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<tr class="memitem:a877b2cba40d8d46dde6fb4209effed19" id="r_a877b2cba40d8d46dde6fb4209effed19"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a877b2cba40d8d46dde6fb4209effed19">add_edge</a> (T u, T v, bool bidir=true)</td></tr>
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<tr class="memitem:a3755ec9e6a842238c7f4aac10b661981" id="r_a3755ec9e6a842238c7f4aac10b661981"><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="#a3755ec9e6a842238c7f4aac10b661981">breadth_first_search</a> (T src)</td></tr>
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<tr class="memitem:a8839fa14bff19d2deab4a618447c13e5" id="r_a8839fa14bff19d2deab4a618447c13e5"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a8839fa14bff19d2deab4a618447c13e5">Graph</a> (size_t N, 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)</td></tr>
<tr class="memdesc:a8839fa14bff19d2deab4a618447c13e5"><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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<tr class="memitem:a8930d1470d132b19e430d1c71f94c904" id="r_a8930d1470d132b19e430d1c71f94c904"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a8930d1470d132b19e430d1c71f94c904">number_of_vertices</a> () const</td></tr>
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Public Attributes</h2></td></tr>
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<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/container/vector.html">std::vector</a>&lt; int &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>neighbors</b></td></tr>
<tr class="memdesc:a59940c462861f2fcf4951d1b6c084e6a"><td class="mdescLeft">&#160;</td><td class="mdescRight">for each vertex it stores a list indicies of its neighbors <br /></td></tr>
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Private Attributes</h2></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><div class="compoundTemplParams">template&lt;typename T&gt;<br />
class graph::Graph&lt; T &gt;</div><p>Class for representing a graph as an adjacency list. Its vertices are indexed 0, 1, ..., N - 1. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a8839fa14bff19d2deab4a618447c13e5">&#9670;&#160;</a></span>Graph()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph</a>&lt; T &gt;<a class="el" href="../../da/d9a/class_graph.html">::Graph</a> </td>
<td>(</td>
<td class="paramtype">size_t</td> <td class="paramname"><span class="paramname"><em>N</em></span>, </td>
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<td class="paramtype">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;</td> <td class="paramname"><span class="paramname"><em>undirected_edges</em></span>&#160;)</td>
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<p>Populate the adjacency list for each vertex in the graph. Assumes that evey edge is a pair of valid vertex indices. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">N</td><td>number of vertices in the graph </td></tr>
<tr><td class="paramname">undirected_edges</td><td>list of graph's undirected edges </td></tr>
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<div class="fragment"><div class="line"><span class="lineno"> 62</span> {</div>
<div class="line"><span class="lineno"> 63</span> <a class="code hl_variable" href="#a59940c462861f2fcf4951d1b6c084e6a">neighbors</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/resize.html">resize</a>(N);</div>
<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;edge : undirected_edges) {</div>
<div class="line"><span class="lineno"> 65</span> <a class="code hl_variable" href="#a59940c462861f2fcf4951d1b6c084e6a">neighbors</a>[edge.first].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(edge.second);</div>
<div class="line"><span class="lineno"> 66</span> <a class="code hl_variable" href="#a59940c462861f2fcf4951d1b6c084e6a">neighbors</a>[edge.second].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(edge.first);</div>
<div class="line"><span class="lineno"> 67</span> }</div>
<div class="line"><span class="lineno"> 68</span> }</div>
<div class="ttc" id="aclassgraph_1_1_graph_html_a59940c462861f2fcf4951d1b6c084e6a"><div class="ttname"><a href="#a59940c462861f2fcf4951d1b6c084e6a">graph::Graph::neighbors</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; int &gt; &gt; neighbors</div><div class="ttdoc">for each vertex it stores a list indicies of its neighbors</div><div class="ttdef"><b>Definition</b> lowest_common_ancestor.cpp:77</div></div>
<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
<div class="ttc" id="aresize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/resize.html">std::vector::resize</a></div><div class="ttdeci">T resize(T... args)</div></div>
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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a877b2cba40d8d46dde6fb4209effed19">&#9670;&#160;</a></span>add_edge()</h2>
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<td class="memname">void <a class="el" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph</a>&lt; T &gt;::add_edge </td>
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<td class="paramtype">T</td> <td class="paramname"><span class="paramname"><em>u</em></span>, </td>
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<td class="paramtype">bool</td> <td class="paramname"><span class="paramname"><em>bidir</em></span><span class="paramdefsep"> = </span><span class="paramdefval">true</span>&#160;)</td>
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<p>add_edge(u,v,bidir) is used to add an edge between node u and node v by default , bidir is made true , i.e graph is bidirectional . It means if edge(u,v) is added then u--&gt;v and v--&gt;u both edges exist.</p>
<p>to make the graph unidirectional pass the third parameter of add_edge as false which will</p>
<div class="fragment"><div class="line"><span class="lineno"> 74</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 75</span><span class="comment"> /**</span></div>
<div class="line"><span class="lineno"> 76</span><span class="comment"> * add_edge(u,v,bidir) is used to add an edge between node u and</span></div>
<div class="line"><span class="lineno"> 77</span><span class="comment"> * node v by default , bidir is made true , i.e graph is</span></div>
<div class="line"><span class="lineno"> 78</span><span class="comment"> * bidirectional . It means if edge(u,v) is added then u--&gt;v and</span></div>
<div class="line"><span class="lineno"> 79</span><span class="comment"> * v--&gt;u both edges exist.</span></div>
<div class="line"><span class="lineno"> 80</span><span class="comment"> *</span></div>
<div class="line"><span class="lineno"> 81</span><span class="comment"> * to make the graph unidirectional pass the third parameter of</span></div>
<div class="line"><span class="lineno"> 82</span><span class="comment"> * add_edge as false which will</span></div>
<div class="line"><span class="lineno"> 83</span><span class="comment"> */</span></div>
<div class="line"><span class="lineno"> 84</span> <a class="code hl_variable" href="#acebf0505d625b043bb9c8c27c7a8def0">adjacency_list</a>[u].push_back(v); <span class="comment">// u--&gt;v edge added</span></div>
<div class="line"><span class="lineno"> 85</span> <span class="keywordflow">if</span> (bidir == <span class="keyword">true</span>) {</div>
<div class="line"><span class="lineno"> 86</span> <span class="comment">// if graph is bidirectional</span></div>
<div class="line"><span class="lineno"> 87</span> <a class="code hl_variable" href="#acebf0505d625b043bb9c8c27c7a8def0">adjacency_list</a>[v].push_back(u); <span class="comment">// v--&gt;u edge added</span></div>
<div class="line"><span class="lineno"> 88</span> }</div>
<div class="line"><span class="lineno"> 89</span> }</div>
<div class="ttc" id="aclassgraph_1_1_graph_html_acebf0505d625b043bb9c8c27c7a8def0"><div class="ttname"><a href="#acebf0505d625b043bb9c8c27c7a8def0">graph::Graph::adjacency_list</a></div><div class="ttdeci">std::map&lt; T, std::list&lt; T &gt; &gt; adjacency_list</div><div class="ttdef"><b>Definition</b> breadth_first_search.cpp:69</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a3755ec9e6a842238c7f4aac10b661981">&#9670;&#160;</a></span>breadth_first_search()</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map</a>&lt; T, bool &gt; <a class="el" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph</a>&lt; T &gt;::breadth_first_search </td>
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<p>this function performs the breadth first search on graph and return a mapping which maps the nodes to a boolean value representing whether the node was traversed or not. </p>
<p>mapping to keep track of all visited nodes</p>
<p>initialise every possible vertex to map to false initially none of the vertices are unvisited</p>
<p>queue to store the nodes which are yet to be traversed</p>
<p>push the source vertex to queue to begin traversing</p>
<p>mark the source vertex as visited</p>
<p>traverse the graph till no connected vertex are left extract a node from queue for further traversal</p>
<p>remove the node from the queue</p>
<p>check every vertex connected to the node which are still unvisited</p>
<p>if the neighbour is unvisited , push it into the queue</p>
<p>mark the neighbour as visited</p>
<div class="fragment"><div class="line"><span class="lineno"> 96</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 97</span><span class="comment"> /// mapping to keep track of all visited nodes</span></div>
<div class="line"><span class="lineno"> 98</span><span class="comment"></span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map&lt;T, bool&gt;</a> visited;<span class="comment"></span></div>
<div class="line"><span class="lineno"> 99</span><span class="comment"> /// initialise every possible vertex to map to false</span></div>
<div class="line"><span class="lineno"> 100</span><span class="comment"> /// initially none of the vertices are unvisited</span></div>
<div class="line"><span class="lineno"> 101</span><span class="comment"></span> <span class="keywordflow">for</span> (<span class="keyword">auto</span> <span class="keyword">const</span> &amp;adjlist : <a class="code hl_variable" href="#acebf0505d625b043bb9c8c27c7a8def0">adjacency_list</a>) {</div>
<div class="line"><span class="lineno"> 102</span> visited[adjlist.first] = <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 103</span> <span class="keywordflow">for</span> (<span class="keyword">auto</span> <span class="keyword">const</span> &amp;<a class="code hl_class" href="../../d5/da1/structnode.html">node</a> : <a class="code hl_variable" href="#acebf0505d625b043bb9c8c27c7a8def0">adjacency_list</a>[adjlist.first]) {</div>
<div class="line"><span class="lineno"> 104</span> visited[<a class="code hl_typedef" href="../../d8/dee/avltree_8cpp.html#a74f0cf18a0e5b832d9994e2f2d022287">node</a>] = <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 105</span> }</div>
<div class="line"><span class="lineno"> 106</span> }</div>
<div class="line"><span class="lineno"> 107</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 108</span><span class="comment"> /// queue to store the nodes which are yet to be traversed</span></div>
<div class="line"><span class="lineno"> 109</span><span class="comment"></span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;T&gt;</a> tracker;</div>
<div class="line"><span class="lineno"> 110</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 111</span><span class="comment"> /// push the source vertex to queue to begin traversing</span></div>
<div class="line"><span class="lineno"> 112</span><span class="comment"></span> tracker.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/push.html">push</a>(src);<span class="comment"></span></div>
<div class="line"><span class="lineno"> 113</span><span class="comment"> /// mark the source vertex as visited</span></div>
<div class="line"><span class="lineno"> 114</span><span class="comment"></span> visited[src] = <span class="keyword">true</span>;</div>
<div class="line"><span class="lineno"> 115</span> <span class="keywordflow">while</span> (!tracker.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/empty.html">empty</a>()) {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 116</span><span class="comment"> /// traverse the graph till no connected vertex are left</span></div>
<div class="line"><span class="lineno"> 117</span><span class="comment"> /// extract a node from queue for further traversal</span></div>
<div class="line"><span class="lineno"> 118</span><span class="comment"></span> T <a class="code hl_class" href="../../d5/da1/structnode.html">node</a> = tracker.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/front.html">front</a>();<span class="comment"></span></div>
<div class="line"><span class="lineno"> 119</span><span class="comment"> /// remove the node from the queue</span></div>
<div class="line"><span class="lineno"> 120</span><span class="comment"></span> tracker.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/pop.html">pop</a>();</div>
<div class="line"><span class="lineno"> 121</span> <span class="keywordflow">for</span> (T <span class="keyword">const</span> &amp;neighbour : <a class="code hl_variable" href="#acebf0505d625b043bb9c8c27c7a8def0">adjacency_list</a>[<a class="code hl_class" href="../../d5/da1/structnode.html">node</a>]) {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 122</span><span class="comment"> /// check every vertex connected to the node which are still</span></div>
<div class="line"><span class="lineno"> 123</span><span class="comment"> /// unvisited</span></div>
<div class="line"><span class="lineno"> 124</span><span class="comment"></span> <span class="keywordflow">if</span> (!visited[neighbour]) {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 125</span><span class="comment"> /// if the neighbour is unvisited , push it into the queue</span></div>
<div class="line"><span class="lineno"> 126</span><span class="comment"></span> tracker.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/push.html">push</a>(neighbour);<span class="comment"></span></div>
<div class="line"><span class="lineno"> 127</span><span class="comment"> /// mark the neighbour as visited</span></div>
<div class="line"><span class="lineno"> 128</span><span class="comment"></span> visited[neighbour] = <span class="keyword">true</span>;</div>
<div class="line"><span class="lineno"> 129</span> }</div>
<div class="line"><span class="lineno"> 130</span> }</div>
<div class="line"><span class="lineno"> 131</span> }</div>
<div class="line"><span class="lineno"> 132</span> <span class="keywordflow">return</span> visited;</div>
<div class="line"><span class="lineno"> 133</span> }</div>
<div class="ttc" id="aavltree_8cpp_html_a74f0cf18a0e5b832d9994e2f2d022287"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#a74f0cf18a0e5b832d9994e2f2d022287">node</a></div><div class="ttdeci">struct node { int data; int height; struct node *left; struct node *right;} node</div><div class="ttdoc">for std::queue</div><div class="ttdef"><b>Definition</b> avltree.cpp:13</div></div>
<div class="ttc" id="aempty_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/empty.html">std::queue::empty</a></div><div class="ttdeci">T empty(T... args)</div></div>
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<div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition</b> binary_search_tree.cpp:11</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a8930d1470d132b19e430d1c71f94c904">&#9670;&#160;</a></span>number_of_vertices()</h2>
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<td class="memname">int <a class="el" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph</a>&lt; T &gt;::number_of_vertices </td>
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<p>Function to get the number of vertices in the graph </p><dl class="section return"><dt>Returns</dt><dd>the number of vertices in the graph. </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 74</span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="#a59940c462861f2fcf4951d1b6c084e6a">neighbors</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); }</div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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<h2 class="groupheader">Member Data Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#acebf0505d625b043bb9c8c27c7a8def0">&#9670;&#160;</a></span>adjacency_list</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map</a>&lt;T, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list</a>&lt;T&gt; &gt; <a class="el" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph</a>&lt; T &gt;::adjacency_list</td>
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<p>adjacency_list maps every vertex to the list of its neighbours in the order in which they are added. </p>
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<hr/>The documentation for this class was generated from the following files:<ul>
<li>graph/<a class="el" href="../../df/d82/breadth__first__search_8cpp.html">breadth_first_search.cpp</a></li>
<li>graph/<a class="el" href="../../de/dde/lowest__common__ancestor_8cpp.html">lowest_common_ancestor.cpp</a></li>
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