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<title>Algorithms_in_C++: graph::Graph Class Reference</title>
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<a href="#pub-methods">Public Member Functions</a> &#124;
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<div class="title">graph::Graph Class Reference</div> </div>
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Inheritance diagram for graph::Graph:</div>
Inheritance diagram for graph::Graph&lt; T &gt;:</div>
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Public Member Functions</h2></td></tr>
<tr class="memitem:a34414f67c2e3ea89774839b36b1575f8"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html#a34414f67c2e3ea89774839b36b1575f8">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:a34414f67c2e3ea89774839b36b1575f8"><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#a34414f67c2e3ea89774839b36b1575f8">More...</a><br /></td></tr>
<tr class="separator:a34414f67c2e3ea89774839b36b1575f8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae2f6992450faa2c3da93edea0818869a"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html#ae2f6992450faa2c3da93edea0818869a">number_of_vertices</a> () const</td></tr>
<tr class="separator:ae2f6992450faa2c3da93edea0818869a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a877b2cba40d8d46dde6fb4209effed19"><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>
<tr class="separator:a877b2cba40d8d46dde6fb4209effed19"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6e3efabd5e401ef0f47c179866e7454e"><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#a6e3efabd5e401ef0f47c179866e7454e">breadth_first_search</a> (T src)</td></tr>
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<tr class="memitem:a8839fa14bff19d2deab4a618447c13e5"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html#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. <a href="../../dc/d61/classgraph_1_1_graph.html#a8839fa14bff19d2deab4a618447c13e5">More...</a><br /></td></tr>
<tr class="separator:a8839fa14bff19d2deab4a618447c13e5"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8930d1470d132b19e430d1c71f94c904"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html#a8930d1470d132b19e430d1c71f94c904">number_of_vertices</a> () const</td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-attribs"></a>
Public Attributes</h2></td></tr>
<tr class="memitem:afe3c12683248e50a7a1688b40156a842"><td class="memItemLeft" align="right" valign="top"><a id="afe3c12683248e50a7a1688b40156a842"></a>
<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"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html#afe3c12683248e50a7a1688b40156a842">neighbors</a></td></tr>
<tr class="memdesc:afe3c12683248e50a7a1688b40156a842"><td class="mdescLeft">&#160;</td><td class="mdescRight">for each vertex it stores a list indicies of its neighbors <br /></td></tr>
<tr class="separator:afe3c12683248e50a7a1688b40156a842"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a59940c462861f2fcf4951d1b6c084e6a"><td class="memItemLeft" align="right" valign="top"><a id="a59940c462861f2fcf4951d1b6c084e6a"></a>
<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"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html#a59940c462861f2fcf4951d1b6c084e6a">neighbors</a></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>
<tr class="separator:a59940c462861f2fcf4951d1b6c084e6a"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-attribs"></a>
Private Attributes</h2></td></tr>
<tr class="memitem:a3ab95bb3ba618a7e883ead8ee696c25c"><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, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list</a>&lt; T &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html#a3ab95bb3ba618a7e883ead8ee696c25c">adjacency_list</a></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Class for representing a graph as an adjacency list. Its vertices are indexed 0, 1, ..., N - 1. </p>
<div class="textblock"><h3>template&lt;typename T&gt;<br />
class graph::Graph&lt; T &gt;</h3>
<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>
<a id="a34414f67c2e3ea89774839b36b1575f8"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a34414f67c2e3ea89774839b36b1575f8">&#9670;&nbsp;</a></span>Graph()</h2>
<a id="a8839fa14bff19d2deab4a618447c13e5"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8839fa14bff19d2deab4a618447c13e5">&#9670;&nbsp;</a></span>Graph()</h2>
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<td class="memname">graph::Graph::Graph </td>
<td class="memname"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph</a>&lt; T &gt;::<a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> </td>
<td>(</td>
<td class="paramtype">size_t&#160;</td>
<td class="paramname"><em>N</em>, </td>
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<div class="fragment"><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#afe3c12683248e50a7a1688b40156a842">neighbors</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/resize.html">resize</a>(N);</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#a59940c462861f2fcf4951d1b6c084e6a">neighbors</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/resize.html">resize</a>(N);</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">auto</span> &amp;edge : undirected_edges) {</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#afe3c12683248e50a7a1688b40156a842">neighbors</a>[edge.first].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(edge.second);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#afe3c12683248e50a7a1688b40156a842">neighbors</a>[edge.second].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(edge.first);</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#a59940c462861f2fcf4951d1b6c084e6a">neighbors</a>[edge.first].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(edge.second);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#a59940c462861f2fcf4951d1b6c084e6a">neighbors</a>[edge.second].<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(edge.first);</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; }</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; }</div>
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Here is the call graph for this function:</div>
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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae2f6992450faa2c3da93edea0818869a">&#9670;&nbsp;</a></span>number_of_vertices()</h2>
<a id="a877b2cba40d8d46dde6fb4209effed19"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a877b2cba40d8d46dde6fb4209effed19">&#9670;&nbsp;</a></span>add_edge()</h2>
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<td class="memname">int graph::Graph::number_of_vertices </td>
<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">bool&#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"><a name="l00072"></a><span class="lineno"> 72</span>&#160; {<span class="comment"></span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160;<span class="comment"> /**</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160;<span class="comment"> * add_edge(u,v,bidir) is used to add an edge between node u and node v</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160;<span class="comment"> * by default , bidir is made true , i.e graph is bidirectional .</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160;<span class="comment"> * It means if edge(u,v) is added then u--&gt;v and v--&gt;u both edges exist.</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160;<span class="comment"> * to make the graph unidirectional pass the third parameter of add_edge as</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160;<span class="comment"> * false which will</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#a3ab95bb3ba618a7e883ead8ee696c25c">adjacency_list</a>[u].push_back(v); <span class="comment">// u--&gt;v edge added</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="keywordflow">if</span>(bidir==<span class="keyword">true</span>){</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <span class="comment">// if graph is bidirectional</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#a3ab95bb3ba618a7e883ead8ee696c25c">adjacency_list</a>[v].push_back(u); <span class="comment">// v--&gt;u edge added</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; }</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6e3efabd5e401ef0f47c179866e7454e">&#9670;&nbsp;</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"><a name="l00094"></a><span class="lineno"> 94</span>&#160; {<span class="comment"></span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160;<span class="comment"> /// mapping to keep track of all visited nodes </span></div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160;<span class="comment"></span> <a class="codeRef" 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"><a name="l00097"></a><span class="lineno"> 97</span>&#160;<span class="comment"> /// initialise every possible vertex to map to false</span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160;<span class="comment"> /// initially none of the vertices are unvisited</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160;<span class="comment"></span> <span class="keywordflow">for</span>(<span class="keyword">auto</span> <span class="keyword">const</span> &amp;adjlist: <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#a3ab95bb3ba618a7e883ead8ee696c25c">adjacency_list</a>){</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; visited[adjlist.first]=<span class="keyword">false</span>;</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a8930d1470d132b19e430d1c71f94c904">&#9670;&nbsp;</a></span>number_of_vertices()</h2>
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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"><a name="l00074"></a><span class="lineno"> 74</span>&#160;{ <span class="keywordflow">return</span> <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#afe3c12683248e50a7a1688b40156a842">neighbors</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); }</div>
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<hr/>The documentation for this class was generated from the following file:<ul>
<h2 class="groupheader">Member Data Documentation</h2>
<a id="a3ab95bb3ba618a7e883ead8ee696c25c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3ab95bb3ba618a7e883ead8ee696c25c">&#9670;&nbsp;</a></span>adjacency_list</h2>
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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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