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<title>Algorithms_in_C++: graph::is_graph_bipartite::Graph Class Reference</title>
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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:a6aef65b40347c4606662cad4dd2e14d3"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html#a6aef65b40347c4606662cad4dd2e14d3">Graph</a> (int size)</td></tr>
<tr class="memdesc:a6aef65b40347c4606662cad4dd2e14d3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor that initializes the graph on creation. <a href="../../de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html#a6aef65b40347c4606662cad4dd2e14d3">More...</a><br /></td></tr>
<tr class="memdesc:a6aef65b40347c4606662cad4dd2e14d3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor that initializes the graph on creation. <br /></td></tr>
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<tr class="memitem:ad8c10df34357b2cd865c81e0c4f0bd8c"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html#ad8c10df34357b2cd865c81e0c4f0bd8c">addEdge</a> (int u, int v)</td></tr>
<tr class="memdesc:ad8c10df34357b2cd865c81e0c4f0bd8c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function that add an edge between two nodes or vertices of graph. <a href="../../de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html#ad8c10df34357b2cd865c81e0c4f0bd8c">More...</a><br /></td></tr>
<tr class="memdesc:ad8c10df34357b2cd865c81e0c4f0bd8c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function that add an edge between two nodes or vertices of graph. <br /></td></tr>
<tr class="separator:ad8c10df34357b2cd865c81e0c4f0bd8c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9b0c6400693a5cfff971f768dd5ca5ca"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html#a9b0c6400693a5cfff971f768dd5ca5ca">is_bipartite</a> ()</td></tr>
<tr class="memdesc:a9b0c6400693a5cfff971f768dd5ca5ca"><td class="mdescLeft">&#160;</td><td class="mdescRight">function to add edges to our graph <a href="../../de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html#a9b0c6400693a5cfff971f768dd5ca5ca">More...</a><br /></td></tr>
<tr class="memdesc:a9b0c6400693a5cfff971f768dd5ca5ca"><td class="mdescLeft">&#160;</td><td class="mdescRight">function to add edges to our graph <br /></td></tr>
<tr class="separator:a9b0c6400693a5cfff971f768dd5ca5ca"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Class for representing graph as an adjacency list. </p>
<div class="textblock"><p>Class for representing graph as an adjacency list. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="a6aef65b40347c4606662cad4dd2e14d3" name="a6aef65b40347c4606662cad4dd2e14d3"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a6aef65b40347c4606662cad4dd2e14d3">&#9670;&#160;</a></span>Graph()</h2>
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<p>function to add edges to our graph </p>
<p >function that checks whether the graph is bipartite or not the function returns true if the graph is a bipartite graph the function returns false if the graph is not a bipartite graph</p>
<p >Here, side refers to the two disjoint subsets of the bipartite graph. Initially, the values of side are set to -1 which is an unassigned state. A for loop is run for every vertex of the graph. If the current edge has no side assigned to it, then a Breadth First Search operation is performed. If two neighbours have the same side then the graph will not be bipartite and the value of check becomes false. If and only if each pair of neighbours have different sides, the value of check will be true and hence the graph bipartite.</p>
<p>function that checks whether the graph is bipartite or not the function returns true if the graph is a bipartite graph the function returns false if the graph is not a bipartite graph</p>
<p>Here, side refers to the two disjoint subsets of the bipartite graph. Initially, the values of side are set to -1 which is an unassigned state. A for loop is run for every vertex of the graph. If the current edge has no side assigned to it, then a Breadth First Search operation is performed. If two neighbours have the same side then the graph will not be bipartite and the value of check becomes false. If and only if each pair of neighbours have different sides, the value of check will be true and hence the graph bipartite.</p>
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if th graph is bipartite </dd>
<dd>
<code>false</code> otherwise </dd></dl>
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<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../df/dce/namespacegraph.html">graph</a></li><li class="navelem"><b>is_graph_bipartite</b></li><li class="navelem"><a class="el" href="../../de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html">Graph</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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@@ -130,18 +130,18 @@ Namespaces</h2></td></tr>
Functions</h2></td></tr>
<tr class="memitem:ae79a9d247691fce0d655fce75f1c04fa"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ae79a9d247691fce0d655fce75f1c04fa"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d07/cycle__sort_8cpp.html#ae79a9d247691fce0d655fce75f1c04fa">sorting::cycle_sort::cycleSort</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;in_arr)</td></tr>
<tr class="memdesc:ae79a9d247691fce0d655fce75f1c04fa"><td class="mdescLeft">&#160;</td><td class="mdescRight">The main function implements cycleSort. <a href="../../de/d07/cycle__sort_8cpp.html#ae79a9d247691fce0d655fce75f1c04fa">More...</a><br /></td></tr>
<tr class="memdesc:ae79a9d247691fce0d655fce75f1c04fa"><td class="mdescLeft">&#160;</td><td class="mdescRight">The main function implements cycleSort. <br /></td></tr>
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<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test implementations. <a href="../../de/d07/cycle__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">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="../../de/d07/cycle__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../de/d07/cycle__sort_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>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implementation of <a href="https://en.wikipedia.org/wiki/Cycle_sort" target="_blank">Cycle sort</a> algorithm. </p>
<p >Cycle Sort is a sorting algorithm that works in \(O(n^2)\) time in the best case and works in \(O(n^2)\) in worst case. If a element is already at its correct position, do nothing. If a element is not at its correct position, we then need to move it to its correct position by computing the correct positions.Therefore, we should make sure the duplicate elements. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/dalaoqi" target="_blank">TsungHan Ho</a> </dd></dl>
<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Cycle_sort" target="_blank">Cycle sort</a> algorithm. </p>
<p>Cycle Sort is a sorting algorithm that works in \(O(n^2)\) time in the best case and works in \(O(n^2)\) in worst case. If a element is already at its correct position, do nothing. If a element is not at its correct position, we then need to move it to its correct position by computing the correct positions.Therefore, we should make sure the duplicate elements. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/dalaoqi" target="_blank">TsungHan Ho</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae79a9d247691fce0d655fce75f1c04fa" name="ae79a9d247691fce0d655fce75f1c04fa"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae79a9d247691fce0d655fce75f1c04fa">&#9670;&#160;</a></span>cycleSort()</h2>
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<li class="navelem"><a class="el" href="../../dir_bb1b521853a9c46347182a9d10420771.html">sorting</a></li><li class="navelem"><a class="el" href="../../de/d07/cycle__sort_8cpp.html">cycle_sort.cpp</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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<head>
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<meta name="generator" content="Doxygen 1.9.5"/>
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<title>Algorithms_in_C++: merge_insertion Namespace Reference</title>
<link href="../../tabs.css" rel="stylesheet" type="text/css"/>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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<p>Combined Intersion-Merge sorting algorithm.
<a href="../../de/d0a/namespacemerge__insertion.html#details">More...</a></p>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Combined Intersion-Merge sorting algorithm. </p>
<div class="textblock"><p>Combined Intersion-Merge sorting algorithm. </p>
</div></div><!-- contents -->
</div><!-- doc-content -->
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<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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Functions</h2></td></tr>
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<tr class="memdesc:a0bc61b3903d9a53061bf31e5d110fe61"><td class="mdescLeft">&#160;</td><td class="mdescRight">using fibonacci search algorithm finds an index of a given element in a sorted array <a href="../../de/d0d/fibonacci__search_8cpp.html#a0bc61b3903d9a53061bf31e5d110fe61">More...</a><br /></td></tr>
<tr class="memdesc:a0bc61b3903d9a53061bf31e5d110fe61"><td class="mdescLeft">&#160;</td><td class="mdescRight">using fibonacci search algorithm finds an index of a given element in a sorted array <br /></td></tr>
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<tr class="memdesc:a5e144326104e57a3808aed7eb098db0d"><td class="mdescLeft">&#160;</td><td class="mdescRight">random tests for checking performance when an array doesn't contain an element <a href="../../de/d0d/fibonacci__search_8cpp.html#a5e144326104e57a3808aed7eb098db0d">More...</a><br /></td></tr>
<tr class="memdesc:a5e144326104e57a3808aed7eb098db0d"><td class="mdescLeft">&#160;</td><td class="mdescRight">random tests for checking performance when an array doesn't contain an element <br /></td></tr>
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<tr class="memitem:a2aa09bef74ee063c1331de0883af4f4f"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d0d/fibonacci__search_8cpp.html#a2aa09bef74ee063c1331de0883af4f4f">random_tests</a> ()</td></tr>
<tr class="memdesc:a2aa09bef74ee063c1331de0883af4f4f"><td class="mdescLeft">&#160;</td><td class="mdescRight">random tests which cover cases when we have one, multiple or zero occurences of the value we're looking for <a href="../../de/d0d/fibonacci__search_8cpp.html#a2aa09bef74ee063c1331de0883af4f4f">More...</a><br /></td></tr>
<tr class="memdesc:a2aa09bef74ee063c1331de0883af4f4f"><td class="mdescLeft">&#160;</td><td class="mdescRight">random tests which cover cases when we have one, multiple or zero occurences of the value we're looking for <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/Fibonacci_search_technique" target="_blank">Fibonacci search algorithm</a> </p>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Fibonacci_search_technique" target="_blank">Fibonacci search algorithm</a> </p>
<dl class="section author"><dt>Author</dt><dd>sprintyaf </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<p >Main Function testing the algorithm </p>
<p>Main Function testing the algorithm </p>
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<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Disjoint-set_data_structure" target="_blank">Disjoint Sets Data Structure (Disjoint Sets)</a> </p>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Disjoint-set_data_structure" target="_blank">Disjoint Sets Data Structure (Disjoint Sets)</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/leoyang429" target="_blank">leoyang429</a></dd></dl>
<p>A disjoint set data structure (also called union find or merge find set) is a data structure that tracks a set of elements partitioned into a number of disjoint (non-overlapping) subsets. Some situations where disjoint sets can be used are- to find connected components of a graph, kruskal's algorithm for finding <a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> Spanning Tree etc. There are two operation which we perform on disjoint sets - 1) Union 2) Find </p>
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<p >Function to create a set </p><dl class="params"><dt>Parameters</dt><dd>
<p>Function to create a set </p><dl class="params"><dt>Parameters</dt><dd>
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<p >Find operation takes a number x and returns the set to which this number belongs to. </p><dl class="params"><dt>Parameters</dt><dd>
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<p >A utility function to check if x and y are from same set or not </p><dl class="params"><dt>Parameters</dt><dd>
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<p >Main function </p>
<p>Main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 93</span> {</div>
<div class="line"><span class="lineno"> 94</span> <span class="comment">// tests CreateSet &amp; Find</span></div>
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<p >Union operation combines two disjoint sets to make a single set in this union function we pass two elements and check if they are from different sets then combine those sets </p><dl class="params"><dt>Parameters</dt><dd>
<p>Union operation combines two disjoint sets to make a single set in this union function we pass two elements and check if they are from different sets then combine those sets </p><dl class="params"><dt>Parameters</dt><dd>
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<tr class="memdesc:a167c24bd817469ae47358d12e034f2d5"><td class="mdescLeft">&#160;</td><td class="mdescRight">A Test to check an simple case. <a href="../../d9/df4/namespacetests.html#a167c24bd817469ae47358d12e034f2d5">More...</a><br /></td></tr>
<tr class="memdesc:a167c24bd817469ae47358d12e034f2d5"><td class="mdescLeft">&#160;</td><td class="mdescRight">A Test to check an simple case. <br /></td></tr>
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<tr class="memdesc:abdd77344d4af8fd56d14a5cabbf2f669"><td class="mdescLeft">&#160;</td><td class="mdescRight">A Test to check an empty vector. <a href="../../d9/df4/namespacetests.html#abdd77344d4af8fd56d14a5cabbf2f669">More...</a><br /></td></tr>
<tr class="memdesc:abdd77344d4af8fd56d14a5cabbf2f669"><td class="mdescLeft">&#160;</td><td class="mdescRight">A Test to check an empty vector. <br /></td></tr>
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<tr class="memdesc:aa515639572647508b94986489aab6d76"><td class="mdescLeft">&#160;</td><td class="mdescRight">A Test to check an invalid shift value. <a href="../../d9/df4/namespacetests.html#aa515639572647508b94986489aab6d76">More...</a><br /></td></tr>
<tr class="memdesc:aa515639572647508b94986489aab6d76"><td class="mdescLeft">&#160;</td><td class="mdescRight">A Test to check an invalid shift value. <br /></td></tr>
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<tr class="memdesc:a2b9769e44683dcb67fe1083ad91e134d"><td class="mdescLeft">&#160;</td><td class="mdescRight">A Test to check a very large input. <a href="../../d9/df4/namespacetests.html#a2b9769e44683dcb67fe1083ad91e134d">More...</a><br /></td></tr>
<tr class="memdesc:a2b9769e44683dcb67fe1083ad91e134d"><td class="mdescLeft">&#160;</td><td class="mdescRight">A Test to check a very large input. <br /></td></tr>
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<tr class="memdesc:af7b81d7a1534216af6a36a80135beb86"><td class="mdescLeft">&#160;</td><td class="mdescRight">A Test to check a shift of zero. <a href="../../d9/df4/namespacetests.html#af7b81d7a1534216af6a36a80135beb86">More...</a><br /></td></tr>
<tr class="memdesc:af7b81d7a1534216af6a36a80135beb86"><td class="mdescLeft">&#160;</td><td class="mdescRight">A Test to check a shift of zero. <br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d33/circular__linked__list_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to test the correctness of the Circular Linked List. <a href="../../de/d33/circular__linked__list_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to test the correctness of the Circular Linked List. <br /></td></tr>
<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d33/circular__linked__list_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">main function <a href="../../de/d33/circular__linked__list_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>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implementation for a <a href="https://www.geeksforgeeks.org/circular-linked-list/" target="_blank">Circular Linked List</a>. </p>
<p >A Circular Linked List is a variation on the regular linked list, in which the last node has a pointer to the first node, which creates a full circle. Consequently, this allows any node to be used as the starting point for the list. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/polarvoid" target="_blank">Alvin</a> </dd></dl>
<div class="textblock"><p>Implementation for a <a href="https://www.geeksforgeeks.org/circular-linked-list/" target="_blank">Circular Linked List</a>. </p>
<p>A Circular Linked List is a variation on the regular linked list, in which the last node has a pointer to the first node, which creates a full circle. Consequently, this allows any node to be used as the starting point for the list. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/polarvoid" target="_blank">Alvin</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<a href="../../de/d36/namespacen__bonacci.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="http://oeis.org/wiki/N-bonacci_numbers" target="_blank">N-bonacci</a> implementation. </p>
<div class="textblock"><p>Functions for the <a href="http://oeis.org/wiki/N-bonacci_numbers" target="_blank">N-bonacci</a> implementation. </p>
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<div class="textblock"><p >Functions for the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm" target="_blank">Karatsuba algorithm for fast multiplication</a> implementation. </p>
<div class="textblock"><p>Functions for the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm" target="_blank">Karatsuba algorithm for fast multiplication</a> implementation. </p>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >This Programme returns the Nth fibonacci as a string. </p>
<p >The method used is manual addition with carry and placing it in a string which is called string addition This makes it have no bounds or limits</p>
<div class="textblock"><p>This Programme returns the Nth fibonacci as a string. </p>
<p>The method used is manual addition with carry and placing it in a string which is called string addition This makes it have no bounds or limits</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/de4/fibonacci__large_8cpp.html" title="Computes N^th Fibonacci number given as input argument. Uses custom build arbitrary integers library ...">fibonacci_large.cpp</a>, <a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html" title="Faster computation of Fibonacci series.">fibonacci_fast.cpp</a>, <a class="el" href="../../d9/d89/fibonacci_8cpp.html" title="Generate fibonacci sequence.">fibonacci.cpp</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a28052eee05d43c2ebc5147c52bd50c35" name="a28052eee05d43c2ebc5147c52bd50c35"></a>
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<p >function to add two string numbers </p><dl class="params"><dt>Parameters</dt><dd>
<p>function to add two string numbers </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">a</td><td>first number in string to add </td></tr>
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<p >Fibonacci iterator </p><dl class="params"><dt>Parameters</dt><dd>
<p>Fibonacci iterator </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>n^th Fibonacci number </td></tr>
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<p >main function </p>
<p>main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 81</span> {</div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordtype">int</span> n;</div>
<div class="line"><span class="lineno"> 83</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter whatever number N you want to find the fibonacci of\n&quot;</span>;</div>
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<div class="textblock"><p >structure of points containing two numbers, respectively x and y such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. </p>
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<div class="textblock"><p >The <a href="https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm" target="_blank">Knuth-Morris-Pratt Algorithm</a> for finding a pattern within a piece of text with complexity O(n + m) </p>
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<li>Preprocess pattern to identify any suffixes that are identical to prefixes. This tells us where to continue from if we get a mismatch between a character in our pattern and the text.</li>
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Functions</h2></td></tr>
<tr class="memitem:a82964ca6180507deb5fafc71050012ba"><td class="memItemLeft" align="right" valign="top">float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d72/geometric__dist_8cpp.html#a82964ca6180507deb5fafc71050012ba">probability::geometric_dist::generate_uniform</a> ()</td></tr>
<tr class="memdesc:a82964ca6180507deb5fafc71050012ba"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a random number between [0,1]. <a href="../../de/d72/geometric__dist_8cpp.html#a82964ca6180507deb5fafc71050012ba">More...</a><br /></td></tr>
<tr class="memdesc:a82964ca6180507deb5fafc71050012ba"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a random number between [0,1]. <br /></td></tr>
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<tr class="memitem:a70fd1cc5c3a2813f28683dc75dcd65b6"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d72/geometric__dist_8cpp.html#a70fd1cc5c3a2813f28683dc75dcd65b6">sample_test</a> (const <a class="el" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html">probability::geometric_dist::geometric_distribution</a> &amp;dist)</td></tr>
<tr class="memdesc:a70fd1cc5c3a2813f28683dc75dcd65b6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Tests the sampling method of the geometric distribution. <a href="../../de/d72/geometric__dist_8cpp.html#a70fd1cc5c3a2813f28683dc75dcd65b6">More...</a><br /></td></tr>
<tr class="memdesc:a70fd1cc5c3a2813f28683dc75dcd65b6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Tests the sampling method of the geometric distribution. <br /></td></tr>
<tr class="separator:a70fd1cc5c3a2813f28683dc75dcd65b6"><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="../../de/d72/geometric__dist_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../de/d72/geometric__dist_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d72/geometric__dist_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../de/d72/geometric__dist_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 ><a href="https://en.wikipedia.org/wiki/Geometric_distribution" target="_blank">Geometric Distribution</a> </p>
<p >The geometric distribution models the experiment of doing Bernoulli trials until a sucess was observed. There are two formulations of the geometric distribution: 1) The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ... } 2) The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set { 0, 1, 2, 3, ... } Here, the first one is implemented.</p>
<p >Common variables used: p - The success probability k - The number of tries</p>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Geometric_distribution" target="_blank">Geometric Distribution</a> </p>
<p>The geometric distribution models the experiment of doing Bernoulli trials until a sucess was observed. There are two formulations of the geometric distribution: 1) The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ... } 2) The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set { 0, 1, 2, 3, ... } Here, the first one is implemented.</p>
<p>Common variables used: p - The success probability k - The number of tries</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/DerAndereDomenic" target="_blank">Domenic Zingsheim</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a82964ca6180507deb5fafc71050012ba" name="a82964ca6180507deb5fafc71050012ba"></a>
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<p>Tests the sampling method of the geometric distribution. </p>
<p >Draws 1000000 random samples and estimates mean and variance These should be close to the expected value and variance of the given distribution to pass. </p><dl class="params"><dt>Parameters</dt><dd>
<p>Draws 1000000 random samples and estimates mean and variance These should be close to the expected value and variance of the given distribution to pass. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">dist</td><td>The distribution to test </td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Compute real eigen values and eigen vectors of a symmetric matrix using <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> method. </p>
<div class="textblock"><p>Compute real eigen values and eigen vectors of a symmetric matrix using <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> method. </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">Macro Definition Documentation</h2>
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<p >limit of range of matrix values </p>
<p>limit of range of matrix values </p>
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<p >create a symmetric square matrix of given size with random elements. A symmetric square matrix will <em>always</em> have real eigen values.</p>
<p>create a symmetric square matrix of given size with random elements. A symmetric square matrix will <em>always</em> have real eigen values.</p>
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<tr><td class="paramdir">[out]</td><td class="paramname">A</td><td>matrix to create (must be pre-allocated in memory) </td></tr>
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<p >main function </p>
<p>main function </p>
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<p >Perform multiplication of two matrices.</p><ul>
<p>Perform multiplication of two matrices.</p><ul>
<li>R2 must be equal to C1</li>
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<p >test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
<p>test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
\[\begin{bmatrix}
5 &amp; 7\\
7 &amp; 11
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<p >test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
<p>test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
\[\begin{bmatrix}
-4&amp; 4&amp; 2&amp; 0&amp; -3\\
4&amp; -4&amp; 4&amp; -3&amp; -1\\
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<tr class="memdesc:a0cba4fbf287ab8cb978ed7f8fef886b1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insertion merge algorithm. <a href="../../de/d7b/merge__insertion__sort_8cpp.html#a0cba4fbf287ab8cb978ed7f8fef886b1">More...</a><br /></td></tr>
<tr class="memdesc:a0cba4fbf287ab8cb978ed7f8fef886b1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insertion merge algorithm. <br /></td></tr>
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<tr class="memitem:af4de4067a9a866ffd985c5b5055ccedf"><td class="memTemplParams" colspan="2">template&lt;typename T , size_t N&gt; </td></tr>
<tr class="memitem:af4de4067a9a866ffd985c5b5055ccedf"><td class="memTemplItemLeft" align="right" valign="top">static void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d7b/merge__insertion__sort_8cpp.html#af4de4067a9a866ffd985c5b5055ccedf">sorting::merge_insertion::merge</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; T, N &gt; *array, size_t min, size_t max, size_t mid)</td></tr>
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<tr class="memdesc:af4de4067a9a866ffd985c5b5055ccedf"><td class="mdescLeft">&#160;</td><td class="mdescRight">Perform merge of data in a window. <br /></td></tr>
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<tr class="memitem:a7161278f18e83b671c6454b139cc5674"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d7b/merge__insertion__sort_8cpp.html#a7161278f18e83b671c6454b139cc5674">sorting::merge_insertion::mergeSort</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; T, N &gt; *array, size_t min, size_t max, size_t threshold)</td></tr>
<tr class="memdesc:a7161278f18e83b671c6454b139cc5674"><td class="mdescLeft">&#160;</td><td class="mdescRight">Final combined algorithm. Algorithm utilizes <a class="el" href="../../de/d7b/merge__insertion__sort_8cpp.html#a0cba4fbf287ab8cb978ed7f8fef886b1" title="Insertion merge algorithm.">sorting::merge_insertion::InsertionSort</a> if window length is less than threshold, else performs merge sort recursively using <a class="el" href="../../de/d7b/merge__insertion__sort_8cpp.html#a7161278f18e83b671c6454b139cc5674" title="Final combined algorithm. Algorithm utilizes sorting::merge_insertion::InsertionSort if window length...">sorting::merge_insertion::mergeSort</a>. <a href="../../de/d7b/merge__insertion__sort_8cpp.html#a7161278f18e83b671c6454b139cc5674">More...</a><br /></td></tr>
<tr class="memdesc:a7161278f18e83b671c6454b139cc5674"><td class="mdescLeft">&#160;</td><td class="mdescRight">Final combined algorithm. Algorithm utilizes <a class="el" href="../../de/d7b/merge__insertion__sort_8cpp.html#a0cba4fbf287ab8cb978ed7f8fef886b1" title="Insertion merge algorithm.">sorting::merge_insertion::InsertionSort</a> if window length is less than threshold, else performs merge sort recursively using <a class="el" href="../../de/d7b/merge__insertion__sort_8cpp.html#a7161278f18e83b671c6454b139cc5674" title="Final combined algorithm. Algorithm utilizes sorting::merge_insertion::InsertionSort if window length...">sorting::merge_insertion::mergeSort</a>. <br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d7b/merge__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to test code using random arrays. <a href="../../de/d7b/merge__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to test code using random arrays. <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="../../de/d7b/merge__insertion__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../de/d7b/merge__insertion__sort_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 >Algorithm that combines insertion sort and merge sort. <a href="https://en.wikipedia.org/wiki/Merge-insertion_sort" target="_blank">Wiki link</a> </p>
<div class="textblock"><p>Algorithm that combines insertion sort and merge sort. <a href="https://en.wikipedia.org/wiki/Merge-insertion_sort" target="_blank">Wiki link</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/sinkyoungdeok" target="_blank">@sinkyoungdeok</a> </dd>
<dd>
<a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Functions for checking whether a graph is bipartite or not. </p>
<div class="textblock"><p>Functions for checking whether a graph is bipartite or not. </p>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >This Programme Converts a given decimal number in the range [0,4000) to both Lower case and Upper case Roman Numeral. </p>
<div class="textblock"><p>This Programme Converts a given decimal number in the range [0,4000) to both Lower case and Upper case Roman Numeral. </p>
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<a id="a88203bd297e8405160c132faa1187780" name="a88203bd297e8405160c132faa1187780"></a>
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<p >This functions fills a string with character c, n times and returns it </p><dl class="section note"><dt>Note</dt><dd>This can probably be replace by <code>memcpy</code> function. </dd></dl>
<p>This functions fills a string with character c, n times and returns it </p><dl class="section note"><dt>Note</dt><dd>This can probably be replace by <code>memcpy</code> function. </dd></dl>
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<p >main function </p>
<p>main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 90</span> {</div>
<div class="line"><span class="lineno"> 91</span> <span class="keywordtype">int</span> n;</div>
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<p >to convert to lowercase Roman Numeral the function works recursively </p>
<p>to convert to lowercase Roman Numeral the function works recursively </p>
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<p >to convert to uppercase Roman Numeral the function works recursively </p>
<p>to convert to uppercase Roman Numeral the function works recursively </p>
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<tr class="memdesc:ab7706341d006e20d1ae58274187a3346"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function calculates the minimum path distance that will cover all the cities starting from the source. <a href="../../df/dce/namespacegraph.html#ab7706341d006e20d1ae58274187a3346">More...</a><br /></td></tr>
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<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<div class="textblock"><p >[Travelling Salesman Problem] (<a href="https://en.wikipedia.org/wiki/Travelling_salesman_problem">https://en.wikipedia.org/wiki/Travelling_salesman_problem</a>) implementation </p>
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<dl class="section author"><dt>Author</dt><dd><a href="http://github.com/Mayank17M" target="_blank">Mayank Mamgain</a></dd></dl>
<p>Travelling salesman problem asks: Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city? TSP can be modeled as an undirected weighted graph, such that cities are the graph's vertices, paths are the graph's edges, and a path's distance is the edge's weight. It is a minimization problem starting and finishing at a specified vertex after having visited each other vertex exactly once. This is the naive implementation of the problem. </p>
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<div class="textblock"><p >Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset Sum</a> problem. </p>
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<div class="textblock"><p >Get list of prime numbers. </p>
<div class="textblock"><p>Get list of prime numbers. </p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d4/d9c/primes__up__to__billion_8cpp.html" title="Compute prime numbers upto 1 billion.">primes_up_to_billion.cpp</a> <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html" title="Get list of prime numbers using Sieve of Eratosthenes.">sieve_of_eratosthenes.cpp</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<p >main function </p>
<p>main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 34</span> {</div>
<div class="line"><span class="lineno"> 35</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Calculate primes up to:\n&gt;&gt; &quot;</span>;</div>
<div class="line"><span class="lineno"> 36</span> <span class="keywordtype">int</span> n = 0;</div>
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<p >Generate an increasingly large number of primes and store in a list </p>
<p>Generate an increasingly large number of primes and store in a list </p>
<div class="fragment"><div class="line"><span class="lineno"> 12</span> {</div>
<div class="line"><span class="lineno"> 13</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> res;</div>
<div class="line"><span class="lineno"> 14</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> is_not_prime(max + 1, <span class="keyword">false</span>);</div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >A link class containing a value and pointer to another link </p>
<div class="textblock"><p>A link class containing a value and pointer to another link </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<p >Creates link with provided value and pointer to next link </p><dl class="params"><dt>Parameters</dt><dd>
<p>Creates link with provided value and pointer to next link </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">value</td><td>is the integer stored in the link </td></tr>
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<p >function returns the pointer to next link </p><dl class="section return"><dt>Returns</dt><dd>the pointer to the next link </dd></dl>
<p>function returns the pointer to next link </p><dl class="section return"><dt>Returns</dt><dd>the pointer to the next link </dd></dl>
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<p >function returns the integer value stored in the link. </p><dl class="section return"><dt>Returns</dt><dd>the integer value stored in the link. </dd></dl>
<p>function returns the integer value stored in the link. </p><dl class="section return"><dt>Returns</dt><dd>the integer value stored in the link. </dd></dl>
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Functions</h2></td></tr>
<tr class="memitem:af0a3e6827f41c151e47451f5ff98b1f1"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dab/ncr__modulo__p_8cpp.html#af0a3e6827f41c151e47451f5ff98b1f1">tests</a> (<a class="el" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html">math::ncr_modulo_p::NCRModuloP</a> ncrObj)</td></tr>
<tr class="memdesc:af0a3e6827f41c151e47451f5ff98b1f1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test implementations. <a href="../../de/dab/ncr__modulo__p_8cpp.html#af0a3e6827f41c151e47451f5ff98b1f1">More...</a><br /></td></tr>
<tr class="memdesc:af0a3e6827f41c151e47451f5ff98b1f1"><td class="mdescLeft">&#160;</td><td class="mdescRight">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="../../de/dab/ncr__modulo__p_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../de/dab/ncr__modulo__p_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 >This program aims at calculating <a href="https://cp-algorithms.com/combinatorics/binomial-coefficients.html" target="_blank">nCr modulo p</a>. </p>
<p >nCr is defined as n! / (r! * (n-r)!) where n! represents factorial of n. In many cases, the value of nCr is too large to fit in a 64 bit integer. Hence, in competitive programming, there are many problems or subproblems to compute nCr modulo p where p is a given number. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/KaustubhDamania" target="_blank">Kaustubh Damania</a> </dd></dl>
<div class="textblock"><p>This program aims at calculating <a href="https://cp-algorithms.com/combinatorics/binomial-coefficients.html" target="_blank">nCr modulo p</a>. </p>
<p>nCr is defined as n! / (r! * (n-r)!) where n! represents factorial of n. In many cases, the value of nCr is too large to fit in a 64 bit integer. Hence, in competitive programming, there are many problems or subproblems to compute nCr modulo p where p is a given number. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/KaustubhDamania" target="_blank">Kaustubh Damania</a> </dd></dl>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<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/Atbash" target="_blank">Atbash Cipher</a> implementation. </p>
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