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annotated.html
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<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
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<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Algorithms_in_C++: Class List</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
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<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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<head>
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<meta name="generator" content="Doxygen 1.9.5"/>
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<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Algorithms_in_C++: Class Index</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
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<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=11"/>
<meta name="generator" content="Doxygen 1.9.5"/>
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<title>Algorithms_in_C++: others/smallest_circle.cpp File Reference</title>
<link href="../../tabs.css" rel="stylesheet" type="text/css"/>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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@@ -141,7 +141,7 @@ Functions</h2></td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Get centre and radius of the <a href="https://en.wikipedia.org/wiki/Smallest-circle_problem" target="_blank">smallest circle</a> that circumscribes given set of points. </p>
<div class="textblock"><p>Get centre and radius of the <a href="https://en.wikipedia.org/wiki/Smallest-circle_problem" target="_blank">smallest circle</a> that circumscribes given set of points. </p>
<dl class="section see"><dt>See also</dt><dd><a href="https://www.nayuki.io/page/smallest-enclosing-circle" target="_blank">other implementation</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a0b0676df8e4da7a08c7ccaecea344903" name="a0b0676df8e4da7a08c7ccaecea344903"></a>
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</tr>
</table>
</div><div class="memdoc">
<p >Find the centre and radius of a circle enclosing a set of points.<br />
<p>Find the centre and radius of a circle enclosing a set of points.<br />
The function returns the radius of the circle and prints the coordinated of the centre of the circle. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">P</td><td>vector of points </td></tr>
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</tr>
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<p >Compute the Euclidian distance between two points \(A\equiv(x_1,y_1)\) and \(B\equiv(x_2,y_2)\) using the formula: </p><p class="formulaDsp">
<p>Compute the Euclidian distance between two points \(A\equiv(x_1,y_1)\) and \(B\equiv(x_2,y_2)\) using the formula: </p><p class="formulaDsp">
\[d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}\]
</p>
<dl class="params"><dt>Parameters</dt><dd>
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<p >Main program </p>
<p>Main program </p>
<div class="fragment"><div class="line"><span class="lineno"> 198</span> {</div>
<div class="line"><span class="lineno"> 199</span> <a class="code hl_function" href="../../d0/d01/smallest__circle_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
<div class="line"><span class="lineno"> 200</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<p >Check if a set of points lie within given circle. This is true if the distance of all the points from the centre of the circle is less than the radius of the circle </p><dl class="params"><dt>Parameters</dt><dd>
<p>Check if a set of points lie within given circle. This is true if the distance of all the points from the centre of the circle is less than the radius of the circle </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">P</td><td>set of points to check </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">Center</td><td>coordinates to centre of the circle </td></tr>
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<p >Test case: result should be: <br />
<p>Test case: result should be: <br />
Circle with <br />
radius 3.318493136080724 <br />
centre at (3.0454545454545454, 1.3181818181818181) </p>
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<p >Test case: result should be: <br />
<p>Test case: result should be: <br />
Circle with <br />
radius 1.4142135623730951 <br />
centre at (1.0, 1.0) </p>
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<p >Test case: result should be: <br />
<p>Test case: result should be: <br />
Circle with <br />
radius 1.821078397711709 <br />
centre at (2.142857142857143, 1.7857142857142856) </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000010">Todo:</a></b></dt><dd>This test fails </dd></dl>
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<p >Compute the area of triangle formed by three points using <a href="https://en.wikipedia.org/wiki/Heron%27s_formula" target="_blank">Heron's formula</a>. If the lengths of the sides of the triangle are \(a,\,b,\,c\) and \(s=\displaystyle\frac{a+b+c}{2}\) is the semi-perimeter then the area is given by </p><p class="formulaDsp">
<p>Compute the area of triangle formed by three points using <a href="https://en.wikipedia.org/wiki/Heron%27s_formula" target="_blank">Heron's formula</a>. If the lengths of the sides of the triangle are \(a,\,b,\,c\) and \(s=\displaystyle\frac{a+b+c}{2}\) is the semi-perimeter then the area is given by </p><p class="formulaDsp">
\[A=\sqrt{s(s-a)(s-b)(s-c)}\]
</p>
<dl class="params"><dt>Parameters</dt><dd>
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@@ -138,8 +138,8 @@ Functions</h2></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Compute statistics for data entered in rreal-time. </p>
<p >This algorithm is really beneficial to compute statistics on data read in realtime. For example, devices reading biometrics data. The algorithm is simple enough to be easily implemented in an embedded system. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
<div class="textblock"><p>Compute statistics for data entered in rreal-time. </p>
<p>This algorithm is really beneficial to compute statistics on data read in realtime. For example, devices reading biometrics data. The algorithm is simple enough to be easily implemented in an embedded system. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a3c04138a5bfe5d72780bb7e82a18e627" name="a3c04138a5bfe5d72780bb7e82a18e627"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&#160;</a></span>main()</h2>
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<p >Main function </p>
<p>Main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 158</span> {</div>
<div class="line"><span class="lineno"> 159</span> <span class="keyword">const</span> <span class="keywordtype">float</span> test_data1[] = {3, 4, 5, -1.4, -3.6, 1.9, 1.};</div>
<div class="line"><span class="lineno"> 160</span> <a class="code hl_function" href="../../d0/d08/realtime__stats_8cpp.html#aa54c915581fcc495489175a4386d59fd">test_function</a>(test_data1, <span class="keyword">sizeof</span>(test_data1) / <span class="keyword">sizeof</span>(test_data1[0]));</div>
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<p >Test the algorithm implementation </p><dl class="params"><dt>Parameters</dt><dd>
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<a href="../../d0/d20/namespaceground__to__ground__projectile__motion.html#details">More...</a></p>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Functions for the Ground to ground <a href="https://en.wikipedia.org/wiki/Projectile_motion" target="_blank">projectile motion</a> equation. </p>
<div class="textblock"><p>Functions for the Ground to ground <a href="https://en.wikipedia.org/wiki/Projectile_motion" target="_blank">projectile motion</a> equation. </p>
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<div class="textblock"><p >Functions for the <a href="https://en.wikipedia.org/wiki/Quicksort" target="_blank">Quick sort implementation</a> in C++. </p>
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<tr class="memdesc:aab373beb3f618b90922528c68797d988"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a character to integer for indexing. <a href="../../d0/d3e/classdata__structures_1_1trie.html#aab373beb3f618b90922528c68797d988">More...</a><br /></td></tr>
<tr class="memdesc:aab373beb3f618b90922528c68797d988"><td class="mdescLeft">&#160;</td><td class="mdescRight">Convert a character to integer for indexing. <br /></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/Trie" target="_blank">Trie</a> implementation for small-case English alphabets <code>a-z</code> </p>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Trie" target="_blank">Trie</a> implementation for small-case English alphabets <code>a-z</code> </p>
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<a id="aab373beb3f618b90922528c68797d988" name="aab373beb3f618b90922528c68797d988"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aab373beb3f618b90922528c68797d988">&#9670;&#160;</a></span>char_to_int()</h2>
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<p >removes the string if it is not a prefix of any other string, if it is then just sets the ::data_structure::trie::isEndofWord to false, else removes the given string </p><dl class="section note"><dt>Note</dt><dd>the function ::data_structure::trie::deleteString might be erroneous </dd></dl>
<p>removes the string if it is not a prefix of any other string, if it is then just sets the ::data_structure::trie::isEndofWord to false, else removes the given string </p><dl class="section note"><dt>Note</dt><dd>the function ::data_structure::trie::deleteString might be erroneous </dd></dl>
<dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000005">Todo:</a></b></dt><dd>review the function ::data_structure::trie::deleteString and the commented lines </dd></dl>
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<p >insert string into the trie </p><dl class="params"><dt>Parameters</dt><dd>
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<p >search a string exists inside a given root trie </p><dl class="params"><dt>Parameters</dt><dd>
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Functions</h2></td></tr>
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<tr class="memdesc:a8a3b522a675ab4cdec2d275f6f7798a1"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <a href="../../d0/d46/finding__number__of__digits__in__a__number_8cpp.html#a8a3b522a675ab4cdec2d275f6f7798a1">More...</a><br /></td></tr>
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<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <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="../../d0/d46/finding__number__of__digits__in__a__number_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d0/d46/finding__number__of__digits__in__a__number_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 >[Program to count digits in an integer](<a href="https://www.geeksforgeeks.org/program-count-digits-integer-3-different-methods">https://www.geeksforgeeks.org/program-count-digits-integer-3-different-methods</a>) </p>
<div class="textblock"><p>[Program to count digits in an integer](<a href="https://www.geeksforgeeks.org/program-count-digits-integer-3-different-methods">https://www.geeksforgeeks.org/program-count-digits-integer-3-different-methods</a>) </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/amino19" target="_blank">aminos 🇮🇳</a></dd></dl>
<p>It is a very basic math of finding number of digits in a given number i.e, we can use it by inputting values whether it can be a positive/negative value, let's say: an integer. There is also a second method: by using "K = floor(log10(N) + 1)", but it's only applicable for numbers (not integers). For more details, refer to the <a href="https://github.com/TheAlgorithms/Algorithms-Explanation/blob/master/en/Basic%20Math/Finding
the number of digits in a number.md" target="_blank">Algorithms-Explanation</a> repository. </p>
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<p>for IO operations </p>
<p >for assert</p>
<p >The main function that checks the number of digits in a number. </p><dl class="params"><dt>Parameters</dt><dd>
<p>for assert</p>
<p>The main function that checks the number of digits in a number. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>the number to check its digits </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>the digits count </dd></dl>
<p >&lt; the variable used for the digits count</p>
<p>&lt; the variable used for the digits count</p>
<div class="fragment"><div class="line"><span class="lineno"> 27</span> {</div>
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<div class="line"><span class="lineno"> 29</span> </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implementation to calculate an estimate of the <a href="https://en.wikipedia.org/wiki/File:Pi_30K.gif" target="_blank">number π (Pi)</a>. </p>
<p >We take a random point P with coordinates (x, y) such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. If x² + y² ≤ 1, then the point is inside the quarter disk of radius 1, otherwise the point is outside. We know that the probability of the point being inside the quarter disk is equal to π/4 double approx(vector&lt;Point&gt; &amp;pts) which will use the points pts (drawn at random) to return an estimate of the number π </p><dl class="section note"><dt>Note</dt><dd>This implementation is better than naive recursive or iterative approach.</dd></dl>
<div class="textblock"><p>Implementation to calculate an estimate of the <a href="https://en.wikipedia.org/wiki/File:Pi_30K.gif" target="_blank">number π (Pi)</a>. </p>
<p>We take a random point P with coordinates (x, y) such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. If x² + y² ≤ 1, then the point is inside the quarter disk of radius 1, otherwise the point is outside. We know that the probability of the point being inside the quarter disk is equal to π/4 double approx(vector&lt;Point&gt; &amp;pts) which will use the points pts (drawn at random) to return an estimate of the number π </p><dl class="section note"><dt>Note</dt><dd>This implementation is better than naive recursive or iterative approach.</dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Qannaf" target="_blank">Qannaf AL-SAHMI</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a0ddf1224851353fc92bfbff6f499fa97" name="a0ddf1224851353fc92bfbff6f499fa97"></a>
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<a href="../../d0/d52/namespacewiggle__sort.html#details">More...</a></p>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Functions for <a href="https://leetcode.com/problems/wiggle-sort-ii/" target="_blank">Wiggle Sort</a> algorithm. </p>
<div class="textblock"><p>Functions for <a href="https://leetcode.com/problems/wiggle-sort-ii/" target="_blank">Wiggle Sort</a> algorithm. </p>
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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:aacdeecac857623e9fbfe92590f3c504d"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d58/classgraph_1_1_rooted_tree.html#aacdeecac857623e9fbfe92590f3c504d">RootedTree</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; int, int &gt; &gt; &amp;undirected_edges, int root_)</td></tr>
<tr class="memdesc:aacdeecac857623e9fbfe92590f3c504d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructs the tree by calculating parent for every vertex. Assumes a valid description of a tree is provided. <a href="../../d0/d58/classgraph_1_1_rooted_tree.html#aacdeecac857623e9fbfe92590f3c504d">More...</a><br /></td></tr>
<tr class="memdesc:aacdeecac857623e9fbfe92590f3c504d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructs the tree by calculating parent for every vertex. Assumes a valid description of a tree is provided. <br /></td></tr>
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<tr class="memitem:a877b2cba40d8d46dde6fb4209effed19 inherit pub_methods_classgraph_1_1_graph"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html#a877b2cba40d8d46dde6fb4209effed19">add_edge</a> (T u, T v, bool bidir=true)</td></tr>
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<tr class="memitem:a3755ec9e6a842238c7f4aac10b661981 inherit pub_methods_classgraph_1_1_graph"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map</a>&lt; T, bool &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html#a3755ec9e6a842238c7f4aac10b661981">breadth_first_search</a> (T src)</td></tr>
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<tr class="memdesc:a8839fa14bff19d2deab4a618447c13e5 inherit pub_methods_classgraph_1_1_graph"><td class="mdescLeft">&#160;</td><td class="mdescRight">Populate the adjacency list for each vertex in the graph. Assumes that evey edge is a pair of valid vertex indices. <a href="../../dc/d61/classgraph_1_1_graph.html#a8839fa14bff19d2deab4a618447c13e5">More...</a><br /></td></tr>
<tr class="memdesc:a8839fa14bff19d2deab4a618447c13e5 inherit pub_methods_classgraph_1_1_graph"><td class="mdescLeft">&#160;</td><td class="mdescRight">Populate the adjacency list for each vertex in the graph. Assumes that evey edge is a pair of valid vertex indices. <br /></td></tr>
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Protected Member Functions</h2></td></tr>
<tr class="memitem:ae6928f3ebd491541e9570e746b877c1e"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d58/classgraph_1_1_rooted_tree.html#ae6928f3ebd491541e9570e746b877c1e">populate_parents</a> ()</td></tr>
<tr class="memdesc:ae6928f3ebd491541e9570e746b877c1e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate the parents for all the vertices in the tree. Implements the breadth first search algorithm starting from the root vertex searching the entire tree and labeling parents for all vertices. <a href="../../d0/d58/classgraph_1_1_rooted_tree.html#ae6928f3ebd491541e9570e746b877c1e">More...</a><br /></td></tr>
<tr class="memdesc:ae6928f3ebd491541e9570e746b877c1e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate the parents for all the vertices in the tree. Implements the breadth first search algorithm starting from the root vertex searching the entire tree and labeling parents for all vertices. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Representation of a rooted tree. For every vertex its parent is precalculated. </p>
<div class="textblock"><p>Representation of a rooted tree. For every vertex its parent is precalculated. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="aacdeecac857623e9fbfe92590f3c504d" name="aacdeecac857623e9fbfe92590f3c504d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aacdeecac857623e9fbfe92590f3c504d">&#9670;&#160;</a></span>RootedTree()</h2>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Data structure for fast searching and insertion in \(O(\log n)\) time. </p>
<p >A skip list is a data structure that is used for storing a sorted list of items with a help of hierarchy of linked lists that connect increasingly sparse subsequences of the items</p>
<p >References used: <a href="https://www.geeksforgeeks.org/skip-list/" target="_blank">GeeksForGeek</a>, <a href="https://iq.opengenus.org/skip-list" target="_blank">OpenGenus</a> for PseudoCode and Code </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/enqidu" target="_blank">enqidu</a> </dd>
<div class="textblock"><p>Data structure for fast searching and insertion in \(O(\log n)\) time. </p>
<p>A skip list is a data structure that is used for storing a sorted list of items with a help of hierarchy of linked lists that connect increasingly sparse subsequences of the items</p>
<p>References used: <a href="https://www.geeksforgeeks.org/skip-list/" target="_blank">GeeksForGeek</a>, <a href="https://iq.opengenus.org/skip-list" target="_blank">OpenGenus</a> for PseudoCode and Code </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/enqidu" target="_blank">enqidu</a> </dd>
<dd>
<a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<p >Main function: Creates and inserts random 2^[number of levels] elements into the skip lists and than displays it </p>
<p>Main function: Creates and inserts random 2^[number of levels] elements into the skip lists and than displays it </p>
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<div class="line"><span class="lineno"> 213</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
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<tr class="memdesc:afca808362c13273ca8c8ae7d58e8eee0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to count the number of children a node in the trie has. <a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#afca808362c13273ca8c8ae7d58e8eee0">More...</a><br /></td></tr>
<tr class="memdesc:afca808362c13273ca8c8ae7d58e8eee0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to count the number of children a node in the trie has. <br /></td></tr>
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<tr class="memitem:a7ecb75b985b1ffc575a880274f855b1c"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a7ecb75b985b1ffc575a880274f855b1c">Insert</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;entry)</td></tr>
<tr class="memdesc:a7ecb75b985b1ffc575a880274f855b1c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to insert a word in the trie. <a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a7ecb75b985b1ffc575a880274f855b1c">More...</a><br /></td></tr>
<tr class="memdesc:a7ecb75b985b1ffc575a880274f855b1c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to insert a word in the trie. <br /></td></tr>
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<tr class="memitem:aefd24626ac47277431c9b8604e064340"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#aefd24626ac47277431c9b8604e064340">Delete</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> entry)</td></tr>
<tr class="memdesc:aefd24626ac47277431c9b8604e064340"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to verify presence and hence delete an entry from the trie. <a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#aefd24626ac47277431c9b8604e064340">More...</a><br /></td></tr>
<tr class="memdesc:aefd24626ac47277431c9b8604e064340"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to verify presence and hence delete an entry from the trie. <br /></td></tr>
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<tr class="memitem:adef6940391f981ab86767775176b7169"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#adef6940391f981ab86767775176b7169">DeleteFrom</a> (<a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html">Tnode</a> *delete_from, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> delete_string, int remove_index)</td></tr>
<tr class="memdesc:adef6940391f981ab86767775176b7169"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function recursively deletes the substring character by character iterating through the string to be deleted. It traverses till the end of word in a recursive fashion, from there it deletes characters one by one till it reaches back to the initial call. <a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#adef6940391f981ab86767775176b7169">More...</a><br /></td></tr>
<tr class="memdesc:adef6940391f981ab86767775176b7169"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function recursively deletes the substring character by character iterating through the string to be deleted. It traverses till the end of word in a recursive fashion, from there it deletes characters one by one till it reaches back to the initial call. <br /></td></tr>
<tr class="separator:adef6940391f981ab86767775176b7169"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4a624fcdf3c3beb2025d69f2cfda8023"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a4a624fcdf3c3beb2025d69f2cfda8023">SearchPresence</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;key)</td></tr>
<tr class="memdesc:a4a624fcdf3c3beb2025d69f2cfda8023"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to check a word's presence in the trie (Basic) <a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a4a624fcdf3c3beb2025d69f2cfda8023">More...</a><br /></td></tr>
<tr class="memdesc:a4a624fcdf3c3beb2025d69f2cfda8023"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to check a word's presence in the trie (Basic) <br /></td></tr>
<tr class="separator:a4a624fcdf3c3beb2025d69f2cfda8023"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a097913c4badec2b60d50a171ecc299fe"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a097913c4badec2b60d50a171ecc299fe">SuggestAutocomplete</a> (<a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html">Tnode</a> *new_root, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;prefix)</td></tr>
<tr class="memdesc:a097913c4badec2b60d50a171ecc299fe"><td class="mdescLeft">&#160;</td><td class="mdescRight">Recursive function to suggest all the entries of trie which have a given common prefix. <a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a097913c4badec2b60d50a171ecc299fe">More...</a><br /></td></tr>
<tr class="memdesc:a097913c4badec2b60d50a171ecc299fe"><td class="mdescLeft">&#160;</td><td class="mdescRight">Recursive function to suggest all the entries of trie which have a given common prefix. <br /></td></tr>
<tr class="separator:a097913c4badec2b60d50a171ecc299fe"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a18b70172ca4fb2811dbfb9a86e48b34c"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a18b70172ca4fb2811dbfb9a86e48b34c">SearchSuggestions</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;key)</td></tr>
<tr class="memdesc:a18b70172ca4fb2811dbfb9a86e48b34c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Lists out all the words in trie with the longest prefix of the search key that is present in the trie. For example - if trie contains "abc", "abcde", "abcdefg", "abcddef" and if the search key is "abcdezz", then the longest common prefix is "abcde" and hence search results will be "abcde", "abcdefg". <a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a18b70172ca4fb2811dbfb9a86e48b34c">More...</a><br /></td></tr>
<tr class="memdesc:a18b70172ca4fb2811dbfb9a86e48b34c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Lists out all the words in trie with the longest prefix of the search key that is present in the trie. For example - if trie contains "abc", "abcde", "abcdefg", "abcddef" and if the search key is "abcdezz", then the longest common prefix is "abcde" and hence search results will be "abcde", "abcdefg". <br /></td></tr>
<tr class="separator:a18b70172ca4fb2811dbfb9a86e48b34c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9e556f52c837190ecf4265b1f05cfe9c"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a9e556f52c837190ecf4265b1f05cfe9c">SuggestFreqAutocomplete</a> (<a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html">Tnode</a> *new_root, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;prefix, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; int, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &gt; &gt; *suggestions)</td></tr>
<tr class="memdesc:a9e556f52c837190ecf4265b1f05cfe9c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Recursive function to suggest most frequently searched entries of trie which have a given common prefix. <a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a9e556f52c837190ecf4265b1f05cfe9c">More...</a><br /></td></tr>
<tr class="memdesc:a9e556f52c837190ecf4265b1f05cfe9c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Recursive function to suggest most frequently searched entries of trie which have a given common prefix. <br /></td></tr>
<tr class="separator:a9e556f52c837190ecf4265b1f05cfe9c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7c5ab271d8042540f64ef16d259d1503"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a7c5ab271d8042540f64ef16d259d1503">SearchFreqSuggestions</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;key)</td></tr>
<tr class="memdesc:a7c5ab271d8042540f64ef16d259d1503"><td class="mdescLeft">&#160;</td><td class="mdescRight">Lists out the most frequent words in trie with the longest prefix of the search key that is present in the trie. For example - if trie contains "abc", "abcde", "abcdefg", "abcddef" and they have been previously searched for 3, 1, 2, 4 times respectively, if the search key is "ab", then the longest common prefix is "ab" and only the top 3 frequencies among the matches would be displayed viz. "abcddef", "abc", "abcdefg". <a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#a7c5ab271d8042540f64ef16d259d1503">More...</a><br /></td></tr>
<tr class="memdesc:a7c5ab271d8042540f64ef16d259d1503"><td class="mdescLeft">&#160;</td><td class="mdescRight">Lists out the most frequent words in trie with the longest prefix of the search key that is present in the trie. For example - if trie contains "abc", "abcde", "abcdefg", "abcddef" and they have been previously searched for 3, 1, 2, 4 times respectively, if the search key is "ab", then the longest common prefix is "ab" and only the top 3 frequencies among the matches would be displayed viz. "abcddef", "abc", "abcdefg". <br /></td></tr>
<tr class="separator:a7c5ab271d8042540f64ef16d259d1503"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aacafb8c9f3ebac7ac6c01d9645bb67b6"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#aacafb8c9f3ebac7ac6c01d9645bb67b6">SelectionTop_3</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; int, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &gt; &gt; *suggestions)</td></tr>
<tr class="memdesc:aacafb8c9f3ebac7ac6c01d9645bb67b6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to display the 3 suggestions with highest frequency of search hits. <a href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html#aacafb8c9f3ebac7ac6c01d9645bb67b6">More...</a><br /></td></tr>
<tr class="memdesc:aacafb8c9f3ebac7ac6c01d9645bb67b6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to display the 3 suggestions with highest frequency of search hits. <br /></td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pri-attribs" name="pri-attribs"></a>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Class defining the structure of trie node and containing the methods to perform operations on them. </p>
<div class="textblock"><p>Class defining the structure of trie node and containing the methods to perform operations on them. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="aef1ef6608e5876312d9ae7f36f469ba7" name="aef1ef6608e5876312d9ae7f36f469ba7"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aef1ef6608e5876312d9ae7f36f469ba7">&#9670;&#160;</a></span>Tnode() <span class="overload">[1/2]</span></h2>
@@ -912,7 +912,7 @@ 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="../../da/d6d/namespaceoperations__on__datastructures.html">operations_on_datastructures</a></li><li class="navelem"><b>trie_operations</b></li><li class="navelem"><a class="el" href="../../d0/d5f/classoperations__on__datastructures_1_1trie__operations_1_1_tnode.html">Tnode</a></li>
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<tr class="memitem:a79a9c914a6c68275b3640303d7faad8a"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d65/namespacedouble__hashing.html#a79a9c914a6c68275b3640303d7faad8a">add</a> (int key)</td></tr>
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<tr class="memitem:a0d90726ed1de7b3d2ae261baed048003"><td class="memItemLeft" align="right" valign="top">size_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">hashFxn</a> (int key)</td></tr>
<tr class="memdesc:a0d90726ed1de7b3d2ae261baed048003"><td class="mdescLeft">&#160;</td><td class="mdescRight">Hash a key. Uses the STL library's <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/hash.html">std::hash()</a></code> function. <a href="../../d0/d65/namespacedouble__hashing.html#a0d90726ed1de7b3d2ae261baed048003">More...</a><br /></td></tr>
<tr class="memdesc:a0d90726ed1de7b3d2ae261baed048003"><td class="mdescLeft">&#160;</td><td class="mdescRight">Hash a key. Uses the STL library's <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/hash.html">std::hash()</a></code> function. <br /></td></tr>
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<tr class="memdesc:a33968a1178289ab61445dd4000df7082"><td class="mdescLeft">&#160;</td><td class="mdescRight">Used for second hash function. <a href="../../d0/d65/namespacedouble__hashing.html#a33968a1178289ab61445dd4000df7082">More...</a><br /></td></tr>
<tr class="memdesc:a33968a1178289ab61445dd4000df7082"><td class="mdescLeft">&#160;</td><td class="mdescRight">Used for second hash function. <br /></td></tr>
<tr class="separator:a33968a1178289ab61445dd4000df7082"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8f8ff4fb018e1bb32d67d8a1885d3200"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d65/namespacedouble__hashing.html#a8f8ff4fb018e1bb32d67d8a1885d3200">doubleHash</a> (int key, bool searching)</td></tr>
<tr class="memdesc:a8f8ff4fb018e1bb32d67d8a1885d3200"><td class="mdescLeft">&#160;</td><td class="mdescRight">Performs double hashing to resolve collisions. <a href="../../d0/d65/namespacedouble__hashing.html#a8f8ff4fb018e1bb32d67d8a1885d3200">More...</a><br /></td></tr>
<tr class="memdesc:a8f8ff4fb018e1bb32d67d8a1885d3200"><td class="mdescLeft">&#160;</td><td class="mdescRight">Performs double hashing to resolve collisions. <br /></td></tr>
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<tr class="memitem:a1e901418c759627557eff359b8db38cd"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d65/namespacedouble__hashing.html#a1e901418c759627557eff359b8db38cd">display</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >An implementation of hash table using <a href="https://en.wikipedia.org/wiki/Double_hashing" target="_blank">double hashing</a> algorithm. </p>
<div class="textblock"><p>An implementation of hash table using <a href="https://en.wikipedia.org/wiki/Double_hashing" target="_blank">double hashing</a> algorithm. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a79a9c914a6c68275b3640303d7faad8a" name="a79a9c914a6c68275b3640303d7faad8a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a79a9c914a6c68275b3640303d7faad8a">&#9670;&#160;</a></span>add()</h2>
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</tr>
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<p >Checks for load factor here </p><dl class="params"><dt>Parameters</dt><dd>
<p>Checks for load factor here </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">key</td><td>key value to add to the table </td></tr>
</table>
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<p >Information about the adding process </p><dl class="params"><dt>Parameters</dt><dd>
<p>Information about the adding process </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">key</td><td>key value to add to table </td></tr>
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<p >Displays the table </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
<p>Displays the table </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 143</span> {</div>
<div class="line"><span class="lineno"> 144</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; totalSize; i++) {</div>
<div class="line"><span class="lineno"> 145</span> <span class="keywordflow">if</span> (table[i].key == notPresent) {</div>
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<p >Finds empty spot in a vector </p><dl class="params"><dt>Parameters</dt><dd>
<p>Finds empty spot in a vector </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">entry</td><td>vector to search in </td></tr>
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<p >Rehashes the table into a bigger table </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
<p>Rehashes the table into a bigger table </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 161</span> {</div>
<div class="line"><span class="lineno"> 162</span> <span class="comment">// Necessary so wall of add info isn&#39;t printed all at once</span></div>
<div class="line"><span class="lineno"> 163</span> rehashing = <span class="keyword">true</span>;</div>
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<p >Information about removal process </p><dl class="params"><dt>Parameters</dt><dd>
<p>Information about removal process </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">key</td><td>key value to remove from table </td></tr>
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<p >Removes key. Leaves tombstone upon removal. </p><dl class="params"><dt>Parameters</dt><dd>
<p>Removes key. Leaves tombstone upon removal. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">key</td><td>key value to remove </td></tr>
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<p >Looks for a matching key </p><dl class="params"><dt>Parameters</dt><dd>
<p>Looks for a matching key </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">entry</td><td>vector to search in </td></tr>
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Functions</h2></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">math::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:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d6d/modular__exponentiation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d6d/modular__exponentiation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d0/d6d/modular__exponentiation_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 >C++ Program for Modular Exponentiation Iteratively. </p>
<p >The task is to calculate the value of an integer a raised to an integer exponent b under modulo c. </p><dl class="section note"><dt>Note</dt><dd>The time complexity of this approach is O(log b).</dd></dl>
<div class="textblock"><p>C++ Program for Modular Exponentiation Iteratively. </p>
<p>The task is to calculate the value of an integer a raised to an integer exponent b under modulo c. </p><dl class="section note"><dt>Note</dt><dd>The time complexity of this approach is O(log b).</dd></dl>
<p>Example: (4^3) % 5 (where ^ stands for exponentiation and % for modulo) (4*4*4) % 5 (4 % 5) * ( (4*4) % 5 ) 4 * (16 % 5) 4 * 1 4 We can also verify the result as 4^3 is 64 and 64 modulo 5 is 4</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Shri2206" target="_blank">Shri2206</a> </dd></dl>
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<p >Function for testing power function. test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
<p>Function for testing power function. test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 60</span> {</div>
<div class="line"><span class="lineno"> 61</span> uint32_t test_case_1 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">math::power</a>(2, 5, 13);</div>
<div class="line"><span class="lineno"> 62</span> assert(test_case_1 == 6);</div>
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<a href="../../d0/d6f/namespaceothers.html#details">More...</a></p>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >for <code>vector</code> </p>
<p >for vector</p>
<p >Other algorithms.</p>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Program to find the Longest Palindormic Subsequence of a string. </p>
<p ><a href="https://en.wikipedia.org/wiki/Palindrome" target="_blank">Palindrome</a> string sequence of characters which reads the same backward as forward <a href="https://en.wikipedia.org/wiki/Subsequence" target="_blank">Subsequence</a> is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.</p>
<div class="textblock"><p>Program to find the Longest Palindormic Subsequence of a string. </p>
<p><a href="https://en.wikipedia.org/wiki/Palindrome" target="_blank">Palindrome</a> string sequence of characters which reads the same backward as forward <a href="https://en.wikipedia.org/wiki/Subsequence" target="_blank">Subsequence</a> is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/anjali1903" target="_blank">Anjali Jha</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<p >Function that returns the longest palindromic subsequence of a string </p>
<p>Function that returns the longest palindromic subsequence of a string </p>
<div class="fragment"><div class="line"><span class="lineno"> 25</span> {</div>
<div class="line"><span class="lineno"> 26</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> b = a;</div>
<div class="line"><span class="lineno"> 27</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/reverse.html">reverse</a>(b.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(), b.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">end</a>());</div>
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<p >Main Function </p>
<p>Main Function </p>
<div class="fragment"><div class="line"><span class="lineno"> 87</span> {</div>
<div class="line"><span class="lineno"> 88</span> <a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">return</span> 0;</div>
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<p >Test function </p>
<p>Test function </p>
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<div class="textblock"><p >C++ Program to calculate the number of positive divisors. </p>
<p >This algorithm uses the prime factorization approach. Any positive integer can be written as a product of its prime factors. <br />
<div class="textblock"><p>C++ Program to calculate the number of positive divisors. </p>
<p>This algorithm uses the prime factorization approach. Any positive integer can be written as a product of its prime factors. <br />
Let \(N = p_1^{e_1} \times p_2^{e_2} \times\cdots\times p_k^{e_k}\) where \(p_1,\, p_2,\, \dots,\, p_k\) are distinct prime factors of \(N\) and \(e_1,\, e_2,\, \dots,\, e_k\) are respective positive integer exponents. <br />
Each positive divisor of \(N\) is in the form \(p_1^{g_1}\times p_2^{g_2}\times\cdots\times p_k^{g_k}\) where \(0\le g_i\le e_i\) are integers for all \(1\le i\le k\). <br />
Finally, there are \((e_1+1) \times (e_2+1)\times\cdots\times (e_k+1)\) positive divisors of \(N\) since we can choose every \(g_i\) independently.</p>
<p >Example: <br />
<p>Example: <br />
\(N = 36 = (3^2 \cdot 2^2)\) <br />
\(\mbox{number_of_positive_divisors}(36) = (2+1) \cdot (2+1) = 9\). <br />
list of positive divisors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.</p>
<p >Similarly, for N = -36 the number of positive divisors remain same. </p>
<p>Similarly, for N = -36 the number of positive divisors remain same. </p>
</div><h2 class="groupheader">Function Documentation</h2>
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<p >Main function </p>
<p>Main function </p>
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<div class="line"><span class="lineno"> 82</span> <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
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<p >Function to compute the number of positive divisors. </p><dl class="params"><dt>Parameters</dt><dd>
<p>Function to compute the number of positive divisors. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
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<p >Test implementations </p>
<p>Test implementations </p>
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<div class="textblock"><p >Functions for the <a href="https://en.wikipedia.org/wiki/Monte_Carlo_integration" target="_blank">Monte Carlo Integration</a> implementation. </p>
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<tr class="memdesc:a140d913e42fb94176a0b2c8b29a80420"><td class="mdescLeft">&#160;</td><td class="mdescRight">bottom-up merge sort which sorts elements in a non-decreasing order <a href="../../d5/d91/namespacesorting.html#a140d913e42fb94176a0b2c8b29a80420">More...</a><br /></td></tr>
<tr class="memdesc:a140d913e42fb94176a0b2c8b29a80420"><td class="mdescLeft">&#160;</td><td class="mdescRight">bottom-up merge sort which sorts elements in a non-decreasing order <br /></td></tr>
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<tr class="memdesc:a27236b8d3df3832e1f1225576a122534"><td class="mdescLeft">&#160;</td><td class="mdescRight">bottom-up merge sort which sorts elements in a non-decreasing order <a href="../../d5/d91/namespacesorting.html#a27236b8d3df3832e1f1225576a122534">More...</a><br /></td></tr>
<tr class="memdesc:a27236b8d3df3832e1f1225576a122534"><td class="mdescLeft">&#160;</td><td class="mdescRight">bottom-up merge sort which sorts elements in a non-decreasing order <br /></td></tr>
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<tr class="memdesc:ae97f4dd815654c4682f564afd718e824"><td class="mdescLeft">&#160;</td><td class="mdescRight">bottom-up merge sort which sorts elements in a non-decreasing order <a href="../../d5/d91/namespacesorting.html#ae97f4dd815654c4682f564afd718e824">More...</a><br /></td></tr>
<tr class="memdesc:ae97f4dd815654c4682f564afd718e824"><td class="mdescLeft">&#160;</td><td class="mdescRight">bottom-up merge sort which sorts elements in a non-decreasing order <br /></td></tr>
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<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/db6/non__recursive__merge__sort_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
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<div class="textblock"><p >Copyright 2020 </p><dl class="section author"><dt>Author</dt><dd>Albirair</dd></dl>
<div class="textblock"><p>Copyright 2020 </p><dl class="section author"><dt>Author</dt><dd>Albirair</dd></dl>
<p>A generic implementation of non-recursive merge sort. </p>
</div><h2 class="groupheader">Function Documentation</h2>
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