504c25c3559"><td class="mdescLeft">&#160;</td><td class="mdescRight">Method that combines two disjoint sets to which i and j belongs to and make a single set having a common representative. <br /></td></tr>
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<tr class="memitem:a64d25c5986742f7c234ed449b2ff7303"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303">isSame</a> (uint64_t i, uint64_t j)</td></tr>
<tr class="memdesc:a64d25c5986742f7c234ed449b2ff7303"><td class="mdescLeft">&#160;</td><td class="mdescRight">A utility function which check whether i and j belongs to same set or not. <a href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303">More...</a><br /></td></tr>
<tr class="memdesc:a64d25c5986742f7c234ed449b2ff7303"><td class="mdescLeft">&#160;</td><td class="mdescRight">A utility function which check whether i and j belongs to same set or not. <br /></td></tr>
<tr class="separator:a64d25c5986742f7c234ed449b2ff7303"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0ce2672c570f4235eafddb0c9a58115a"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt; uint64_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#a0ce2672c570f4235eafddb0c9a58115a">get</a> (uint64_t i)</td></tr>
<tr class="memdesc:a0ce2672c570f4235eafddb0c9a58115a"><td class="mdescLeft">&#160;</td><td class="mdescRight">prints the minimum, maximum and size of the set to which i belongs to <a href="../../dd/d1f/classdsu.html#a0ce2672c570f4235eafddb0c9a58115a">More...</a><br /></td></tr>
<tr class="memdesc:a0ce2672c570f4235eafddb0c9a58115a"><td class="mdescLeft">&#160;</td><td class="mdescRight">prints the minimum, maximum and size of the set to which i belongs to <br /></td></tr>
<tr class="separator:a0ce2672c570f4235eafddb0c9a58115a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1c24228b0f2f49220133fb8c3566a55c"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#a1c24228b0f2f49220133fb8c3566a55c">size</a> (uint64_t i)</td></tr>
<tr class="memdesc:a1c24228b0f2f49220133fb8c3566a55c"><td class="mdescLeft">&#160;</td><td class="mdescRight">A utility function that returns the size of the set to which i belongs to. <a href="../../dd/d1f/classdsu.html#a1c24228b0f2f49220133fb8c3566a55c">More...</a><br /></td></tr>
<tr class="memdesc:a1c24228b0f2f49220133fb8c3566a55c"><td class="mdescLeft">&#160;</td><td class="mdescRight">A utility function that returns the size of the set to which i belongs to. <br /></td></tr>
<tr class="separator:a1c24228b0f2f49220133fb8c3566a55c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a696141b8b092466767f4bfe1c5e46cde"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#a696141b8b092466767f4bfe1c5e46cde">get_max</a> (uint64_t i)</td></tr>
<tr class="memdesc:a696141b8b092466767f4bfe1c5e46cde"><td class="mdescLeft">&#160;</td><td class="mdescRight">A utility function that returns the max element of the set to which i belongs to. <a href="../../dd/d1f/classdsu.html#a696141b8b092466767f4bfe1c5e46cde">More...</a><br /></td></tr>
<tr class="memdesc:a696141b8b092466767f4bfe1c5e46cde"><td class="mdescLeft">&#160;</td><td class="mdescRight">A utility function that returns the max element of the set to which i belongs to. <br /></td></tr>
<tr class="separator:a696141b8b092466767f4bfe1c5e46cde"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac713a5b496d0405c82e2808a85e58415"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#ac713a5b496d0405c82e2808a85e58415">get_min</a> (uint64_t i)</td></tr>
<tr class="memdesc:ac713a5b496d0405c82e2808a85e58415"><td class="mdescLeft">&#160;</td><td class="mdescRight">A utility function that returns the min element of the set to which i belongs to. <a href="../../dd/d1f/classdsu.html#ac713a5b496d0405c82e2808a85e58415">More...</a><br /></td></tr>
<tr class="memdesc:ac713a5b496d0405c82e2808a85e58415"><td class="mdescLeft">&#160;</td><td class="mdescRight">A utility function that returns the min element of the set to which i belongs to. <br /></td></tr>
<tr class="separator:ac713a5b496d0405c82e2808a85e58415"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a126e3002a464e53cd54b07ba56482a72"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#a126e3002a464e53cd54b07ba56482a72">dsu</a> (uint64_t n)</td></tr>
<tr class="memdesc:a126e3002a464e53cd54b07ba56482a72"><td class="mdescLeft">&#160;</td><td class="mdescRight">constructor for initialising all data members <a href="../../dd/d1f/classdsu.html#a126e3002a464e53cd54b07ba56482a72">More...</a><br /></td></tr>
<tr class="memdesc:a126e3002a464e53cd54b07ba56482a72"><td class="mdescLeft">&#160;</td><td class="mdescRight">constructor for initialising all data members <br /></td></tr>
<tr class="separator:a126e3002a464e53cd54b07ba56482a72"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a16851f78fe390fc1430905c83d6a2f1c"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a> (uint64_t i)</td></tr>
<tr class="memdesc:a16851f78fe390fc1430905c83d6a2f1c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Method to find the representative of the set to which i belongs to, T(n) = O(logN) <a href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">More...</a><br /></td></tr>
<tr class="memdesc:a16851f78fe390fc1430905c83d6a2f1c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Method to find the representative of the set to which i belongs to, T(n) = O(logN) <br /></td></tr>
<tr class="separator:a16851f78fe390fc1430905c83d6a2f1c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a81897528bdb53fd5e796d75d7dbc430f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a> (uint64_t i, uint64_t j)</td></tr>
<tr class="memdesc:a81897528bdb53fd5e796d75d7dbc430f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Method that combines two disjoint sets to which i and j belongs to and make a single set having a common representative. <a href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">More...</a><br /></td></tr>
<tr class="memdesc:a81897528bdb53fd5e796d75d7dbc430f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Method that combines two disjoint sets to which i and j belongs to and make a single set having a common representative. <br /></td></tr>
<tr class="separator:a81897528bdb53fd5e796d75d7dbc430f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a64d25c5986742f7c234ed449b2ff7303"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303">isSame</a> (uint64_t i, uint64_t j)</td></tr>
<tr class="memdesc:a64d25c5986742f7c234ed449b2ff7303"><td class="mdescLeft">&#160;</td><td class="mdescRight">A utility function which check whether i and j belongs to same set or not. <a href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303">More...</a><br /></td></tr>
<tr class="memdesc:a64d25c5986742f7c234ed449b2ff7303"><td class="mdescLeft">&#160;</td><td class="mdescRight">A utility function which check whether i and j belongs to same set or not. <br /></td></tr>
<tr class="separator:a64d25c5986742f7c234ed449b2ff7303"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab8ee27083a3c2e2df80755165a2ec280"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt; uint64_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html#ab8ee27083a3c2e2df80755165a2ec280">getParents</a> (uint64_t i)</td></tr>
<tr class="memdesc:ab8ee27083a3c2e2df80755165a2ec280"><td class="mdescLeft">&#160;</td><td class="mdescRight">Method to print all the parents of i, or the path from i to representative. <a href="../../dd/d1f/classdsu.html#ab8ee27083a3c2e2df80755165a2ec280">More...</a><br /></td></tr>
<tr class="memdesc:ab8ee27083a3c2e2df80755165a2ec280"><td class="mdescLeft">&#160;</td><td class="mdescRight">Method to print all the parents of i, or the path from i to representative. <br /></td></tr>
<tr class="separator:ab8ee27083a3c2e2df80755165a2ec280"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pri-attribs" name="pri-attribs"></a>
@@ -180,7 +180,7 @@ Private Attributes</h2></td></tr>
<tr class="separator:a1d77aad7fc39fe7140d834cd347e5c63"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Disjoint sets union data structure, class based representation. </p>
<div class="textblock"><p>Disjoint sets union data structure, class based representation. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>number of elements </td></tr>
@@ -219,9 +219,9 @@ Private Attributes</h2></td></tr>
</table>
</dd>
</dl>
<p >initially, all of them are their own parents</p>
<p >initially all have depth are equals to zero</p>
<p >initially set size will be equals to one</p>
<p>initially, all of them are their own parents</p>
<p>initially all have depth are equals to zero</p>
<p>initially set size will be equals to one</p>
<div class="fragment"><div class="line"><span class="lineno"> 45</span> {</div>
<div class="line"><span class="lineno"> 46</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(n, 0);<span class="comment"></span></div>
<div class="line"><span class="lineno"> 47</span><span class="comment"> /// initially, all of them are their own parents</span></div>
@@ -289,7 +289,7 @@ Here is the call graph for this function:</div>
</table>
</dd>
</dl>
<p >initially all of them are their own parents</p>
<p>initially all of them are their own parents</p>
<div class="fragment"><div class="line"><span class="lineno"> 44</span> {</div>
<div class="line"><span class="lineno"> 45</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(n, 0);<span class="comment"></span></div>
<div class="line"><span class="lineno"> 46</span><span class="comment"> /// initially all of them are their own parents</span></div>
@@ -343,7 +343,7 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>representative of the set to which i belongs to. </dd></dl>
<p >using path compression</p>
<p>using path compression</p>
<div class="fragment"><div class="line"><span class="lineno"> 73</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 74</span><span class="comment"> /// using path compression</span></div>
<div class="line"><span class="lineno"> 75</span><span class="comment"></span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] == i) {</div>
@@ -393,7 +393,7 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>representative of the set to which i belongs to </dd></dl>
<p >using union-rank</p>
<p>using union-rank</p>
<div class="fragment"><div class="line"><span class="lineno"> 61</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 62</span><span class="comment"> /// using union-rank</span></div>
<div class="line"><span class="lineno"> 63</span><span class="comment"></span> <span class="keywordflow">while</span> (i != <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i]) {</div>
@@ -789,12 +789,12 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p >check if both belongs to the same set or not</p>
<p >always keeping the min as x shallow tree</p>
<p >making the shallower root's parent the deeper root</p>
<p >if same depth, then increase one's depth</p>
<p >total size of the resultant set</p>
<p >changing the maximum elements</p>
<p>check if both belongs to the same set or not</p>
<p>always keeping the min as x shallow tree</p>
<p>making the shallower root's parent the deeper root</p>
<p>if same depth, then increase one's depth</p>
<p>total size of the resultant set</p>
<p>changing the maximum elements</p>
<div class="fragment"><div class="line"><span class="lineno"> 87</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 88</span><span class="comment"> /// check if both belongs to the same set or not</span></div>
<div class="line"><span class="lineno"> 89</span><span class="comment"></span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303">isSame</a>(i, j)) {</div>
@@ -879,12 +879,12 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p >checks if both belongs to same set or not</p>
<p >we find representative of the i and j</p>
<p >always keeping the min as x in order to create a shallow tree</p>
<p >making the shallower tree, root parent of the deeper root</p>
<p >if same depth, then increase one's depth</p>
<p >total size of the resultant set</p>
<p>checks if both belongs to same set or not</p>
<p>we find representative of the i and j</p>
<p>always keeping the min as x in order to create a shallow tree</p>
<p>making the shallower tree, root parent of the deeper root</p>
<p>if same depth, then increase one's depth</p>
<p>total size of the resultant set</p>
<div class="fragment"><div class="line"><span class="lineno"> 75</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 76</span><span class="comment"> /// checks if both belongs to same set or not</span></div>
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<div class="textblock"><p >Dynamic Programming algorithms. </p>
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<tr class="memitem:a85a6ec58b5064d63d4f0df3854496713"><td class="memItemLeft" align="right" valign="top">static float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a> (float x)</td></tr>
<tr class="memdesc:a85a6ec58b5064d63d4f0df3854496713"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function gives the value of f(x) for given x. <a href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">More...</a><br /></td></tr>
<tr class="memdesc:a85a6ec58b5064d63d4f0df3854496713"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function gives the value of f(x) for given x. <br /></td></tr>
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<tr class="memdesc:a7d69b49dc37da1c02b3ab8c7fe783494"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function finds root of the equation in given interval i.e. (x1,x2). <a href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">More...</a><br /></td></tr>
<tr class="memdesc:a7d69b49dc37da1c02b3ab8c7fe783494"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function finds root of the equation in given interval i.e. (x1,x2). <br /></td></tr>
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<tr class="memdesc:a85cb7bfb90abc898e042d624372c5345"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function prints roots of the equation. <a href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">More...</a><br /></td></tr>
<tr class="memdesc:a85cb7bfb90abc898e042d624372c5345"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function prints roots of the equation. <br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../dd/d29/false__position_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Regula_falsi" target="_blank">false position method</a>, also known as the Secant method. </p>
<p >First, multiple intervals are selected with the interval gap provided. Separate recursive function called for every root. Roots are printed Separatelt.</p>
<p >For an interval [a,b] \(a\) and \(b\) such that \(f(a)&lt;0\) and \(f(b)&gt;0\), then the \((i+1)^\text{th}\) approximation is given by: </p><p class="formulaDsp">
<div class="textblock"><p>Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Regula_falsi" target="_blank">false position method</a>, also known as the Secant method. </p>
<p>First, multiple intervals are selected with the interval gap provided. Separate recursive function called for every root. Roots are printed Separatelt.</p>
<p>For an interval [a,b] \(a\) and \(b\) such that \(f(a)&lt;0\) and \(f(b)&gt;0\), then the \((i+1)^\text{th}\) approximation is given by: </p><p class="formulaDsp">
\[
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@@ -123,7 +123,7 @@ Classes</h2></td></tr>
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<tr class="memitem:a6af57e9f25d0d0a2d59eea5a4a802908"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d2f/class_trie.html#a6af57e9f25d0d0a2d59eea5a4a802908">Trie</a> ()</td></tr>
<tr class="memdesc:a6af57e9f25d0d0a2d59eea5a4a802908"><td class="mdescLeft">&#160;</td><td class="mdescRight">constructor to initialise the root of the trie. <a href="../../dd/d2f/class_trie.html#a6af57e9f25d0d0a2d59eea5a4a802908">More...</a><br /></td></tr>
<tr class="memdesc:a6af57e9f25d0d0a2d59eea5a4a802908"><td class="mdescLeft">&#160;</td><td class="mdescRight">constructor to initialise the root of the trie. <br /></td></tr>
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<tr class="memitem:afd8b79959009b554e98ea7128b2886f2"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d2f/class_trie.html#afd8b79959009b554e98ea7128b2886f2">insert</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;word)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >A basic implementation of trie class to store only lower-case strings. You can extend the implementation to all the ASCII characters by changing the value of @ ALPHABETS to 128. </p>
<div class="textblock"><p>A basic implementation of trie class to store only lower-case strings. You can extend the implementation to all the ASCII characters by changing the value of @ ALPHABETS to 128. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="a6af57e9f25d0d0a2d59eea5a4a802908" name="a6af57e9f25d0d0a2d59eea5a4a802908"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a6af57e9f25d0d0a2d59eea5a4a802908">&#9670;&#160;</a></span>Trie()</h2>
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<p >Function to check if a node has some children which can form words. </p><dl class="params"><dt>Parameters</dt><dd>
<p>Function to check if a node has some children which can form words. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">node</td><td>whose character array of pointers need to be checked for children. </td></tr>
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</tr>
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<p >Insert a word into the trie. </p><dl class="params"><dt>Parameters</dt><dd>
<p>Insert a word into the trie. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">word</td><td>which needs to be inserted into the string. </td></tr>
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</tr>
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<p >A recursive helper function to remove a word from the trie. First, it recursively traverses to the location of last character of word in the trie. However, if the word is not found, the function returns a runtime error. Upon successfully reaching the last character of word in trie, if sets the isEndOfWord to false and deletes the node if and only if it has no children, else it returns the current node. </p><dl class="params"><dt>Parameters</dt><dd>
<p>A recursive helper function to remove a word from the trie. First, it recursively traverses to the location of last character of word in the trie. However, if the word is not found, the function returns a runtime error. Upon successfully reaching the last character of word in trie, if sets the isEndOfWord to false and deletes the node if and only if it has no children, else it returns the current node. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">word</td><td>is the string which needs to be removed from trie. </td></tr>
<tr><td class="paramname">curr</td><td>is the current node we are at. </td></tr>
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</tr>
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<p >Search if a word is present in trie or not. </p><dl class="params"><dt>Parameters</dt><dd>
<p>Search if a word is present in trie or not. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">word</td><td>which is needed to be searched in the trie. </td></tr>
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@@ -467,7 +467,7 @@ False if word is not found in trie or isEndOfWord is set to false. </dd></dl>
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<li class="navelem"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></li>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
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<tr class="memdesc:ad5219979ea9a8baa3a273a9ec0f0c670"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html" title="2-3-4 tree node class">Node</a> constructor. <br /></td></tr>
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<tr class="memdesc:aac82e17daa088ede9ee00dc69c1e6f06"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the item count that current saved in the node. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#aac82e17daa088ede9ee00dc69c1e6f06">More...</a><br /></td></tr>
<tr class="memdesc:aac82e17daa088ede9ee00dc69c1e6f06"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the item count that current saved in the node. <br /></td></tr>
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<tr class="memdesc:af564fd4b0992fff69f90de201542d3d1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set the item count of the node. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#af564fd4b0992fff69f90de201542d3d1">More...</a><br /></td></tr>
<tr class="memdesc:af564fd4b0992fff69f90de201542d3d1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set the item count of the node. <br /></td></tr>
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<tr class="memdesc:a607d8201b00b142bf1d6a34df2f936e8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Check if node is a leaf. <br /></td></tr>
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<tr class="memdesc:a4a37381c0ef93d5ae2118b2e554974dd"><td class="mdescLeft">&#160;</td><td class="mdescRight">Check if node is a full (4-node) <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a4a37381c0ef93d5ae2118b2e554974dd">More...</a><br /></td></tr>
<tr class="memdesc:a4a37381c0ef93d5ae2118b2e554974dd"><td class="mdescLeft">&#160;</td><td class="mdescRight">Check if node is a full (4-node) <br /></td></tr>
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<tr class="memdesc:afd9f83e2d5d7f22f79c1348e98914631"><td class="mdescLeft">&#160;</td><td class="mdescRight">Check if node is a 2-node. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#afd9f83e2d5d7f22f79c1348e98914631">More...</a><br /></td></tr>
<tr class="memdesc:afd9f83e2d5d7f22f79c1348e98914631"><td class="mdescLeft">&#160;</td><td class="mdescRight">Check if node is a 2-node. <br /></td></tr>
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<tr class="memdesc:a6c5f929afcbad5219646990edee22e18"><td class="mdescLeft">&#160;</td><td class="mdescRight">Check if node is a 3-node or 4-node, this is useful when we delete item from 2-3-4 tree. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a6c5f929afcbad5219646990edee22e18">More...</a><br /></td></tr>
<tr class="memdesc:a6c5f929afcbad5219646990edee22e18"><td class="mdescLeft">&#160;</td><td class="mdescRight">Check if node is a 3-node or 4-node, this is useful when we delete item from 2-3-4 tree. <br /></td></tr>
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<tr class="memitem:a22fd25c6c811c64b6b27b0850d8c532f"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a22fd25c6c811c64b6b27b0850d8c532f">Contains</a> (int64_t item)</td></tr>
<tr class="memdesc:a22fd25c6c811c64b6b27b0850d8c532f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Check if item is in the node. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a22fd25c6c811c64b6b27b0850d8c532f">More...</a><br /></td></tr>
<tr class="memdesc:a22fd25c6c811c64b6b27b0850d8c532f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Check if item is in the node. <br /></td></tr>
<tr class="separator:a22fd25c6c811c64b6b27b0850d8c532f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a650f0ef26b7450e1addb5d80bb0ed629"><td class="memItemLeft" align="right" valign="top">int8_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a650f0ef26b7450e1addb5d80bb0ed629">GetItemIndex</a> (int64_t item)</td></tr>
<tr class="memdesc:a650f0ef26b7450e1addb5d80bb0ed629"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the index of the item in the node, 0-based. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a650f0ef26b7450e1addb5d80bb0ed629">More...</a><br /></td></tr>
<tr class="memdesc:a650f0ef26b7450e1addb5d80bb0ed629"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the index of the item in the node, 0-based. <br /></td></tr>
<tr class="separator:a650f0ef26b7450e1addb5d80bb0ed629"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2753b6053b8c86c5bd987a44fdfa0a57"><td class="memItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a2753b6053b8c86c5bd987a44fdfa0a57">GetMaxItem</a> ()</td></tr>
<tr class="memdesc:a2753b6053b8c86c5bd987a44fdfa0a57"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get max item (rightmost) in the current node. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a2753b6053b8c86c5bd987a44fdfa0a57">More...</a><br /></td></tr>
<tr class="memdesc:a2753b6053b8c86c5bd987a44fdfa0a57"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get max item (rightmost) in the current node. <br /></td></tr>
<tr class="separator:a2753b6053b8c86c5bd987a44fdfa0a57"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5438d0a47850f520b2262b5a42f75b71"><td class="memItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a5438d0a47850f520b2262b5a42f75b71">GetMinItem</a> ()</td></tr>
<tr class="memdesc:a5438d0a47850f520b2262b5a42f75b71"><td class="mdescLeft">&#160;</td><td class="mdescRight">get min item (leftmost) in the current node <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a5438d0a47850f520b2262b5a42f75b71">More...</a><br /></td></tr>
<tr class="memdesc:a5438d0a47850f520b2262b5a42f75b71"><td class="mdescLeft">&#160;</td><td class="mdescRight">get min item (leftmost) in the current node <br /></td></tr>
<tr class="separator:a5438d0a47850f520b2262b5a42f75b71"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4808acb43668ff8cfd6f7cb44ceedad3"><td class="memItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a4808acb43668ff8cfd6f7cb44ceedad3">GetItem</a> (int8_t index)</td></tr>
<tr class="memdesc:a4808acb43668ff8cfd6f7cb44ceedad3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get item of the \index index. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a4808acb43668ff8cfd6f7cb44ceedad3">More...</a><br /></td></tr>
<tr class="memdesc:a4808acb43668ff8cfd6f7cb44ceedad3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get item of the \index index. <br /></td></tr>
<tr class="separator:a4808acb43668ff8cfd6f7cb44ceedad3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aaa89a3016b5dd1be3552321c34343cbc"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#aaa89a3016b5dd1be3552321c34343cbc">SetItem</a> (int8_t index, int64_t new_item)</td></tr>
<tr class="memdesc:aaa89a3016b5dd1be3552321c34343cbc"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set item value at position of index. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#aaa89a3016b5dd1be3552321c34343cbc">More...</a><br /></td></tr>
<tr class="memdesc:aaa89a3016b5dd1be3552321c34343cbc"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set item value at position of index. <br /></td></tr>
<tr class="separator:aaa89a3016b5dd1be3552321c34343cbc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8e809ae85ae00e937f67ddb76951b6bb"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8e809ae85ae00e937f67ddb76951b6bb">InsertItem</a> (int item)</td></tr>
<tr class="memdesc:a8e809ae85ae00e937f67ddb76951b6bb"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insert item to the proper position of the node and return the position index. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a8e809ae85ae00e937f67ddb76951b6bb">More...</a><br /></td></tr>
<tr class="memdesc:a8e809ae85ae00e937f67ddb76951b6bb"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insert item to the proper position of the node and return the position index. <br /></td></tr>
<tr class="separator:a8e809ae85ae00e937f67ddb76951b6bb"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a306a30931f54c84098b38d6bc8f4a956"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a306a30931f54c84098b38d6bc8f4a956">InsertItemByIndex</a> (int8_t index, int64_t item, <a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html">Node</a> *with_child, bool to_left=true)</td></tr>
<tr class="memdesc:a306a30931f54c84098b38d6bc8f4a956"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insert a value to the index position. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a306a30931f54c84098b38d6bc8f4a956">More...</a><br /></td></tr>
<tr class="memdesc:a306a30931f54c84098b38d6bc8f4a956"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insert a value to the index position. <br /></td></tr>
<tr class="separator:a306a30931f54c84098b38d6bc8f4a956"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a28944bb16ec22650b47fe3e80e3e13f8"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a28944bb16ec22650b47fe3e80e3e13f8">RemoveItemByIndex</a> (int8_t index, bool keep_left)</td></tr>
<tr class="memdesc:a28944bb16ec22650b47fe3e80e3e13f8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insert a value to the index position. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a28944bb16ec22650b47fe3e80e3e13f8">More...</a><br /></td></tr>
<tr class="memdesc:a28944bb16ec22650b47fe3e80e3e13f8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insert a value to the index position. <br /></td></tr>
<tr class="separator:a28944bb16ec22650b47fe3e80e3e13f8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad632a0440295bc88ceadae7478fe0d37"><td class="memItemLeft" align="right" valign="top">int8_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad632a0440295bc88ceadae7478fe0d37">GetChildIndex</a> (<a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html">Node</a> *child)</td></tr>
<tr class="memdesc:ad632a0440295bc88ceadae7478fe0d37"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the child's index of the children array. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ad632a0440295bc88ceadae7478fe0d37">More...</a><br /></td></tr>
<tr class="memdesc:ad632a0440295bc88ceadae7478fe0d37"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the child's index of the children array. <br /></td></tr>
<tr class="separator:ad632a0440295bc88ceadae7478fe0d37"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a164574a9209b5df66368530d090b32c4"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a164574a9209b5df66368530d090b32c4">GetChild</a> (int8_t index)</td></tr>
<tr class="memdesc:a164574a9209b5df66368530d090b32c4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the child pointer at position of index. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a164574a9209b5df66368530d090b32c4">More...</a><br /></td></tr>
<tr class="memdesc:a164574a9209b5df66368530d090b32c4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the child pointer at position of index. <br /></td></tr>
<tr class="separator:a164574a9209b5df66368530d090b32c4"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab4e5f7b7b260bb81d9441652cc124c74"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ab4e5f7b7b260bb81d9441652cc124c74">SetChild</a> (int8_t index, <a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html">Node</a> *child)</td></tr>
<tr class="memdesc:ab4e5f7b7b260bb81d9441652cc124c74"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set child pointer to the position of index. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ab4e5f7b7b260bb81d9441652cc124c74">More...</a><br /></td></tr>
<tr class="memdesc:ab4e5f7b7b260bb81d9441652cc124c74"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set child pointer to the position of index. <br /></td></tr>
<tr class="separator:ab4e5f7b7b260bb81d9441652cc124c74"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a731f9ae385840cf0a06d55e7f9924a94"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a731f9ae385840cf0a06d55e7f9924a94">GetRightmostChild</a> ()</td></tr>
<tr class="memdesc:a731f9ae385840cf0a06d55e7f9924a94"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get rightmose child of the current node. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a731f9ae385840cf0a06d55e7f9924a94">More...</a><br /></td></tr>
<tr class="memdesc:a731f9ae385840cf0a06d55e7f9924a94"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get rightmose child of the current node. <br /></td></tr>
<tr class="separator:a731f9ae385840cf0a06d55e7f9924a94"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac6f619a1605cb46196360889fff4529e"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ac6f619a1605cb46196360889fff4529e">GetLeftmostChild</a> ()</td></tr>
<tr class="memdesc:ac6f619a1605cb46196360889fff4529e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get leftmose child of the current node. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ac6f619a1605cb46196360889fff4529e">More...</a><br /></td></tr>
<tr class="memdesc:ac6f619a1605cb46196360889fff4529e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get leftmose child of the current node. <br /></td></tr>
<tr class="separator:ac6f619a1605cb46196360889fff4529e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab654d7376d3449fdc78edab0e7fed06e"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ab654d7376d3449fdc78edab0e7fed06e">GetItemLeftChild</a> (int8_t item_index)</td></tr>
<tr class="memdesc:ab654d7376d3449fdc78edab0e7fed06e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get left child of item at item_index. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#ab654d7376d3449fdc78edab0e7fed06e">More...</a><br /></td></tr>
<tr class="memdesc:ab654d7376d3449fdc78edab0e7fed06e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get left child of item at item_index. <br /></td></tr>
<tr class="separator:ab654d7376d3449fdc78edab0e7fed06e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a441cbee9896391f2b167d5aa7b4f8c95"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a441cbee9896391f2b167d5aa7b4f8c95">GetItemRightChild</a> (int8_t item_index)</td></tr>
<tr class="memdesc:a441cbee9896391f2b167d5aa7b4f8c95"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get right child of item at item_index. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a441cbee9896391f2b167d5aa7b4f8c95">More...</a><br /></td></tr>
<tr class="memdesc:a441cbee9896391f2b167d5aa7b4f8c95"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get right child of item at item_index. <br /></td></tr>
<tr class="separator:a441cbee9896391f2b167d5aa7b4f8c95"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a91322b3bb0b2b2175eb56e9e10d7db46"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html">Node</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a91322b3bb0b2b2175eb56e9e10d7db46">GetNextPossibleChild</a> (int64_t item)</td></tr>
<tr class="memdesc:a91322b3bb0b2b2175eb56e9e10d7db46"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get next node which is possibly contains item. <a href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html#a91322b3bb0b2b2175eb56e9e10d7db46">More...</a><br /></td></tr>
<tr class="memdesc:a91322b3bb0b2b2175eb56e9e10d7db46"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get next node which is possibly contains item. <br /></td></tr>
<tr class="separator:a91322b3bb0b2b2175eb56e9e10d7db46"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pri-attribs" name="pri-attribs"></a>
@@ -205,7 +205,7 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
<tr class="separator:a934e6d53cfefae2b971e1241a8a4c921"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >2-3-4 tree node class </p>
<div class="textblock"><p>2-3-4 tree node class </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="ad5219979ea9a8baa3a273a9ec0f0c670" name="ad5219979ea9a8baa3a273a9ec0f0c670"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad5219979ea9a8baa3a273a9ec0f0c670">&#9670;&#160;</a></span>Node()</h2>
@@ -748,7 +748,7 @@ int8_t&#160;</td><td class="memItemRight" valign="bottom"><b>count</b> = 0</td><
</div><div class="memdoc">
<p>Insert item to the proper position of the node and return the position index. </p>
<p >This is a helper function we use during insertion. Please mind that when insert a item, we aslo need to take care of two child pointers. One is the original child pointer at the insertion position. It can be placed as new item's either left child or right child. And the other is the new child that should be added. For our dedicated situation here, we choose to use the original child as the new item's left child, and add a null pointer to its right child. So after use the function, please update these two children pointer manually.</p>
<p>This is a helper function we use during insertion. Please mind that when insert a item, we aslo need to take care of two child pointers. One is the original child pointer at the insertion position. It can be placed as new item's either left child or right child. And the other is the new child that should be added. For our dedicated situation here, we choose to use the original child as the new item's left child, and add a null pointer to its right child. So after use the function, please update these two children pointer manually.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">item</td><td>value to be inserted to the node </td></tr>
@@ -1111,7 +1111,7 @@ Here is the call graph for this function:</div>
</div><div class="memdoc">
<p>Set the item count of the node. </p>
<p >This is only used when we spliting and merging node where we need to do some raw operation manually. In common inserting and removing operation the count is maintained automatically.</p>
<p>This is only used when we spliting and merging node where we need to do some raw operation manually. In common inserting and removing operation the count is maintained automatically.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">c</td><td>the count to set </td></tr>
@@ -1181,7 +1181,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../d5/d3c/namespacedata__structures.html">data_structures</a></li><li class="navelem"><b>tree_234</b></li><li class="navelem"><a class="el" href="../../dd/d40/classdata__structures_1_1tree__234_1_1_node.html">Node</a></li>
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.5 </li>
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<title>Algorithms_in_C++: MD5 Namespace Reference</title>
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<p>Functions for the <a href="https://en.wikipedia.org/wiki/MD5" target="_blank">MD5</a> algorithm implementation.
<a href="../../dd/d43/namespace_m_d5.html#details">More...</a></p>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Functions for the <a href="https://en.wikipedia.org/wiki/MD5" target="_blank">MD5</a> algorithm implementation. </p>
<div class="textblock"><p>Functions for the <a href="https://en.wikipedia.org/wiki/MD5" target="_blank">MD5</a> algorithm implementation. </p>
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<li class="navelem"><a class="el" href="../../dd/d43/namespace_m_d5.html">MD5</a></li>
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<tr class="separator:abf7f2a6d91f1ca6c89698792aea3f188"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a971ce57e368f2f631cf1f4ff3f864049"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a971ce57e368f2f631cf1f4ff3f864049"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a971ce57e368f2f631cf1f4ff3f864049">square_area</a> (T length)</td></tr>
<tr class="memdesc:a971ce57e368f2f631cf1f4ff3f864049"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Square" target="_blank">square</a> (l * l) <a href="../../dd/d47/namespacemath.html#a971ce57e368f2f631cf1f4ff3f864049">More...</a><br /></td></tr>
<tr class="memdesc:a971ce57e368f2f631cf1f4ff3f864049"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Square" target="_blank">square</a> (l * l) <br /></td></tr>
<tr class="separator:a971ce57e368f2f631cf1f4ff3f864049"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab31d141f7c5b551746b1eee0eb4dedca"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ab31d141f7c5b551746b1eee0eb4dedca"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ab31d141f7c5b551746b1eee0eb4dedca">rect_area</a> (T length, T width)</td></tr>
<tr class="memdesc:ab31d141f7c5b551746b1eee0eb4dedca"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Rectangle" target="_blank">rectangle</a> (l * w) <a href="../../dd/d47/namespacemath.html#ab31d141f7c5b551746b1eee0eb4dedca">More...</a><br /></td></tr>
<tr class="memdesc:ab31d141f7c5b551746b1eee0eb4dedca"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Rectangle" target="_blank">rectangle</a> (l * w) <br /></td></tr>
<tr class="separator:ab31d141f7c5b551746b1eee0eb4dedca"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab3b920cc56442abd92279ba23b50f4dc"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ab3b920cc56442abd92279ba23b50f4dc"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ab3b920cc56442abd92279ba23b50f4dc">triangle_area</a> (T base, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
<tr class="memdesc:ab3b920cc56442abd92279ba23b50f4dc"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Triangle" target="_blank">triangle</a> (b * h / 2) <a href="../../dd/d47/namespacemath.html#ab3b920cc56442abd92279ba23b50f4dc">More...</a><br /></td></tr>
<tr class="memdesc:ab3b920cc56442abd92279ba23b50f4dc"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Triangle" target="_blank">triangle</a> (b * h / 2) <br /></td></tr>
<tr class="separator:ab3b920cc56442abd92279ba23b50f4dc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a40e36c67da78d2131408c57ee091ad75"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a40e36c67da78d2131408c57ee091ad75"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a40e36c67da78d2131408c57ee091ad75">circle_area</a> (T radius)</td></tr>
<tr class="memdesc:a40e36c67da78d2131408c57ee091ad75"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Area_of_a_circle" target="_blank">circle</a> (pi <a href="../../dd/d47/namespacemath.html#a40e36c67da78d2131408c57ee091ad75">More...</a><br /></td></tr>
<tr class="memdesc:a40e36c67da78d2131408c57ee091ad75"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Area_of_a_circle" target="_blank">circle</a> (pi <br /></td></tr>
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<tr class="memitem:a5de184925e68658f15415dd53954df4f"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a5de184925e68658f15415dd53954df4f"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a5de184925e68658f15415dd53954df4f">parallelogram_area</a> (T base, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
<tr class="memdesc:a5de184925e68658f15415dd53954df4f"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Parallelogram" target="_blank">parallelogram</a> (b * h) <a href="../../dd/d47/namespacemath.html#a5de184925e68658f15415dd53954df4f">More...</a><br /></td></tr>
<tr class="memdesc:a5de184925e68658f15415dd53954df4f"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Parallelogram" target="_blank">parallelogram</a> (b * h) <br /></td></tr>
<tr class="separator:a5de184925e68658f15415dd53954df4f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abc46c784a297fc1d2eb8b33a327fba4c"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:abc46c784a297fc1d2eb8b33a327fba4c"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#abc46c784a297fc1d2eb8b33a327fba4c">cube_surface_area</a> (T length)</td></tr>
<tr class="memdesc:abc46c784a297fc1d2eb8b33a327fba4c"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface area of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> ( 6 * (l <a href="../../dd/d47/namespacemath.html#abc46c784a297fc1d2eb8b33a327fba4c">More...</a><br /></td></tr>
<tr class="memdesc:abc46c784a297fc1d2eb8b33a327fba4c"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface area of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> ( 6 * (l <br /></td></tr>
<tr class="separator:abc46c784a297fc1d2eb8b33a327fba4c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab7f29862d30df351c317eedd60a0c656"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ab7f29862d30df351c317eedd60a0c656"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ab7f29862d30df351c317eedd60a0c656">sphere_surface_area</a> (T radius)</td></tr>
<tr class="memdesc:ab7f29862d30df351c317eedd60a0c656"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface area of a <a href="https://en.wikipedia.org/wiki/Sphere" target="_blank">sphere</a> ( 4 * pi * r^2) <a href="../../dd/d47/namespacemath.html#ab7f29862d30df351c317eedd60a0c656">More...</a><br /></td></tr>
<tr class="memdesc:ab7f29862d30df351c317eedd60a0c656"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface area of a <a href="https://en.wikipedia.org/wiki/Sphere" target="_blank">sphere</a> ( 4 * pi * r^2) <br /></td></tr>
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<tr class="memitem:ac5803413618fcfb922cb32c6db0fc864"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ac5803413618fcfb922cb32c6db0fc864"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ac5803413618fcfb922cb32c6db0fc864">cylinder_surface_area</a> (T radius, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
<tr class="memdesc:ac5803413618fcfb922cb32c6db0fc864"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface area of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> (2 * pi * r * h + 2 * pi * r^2) <a href="../../dd/d47/namespacemath.html#ac5803413618fcfb922cb32c6db0fc864">More...</a><br /></td></tr>
<tr class="memdesc:ac5803413618fcfb922cb32c6db0fc864"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface area of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> (2 * pi * r * h + 2 * pi * r^2) <br /></td></tr>
<tr class="separator:ac5803413618fcfb922cb32c6db0fc864"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aec65db4e5c7317323227f026fe50ef11"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">integral_approx</a> (double lb, double ub, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt; double(double)&gt; &amp;func, double delta=.0001)</td></tr>
<tr class="memdesc:aec65db4e5c7317323227f026fe50ef11"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes integral approximation. <a href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">More...</a><br /></td></tr>
<tr class="memdesc:aec65db4e5c7317323227f026fe50ef11"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes integral approximation. <br /></td></tr>
<tr class="separator:aec65db4e5c7317323227f026fe50ef11"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a50936ee98f4d40f17823befc65a32aec"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">test_eval</a> (double approx, double expected, double threshold)</td></tr>
<tr class="memdesc:a50936ee98f4d40f17823befc65a32aec"><td class="mdescLeft">&#160;</td><td class="mdescRight">Wrapper to evaluate if the approximated value is within <code>.XX%</code> threshold of the exact value. <a href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">More...</a><br /></td></tr>
<tr class="memdesc:a50936ee98f4d40f17823befc65a32aec"><td class="mdescLeft">&#160;</td><td class="mdescRight">Wrapper to evaluate if the approximated value is within <code>.XX%</code> threshold of the exact value. <br /></td></tr>
<tr class="separator:a50936ee98f4d40f17823befc65a32aec"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afa39ec943a4836c878e1614fd89b146f"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">largestPower</a> (uint32_t n, const uint16_t &amp;p)</td></tr>
<tr class="memdesc:afa39ec943a4836c878e1614fd89b146f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to calculate largest power. <a href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">More...</a><br /></td></tr>
<tr class="memdesc:afa39ec943a4836c878e1614fd89b146f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to calculate largest power. <br /></td></tr>
<tr class="separator:afa39ec943a4836c878e1614fd89b146f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a04065193d190d605e1f0d0d93a87e244"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">lcmSum</a> (const uint16_t &amp;num)</td></tr>
<tr class="separator:a04065193d190d605e1f0d0d93a87e244"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8d8e81a7cd59644b311ef9adb268f5f0"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a8d8e81a7cd59644b311ef9adb268f5f0">magic_number</a> (const uint64_t &amp;n)</td></tr>
<tr class="separator:a8d8e81a7cd59644b311ef9adb268f5f0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afcd07701d73ed65cd616bcba02737f3d"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">power</a> (uint64_t a, uint64_t b, uint64_t c)</td></tr>
<tr class="memdesc:afcd07701d73ed65cd616bcba02737f3d"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function calculates a raised to exponent b under modulo c using modular exponentiation. <a href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">More...</a><br /></td></tr>
<tr class="memdesc:afcd07701d73ed65cd616bcba02737f3d"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function calculates a raised to exponent b under modulo c using modular exponentiation. <br /></td></tr>
<tr class="separator:afcd07701d73ed65cd616bcba02737f3d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6e2dff75c5de70455b90c799d6ad6967"><td class="memTemplParams" colspan="2">template&lt;class T &gt; </td></tr>
<tr class="memitem:a6e2dff75c5de70455b90c799d6ad6967"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a6e2dff75c5de70455b90c799d6ad6967">n_choose_r</a> (T n, T r)</td></tr>
<tr class="memdesc:a6e2dff75c5de70455b90c799d6ad6967"><td class="mdescLeft">&#160;</td><td class="mdescRight">This is the function implementation of \( \binom{n}{r} \). <a href="../../dd/d47/namespacemath.html#a6e2dff75c5de70455b90c799d6ad6967">More...</a><br /></td></tr>
<tr class="memdesc:a6e2dff75c5de70455b90c799d6ad6967"><td class="mdescLeft">&#160;</td><td class="mdescRight">This is the function implementation of \( \binom{n}{r} \). <br /></td></tr>
<tr class="separator:a6e2dff75c5de70455b90c799d6ad6967"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9236348755183644f1225e162d01ab14"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a9236348755183644f1225e162d01ab14"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a9236348755183644f1225e162d01ab14">square_perimeter</a> (T length)</td></tr>
<tr class="memdesc:a9236348755183644f1225e162d01ab14"><td class="mdescLeft">&#160;</td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/Square" target="_blank">square</a> (4 * l) <a href="../../dd/d47/namespacemath.html#a9236348755183644f1225e162d01ab14">More...</a><br /></td></tr>
<tr class="memdesc:a9236348755183644f1225e162d01ab14"><td class="mdescLeft">&#160;</td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/Square" target="_blank">square</a> (4 * l) <br /></td></tr>
<tr class="separator:a9236348755183644f1225e162d01ab14"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a428769a16e9525e56588d7c7709d25a6"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a428769a16e9525e56588d7c7709d25a6"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a428769a16e9525e56588d7c7709d25a6">rect_perimeter</a> (T length, T width)</td></tr>
<tr class="memdesc:a428769a16e9525e56588d7c7709d25a6"><td class="mdescLeft">&#160;</td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/Rectangle" target="_blank">rectangle</a> ( 2(l + w) ) <a href="../../dd/d47/namespacemath.html#a428769a16e9525e56588d7c7709d25a6">More...</a><br /></td></tr>
<tr class="memdesc:a428769a16e9525e56588d7c7709d25a6"><td class="mdescLeft">&#160;</td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/Rectangle" target="_blank">rectangle</a> ( 2(l + w) ) <br /></td></tr>
<tr class="separator:a428769a16e9525e56588d7c7709d25a6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3d1e4db743b189f309327572663415f3"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a3d1e4db743b189f309327572663415f3"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a3d1e4db743b189f309327572663415f3">triangle_perimeter</a> (T base, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>, T hypotenuse)</td></tr>
<tr class="memdesc:a3d1e4db743b189f309327572663415f3"><td class="mdescLeft">&#160;</td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/Triangle" target="_blank">triangle</a> (a + b + c) <a href="../../dd/d47/namespacemath.html#a3d1e4db743b189f309327572663415f3">More...</a><br /></td></tr>
<tr class="memdesc:a3d1e4db743b189f309327572663415f3"><td class="mdescLeft">&#160;</td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/Triangle" target="_blank">triangle</a> (a + b + c) <br /></td></tr>
<tr class="separator:a3d1e4db743b189f309327572663415f3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad0acf82b7bc920182bf8322d1e103953"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ad0acf82b7bc920182bf8322d1e103953"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ad0acf82b7bc920182bf8322d1e103953">circle_perimeter</a> (T radius)</td></tr>
<tr class="memdesc:ad0acf82b7bc920182bf8322d1e103953"><td class="mdescLeft">&#160;</td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/perimeter_of_a_circle" target="_blank">circle</a> (2 * pi * r) <a href="../../dd/d47/namespacemath.html#ad0acf82b7bc920182bf8322d1e103953">More...</a><br /></td></tr>
<tr class="memdesc:ad0acf82b7bc920182bf8322d1e103953"><td class="mdescLeft">&#160;</td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/perimeter_of_a_circle" target="_blank">circle</a> (2 * pi * r) <br /></td></tr>
<tr class="separator:ad0acf82b7bc920182bf8322d1e103953"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0efb235330ff48e14fd31faaccbcebb3"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a0efb235330ff48e14fd31faaccbcebb3"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a0efb235330ff48e14fd31faaccbcebb3">parallelogram_perimeter</a> (T base, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
<tr class="memdesc:a0efb235330ff48e14fd31faaccbcebb3"><td class="mdescLeft">&#160;</td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/Parallelogram" target="_blank">parallelogram</a> 2(b + h) <a href="../../dd/d47/namespacemath.html#a0efb235330ff48e14fd31faaccbcebb3">More...</a><br /></td></tr>
<tr class="memdesc:a0efb235330ff48e14fd31faaccbcebb3"><td class="mdescLeft">&#160;</td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/Parallelogram" target="_blank">parallelogram</a> 2(b + h) <br /></td></tr>
<tr class="separator:a0efb235330ff48e14fd31faaccbcebb3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8998ca7b1886d1d7d00aef3b457a9b1b"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a8998ca7b1886d1d7d00aef3b457a9b1b"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a8998ca7b1886d1d7d00aef3b457a9b1b">cube_surface_perimeter</a> (T length)</td></tr>
<tr class="memdesc:a8998ca7b1886d1d7d00aef3b457a9b1b"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface perimeter of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> ( 12 <a href="../../dd/d47/namespacemath.html#a8998ca7b1886d1d7d00aef3b457a9b1b">More...</a><br /></td></tr>
<tr class="memdesc:a8998ca7b1886d1d7d00aef3b457a9b1b"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface perimeter of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> ( 12 <br /></td></tr>
<tr class="separator:a8998ca7b1886d1d7d00aef3b457a9b1b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa8592c3279c41a2c6d4d64eeb488f63f"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:aa8592c3279c41a2c6d4d64eeb488f63f"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#aa8592c3279c41a2c6d4d64eeb488f63f">n_polygon_surface_perimeter</a> (T sides, T length)</td></tr>
<tr class="memdesc:aa8592c3279c41a2c6d4d64eeb488f63f"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface perimeter of a <a href="https://www.cuemath.com/measurement/perimeter-of-polygon/" target="_blank">n-polygon</a> ( n * l) <a href="../../dd/d47/namespacemath.html#aa8592c3279c41a2c6d4d64eeb488f63f">More...</a><br /></td></tr>
<tr class="memdesc:aa8592c3279c41a2c6d4d64eeb488f63f"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface perimeter of a <a href="https://www.cuemath.com/measurement/perimeter-of-polygon/" target="_blank">n-polygon</a> ( n * l) <br /></td></tr>
<tr class="separator:aa8592c3279c41a2c6d4d64eeb488f63f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1d4df7a4e43a2eac1acc0ac610487c73"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a1d4df7a4e43a2eac1acc0ac610487c73"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a1d4df7a4e43a2eac1acc0ac610487c73">cylinder_surface_perimeter</a> (T radius, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
<tr class="memdesc:a1d4df7a4e43a2eac1acc0ac610487c73"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface perimeter of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> (2 * radius + 2 * height) <a href="../../dd/d47/namespacemath.html#a1d4df7a4e43a2eac1acc0ac610487c73">More...</a><br /></td></tr>
<tr class="memdesc:a1d4df7a4e43a2eac1acc0ac610487c73"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface perimeter of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> (2 * radius + 2 * height) <br /></td></tr>
<tr class="separator:a1d4df7a4e43a2eac1acc0ac610487c73"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8a48be4d7f14e34c5c92925bc1cbf3bb"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a8a48be4d7f14e34c5c92925bc1cbf3bb">power_of_two</a> (int n)</td></tr>
<tr class="memdesc:a8a48be4d7f14e34c5c92925bc1cbf3bb"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function finds whether a number is power of 2 or not. <a href="../../dd/d47/namespacemath.html#a8a48be4d7f14e34c5c92925bc1cbf3bb">More...</a><br /></td></tr>
<tr class="memdesc:a8a48be4d7f14e34c5c92925bc1cbf3bb"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function finds whether a number is power of 2 or not. <br /></td></tr>
<tr class="separator:a8a48be4d7f14e34c5c92925bc1cbf3bb"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae1ca505751f5a6d3977b86372cfe75ea"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ae1ca505751f5a6d3977b86372cfe75ea">binomialCoeffSum</a> (uint64_t n)</td></tr>
<tr class="separator:ae1ca505751f5a6d3977b86372cfe75ea"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae413098478fa38acaac887b7654f0725"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ae413098478fa38acaac887b7654f0725"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ae413098478fa38acaac887b7654f0725">cube_volume</a> (T length)</td></tr>
<tr class="memdesc:ae413098478fa38acaac887b7654f0725"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> <a href="../../dd/d47/namespacemath.html#ae413098478fa38acaac887b7654f0725">More...</a><br /></td></tr>
<tr class="memdesc:ae413098478fa38acaac887b7654f0725"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> <br /></td></tr>
<tr class="separator:ae413098478fa38acaac887b7654f0725"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3fdc74c24697ec5bb5c3698c96117c12"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a3fdc74c24697ec5bb5c3698c96117c12"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a3fdc74c24697ec5bb5c3698c96117c12">rect_prism_volume</a> (T length, T width, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
<tr class="memdesc:a3fdc74c24697ec5bb5c3698c96117c12"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cuboid" target="_blank">rectangular</a> prism. <a href="../../dd/d47/namespacemath.html#a3fdc74c24697ec5bb5c3698c96117c12">More...</a><br /></td></tr>
<tr class="memdesc:a3fdc74c24697ec5bb5c3698c96117c12"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cuboid" target="_blank">rectangular</a> prism. <br /></td></tr>
<tr class="separator:a3fdc74c24697ec5bb5c3698c96117c12"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3fe35440c27758ecc2287e08217d63a7"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a3fe35440c27758ecc2287e08217d63a7"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a3fe35440c27758ecc2287e08217d63a7">cone_volume</a> (T radius, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>, double PI=3.14)</td></tr>
<tr class="memdesc:a3fe35440c27758ecc2287e08217d63a7"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cone" target="_blank">cone</a> <a href="../../dd/d47/namespacemath.html#a3fe35440c27758ecc2287e08217d63a7">More...</a><br /></td></tr>
<tr class="memdesc:a3fe35440c27758ecc2287e08217d63a7"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cone" target="_blank">cone</a> <br /></td></tr>
<tr class="separator:a3fe35440c27758ecc2287e08217d63a7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2d704a7b72a6b2db8b76c8581b577b2c"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a2d704a7b72a6b2db8b76c8581b577b2c"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a2d704a7b72a6b2db8b76c8581b577b2c">triangle_prism_volume</a> (T base, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>, T depth)</td></tr>
<tr class="memdesc:a2d704a7b72a6b2db8b76c8581b577b2c"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Triangular_prism" target="_blank">triangular</a> prism. <a href="../../dd/d47/namespacemath.html#a2d704a7b72a6b2db8b76c8581b577b2c">More...</a><br /></td></tr>
<tr class="memdesc:a2d704a7b72a6b2db8b76c8581b577b2c"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Triangular_prism" target="_blank">triangular</a> prism. <br /></td></tr>
<tr class="separator:a2d704a7b72a6b2db8b76c8581b577b2c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a94db02b3c9e55a69ac1696f30e2f761c"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a94db02b3c9e55a69ac1696f30e2f761c"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a94db02b3c9e55a69ac1696f30e2f761c">pyramid_volume</a> (T length, T width, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
<tr class="memdesc:a94db02b3c9e55a69ac1696f30e2f761c"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Pyramid_(geometry)" target="_blank">pyramid</a> <a href="../../dd/d47/namespacemath.html#a94db02b3c9e55a69ac1696f30e2f761c">More...</a><br /></td></tr>
<tr class="memdesc:a94db02b3c9e55a69ac1696f30e2f761c"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Pyramid_(geometry)" target="_blank">pyramid</a> <br /></td></tr>
<tr class="separator:a94db02b3c9e55a69ac1696f30e2f761c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a34d66a77c19ce9b8b3a3d14352b34551"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a34d66a77c19ce9b8b3a3d14352b34551"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a34d66a77c19ce9b8b3a3d14352b34551">sphere_volume</a> (T radius, double PI=3.14)</td></tr>
<tr class="memdesc:a34d66a77c19ce9b8b3a3d14352b34551"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Sphere" target="_blank">sphere</a> <a href="../../dd/d47/namespacemath.html#a34d66a77c19ce9b8b3a3d14352b34551">More...</a><br /></td></tr>
<tr class="memdesc:a34d66a77c19ce9b8b3a3d14352b34551"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Sphere" target="_blank">sphere</a> <br /></td></tr>
<tr class="separator:a34d66a77c19ce9b8b3a3d14352b34551"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abde24398be43538c62e4a496968e60ca"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:abde24398be43538c62e4a496968e60ca"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#abde24398be43538c62e4a496968e60ca">cylinder_volume</a> (T radius, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>, double PI=3.14)</td></tr>
<tr class="memdesc:abde24398be43538c62e4a496968e60ca"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> <a href="../../dd/d47/namespacemath.html#abde24398be43538c62e4a496968e60ca">More...</a><br /></td></tr>
<tr class="memdesc:abde24398be43538c62e4a496968e60ca"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> <br /></td></tr>
<tr class="separator:abde24398be43538c62e4a496968e60ca"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a> </p>
<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
<p >for io operations</p>
<p >Evaluate recurrence relation using <a href="https://www.hackerearth.com/practice/notes/matrix-exponentiation-1/" target="_blank">matrix exponentiation</a>.</p>
<p >for assert</p>
<p >Math algorithms.</p>
<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p >for IO operations</p>
<p >for M_PI definition and pow()</p>
<p >for IO operations for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p >Mathematical algorithms</p>
<p >for assert for uint16_t datatype for IO operations</p>
<p >Mathematical algorithms</p>
<p >for assert for int32_t type for atoi</p>
<p >Mathematical algorithms</p>
<p >for assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
<p >Mathematical algorithms</p>
<p >for assert for mathematical functions for passing in functions</p>
<p >Mathematical functions</p>
<p >for math functions for fixed size data types for time to initialize rng for function pointers for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> for random number generation for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
<p >Mathematical algorithms</p>
<p >Given a recurrence relation; evaluate the value of nth term. For e.g., For fibonacci series, recurrence series is <code>f(n) = f(n-1) + f(n-2)</code> where <code>f(0) = 0</code> and <code>f(1) = 1</code>. Note that the method used only demonstrates recurrence relation with one variable (n), unlike <code>nCr</code> problem, since it has two (n, r)</p>
<div class="textblock"><p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a> </p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
<p>for io operations</p>
<p>Evaluate recurrence relation using <a href="https://www.hackerearth.com/practice/notes/matrix-exponentiation-1/" target="_blank">matrix exponentiation</a>.</p>
<p>for assert</p>
<p>Math algorithms.</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p>for IO operations</p>
<p>for M_PI definition and pow()</p>
<p>for IO operations for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p>Mathematical algorithms</p>
<p>for assert for uint16_t datatype for IO operations</p>
<p>Mathematical algorithms</p>
<p>for assert for int32_t type for atoi</p>
<p>Mathematical algorithms</p>
<p>for assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
<p>Mathematical algorithms</p>
<p>for assert for mathematical functions for passing in functions</p>
<p>Mathematical functions</p>
<p>for math functions for fixed size data types for time to initialize rng for function pointers for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> for random number generation for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
<p>Mathematical algorithms</p>
<p>Given a recurrence relation; evaluate the value of nth term. For e.g., For fibonacci series, recurrence series is <code>f(n) = f(n-1) + f(n-2)</code> where <code>f(0) = 0</code> and <code>f(1) = 1</code>. Note that the method used only demonstrates recurrence relation with one variable (n), unlike <code>nCr</code> problem, since it has two (n, r)</p>
<h3><a class="anchor" id="autotoc_md84"></a>
Algorithm</h3>
<p >This problem can be solved using matrix exponentiation method. </p><dl class="section see"><dt>See also</dt><dd>here for simple <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_exponentiation.cpp" target="_blank">number exponentiation algorithm</a> or <a href="https://en.wikipedia.org/wiki/Exponentiation_by_squaring" target="_blank">explaination here</a>. </dd></dl>
<p>This problem can be solved using matrix exponentiation method. </p><dl class="section see"><dt>See also</dt><dd>here for simple <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_exponentiation.cpp" target="_blank">number exponentiation algorithm</a> or <a href="https://en.wikipedia.org/wiki/Exponentiation_by_squaring" target="_blank">explaination here</a>. </dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/AshishYUO" target="_blank">Ashish Daulatabad</a> for assert for IO operations for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> STL</dd></dl>
<p>Mathematical algorithms</p>
<p >for assert</p>
<p >Mathematical algorithms</p>
<p >for std::is_equal, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a> for assert for IO operations</p>
<p >Mathematical algorithms</p>
<p >for assert for io operations</p>
<p >Mathematical algorithms</p>
<p >for assert for M_PI definition and pow() for uint16_t datatype</p>
<p >Mathematical algorithms</p>
<p >for IO operations</p>
<p >Mathematical algorithms</p>
<p >for assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a></p>
<p >Mathematical algorithms </p>
<p>for assert</p>
<p>Mathematical algorithms</p>
<p>for std::is_equal, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a> for assert for IO operations</p>
<p>Mathematical algorithms</p>
<p>for assert for io operations</p>
<p>Mathematical algorithms</p>
<p>for assert for M_PI definition and pow() for uint16_t datatype</p>
<p>Mathematical algorithms</p>
<p>for IO operations</p>
<p>Mathematical algorithms</p>
<p>for assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a></p>
<p>Mathematical algorithms </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="abf7f2a6d91f1ca6c89698792aea3f188" name="abf7f2a6d91f1ca6c89698792aea3f188"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abf7f2a6d91f1ca6c89698792aea3f188">&#9670;&#160;</a></span>approximate_pi()</h2>
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</tr>
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<p >This function use the points pts (drawn at random) to return an estimate of the number π using the given points </p><dl class="params"><dt>Parameters</dt><dd>
<p>This function use the points pts (drawn at random) to return an estimate of the number π using the given points </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">pts</td><td>Each item of pts contains a point. A point is represented by a structure containing exactly two numbers, respectively x and y such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. pts always contains at least one item </td></tr>
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@@ -334,7 +334,7 @@ Algorithm</h3>
</tr>
</table>
</div><div class="memdoc">
<p >Function to calculate sum of binomial coefficients </p><dl class="params"><dt>Parameters</dt><dd>
<p>Function to calculate sum of binomial coefficients </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>number </td></tr>
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<p >Function to compute sum of euler totients in sumOfEulerTotient vector </p><dl class="params"><dt>Parameters</dt><dd>
<p>Function to compute sum of euler totients in sumOfEulerTotient vector </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
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<p >Function to check if the given number is magic number or not. </p><dl class="params"><dt>Parameters</dt><dd>
<p>Function to check if the given number is magic number or not. </p><dl class="params"><dt>Parameters</dt><dd>
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</div><div class="memdoc">
<p>This is the function implementation of \( \binom{n}{r} \). </p>
<p >We are calculating the ans with iterations instead of calculating three different factorials. Also, we are using the fact that \( \frac{n!}{r! (n-r)!} = \frac{(n - r + 1) \times \cdots \times n}{1 \times
<p>We are calculating the ans with iterations instead of calculating three different factorials. Also, we are using the fact that \( \frac{n!}{r! (n-r)!} = \frac{(n - r + 1) \times \cdots \times n}{1 \times
\cdots \times r} \) </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Only for integer types such as long, int_64 etc </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>a raised to power b modulo c </dd></dl>
<p >Initialize the answer to be returned</p>
<p >Update a if it is more than or equal to c</p>
<p >In case a is divisible by c;</p>
<p >If b is odd, multiply a with answer</p>
<p >b must be even now</p>
<p >b = b/2</p>
<p>Initialize the answer to be returned</p>
<p>Update a if it is more than or equal to c</p>
<p>In case a is divisible by c;</p>
<p>If b is odd, multiply a with answer</p>
<p>b must be even now</p>
<p>b = b/2</p>
<div class="fragment"><div class="line"><span class="lineno"> 35</span> {</div>
<div class="line"><span class="lineno"> 36</span> uint64_t ans = 1; <span class="comment">/// Initialize the answer to be returned</span></div>
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<dl class="section return"><dt>Returns</dt><dd>1 if <code>n</code> IS the power of 2 </dd>
<dd>
0 if n is NOT a power of 2 </dd></dl>
<p >result stores the bitwise and of n and n-1</p>
<p>result stores the bitwise and of n and n-1</p>
<div class="fragment"><div class="line"><span class="lineno"> 42</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 43</span><span class="comment"> /// result stores the</span></div>
<div class="line"><span class="lineno"> 44</span><span class="comment"> /// bitwise and of n and n-1</span></div>
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<p>Functions for the <a href="https://en.wikipedia.org/wiki/Geometric_distribution" target="_blank">Geometric Distribution</a> algorithm implementation.
<a href="../../dd/d8a/namespacegeometric__dist.html#details">More...</a></p>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Functions for the <a href="https://en.wikipedia.org/wiki/Geometric_distribution" target="_blank">Geometric Distribution</a> algorithm implementation. </p>
<div class="textblock"><p>Functions for the <a href="https://en.wikipedia.org/wiki/Geometric_distribution" target="_blank">Geometric Distribution</a> algorithm implementation. </p>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >n --&gt; No. of elements present in input array. bit[0..n] --&gt; Array that represents Binary Indexed Tree. </p>
<div class="textblock"><p>n --&gt; No. of elements present in input array. bit[0..n] --&gt; Array that represents Binary Indexed Tree. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="aaddab1f03d4941212a82cc647b1adb17" name="aaddab1f03d4941212a82cc647b1adb17"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aaddab1f03d4941212a82cc647b1adb17">&#9670;&#160;</a></span>FenwickTree() <span class="overload">[1/2]</span></h2>
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<p >Constructor </p><dl class="params"><dt>Parameters</dt><dd>
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<p >Constructor </p><dl class="params"><dt>Parameters</dt><dd>
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<p >Returns the highest power of two which is not more than x </p>
<p>Returns the highest power of two which is not more than x </p>
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<p >Get prefix sum upto id </p>
<p>Get prefix sum upto id </p>
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<p >Returns the prefix sum in range from l to r </p>
<p>Returns the prefix sum in range from l to r </p>
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<p >Add val at id </p>
<p>Add val at id </p>
<div class="fragment"><div class="line"><span class="lineno"> 45</span> {</div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordtype">id</span>++;</div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:aa5c0486c7f29f323a2aced2ab33af420"><td class="memItemLeft" align="right" valign="top">uint32_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#aa5c0486c7f29f323a2aced2ab33af420">get</a> (size_t i, size_t j) const</td></tr>
<tr class="memdesc:aa5c0486c7f29f323a2aced2ab33af420"><td class="mdescLeft">&#160;</td><td class="mdescRight">get the value from i units from right and j units from left side of the board <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#aa5c0486c7f29f323a2aced2ab33af420">More...</a><br /></td></tr>
<tr class="memdesc:aa5c0486c7f29f323a2aced2ab33af420"><td class="mdescLeft">&#160;</td><td class="mdescRight">get the value from i units from right and j units from left side of the board <br /></td></tr>
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<tr class="memitem:ade14b0e1a88543b91426e2008e4d0f99"><td class="memItemLeft" align="right" valign="top"><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; uint32_t, N &gt;, N &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#ade14b0e1a88543b91426e2008e4d0f99">get_state</a> ()</td></tr>
<tr class="memdesc:ade14b0e1a88543b91426e2008e4d0f99"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the current state of the board. <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#ade14b0e1a88543b91426e2008e4d0f99">More...</a><br /></td></tr>
<tr class="memdesc:ade14b0e1a88543b91426e2008e4d0f99"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the current state of the board. <br /></td></tr>
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<tr class="memitem:ae145ac4a0d2ec58945b58fad3c04f00f"><td class="memItemLeft" align="right" valign="top">size_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#ae145ac4a0d2ec58945b58fad3c04f00f">get_size</a> () const</td></tr>
<tr class="memdesc:ae145ac4a0d2ec58945b58fad3c04f00f"><td class="mdescLeft">&#160;</td><td class="mdescRight">returns the size of the <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html" title="A class defining EightPuzzle/15-Puzzle game.">EightPuzzle</a> (number of row / column) <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#ae145ac4a0d2ec58945b58fad3c04f00f">More...</a><br /></td></tr>
<tr class="memdesc:ae145ac4a0d2ec58945b58fad3c04f00f"><td class="mdescLeft">&#160;</td><td class="mdescRight">returns the size of the <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html" title="A class defining EightPuzzle/15-Puzzle game.">EightPuzzle</a> (number of row / column) <br /></td></tr>
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<tr class="memitem:a3dc09f4742a0e1167ed202f7bf94721b"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a3dc09f4742a0e1167ed202f7bf94721b">EightPuzzle</a> ()</td></tr>
<tr class="memdesc:a3dc09f4742a0e1167ed202f7bf94721b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default constructor for <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html" title="A class defining EightPuzzle/15-Puzzle game.">EightPuzzle</a>. <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a3dc09f4742a0e1167ed202f7bf94721b">More...</a><br /></td></tr>
<tr class="memdesc:a3dc09f4742a0e1167ed202f7bf94721b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default constructor for <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html" title="A class defining EightPuzzle/15-Puzzle game.">EightPuzzle</a>. <br /></td></tr>
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<tr class="memdesc:ab7fd890a7ccf756e4b3313087b76a8c2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Parameterized Constructor for <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html" title="A class defining EightPuzzle/15-Puzzle game.">EightPuzzle</a>. <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#ab7fd890a7ccf756e4b3313087b76a8c2">More...</a><br /></td></tr>
<tr class="memdesc:ab7fd890a7ccf756e4b3313087b76a8c2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Parameterized Constructor for <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html" title="A class defining EightPuzzle/15-Puzzle game.">EightPuzzle</a>. <br /></td></tr>
<tr class="separator:ab7fd890a7ccf756e4b3313087b76a8c2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad45fde095ac00effe1fe00b1d85ff9c7"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#ad45fde095ac00effe1fe00b1d85ff9c7">EightPuzzle</a> (const <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a>&lt; N &gt; &amp;A)</td></tr>
<tr class="memdesc:ad45fde095ac00effe1fe00b1d85ff9c7"><td class="mdescLeft">&#160;</td><td class="mdescRight">Copy constructor. <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#ad45fde095ac00effe1fe00b1d85ff9c7">More...</a><br /></td></tr>
<tr class="memdesc:ad45fde095ac00effe1fe00b1d85ff9c7"><td class="mdescLeft">&#160;</td><td class="mdescRight">Copy constructor. <br /></td></tr>
<tr class="separator:ad45fde095ac00effe1fe00b1d85ff9c7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af22395b8e9e04222aa93a329523faef9"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#af22395b8e9e04222aa93a329523faef9">EightPuzzle</a> (const <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a>&lt; N &gt; &amp;&amp;A) noexcept</td></tr>
<tr class="memdesc:af22395b8e9e04222aa93a329523faef9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Move constructor. <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#af22395b8e9e04222aa93a329523faef9">More...</a><br /></td></tr>
<tr class="memdesc:af22395b8e9e04222aa93a329523faef9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Move constructor. <br /></td></tr>
<tr class="separator:af22395b8e9e04222aa93a329523faef9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a194c2973b51a5467fc17064a4ea4e6f9"><td class="memItemLeft" align="right" valign="top"><a id="a194c2973b51a5467fc17064a4ea4e6f9" name="a194c2973b51a5467fc17064a4ea4e6f9"></a>
&#160;</td><td class="memItemRight" valign="bottom"><b>~EightPuzzle</b> ()=default</td></tr>
<tr class="memdesc:a194c2973b51a5467fc17064a4ea4e6f9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Destructor of <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html" title="A class defining EightPuzzle/15-Puzzle game.">EightPuzzle</a>. <br /></td></tr>
<tr class="separator:a194c2973b51a5467fc17064a4ea4e6f9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a467e722dc1fcc82bfb4cef55744e04e2"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a467e722dc1fcc82bfb4cef55744e04e2">operator=</a> (const <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a> &amp;A)</td></tr>
<tr class="memdesc:a467e722dc1fcc82bfb4cef55744e04e2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Copy assignment operator. <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a467e722dc1fcc82bfb4cef55744e04e2">More...</a><br /></td></tr>
<tr class="memdesc:a467e722dc1fcc82bfb4cef55744e04e2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Copy assignment operator. <br /></td></tr>
<tr class="separator:a467e722dc1fcc82bfb4cef55744e04e2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1802cf6197a255055cb734d626abc101"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a1802cf6197a255055cb734d626abc101">operator=</a> (<a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a> &amp;&amp;A) noexcept</td></tr>
<tr class="memdesc:a1802cf6197a255055cb734d626abc101"><td class="mdescLeft">&#160;</td><td class="mdescRight">Move assignment operator. <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a1802cf6197a255055cb734d626abc101">More...</a><br /></td></tr>
<tr class="memdesc:a1802cf6197a255055cb734d626abc101"><td class="mdescLeft">&#160;</td><td class="mdescRight">Move assignment operator. <br /></td></tr>
<tr class="separator:a1802cf6197a255055cb734d626abc101"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a26a976171392d257ca0f814ed73e0658"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a>&lt; N &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a26a976171392d257ca0f814ed73e0658">generate_possible_moves</a> ()</td></tr>
<tr class="memdesc:a26a976171392d257ca0f814ed73e0658"><td class="mdescLeft">&#160;</td><td class="mdescRight">Find all possible states after processing all possible moves, given the current state of the puzzle. <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a26a976171392d257ca0f814ed73e0658">More...</a><br /></td></tr>
<tr class="memdesc:a26a976171392d257ca0f814ed73e0658"><td class="mdescLeft">&#160;</td><td class="mdescRight">Find all possible states after processing all possible moves, given the current state of the puzzle. <br /></td></tr>
<tr class="separator:a26a976171392d257ca0f814ed73e0658"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa17e0227321b109ed91e156ac1332915"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#aa17e0227321b109ed91e156ac1332915">operator==</a> (const <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a>&lt; N &gt; &amp;check) const</td></tr>
<tr class="memdesc:aa17e0227321b109ed91e156ac1332915"><td class="mdescLeft">&#160;</td><td class="mdescRight">check whether two boards are equal <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#aa17e0227321b109ed91e156ac1332915">More...</a><br /></td></tr>
<tr class="memdesc:aa17e0227321b109ed91e156ac1332915"><td class="mdescLeft">&#160;</td><td class="mdescRight">check whether two boards are equal <br /></td></tr>
<tr class="separator:aa17e0227321b109ed91e156ac1332915"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a64815f10cf9fb9fdb4cc92731ccf10ba"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a64815f10cf9fb9fdb4cc92731ccf10ba">operator&lt;</a> (const <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a>&lt; N &gt; &amp;check) const</td></tr>
<tr class="memdesc:a64815f10cf9fb9fdb4cc92731ccf10ba"><td class="mdescLeft">&#160;</td><td class="mdescRight">check whether one board is lexicographically smaller <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a64815f10cf9fb9fdb4cc92731ccf10ba">More...</a><br /></td></tr>
<tr class="memdesc:a64815f10cf9fb9fdb4cc92731ccf10ba"><td class="mdescLeft">&#160;</td><td class="mdescRight">check whether one board is lexicographically smaller <br /></td></tr>
<tr class="separator:a64815f10cf9fb9fdb4cc92731ccf10ba"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af778034b2942ecac6df1e9ec8b5412ee"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#af778034b2942ecac6df1e9ec8b5412ee">operator&lt;=</a> (const <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a>&lt; N &gt; &amp;check) const</td></tr>
<tr class="memdesc:af778034b2942ecac6df1e9ec8b5412ee"><td class="mdescLeft">&#160;</td><td class="mdescRight">check whether one board is lexicographically smaller or equal <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#af778034b2942ecac6df1e9ec8b5412ee">More...</a><br /></td></tr>
<tr class="memdesc:af778034b2942ecac6df1e9ec8b5412ee"><td class="mdescLeft">&#160;</td><td class="mdescRight">check whether one board is lexicographically smaller or equal <br /></td></tr>
<tr class="separator:af778034b2942ecac6df1e9ec8b5412ee"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pri-methods" name="pri-methods"></a>
Private Member Functions</h2></td></tr>
<tr class="memitem:a94f794bf44f424b1b0ca6ef9f4f6ebd3"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; uint32_t, uint32_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a94f794bf44f424b1b0ca6ef9f4f6ebd3">find_zero</a> ()</td></tr>
<tr class="memdesc:a94f794bf44f424b1b0ca6ef9f4f6ebd3"><td class="mdescLeft">&#160;</td><td class="mdescRight">A helper array to evaluate the next state from current state;. <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a94f794bf44f424b1b0ca6ef9f4f6ebd3">More...</a><br /></td></tr>
<tr class="memdesc:a94f794bf44f424b1b0ca6ef9f4f6ebd3"><td class="mdescLeft">&#160;</td><td class="mdescRight">A helper array to evaluate the next state from current state;. <br /></td></tr>
<tr class="separator:a94f794bf44f424b1b0ca6ef9f4f6ebd3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a48d054230468b79037964f474d842b6e"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a48d054230468b79037964f474d842b6e">in_range</a> (const uint32_t value) const</td></tr>
<tr class="memdesc:a48d054230468b79037964f474d842b6e"><td class="mdescLeft">&#160;</td><td class="mdescRight">check whether the index value is bounded within the puzzle area <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a48d054230468b79037964f474d842b6e">More...</a><br /></td></tr>
<tr class="memdesc:a48d054230468b79037964f474d842b6e"><td class="mdescLeft">&#160;</td><td class="mdescRight">check whether the index value is bounded within the puzzle area <br /></td></tr>
<tr class="separator:a48d054230468b79037964f474d842b6e"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pri-attribs" name="pri-attribs"></a>
@@ -177,19 +177,19 @@ Private Attributes</h2></td></tr>
<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; uint32_t, N &gt;, N &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>board</b></td></tr>
<tr class="separator:a35d8f14ca17218f236c09ff9ad864f9c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa73857052e69b86347859d9148933f71"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; int8_t, int8_t &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#aa73857052e69b86347859d9148933f71">moves</a></td></tr>
<tr class="memdesc:aa73857052e69b86347859d9148933f71"><td class="mdescLeft">&#160;</td><td class="mdescRight">N x N array to store the current state of the Puzzle. <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#aa73857052e69b86347859d9148933f71">More...</a><br /></td></tr>
<tr class="memdesc:aa73857052e69b86347859d9148933f71"><td class="mdescLeft">&#160;</td><td class="mdescRight">N x N array to store the current state of the Puzzle. <br /></td></tr>
<tr class="separator:aa73857052e69b86347859d9148933f71"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="friends" name="friends"></a>
Friends</h2></td></tr>
<tr class="memitem:a9517e162e2988f7db052296bd550a742"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a9517e162e2988f7db052296bd550a742">operator&lt;&lt;</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;op, const <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a>&lt; N &gt; &amp;SomeState)</td></tr>
<tr class="memdesc:a9517e162e2988f7db052296bd550a742"><td class="mdescLeft">&#160;</td><td class="mdescRight">friend operator to display EightPuzzle&lt;&gt; <a href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html#a9517e162e2988f7db052296bd550a742">More...</a><br /></td></tr>
<tr class="memdesc:a9517e162e2988f7db052296bd550a742"><td class="mdescLeft">&#160;</td><td class="mdescRight">friend operator to display EightPuzzle&lt;&gt; <br /></td></tr>
<tr class="separator:a9517e162e2988f7db052296bd550a742"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><div class="compoundTemplParams">template&lt;size_t N = 3&gt;<br />
class machine_learning::aystar_search::EightPuzzle&lt; N &gt;</div><p >A class defining <a href="https://en.wikipedia.org/wiki/15_puzzle" target="_blank">EightPuzzle/15-Puzzle game</a>. </p>
<p >A well known 3 x 3 puzzle of the form ` 1 2 3 4 5 6 7 8 0 <code> where</code>0` represents an empty space in the puzzle Given any random state, the goal is to achieve the above configuration (or any other configuration if possible) </p><dl class="tparams"><dt>Template Parameters</dt><dd>
class machine_learning::aystar_search::EightPuzzle&lt; N &gt;</div><p>A class defining <a href="https://en.wikipedia.org/wiki/15_puzzle" target="_blank">EightPuzzle/15-Puzzle game</a>. </p>
<p>A well known 3 x 3 puzzle of the form ` 1 2 3 4 5 6 7 8 0 <code> where</code>0` represents an empty space in the puzzle Given any random state, the goal is to achieve the above configuration (or any other configuration if possible) </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">N</td><td>size of the square Puzzle, default is set to 3 (since it is <a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html" title="A class defining EightPuzzle/15-Puzzle game.">EightPuzzle</a>) </td></tr>
</table>
@@ -372,7 +372,7 @@ template&lt;size_t N = 3&gt; </div>
</div><div class="memdoc">
<p>A helper array to evaluate the next state from current state;. </p>
<p >Finds an empty space in puzzle (in this case; a zero) </p><dl class="section return"><dt>Returns</dt><dd>a pair indicating integer distances from top and right respectively, else returns -1, -1 </dd></dl>
<p>Finds an empty space in puzzle (in this case; a zero) </p><dl class="section return"><dt>Returns</dt><dd>a pair indicating integer distances from top and right respectively, else returns -1, -1 </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 75</span> {</div>
<div class="line"><span class="lineno"> 76</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++i) {</div>
<div class="line"><span class="lineno"> 77</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; ++j) {</div>
@@ -923,7 +923,7 @@ template&lt;size_t N = 3&gt; </div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../d8/d77/namespacemachine__learning.html">machine_learning</a></li><li class="navelem"><b>aystar_search</b></li><li class="navelem"><a class="el" href="../../dd/d9c/classmachine__learning_1_1aystar__search_1_1_eight_puzzle.html">EightPuzzle</a></li>
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.5 </li>
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