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&#160;<span id="projectnumber">1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<a href="#nested-classes">Classes</a> &#124;
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<p><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> algorithms.
<a href="../../df/dce/namespacegraph.html#details">More...</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="nested-classes"></a>
Classes</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d69/classgraph_1_1_h_k_graph.html">HKGraph</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Represents Bipartite graph for Hopcroft Karp implementation. <a href="../../d8/d69/classgraph_1_1_h_k_graph.html#details">More...</a><br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html">LowestCommonAncestor</a></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d58/classgraph_1_1_rooted_tree.html">RootedTree</a></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a372ff051a7bc6c91d34a7b58edf8dfce"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a372ff051a7bc6c91d34a7b58edf8dfce">addEdge</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&gt; *adj, int u, int v)</td></tr>
<tr class="memdesc:a372ff051a7bc6c91d34a7b58edf8dfce"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function that add edge between two nodes or vertices of graph. <a href="../../df/dce/namespacegraph.html#a372ff051a7bc6c91d34a7b58edf8dfce">More...</a><br /></td></tr>
<tr class="separator:a372ff051a7bc6c91d34a7b58edf8dfce"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8e9885e0dd49fcf8262a9868124deac9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a8e9885e0dd49fcf8262a9868124deac9">explore</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&gt; *adj, int u, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt; *visited)</td></tr>
<tr class="memdesc:a8e9885e0dd49fcf8262a9868124deac9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Utility function for depth first seach algorithm this function explores the vertex which is passed into. <a href="../../df/dce/namespacegraph.html#a8e9885e0dd49fcf8262a9868124deac9">More...</a><br /></td></tr>
<tr class="separator:a8e9885e0dd49fcf8262a9868124deac9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9fc2ded2807582edf398e6d7c7114914"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a9fc2ded2807582edf398e6d7c7114914">getConnectedComponents</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&gt; *adj)</td></tr>
<tr class="memdesc:a9fc2ded2807582edf398e6d7c7114914"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function that perfoms depth first search algorithm on graph and calculated the number of connected components. <a href="../../df/dce/namespacegraph.html#a9fc2ded2807582edf398e6d7c7114914">More...</a><br /></td></tr>
<tr class="separator:a9fc2ded2807582edf398e6d7c7114914"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a33d8f7759375aee956643d76df491b7b"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a33d8f7759375aee956643d76df491b7b">addEdge</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; size_t &gt;&gt; *adj, size_t u, size_t v)</td></tr>
<tr class="memdesc:a33d8f7759375aee956643d76df491b7b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Adds and edge between two vertices of graph say u and v in this case. <a href="../../df/dce/namespacegraph.html#a33d8f7759375aee956643d76df491b7b">More...</a><br /></td></tr>
<tr class="separator:a33d8f7759375aee956643d76df491b7b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a48acac475cb48614279e7ea784c32fc3"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a48acac475cb48614279e7ea784c32fc3">explore</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; size_t &gt;&gt; &amp;adj, size_t v, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt; *visited)</td></tr>
<tr class="memdesc:a48acac475cb48614279e7ea784c32fc3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Explores the given vertex, exploring a vertex means traversing over all the vertices which are connected to the vertex that is currently being explored. <a href="../../df/dce/namespacegraph.html#a48acac475cb48614279e7ea784c32fc3">More...</a><br /></td></tr>
<tr class="separator:a48acac475cb48614279e7ea784c32fc3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2e6017a54d445819ede9adcf33240e1a"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a2e6017a54d445819ede9adcf33240e1a">depth_first_search</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; size_t &gt;&gt; &amp;adj, size_t start)</td></tr>
<tr class="memdesc:a2e6017a54d445819ede9adcf33240e1a"><td class="mdescLeft">&#160;</td><td class="mdescRight">initiates depth first search algorithm. <a href="../../df/dce/namespacegraph.html#a2e6017a54d445819ede9adcf33240e1a">More...</a><br /></td></tr>
<tr class="separator:a2e6017a54d445819ede9adcf33240e1a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a454891267187a5ec6c6e3f3ad5203ff1"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a454891267187a5ec6c6e3f3ad5203ff1">addEdge</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; int, int &gt;&gt;&gt; *adj, int u, int v, int w)</td></tr>
<tr class="memdesc:a454891267187a5ec6c6e3f3ad5203ff1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function that add edge between two nodes or vertices of graph. <a href="../../df/dce/namespacegraph.html#a454891267187a5ec6c6e3f3ad5203ff1">More...</a><br /></td></tr>
<tr class="separator:a454891267187a5ec6c6e3f3ad5203ff1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a868530bfaed30e57290a76d5b4402d50"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a868530bfaed30e57290a76d5b4402d50">dijkstra</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; int, int &gt;&gt;&gt; *adj, int s, int t)</td></tr>
<tr class="memdesc:a868530bfaed30e57290a76d5b4402d50"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function runs the dijkstra algorithm for some source vertex and target vertex in the graph and returns the shortest distance of target from the source. <a href="../../df/dce/namespacegraph.html#a868530bfaed30e57290a76d5b4402d50">More...</a><br /></td></tr>
<tr class="separator:a868530bfaed30e57290a76d5b4402d50"><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><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> algorithms. </p>
<p><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> Algorithms. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a372ff051a7bc6c91d34a7b58edf8dfce"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a372ff051a7bc6c91d34a7b58edf8dfce">&#9670;&nbsp;</a></span>addEdge() <span class="overload">[1/3]</span></h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void graph::addEdge </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&gt; *&#160;</td>
<td class="paramname"><em>adj</em>, </td>
</tr>
<tr>
<td class="paramkey"></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 that add edge between two nodes or vertices of graph. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">adj</td><td>adjacency list of graph. </td></tr>
<tr><td class="paramname">u</td><td>any node or vertex of graph. </td></tr>
<tr><td class="paramname">v</td><td>any node or vertex of graph. </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; (*adj)[u - 1].push_back(v - 1);</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; (*adj)[v - 1].push_back(u - 1);</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160;}</div>
</div><!-- fragment -->
</div>
</div>
<a id="a33d8f7759375aee956643d76df491b7b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a33d8f7759375aee956643d76df491b7b">&#9670;&nbsp;</a></span>addEdge() <span class="overload">[2/3]</span></h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void graph::addEdge </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; size_t &gt;&gt; *&#160;</td>
<td class="paramname"><em>adj</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">size_t&#160;</td>
<td class="paramname"><em>u</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">size_t&#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>Adds and edge between two vertices of graph say u and v in this case. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">adj</td><td>Adjacency list representation of graph </td></tr>
<tr><td class="paramname">u</td><td>first vertex </td></tr>
<tr><td class="paramname">v</td><td>second vertex </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; {</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="comment">/*</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160;<span class="comment"> * Here we are considering undirected graph that&#39;s the</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160;<span class="comment"> * reason we are adding v to the adjacency list representation of u</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160;<span class="comment"> * and also adding u to the adjacency list representation of v</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; (*adj)[u - 1].push_back(v - 1);</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; (*adj)[v - 1].push_back(u - 1);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160;}</div>
</div><!-- fragment -->
</div>
</div>
<a id="a454891267187a5ec6c6e3f3ad5203ff1"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a454891267187a5ec6c6e3f3ad5203ff1">&#9670;&nbsp;</a></span>addEdge() <span class="overload">[3/3]</span></h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void graph::addEdge </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; int, int &gt;&gt;&gt; *&#160;</td>
<td class="paramname"><em>adj</em>, </td>
</tr>
<tr>
<td class="paramkey"></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>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>w</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Function that add edge between two nodes or vertices of graph. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">u</td><td>any node or vertex of graph </td></tr>
<tr><td class="paramname">v</td><td>any node or vertex of graph </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; {</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; (*adj)[u - 1].push_back(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(v - 1, w));</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="comment">// (*adj)[v - 1].push_back(std::make_pair(u - 1, w));</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a2e6017a54d445819ede9adcf33240e1a">&#9670;&nbsp;</a></span>depth_first_search()</h2>
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<td class="memname">void graph::depth_first_search </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; size_t &gt;&gt; &amp;&#160;</td>
<td class="paramname"><em>adj</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">size_t&#160;</td>
<td class="paramname"><em>start</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
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<p>initiates depth first search algorithm. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">adj</td><td>adjacency list of graph </td></tr>
<tr><td class="paramname">start</td><td>vertex from where DFS starts traversing. </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; {</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="keywordtype">size_t</span> vertices = adj.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; </div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> visited(vertices, <span class="keyword">false</span>);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#a48acac475cb48614279e7ea784c32fc3">explore</a>(adj, start, &amp;visited);</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a868530bfaed30e57290a76d5b4402d50">&#9670;&nbsp;</a></span>dijkstra()</h2>
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<td class="memname">int graph::dijkstra </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; int, int &gt;&gt;&gt; *&#160;</td>
<td class="paramname"><em>adj</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>s</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>t</em>&#160;</td>
</tr>
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<td></td>
<td>)</td>
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<p>Function runs the dijkstra algorithm for some source vertex and target vertex in the graph and returns the shortest distance of target from the source. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">adj</td><td>input graph </td></tr>
<tr><td class="paramname">s</td><td>source vertex </td></tr>
<tr><td class="paramname">t</td><td>target vertex</td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>shortest distance if target is reachable from source else -1 in case if target is not reachable from source. </dd></dl>
<p>n denotes the number of vertices in graph</p>
<p>setting all the distances initially to INF</p>
<p>creating a min heap using priority queue first element of pair contains the distance second element of pair contains the vertex</p>
<p>pushing the source vertex 's' with 0 distance in min heap</p>
<p>marking the distance of source as 0</p>
<p>second element of pair denotes the node / vertex</p>
<p>first element of pair denotes the distance</p>
<p>for all the reachable vertex from the currently exploring vertex we will try to minimize the distance</p>
<p>minimizing distances</p>
<div class="fragment"><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; {<span class="comment"></span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160;<span class="comment"> /// n denotes the number of vertices in graph</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160;<span class="comment"></span> <span class="keywordtype">int</span> n = adj-&gt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160;<span class="comment"> /// setting all the distances initially to INF</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160;<span class="comment"></span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> dist(n, INF);</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160;<span class="comment"> /// creating a min heap using priority queue</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160;<span class="comment"> /// first element of pair contains the distance</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160;<span class="comment"> /// second element of pair contains the vertex</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160;<span class="comment"></span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue&lt;std::pair&lt;int, int&gt;</a>, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::pair&lt;int, int&gt;</a>&gt;,</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/greater.html">std::greater&lt;std::pair&lt;int, int&gt;</a>&gt;&gt;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; pq;</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160;<span class="comment"> /// pushing the source vertex &#39;s&#39; with 0 distance in min heap</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160;<span class="comment"></span> pq.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/push.html">push</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(0, s));</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160;<span class="comment"> /// marking the distance of source as 0</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160;<span class="comment"></span> dist[s] = 0;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; </div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="keywordflow">while</span> (!pq.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/empty.html">empty</a>()) {<span class="comment"></span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160;<span class="comment"> /// second element of pair denotes the node / vertex</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160;<span class="comment"></span> <span class="keywordtype">int</span> currentNode = pq.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/top.html">top</a>().second;</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160;<span class="comment"> /// first element of pair denotes the distance</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160;<span class="comment"></span> <span class="keywordtype">int</span> currentDist = pq.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/top.html">top</a>().first;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; </div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; pq.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/pop.html">pop</a>();</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160;<span class="comment"> /// for all the reachable vertex from the currently exploring vertex</span></div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160;<span class="comment"> /// we will try to minimize the distance</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160;<span class="comment"></span> <span class="keywordflow">for</span> (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a> edge : (*adj)[currentNode]) {<span class="comment"></span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160;<span class="comment"> /// minimizing distances</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160;<span class="comment"></span> <span class="keywordflow">if</span> (currentDist + edge.second &lt; dist[edge.first]) {</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; dist[edge.first] = currentDist + edge.second;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; pq.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/push.html">push</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(dist[edge.first], edge.first));</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; }</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; }</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; }</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <span class="keywordflow">if</span> (dist[t] != INF) {</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; <span class="keywordflow">return</span> dist[t];</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; }</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; <span class="keywordflow">return</span> -1;</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a8e9885e0dd49fcf8262a9868124deac9">&#9670;&nbsp;</a></span>explore() <span class="overload">[1/2]</span></h2>
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<td class="memname">void graph::explore </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&gt; *&#160;</td>
<td class="paramname"><em>adj</em>, </td>
</tr>
<tr>
<td class="paramkey"></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"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt; *&#160;</td>
<td class="paramname"><em>visited</em>&#160;</td>
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<p>Utility function for depth first seach algorithm this function explores the vertex which is passed into. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">adj</td><td>adjacency list of graph. </td></tr>
<tr><td class="paramname">u</td><td>vertex or node to be explored. </td></tr>
<tr><td class="paramname">visited</td><td>already visited vertices. </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; {</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; (*visited)[u] = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">auto</span> v : (*adj)[u]) {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordflow">if</span> (!(*visited)[v]) {</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#a8e9885e0dd49fcf8262a9868124deac9">explore</a>(adj, v, visited);</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; }</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; }</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160;}</div>
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<td class="memname">void graph::explore </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; size_t &gt;&gt; &amp;&#160;</td>
<td class="paramname"><em>adj</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">size_t&#160;</td>
<td class="paramname"><em>v</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt; *&#160;</td>
<td class="paramname"><em>visited</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
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<p>Explores the given vertex, exploring a vertex means traversing over all the vertices which are connected to the vertex that is currently being explored. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">adj</td><td>garph </td></tr>
<tr><td class="paramname">v</td><td>vertex to be explored </td></tr>
<tr><td class="paramname">visited</td><td>already visited vertices </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; {</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; v + 1 &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; (*visited)[v] = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">auto</span> x : adj[v]) {</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="keywordflow">if</span> (!(*visited)[x]) {</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#a48acac475cb48614279e7ea784c32fc3">explore</a>(adj, x, visited);</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; }</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; }</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9fc2ded2807582edf398e6d7c7114914">&#9670;&nbsp;</a></span>getConnectedComponents()</h2>
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<td class="memname">int graph::getConnectedComponents </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&gt; *&#160;</td>
<td class="paramname"><em>adj</em></td><td>)</td>
<td></td>
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<p>Function that perfoms depth first search algorithm on graph and calculated the number of connected components. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">adj</td><td>adjacency list of graph.</td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>connected_components number of connected components in graph. </dd></dl>
<div class="fragment"><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; {</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="keywordtype">int</span> n = adj-&gt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <span class="keywordtype">int</span> connected_components = 0;</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> visited(n, <span class="keyword">false</span>);</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <span class="keywordflow">if</span> (!visited[i]) {</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#a8e9885e0dd49fcf8262a9868124deac9">explore</a>(adj, i, &amp;visited);</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; connected_components++;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; }</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; }</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <span class="keywordflow">return</span> connected_components;</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160;}</div>
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