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<div class="headertitle"><div class="title">graph::HKGraph Class Reference</div></div>
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<p>Represents Bipartite graph for Hopcroft Karp implementation.
<a href="../../d8/d69/classgraph_1_1_h_k_graph.html#details">More...</a></p>
<table class="memberdecls">
<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:af02b0c83911070ac6d95fc9905e58aa9"><td class="memItemLeft" align="right" valign="top"><a id="af02b0c83911070ac6d95fc9905e58aa9" name="af02b0c83911070ac6d95fc9905e58aa9"></a>
&#160;</td><td class="memItemRight" valign="bottom"><b>HKGraph</b> ()</td></tr>
<tr class="memdesc:af02b0c83911070ac6d95fc9905e58aa9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor for initialization. <br /></td></tr>
<tr class="separator:af02b0c83911070ac6d95fc9905e58aa9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0da5aa674d3b3e54a38251ee60d7cd64"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a0da5aa674d3b3e54a38251ee60d7cd64">HKGraph</a> (int <a class="el" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a>, int <a class="el" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6f5a9fdbb83ef731d739ba6707e21c3c">n</a>)</td></tr>
<tr class="memdesc:a0da5aa674d3b3e54a38251ee60d7cd64"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor for initialization. <a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a0da5aa674d3b3e54a38251ee60d7cd64">More...</a><br /></td></tr>
<tr class="separator:a0da5aa674d3b3e54a38251ee60d7cd64"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3b49011c09cf90a116ab53bef61cd95a"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3b49011c09cf90a116ab53bef61cd95a">addEdge</a> (int u, int v)</td></tr>
<tr class="memdesc:a3b49011c09cf90a116ab53bef61cd95a"><td class="mdescLeft">&#160;</td><td class="mdescRight">function to add edge from u to v <a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3b49011c09cf90a116ab53bef61cd95a">More...</a><br /></td></tr>
<tr class="separator:a3b49011c09cf90a116ab53bef61cd95a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7491add14d9fc04f679114ca6d6f0f93"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a7491add14d9fc04f679114ca6d6f0f93">bfs</a> ()</td></tr>
<tr class="memdesc:a7491add14d9fc04f679114ca6d6f0f93"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function checks for the possibility of augmented path availability. <a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a7491add14d9fc04f679114ca6d6f0f93">More...</a><br /></td></tr>
<tr class="separator:a7491add14d9fc04f679114ca6d6f0f93"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae794950cb3407b6b47d3dc986cf714c0"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d69/classgraph_1_1_h_k_graph.html#ae794950cb3407b6b47d3dc986cf714c0">dfs</a> (int u)</td></tr>
<tr class="memdesc:ae794950cb3407b6b47d3dc986cf714c0"><td class="mdescLeft">&#160;</td><td class="mdescRight">This functions checks whether an augmenting path is available exists beginning with free vertex u. <a href="../../d8/d69/classgraph_1_1_h_k_graph.html#ae794950cb3407b6b47d3dc986cf714c0">More...</a><br /></td></tr>
<tr class="separator:ae794950cb3407b6b47d3dc986cf714c0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9dbda80d02bdc26c3e8ff7330c9be75d"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a9dbda80d02bdc26c3e8ff7330c9be75d">hopcroftKarpAlgorithm</a> ()</td></tr>
<tr class="memdesc:a9dbda80d02bdc26c3e8ff7330c9be75d"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function counts the number of augmenting paths between left and right sides of the Bipartite graph. <a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a9dbda80d02bdc26c3e8ff7330c9be75d">More...</a><br /></td></tr>
<tr class="separator:a9dbda80d02bdc26c3e8ff7330c9be75d"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pri-attribs" name="pri-attribs"></a>
Private Attributes</h2></td></tr>
<tr class="memitem:a3d9101e3b4598159005fd028b9b0ff74"><td class="memItemLeft" align="right" valign="top"><a id="a3d9101e3b4598159005fd028b9b0ff74" name="a3d9101e3b4598159005fd028b9b0ff74"></a>
int&#160;</td><td class="memItemRight" valign="bottom"><b>m</b> {}</td></tr>
<tr class="memdesc:a3d9101e3b4598159005fd028b9b0ff74"><td class="mdescLeft">&#160;</td><td class="mdescRight">m is the number of vertices on left side of Bipartite <a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> <br /></td></tr>
<tr class="separator:a3d9101e3b4598159005fd028b9b0ff74"><td class="memSeparator" colspan="2">&#160;</td></tr>
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int&#160;</td><td class="memItemRight" valign="bottom"><b>n</b> {}</td></tr>
<tr class="memdesc:a6f5a9fdbb83ef731d739ba6707e21c3c"><td class="mdescLeft">&#160;</td><td class="mdescRight">n is the number of vertices on right side of Bipartite <a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> <br /></td></tr>
<tr class="separator:a6f5a9fdbb83ef731d739ba6707e21c3c"><td class="memSeparator" colspan="2">&#160;</td></tr>
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const int&#160;</td><td class="memItemRight" valign="bottom"><b>NIL</b> {0}</td></tr>
<tr class="separator:ae6d069bd16d6eafa6e08c7e5f735eda6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a44742cb9cfecd1a4493970af9b8bbb15"><td class="memItemLeft" align="right" valign="top"><a id="a44742cb9cfecd1a4493970af9b8bbb15" name="a44742cb9cfecd1a4493970af9b8bbb15"></a>
const int&#160;</td><td class="memItemRight" valign="bottom"><b>INF</b> {INT_MAX}</td></tr>
<tr class="separator:a44742cb9cfecd1a4493970af9b8bbb15"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a35893def7a1c5cd60907b4893117796f"><td class="memItemLeft" align="right" valign="top"><a id="a35893def7a1c5cd60907b4893117796f" name="a35893def7a1c5cd60907b4893117796f"></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/list.html">std::list</a>&lt; int &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>adj</b></td></tr>
<tr class="memdesc:a35893def7a1c5cd60907b4893117796f"><td class="mdescLeft">&#160;</td><td class="mdescRight">adj[u] stores adjacents of left side and 0 is used for dummy vertex <br /></td></tr>
<tr class="separator:a35893def7a1c5cd60907b4893117796f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a86ebff8a70cbfedd05281993d5d1987b"><td class="memItemLeft" align="right" valign="top"><a id="a86ebff8a70cbfedd05281993d5d1987b" name="a86ebff8a70cbfedd05281993d5d1987b"></a>
<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>pair_u</b></td></tr>
<tr class="memdesc:a86ebff8a70cbfedd05281993d5d1987b"><td class="mdescLeft">&#160;</td><td class="mdescRight">value of vertex 'u' ranges from 1 to m <br /></td></tr>
<tr class="separator:a86ebff8a70cbfedd05281993d5d1987b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a976ee239402cc2726a280e781c706d77"><td class="memItemLeft" align="right" valign="top"><a id="a976ee239402cc2726a280e781c706d77" name="a976ee239402cc2726a280e781c706d77"></a>
<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>pair_v</b></td></tr>
<tr class="memdesc:a976ee239402cc2726a280e781c706d77"><td class="mdescLeft">&#160;</td><td class="mdescRight">value of vertex 'v' ranges from 1 to n <br /></td></tr>
<tr class="separator:a976ee239402cc2726a280e781c706d77"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6a0228bbba3818447fcf6b56128b552a"><td class="memItemLeft" align="right" valign="top"><a id="a6a0228bbba3818447fcf6b56128b552a" name="a6a0228bbba3818447fcf6b56128b552a"></a>
<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>dist</b></td></tr>
<tr class="memdesc:a6a0228bbba3818447fcf6b56128b552a"><td class="mdescLeft">&#160;</td><td class="mdescRight">dist represents the distance between vertex 'u' and vertex 'v' <br /></td></tr>
<tr class="separator:a6a0228bbba3818447fcf6b56128b552a"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Represents Bipartite graph for Hopcroft Karp implementation. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="a0da5aa674d3b3e54a38251ee60d7cd64" name="a0da5aa674d3b3e54a38251ee60d7cd64"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0da5aa674d3b3e54a38251ee60d7cd64">&#9670;&nbsp;</a></span>HKGraph()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
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<td class="memname">graph::HKGraph::HKGraph </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Constructor for initialization. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">m</td><td>is the number of vertices on left side of Bipartite <a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> </td></tr>
<tr><td class="paramname">n</td><td>is the number of vertices on right side of Bipartite <a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> {</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> this-&gt;<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a> = <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a>;</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> this-&gt;<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6f5a9fdbb83ef731d739ba6707e21c3c">n</a> = <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6f5a9fdbb83ef731d739ba6707e21c3c">n</a>;</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::list&lt;int&gt;</a> &gt;(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a> + 1);</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span>}</div>
<div class="ttc" id="aclassgraph_1_1_h_k_graph_html_a35893def7a1c5cd60907b4893117796f"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">graph::HKGraph::adj</a></div><div class="ttdeci">std::vector&lt; std::list&lt; int &gt; &gt; adj</div><div class="ttdoc">adj[u] stores adjacents of left side and 0 is used for dummy vertex</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:73</div></div>
<div class="ttc" id="aclassgraph_1_1_h_k_graph_html_a3d9101e3b4598159005fd028b9b0ff74"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">graph::HKGraph::m</a></div><div class="ttdeci">int m</div><div class="ttdoc">m is the number of vertices on left side of Bipartite Graph</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:68</div></div>
<div class="ttc" id="aclassgraph_1_1_h_k_graph_html_a6f5a9fdbb83ef731d739ba6707e21c3c"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6f5a9fdbb83ef731d739ba6707e21c3c">graph::HKGraph::n</a></div><div class="ttdeci">int n</div><div class="ttdoc">n is the number of vertices on right side of Bipartite Graph</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:69</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
</div><!-- fragment -->
</div>
</div>
<h2 class="groupheader">Member Function Documentation</h2>
<a id="a3b49011c09cf90a116ab53bef61cd95a" name="a3b49011c09cf90a116ab53bef61cd95a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3b49011c09cf90a116ab53bef61cd95a">&#9670;&nbsp;</a></span>addEdge()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void graph::HKGraph::addEdge </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>u</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>v</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>function to add edge from u to v </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">u</td><td>is the position of first vertex </td></tr>
<tr><td class="paramname">v</td><td>is the position of second vertex </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span>{</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].push_back(v); <span class="comment">// Add v to u’s list.</span></div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a7491add14d9fc04f679114ca6d6f0f93">&#9670;&nbsp;</a></span>bfs()</h2>
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<td class="memname">bool graph::HKGraph::bfs </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td></td>
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</div><div class="memdoc">
<p>This function checks for the possibility of augmented path availability. </p>
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if there is an augmenting path available </dd>
<dd>
<code>false</code> if there is no augmenting path available </dd></dl>
<div class="fragment"><div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span>{</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;int&gt;</a> q; <span class="comment">// an integer queue for bfs</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> </div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="comment">// First layer of vertices (set distance as 0)</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> u = 1; u &lt;= <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a>; u++)</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> {</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="comment">// If this is a free vertex, add it to queue</span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a>[u] == NIL){</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] = 0; <span class="comment">// u is not matched so distance is 0</span></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> q.push(u);</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> }</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> </div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordflow">else</span>{</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] = INF; <span class="comment">// set distance as infinite so that this vertex is considered next time for availibility</span></div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> }</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> }</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> </div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> </div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[NIL] = INF; <span class="comment">// Initialize distance to NIL as infinite</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> </div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="comment">// q is going to contain vertices of left side only.</span></div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordflow">while</span> (!q.empty())</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> {</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keywordtype">int</span> u = q.front(); <span class="comment">// dequeue a vertex</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> q.pop();</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> </div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="comment">// If this node is not NIL and can provide a shorter path to NIL then</span></div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] &lt; <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[NIL])</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> {</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="comment">// Get all the adjacent vertices of the dequeued vertex u</span></div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list&lt;int&gt;::iterator</a> it;</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="keywordflow">for</span> (it = <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">begin</a>(); it != <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].end(); ++it)</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> {</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keywordtype">int</span> v = *it;</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> </div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="comment">// If pair of v is not considered so far i.e. (v, pair_v[v]) is not yet explored edge.</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]] == INF)</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> {</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]] = <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] + 1; </div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> q.push(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]); <span class="comment">// Consider the pair and push it to queue</span></div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> }</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> }</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> }</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> }</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> </div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> </div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> </div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keywordflow">return</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[NIL] != INF); <span class="comment">// If we could come back to NIL using alternating path of distinct vertices then there is an augmenting path available</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span>}</div>
<div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
<div class="ttc" id="aclassgraph_1_1_h_k_graph_html_a6a0228bbba3818447fcf6b56128b552a"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">graph::HKGraph::dist</a></div><div class="ttdeci">std::vector&lt; int &gt; dist</div><div class="ttdoc">dist represents the distance between vertex 'u' and vertex 'v'</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:77</div></div>
<div class="ttc" id="aclassgraph_1_1_h_k_graph_html_a86ebff8a70cbfedd05281993d5d1987b"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">graph::HKGraph::pair_u</a></div><div class="ttdeci">std::vector&lt; int &gt; pair_u</div><div class="ttdoc">value of vertex 'u' ranges from 1 to m</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:75</div></div>
<div class="ttc" id="aclassgraph_1_1_h_k_graph_html_a976ee239402cc2726a280e781c706d77"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">graph::HKGraph::pair_v</a></div><div class="ttdeci">std::vector&lt; int &gt; pair_v</div><div class="ttdoc">value of vertex 'v' ranges from 1 to n</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:76</div></div>
<div class="ttc" id="alist_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/list.html">std::list</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae794950cb3407b6b47d3dc986cf714c0">&#9670;&nbsp;</a></span>dfs()</h2>
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<td class="memname">bool graph::HKGraph::dfs </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>u</em></td><td>)</td>
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</div><div class="memdoc">
<p>This functions checks whether an augmenting path is available exists beginning with free vertex u. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">u</td><td>represents position of vertex </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if there is an augmenting path beginning with free vertex u </dd>
<dd>
<code>false</code> if there is no augmenting path beginning with free vertex u </dd></dl>
<div class="fragment"><div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span>{</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keywordflow">if</span> (u != NIL)</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> {</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list&lt;int&gt;::iterator</a> it;</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="keywordflow">for</span> (it = <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">begin</a>(); it != <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a35893def7a1c5cd60907b4893117796f">adj</a>[u].end(); ++it)</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> {</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> </div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="keywordtype">int</span> v = *it; <span class="comment">// Adjacent vertex of u</span></div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> </div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="comment">// Follow the distances set by BFS search</span></div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]] == <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] + 1)</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> {</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="comment">// If dfs for pair of v also return true then new matching possible, store the matching</span></div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d8/d69/classgraph_1_1_h_k_graph.html#ae794950cb3407b6b47d3dc986cf714c0">dfs</a>(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]) == <span class="keyword">true</span>)</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> { </div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a>[v] = u;</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a>[u] = v;</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> }</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> }</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> }</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> </div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> </div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] = INF; <span class="comment">// If there is no augmenting path beginning with u then set distance to infinite.</span></div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> }</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span>}</div>
<div class="ttc" id="aclassgraph_1_1_h_k_graph_html_ae794950cb3407b6b47d3dc986cf714c0"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#ae794950cb3407b6b47d3dc986cf714c0">graph::HKGraph::dfs</a></div><div class="ttdeci">bool dfs(int u)</div><div class="ttdoc">This functions checks whether an augmenting path is available exists beginning with free vertex u.</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:191</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9dbda80d02bdc26c3e8ff7330c9be75d">&#9670;&nbsp;</a></span>hopcroftKarpAlgorithm()</h2>
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<td class="memname">int graph::HKGraph::hopcroftKarpAlgorithm </td>
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<td class="paramname"></td><td>)</td>
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<p>This function counts the number of augmenting paths between left and right sides of the Bipartite graph. </p>
<dl class="section return"><dt>Returns</dt><dd>size of maximum matching </dd></dl>
<div class="fragment"><div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span>{</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// pair_u[u] stores pair of u in matching on left side of Bipartite Graph.</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="comment">// If u doesn&#39;t have any pair, then pair_u[u] is NIL</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a> + 1,NIL); </div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> </div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// pair_v[v] stores pair of v in matching on right side of Biparite Graph.</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// If v doesn&#39;t have any pair, then pair_u[v] is NIL</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a976ee239402cc2726a280e781c706d77">pair_v</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6f5a9fdbb83ef731d739ba6707e21c3c">n</a> + 1,NIL); </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a6a0228bbba3818447fcf6b56128b552a">dist</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a> + 1); <span class="comment">// dist[u] stores distance of left side vertices</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> </div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = 0; <span class="comment">// Initialize result</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> </div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="comment">// Keep updating the result while there is an augmenting path possible.</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="keywordflow">while</span> (<a class="code hl_function" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a7491add14d9fc04f679114ca6d6f0f93">bfs</a>())</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> {</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="comment">// Find a free vertex to check for a matching</span></div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> u = 1; u &lt;= <a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a3d9101e3b4598159005fd028b9b0ff74">m</a>; u++){</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// If current vertex is free and there is</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// an augmenting path from current vertex</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="comment">// then increment the result</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d8/d69/classgraph_1_1_h_k_graph.html#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a>[u] == NIL &amp;&amp; <a class="code hl_function" href="../../d8/d69/classgraph_1_1_h_k_graph.html#ae794950cb3407b6b47d3dc986cf714c0">dfs</a>(u)){</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>++;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> }</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> }</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> }</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span>}</div>
<div class="ttc" id="aclassgraph_1_1_h_k_graph_html_a7491add14d9fc04f679114ca6d6f0f93"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html#a7491add14d9fc04f679114ca6d6f0f93">graph::HKGraph::bfs</a></div><div class="ttdeci">bool bfs()</div><div class="ttdoc">This function checks for the possibility of augmented path availability.</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:133</div></div>
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
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