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<p>Represents Bipartite graph for Hopcroft Karp implementation.
<a href="#details">More...</a></p>
<div class="dynheader">
Collaboration diagram for HKGraph:</div>
<div class="dyncontent">
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<center><span class="legend">[<a target="top" href="../../graph_legend.html">legend</a>]</span></center></div>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-pub-methods" class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:af02b0c83911070ac6d95fc9905e58aa9" id="r_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="memitem:a0da5aa674d3b3e54a38251ee60d7cd64" id="r_a0da5aa674d3b3e54a38251ee60d7cd64"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a0da5aa674d3b3e54a38251ee60d7cd64">HKGraph</a> (int <a class="el" href="#a3d9101e3b4598159005fd028b9b0ff74">m</a>, int <a class="el" href="#a6f5a9fdbb83ef731d739ba6707e21c3c">n</a>)</td></tr>
<tr class="memdesc:a0da5aa674d3b3e54a38251ee60d7cd64"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor for initialization. <br /></td></tr>
<tr class="memitem:a3b49011c09cf90a116ab53bef61cd95a" id="r_a3b49011c09cf90a116ab53bef61cd95a"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#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 <br /></td></tr>
<tr class="memitem:a7491add14d9fc04f679114ca6d6f0f93" id="r_a7491add14d9fc04f679114ca6d6f0f93"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#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. <br /></td></tr>
<tr class="memitem:ae794950cb3407b6b47d3dc986cf714c0" id="r_ae794950cb3407b6b47d3dc986cf714c0"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#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. <br /></td></tr>
<tr class="memitem:a9dbda80d02bdc26c3e8ff7330c9be75d" id="r_a9dbda80d02bdc26c3e8ff7330c9be75d"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#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. <br /></td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-pri-attribs" class="groupheader"><a id="pri-attribs" name="pri-attribs"></a>
Private Attributes</h2></td></tr>
<tr class="memitem:a3d9101e3b4598159005fd028b9b0ff74" id="r_a3d9101e3b4598159005fd028b9b0ff74"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a3d9101e3b4598159005fd028b9b0ff74">m</a> {}</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="../../da/d9a/class_graph.html">Graph</a> <br /></td></tr>
<tr class="memitem:a6f5a9fdbb83ef731d739ba6707e21c3c" id="r_a6f5a9fdbb83ef731d739ba6707e21c3c"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a6f5a9fdbb83ef731d739ba6707e21c3c">n</a> {}</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="../../da/d9a/class_graph.html">Graph</a> <br /></td></tr>
<tr class="memitem:ae6d069bd16d6eafa6e08c7e5f735eda6" id="r_ae6d069bd16d6eafa6e08c7e5f735eda6"><td class="memItemLeft" align="right" valign="top">const int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae6d069bd16d6eafa6e08c7e5f735eda6">NIL</a> {0}</td></tr>
<tr class="memitem:a44742cb9cfecd1a4493970af9b8bbb15" id="r_a44742cb9cfecd1a4493970af9b8bbb15"><td class="memItemLeft" align="right" valign="top">const int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a44742cb9cfecd1a4493970af9b8bbb15">INF</a> {INT_MAX}</td></tr>
<tr class="memitem:a35893def7a1c5cd60907b4893117796f" id="r_a35893def7a1c5cd60907b4893117796f"><td class="memItemLeft" align="right" valign="top">std::vector&lt; std::list&lt; int &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a35893def7a1c5cd60907b4893117796f">adj</a></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="memitem:a86ebff8a70cbfedd05281993d5d1987b" id="r_a86ebff8a70cbfedd05281993d5d1987b"><td class="memItemLeft" align="right" valign="top">std::vector&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a></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="memitem:a976ee239402cc2726a280e781c706d77" id="r_a976ee239402cc2726a280e781c706d77"><td class="memItemLeft" align="right" valign="top">std::vector&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a976ee239402cc2726a280e781c706d77">pair_v</a></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="memitem:a6a0228bbba3818447fcf6b56128b552a" id="r_a6a0228bbba3818447fcf6b56128b552a"><td class="memItemLeft" align="right" valign="top">std::vector&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a6a0228bbba3818447fcf6b56128b552a">dist</a></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>
</table>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Represents Bipartite graph for Hopcroft Karp implementation. </p>
<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00066">66</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
</div><a name="doc-constructors" id="doc-constructors"></a><h2 id="header-doc-constructors" class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="a0da5aa674d3b3e54a38251ee60d7cd64" name="a0da5aa674d3b3e54a38251ee60d7cd64"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0da5aa674d3b3e54a38251ee60d7cd64">&#9670;&#160;</a></span>HKGraph()</h2>
<div class="memitem">
<div class="memproto">
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<td class="memname">graph::HKGraph::HKGraph </td>
<td>(</td>
<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>m</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>n</em></span>&#160;)</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="../../da/d9a/class_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="../../da/d9a/class_graph.html">Graph</a> </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00231">231</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 231</span> {</div>
<div class="line"><span class="lineno"> 232</span> this-&gt;<a class="code hl_variable" href="#a3d9101e3b4598159005fd028b9b0ff74">m</a> = <a class="code hl_variable" href="#a3d9101e3b4598159005fd028b9b0ff74">m</a>;</div>
<div class="line"><span class="lineno"> 233</span> this-&gt;<a class="code hl_variable" href="#a6f5a9fdbb83ef731d739ba6707e21c3c">n</a> = <a class="code hl_variable" href="#a6f5a9fdbb83ef731d739ba6707e21c3c">n</a>;</div>
<div class="line"><span class="lineno"> 234</span> <a class="code hl_variable" href="#a35893def7a1c5cd60907b4893117796f">adj</a> = std::vector&lt;std::list&lt;int&gt; &gt;(<a class="code hl_variable" href="#a3d9101e3b4598159005fd028b9b0ff74">m</a> + 1);</div>
<div class="line"><span class="lineno"> 235</span>}</div>
<div class="ttc" id="aclass_h_k_graph_html_a35893def7a1c5cd60907b4893117796f"><div class="ttname"><a href="#a35893def7a1c5cd60907b4893117796f">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> <a href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00073">hopcroft_karp.cpp:73</a></div></div>
<div class="ttc" id="aclass_h_k_graph_html_a3d9101e3b4598159005fd028b9b0ff74"><div class="ttname"><a href="#a3d9101e3b4598159005fd028b9b0ff74">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> <a href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00068">hopcroft_karp.cpp:68</a></div></div>
<div class="ttc" id="aclass_h_k_graph_html_a6f5a9fdbb83ef731d739ba6707e21c3c"><div class="ttname"><a href="#a6f5a9fdbb83ef731d739ba6707e21c3c">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> <a href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00069">hopcroft_karp.cpp:69</a></div></div>
</div><!-- fragment -->
</div>
</div>
<a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Member Function Documentation</h2>
<a id="a3b49011c09cf90a116ab53bef61cd95a" name="a3b49011c09cf90a116ab53bef61cd95a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3b49011c09cf90a116ab53bef61cd95a">&#9670;&#160;</a></span>addEdge()</h2>
<div class="memitem">
<div class="memproto">
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<tr>
<td class="memname">void graph::HKGraph::addEdge </td>
<td>(</td>
<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>u</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>v</em></span>&#160;)</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>
<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00242">242</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 243</span>{</div>
<div class="line"><span class="lineno"> 244</span> <a class="code hl_variable" href="#a35893def7a1c5cd60907b4893117796f">adj</a>[u].push_back(v); <span class="comment">// Add v to u’s list.</span></div>
<div class="line"><span class="lineno"> 245</span>}</div>
</div><!-- fragment -->
</div>
</div>
<a id="a7491add14d9fc04f679114ca6d6f0f93" name="a7491add14d9fc04f679114ca6d6f0f93"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7491add14d9fc04f679114ca6d6f0f93">&#9670;&#160;</a></span>bfs()</h2>
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<td class="memname">bool graph::HKGraph::bfs </td>
<td>(</td>
<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>This function checks for the possibility of augmented path availability. </p>
<dl class="section return"><dt>Returns</dt><dd><span class="tt">true</span> if there is an augmenting path available </dd>
<dd>
<span class="tt">false</span> if there is no augmenting path available </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00133">133</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 134</span>{</div>
<div class="line"><span class="lineno"> 135</span> std::queue&lt;int&gt; q; <span class="comment">// an integer queue for bfs</span></div>
<div class="line"><span class="lineno"> 136</span> </div>
<div class="line"><span class="lineno"> 137</span> <span class="comment">// First layer of vertices (set distance as 0)</span></div>
<div class="line"><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="#a3d9101e3b4598159005fd028b9b0ff74">m</a>; u++)</div>
<div class="line"><span class="lineno"> 139</span> {</div>
<div class="line"><span class="lineno"> 140</span> <span class="comment">// If this is a free vertex, add it to queue</span></div>
<div class="line"><span class="lineno"> 141</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a>[u] == NIL){</div>
<div class="line"><span class="lineno"> 142</span> </div>
<div class="line"><span class="lineno"> 143</span> <a class="code hl_variable" href="#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] = 0; <span class="comment">// u is not matched so distance is 0</span></div>
<div class="line"><span class="lineno"> 144</span> q.push(u);</div>
<div class="line"><span class="lineno"> 145</span> }</div>
<div class="line"><span class="lineno"> 146</span> </div>
<div class="line"><span class="lineno"> 147</span> <span class="keywordflow">else</span>{</div>
<div class="line"><span class="lineno"> 148</span> <a class="code hl_variable" href="#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"><span class="lineno"> 149</span> }</div>
<div class="line"><span class="lineno"> 150</span> }</div>
<div class="line"><span class="lineno"> 151</span> </div>
<div class="line"><span class="lineno"> 152</span> </div>
<div class="line"><span class="lineno"> 153</span> <a class="code hl_variable" href="#a6a0228bbba3818447fcf6b56128b552a">dist</a>[NIL] = INF; <span class="comment">// Initialize distance to NIL as infinite</span></div>
<div class="line"><span class="lineno"> 154</span> </div>
<div class="line"><span class="lineno"> 155</span> <span class="comment">// q is going to contain vertices of left side only.</span></div>
<div class="line"><span class="lineno"> 156</span> <span class="keywordflow">while</span> (!q.empty())</div>
<div class="line"><span class="lineno"> 157</span> {</div>
<div class="line"><span class="lineno"> 158</span> <span class="keywordtype">int</span> u = q.front(); <span class="comment">// dequeue a vertex</span></div>
<div class="line"><span class="lineno"> 159</span> q.pop();</div>
<div class="line"><span class="lineno"> 160</span> </div>
<div class="line"><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"><span class="lineno"> 162</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] &lt; <a class="code hl_variable" href="#a6a0228bbba3818447fcf6b56128b552a">dist</a>[NIL])</div>
<div class="line"><span class="lineno"> 163</span> {</div>
<div class="line"><span class="lineno"> 164</span> <span class="comment">// Get all the adjacent vertices of the dequeued vertex u</span></div>
<div class="line"><span class="lineno"> 165</span> std::list&lt;int&gt;::iterator it;</div>
<div class="line"><span class="lineno"> 166</span> <span class="keywordflow">for</span> (it = <a class="code hl_variable" href="#a35893def7a1c5cd60907b4893117796f">adj</a>[u].begin(); it != <a class="code hl_variable" href="#a35893def7a1c5cd60907b4893117796f">adj</a>[u].end(); ++it)</div>
<div class="line"><span class="lineno"> 167</span> {</div>
<div class="line"><span class="lineno"> 168</span> <span class="keywordtype">int</span> v = *it;</div>
<div class="line"><span class="lineno"> 169</span> </div>
<div class="line"><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"><span class="lineno"> 171</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#a6a0228bbba3818447fcf6b56128b552a">dist</a>[<a class="code hl_variable" href="#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]] == INF)</div>
<div class="line"><span class="lineno"> 172</span> {</div>
<div class="line"><span class="lineno"> 173</span> <a class="code hl_variable" href="#a6a0228bbba3818447fcf6b56128b552a">dist</a>[<a class="code hl_variable" href="#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]] = <a class="code hl_variable" href="#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] + 1; </div>
<div class="line"><span class="lineno"> 174</span> q.push(<a class="code hl_variable" href="#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]); <span class="comment">// Consider the pair and push it to queue</span></div>
<div class="line"><span class="lineno"> 175</span> }</div>
<div class="line"><span class="lineno"> 176</span> }</div>
<div class="line"><span class="lineno"> 177</span> }</div>
<div class="line"><span class="lineno"> 178</span> }</div>
<div class="line"><span class="lineno"> 179</span> </div>
<div class="line"><span class="lineno"> 180</span> </div>
<div class="line"><span class="lineno"> 181</span> </div>
<div class="line"><span class="lineno"> 182</span> <span class="keywordflow">return</span> (<a class="code hl_variable" href="#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"><span class="lineno"> 183</span>}</div>
<div class="ttc" id="aclass_h_k_graph_html_a6a0228bbba3818447fcf6b56128b552a"><div class="ttname"><a href="#a6a0228bbba3818447fcf6b56128b552a">HKGraph::dist</a></div><div class="ttdeci">std::vector&lt; int &gt; dist</div><div class="ttdoc">dist represents the distance between vertex &#39;u&#39; and vertex &#39;v&#39;</div><div class="ttdef"><b>Definition</b> <a href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00077">hopcroft_karp.cpp:77</a></div></div>
<div class="ttc" id="aclass_h_k_graph_html_a86ebff8a70cbfedd05281993d5d1987b"><div class="ttname"><a href="#a86ebff8a70cbfedd05281993d5d1987b">HKGraph::pair_u</a></div><div class="ttdeci">std::vector&lt; int &gt; pair_u</div><div class="ttdoc">value of vertex &#39;u&#39; ranges from 1 to m</div><div class="ttdef"><b>Definition</b> <a href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00075">hopcroft_karp.cpp:75</a></div></div>
<div class="ttc" id="aclass_h_k_graph_html_a976ee239402cc2726a280e781c706d77"><div class="ttname"><a href="#a976ee239402cc2726a280e781c706d77">HKGraph::pair_v</a></div><div class="ttdeci">std::vector&lt; int &gt; pair_v</div><div class="ttdoc">value of vertex &#39;v&#39; ranges from 1 to n</div><div class="ttdef"><b>Definition</b> <a href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00076">hopcroft_karp.cpp:76</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae794950cb3407b6b47d3dc986cf714c0">&#9670;&#160;</a></span>dfs()</h2>
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<td class="memname">bool graph::HKGraph::dfs </td>
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<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>
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<dl class="section return"><dt>Returns</dt><dd><span class="tt">true</span> if there is an augmenting path beginning with free vertex u </dd>
<dd>
<span class="tt">false</span> if there is no augmenting path beginning with free vertex u </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00191">191</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 192</span>{</div>
<div class="line"><span class="lineno"> 193</span> <span class="keywordflow">if</span> (u != NIL)</div>
<div class="line"><span class="lineno"> 194</span> {</div>
<div class="line"><span class="lineno"> 195</span> std::list&lt;int&gt;::iterator it;</div>
<div class="line"><span class="lineno"> 196</span> <span class="keywordflow">for</span> (it = <a class="code hl_variable" href="#a35893def7a1c5cd60907b4893117796f">adj</a>[u].begin(); it != <a class="code hl_variable" href="#a35893def7a1c5cd60907b4893117796f">adj</a>[u].end(); ++it)</div>
<div class="line"><span class="lineno"> 197</span> {</div>
<div class="line"><span class="lineno"> 198</span> </div>
<div class="line"><span class="lineno"> 199</span> <span class="keywordtype">int</span> v = *it; <span class="comment">// Adjacent vertex of u</span></div>
<div class="line"><span class="lineno"> 200</span> </div>
<div class="line"><span class="lineno"> 201</span> <span class="comment">// Follow the distances set by BFS search</span></div>
<div class="line"><span class="lineno"> 202</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#a6a0228bbba3818447fcf6b56128b552a">dist</a>[<a class="code hl_variable" href="#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]] == <a class="code hl_variable" href="#a6a0228bbba3818447fcf6b56128b552a">dist</a>[u] + 1)</div>
<div class="line"><span class="lineno"> 203</span> {</div>
<div class="line"><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"><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="#a976ee239402cc2726a280e781c706d77">pair_v</a>[v]) == <span class="keyword">true</span>)</div>
<div class="line"><span class="lineno"> 206</span> { </div>
<div class="line"><span class="lineno"> 207</span> <a class="code hl_variable" href="#a976ee239402cc2726a280e781c706d77">pair_v</a>[v] = u;</div>
<div class="line"><span class="lineno"> 208</span> <a class="code hl_variable" href="#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a>[u] = v;</div>
<div class="line"><span class="lineno"> 209</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><span class="lineno"> 210</span> }</div>
<div class="line"><span class="lineno"> 211</span> }</div>
<div class="line"><span class="lineno"> 212</span> }</div>
<div class="line"><span class="lineno"> 213</span> </div>
<div class="line"><span class="lineno"> 214</span> </div>
<div class="line"><span class="lineno"> 215</span> <a class="code hl_variable" href="#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"><span class="lineno"> 216</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 217</span> }</div>
<div class="line"><span class="lineno"> 218</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><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> <a href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00191">hopcroft_karp.cpp:191</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9dbda80d02bdc26c3e8ff7330c9be75d">&#9670;&#160;</a></span>hopcroftKarpAlgorithm()</h2>
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<td class="memname">int graph::HKGraph::hopcroftKarpAlgorithm </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>
<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00095">95</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 96</span>{</div>
<div class="line"><span class="lineno"> 97</span> </div>
<div class="line"><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"><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"><span class="lineno"> 100</span> <a class="code hl_variable" href="#a86ebff8a70cbfedd05281993d5d1987b">pair_u</a> = std::vector&lt;int&gt;(<a class="code hl_variable" href="#a3d9101e3b4598159005fd028b9b0ff74">m</a> + 1,NIL); </div>
<div class="line"><span class="lineno"> 101</span> </div>
<div class="line"><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"><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"><span class="lineno"> 104</span> <a class="code hl_variable" href="#a976ee239402cc2726a280e781c706d77">pair_v</a> = std::vector&lt;int&gt;(<a class="code hl_variable" href="#a6f5a9fdbb83ef731d739ba6707e21c3c">n</a> + 1,NIL); </div>
<div class="line"><span class="lineno"> 105</span> </div>
<div class="line"><span class="lineno"> 106</span> <a class="code hl_variable" href="#a6a0228bbba3818447fcf6b56128b552a">dist</a> = std::vector&lt;int&gt;(<a class="code hl_variable" href="#a3d9101e3b4598159005fd028b9b0ff74">m</a> + 1); <span class="comment">// dist[u] stores distance of left side vertices</span></div>
<div class="line"><span class="lineno"> 107</span> </div>
<div class="line"><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"><span class="lineno"> 109</span> </div>
<div class="line"><span class="lineno"> 110</span> <span class="comment">// Keep updating the result while there is an augmenting path possible.</span></div>
<div class="line"><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"><span class="lineno"> 112</span> {</div>
<div class="line"><span class="lineno"> 113</span> <span class="comment">// Find a free vertex to check for a matching</span></div>
<div class="line"><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="#a3d9101e3b4598159005fd028b9b0ff74">m</a>; u++){</div>
<div class="line"><span class="lineno"> 115</span> </div>
<div class="line"><span class="lineno"> 116</span> <span class="comment">// If current vertex is free and there is</span></div>
<div class="line"><span class="lineno"> 117</span> <span class="comment">// an augmenting path from current vertex</span></div>
<div class="line"><span class="lineno"> 118</span> <span class="comment">// then increment the result</span></div>
<div class="line"><span class="lineno"> 119</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#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"><span class="lineno"> 120</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>++;</div>
<div class="line"><span class="lineno"> 121</span> }</div>
<div class="line"><span class="lineno"> 122</span> }</div>
<div class="line"><span class="lineno"> 123</span> }</div>
<div class="line"><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"><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> <a href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00133">hopcroft_karp.cpp:133</a></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> <a href="../../de/dc3/fibonacci__sum_8cpp_source.html#l00077">fibonacci_sum.cpp:77</a></div></div>
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<a name="doc-variable-members" id="doc-variable-members"></a><h2 id="header-doc-variable-members" class="groupheader">Member Data Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a35893def7a1c5cd60907b4893117796f">&#9670;&#160;</a></span>adj</h2>
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<td class="memname">std::vector&lt;std::list&lt;int&gt; &gt; graph::HKGraph::adj</td>
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<p>adj[u] stores adjacents of left side and 0 is used for dummy vertex </p>
<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00073">73</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a6a0228bbba3818447fcf6b56128b552a">&#9670;&#160;</a></span>dist</h2>
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<td class="memname">std::vector&lt;int&gt; graph::HKGraph::dist</td>
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<p>dist represents the distance between vertex 'u' and vertex 'v' </p>
<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00077">77</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a44742cb9cfecd1a4493970af9b8bbb15">&#9670;&#160;</a></span>INF</h2>
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<td class="memname">const int graph::HKGraph::INF {INT_MAX}</td>
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<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00071">71</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 71</span>{INT_MAX};</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a3d9101e3b4598159005fd028b9b0ff74">&#9670;&#160;</a></span>m</h2>
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<td class="memname">int graph::HKGraph::m {}</td>
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<p>m is the number of vertices on left side of Bipartite <a class="el" href="../../da/d9a/class_graph.html">Graph</a> </p>
<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00068">68</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 68</span>{}; </div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6f5a9fdbb83ef731d739ba6707e21c3c">&#9670;&#160;</a></span>n</h2>
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<td class="memname">int graph::HKGraph::n {}</td>
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<p>n is the number of vertices on right side of Bipartite <a class="el" href="../../da/d9a/class_graph.html">Graph</a> </p>
<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00069">69</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 69</span>{}; </div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae6d069bd16d6eafa6e08c7e5f735eda6">&#9670;&#160;</a></span>NIL</h2>
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<td class="memname">const int graph::HKGraph::NIL {0}</td>
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<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00070">70</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 70</span>{0};</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a86ebff8a70cbfedd05281993d5d1987b">&#9670;&#160;</a></span>pair_u</h2>
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<td class="memname">std::vector&lt;int&gt; graph::HKGraph::pair_u</td>
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<p>value of vertex 'u' ranges from 1 to m </p>
<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00075">75</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
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<a id="a976ee239402cc2726a280e781c706d77" name="a976ee239402cc2726a280e781c706d77"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a976ee239402cc2726a280e781c706d77">&#9670;&#160;</a></span>pair_v</h2>
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<td class="memname">std::vector&lt;int&gt; graph::HKGraph::pair_v</td>
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<p>value of vertex 'v' ranges from 1 to n </p>
<p class="definition">Definition at line <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html#l00076">76</a> of file <a class="el" href="../../d1/d9a/hopcroft__karp_8cpp_source.html">hopcroft_karp.cpp</a>.</p>
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<hr/>The documentation for this class was generated from the following file:<ul>
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