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Collaboration diagram for graph::Graph< T >:</div>
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Public Member Functions</h2></td></tr>
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<tr class="memitem:a877b2cba40d8d46dde6fb4209effed19"><td class="memItemLeft" align="right" valign="top">void </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="separator:a877b2cba40d8d46dde6fb4209effed19"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ab1a1a96cd4cddf0d4feb02855c4c16af"><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>< T, bool > </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html#ab1a1a96cd4cddf0d4feb02855c4c16af">breadth_first_search</a> (T src)</td></tr>
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<tr class="separator:ab1a1a96cd4cddf0d4feb02855c4c16af"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a8839fa14bff19d2deab4a618447c13e5"><td class="memItemLeft" align="right" valign="top"> </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>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>< int, int > > &undirected_edges)</td></tr>
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<tr class="memdesc:a8839fa14bff19d2deab4a618447c13e5"><td class="mdescLeft"> </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>
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<tr class="separator:a8839fa14bff19d2deab4a618447c13e5"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a8930d1470d132b19e430d1c71f94c904"><td class="memItemLeft" align="right" valign="top">int </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">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-attribs"></a>
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Public Attributes</h2></td></tr>
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<tr class="memitem:a59940c462861f2fcf4951d1b6c084e6a"><td class="memItemLeft" align="right" valign="top"><a id="a59940c462861f2fcf4951d1b6c084e6a"></a>
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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< int > > </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html#a59940c462861f2fcf4951d1b6c084e6a">neighbors</a></td></tr>
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<tr class="memdesc:a59940c462861f2fcf4951d1b6c084e6a"><td class="mdescLeft"> </td><td class="mdescRight">for each vertex it stores a list indicies of its neighbors <br /></td></tr>
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<tr class="separator:a59940c462861f2fcf4951d1b6c084e6a"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-attribs"></a>
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Private Attributes</h2></td></tr>
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<tr class="memitem:acebf0505d625b043bb9c8c27c7a8def0"><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>< T, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list</a>< T > > </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html#acebf0505d625b043bb9c8c27c7a8def0">adjacency_list</a></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><h3>template<typename T><br />
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class graph::Graph< T ></h3>
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<p>Class for representing a graph as an adjacency list. Its vertices are indexed 0, 1, ..., N - 1. </p>
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</div><h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<a id="a8839fa14bff19d2deab4a618447c13e5"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a8839fa14bff19d2deab4a618447c13e5">◆ </a></span>Graph()</h2>
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template<typename T > </div>
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<td class="memname"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph</a>< T >::<a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> </td>
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<td>(</td>
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<td class="paramtype">size_t </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>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>< int, int > > & </td>
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<td class="paramname"><em>undirected_edges</em> </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>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">N</td><td>number of vertices in the graph </td></tr>
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<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"><a name="l00062"></a><span class="lineno"> 62</span>  {</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <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>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keywordflow">for</span> (<span class="keyword">auto</span> &edge : undirected_edges) {</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <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>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <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>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  }</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  }</div>
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<div class="ttc" id="aclassgraph_1_1_graph_html_a59940c462861f2fcf4951d1b6c084e6a"><div class="ttname"><a href="../../dc/d61/classgraph_1_1_graph.html#a59940c462861f2fcf4951d1b6c084e6a">graph::Graph::neighbors</a></div><div class="ttdeci">std::vector< std::vector< int > > 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>
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<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>
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<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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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d61/classgraph_1_1_graph_a8839fa14bff19d2deab4a618447c13e5_cgraph.svg" width="354" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<h2 class="groupheader">Member Function Documentation</h2>
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<a id="a877b2cba40d8d46dde6fb4209effed19"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a877b2cba40d8d46dde6fb4209effed19">◆ </a></span>add_edge()</h2>
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template<typename T > </div>
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<td class="memname">void <a class="el" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph</a>< T >::add_edge </td>
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<td>(</td>
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<td class="paramtype">T </td>
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<td class="paramtype">bool </td>
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<td class="paramname"><em>bidir</em> = <code>true</code> </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-->v and v-->u both edges exist.</p>
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<p>to make the graph unidirectional pass the third parameter of add_edge as false which will</p>
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<div class="fragment"><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  {<span class="comment"></span></div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment"> /**</span></div>
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<div class="line"><a name="l00076"></a><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>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> * node v by default , bidir is made true , i.e graph is</span></div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"> * bidirectional . It means if edge(u,v) is added then u-->v and</span></div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"> * v-->u both edges exist.</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment"> *</span></div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"> * to make the graph unidirectional pass the third parameter of</span></div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"> * add_edge as false which will</span></div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"> */</span></div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#acebf0505d625b043bb9c8c27c7a8def0">adjacency_list</a>[u].push_back(v); <span class="comment">// u-->v edge added</span></div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">if</span> (bidir == <span class="keyword">true</span>) {</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="comment">// if graph is bidirectional</span></div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#acebf0505d625b043bb9c8c27c7a8def0">adjacency_list</a>[v].push_back(u); <span class="comment">// v-->u edge added</span></div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  }</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  }</div>
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<div class="ttc" id="aclassgraph_1_1_graph_html_acebf0505d625b043bb9c8c27c7a8def0"><div class="ttname"><a href="../../dc/d61/classgraph_1_1_graph.html#acebf0505d625b043bb9c8c27c7a8def0">graph::Graph::adjacency_list</a></div><div class="ttdeci">std::map< T, std::list< T > > 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="#ab1a1a96cd4cddf0d4feb02855c4c16af">◆ </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><T, bool> <a class="el" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph</a>< T >::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>
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<p>mapping to keep track of all visited nodes</p>
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<p>initialise every possible vertex to map to false initially none of the vertices are unvisited</p>
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<p>queue to store the nodes which are yet to be traversed</p>
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<p>push the source vertex to queue to begin traversing</p>
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<p>mark the source vertex as visited</p>
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<p>traverse the graph till no connected vertex are left extract a node from queue for further traversal</p>
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<p>remove the node from the queue</p>
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<p>check every vertex connected to the node which are still unvisited</p>
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<p>if the neighbour is unvisited , push it into the queue</p>
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<p>mark the neighbour as visited</p>
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<div class="fragment"><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  {<span class="comment"></span></div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment"> /// mapping to keep track of all visited nodes</span></div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"></span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map<T, bool></a> visited;<span class="comment"></span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment"> /// initialise every possible vertex to map to false</span></div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment"> /// initially none of the vertices are unvisited</span></div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment"></span> <span class="keywordflow">for</span> (<span class="keyword">auto</span> <span class="keyword">const</span> &adjlist : <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#acebf0505d625b043bb9c8c27c7a8def0">adjacency_list</a>) {</div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  visited[adjlist.first] = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordflow">for</span> (<span class="keyword">auto</span> <span class="keyword">const</span> &<a class="code" href="../../d5/da1/structnode.html">node</a> : <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#acebf0505d625b043bb9c8c27c7a8def0">adjacency_list</a>[adjlist.first]) {</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  visited[<a class="code" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>] = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  }</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  }</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment"></span> </div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment"> /// queue to store the nodes which are yet to be traversed</span></div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment"></span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue<T></a> tracker;</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment"></span> </div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment"> /// push the source vertex to queue to begin traversing</span></div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment"></span> tracker.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/push.html">push</a>(src);<span class="comment"></span></div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment"> /// mark the source vertex as visited</span></div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment"></span> visited[src] = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keywordflow">while</span> (!tracker.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/empty.html">empty</a>()) {<span class="comment"></span></div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"> /// traverse the graph till no connected vertex are left</span></div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment"> /// extract a node from queue for further traversal</span></div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"></span> T <a class="code" href="../../d5/da1/structnode.html">node</a> = tracker.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/front.html">front</a>();<span class="comment"></span></div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment"> /// remove the node from the queue</span></div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment"></span> tracker.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/pop.html">pop</a>();</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keywordflow">for</span> (T <span class="keyword">const</span> &neighbour : <a class="code" href="../../dc/d61/classgraph_1_1_graph.html#acebf0505d625b043bb9c8c27c7a8def0">adjacency_list</a>[<a class="code" href="../../d5/da1/structnode.html">node</a>]) {<span class="comment"></span></div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment"> /// check every vertex connected to the node which are still</span></div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment"> /// unvisited</span></div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment"></span> <span class="keywordflow">if</span> (!visited[neighbour]) {<span class="comment"></span></div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment"> /// if the neighbour is unvisited , push it into the queue</span></div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment"></span> tracker.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue/push.html">push</a>(neighbour);<span class="comment"></span></div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="comment"> /// mark the neighbour as visited</span></div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment"></span> visited[neighbour] = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  }</div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  }</div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  }</div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordflow">return</span> visited;</div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  }</div>
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<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="afront_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/front.html">std::queue::front</a></div><div class="ttdeci">T front(T... args)</div></div>
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<div class="ttc" id="ahash__search_8cpp_html_a8ca8dcb494104d273679e219e53d0555"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a></div><div class="ttdeci">struct list node</div></div>
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<div class="ttc" id="apush_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue/push.html">std::queue::push</a></div><div class="ttdeci">T push(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> avltree.cpp:13</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a8930d1470d132b19e430d1c71f94c904">◆ </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>< T >::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>
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<div class="fragment"><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> { <span class="keywordflow">return</span> <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/size.html">size</a>(); }</div>
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<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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<a id="acebf0505d625b043bb9c8c27c7a8def0"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#acebf0505d625b043bb9c8c27c7a8def0">◆ </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><T, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list</a><T> > <a class="el" href="../../dc/d61/classgraph_1_1_graph.html">graph::Graph</a>< T >::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>
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<li>graph/<a class="el" href="../../df/d82/breadth__first__search_8cpp.html">breadth_first_search.cpp</a></li>
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<li>graph/<a class="el" href="../../de/dde/lowest__common__ancestor_8cpp.html">lowest_common_ancestor.cpp</a></li>
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