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<tr class="memdesc:a3ae80bc4c6a79d041b4f3a6589eb7fb8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Utility function for depth first seach algorithm this function explores the vertex which is passed into. <br /></td></tr>
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<tr class="memdesc:ad4016cfc80485a43748895a2c26c7d08"><td class="mdescLeft">&#160;</td><td class="mdescRight">Adds and edge between two vertices of graph say u and v in this case. <br /></td></tr>
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<tr class="memdesc:a64c1db5aad7502c6f08e4652f6edd463"><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. <br /></td></tr>
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<tr class="memdesc:a0e30e0dca68cb6e4f671440819b35b6a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function that add edge between two nodes or vertices of graph. <br /></td></tr>
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<tr class="memdesc:a8e1b547cd407c0774e63f0dc95cda9e7"><td class="mdescLeft">&#160;</td><td class="mdescRight">function to check whether the passed graph is bipartite or not <br /></td></tr>
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<tr class="memdesc:a84b0551489c613a681cc83b34450da4b"><td class="mdescLeft">&#160;</td><td class="mdescRight">returns true if the given graph is bipartite else returns false <br /></td></tr>
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<tr class="memitem:ab7706341d006e20d1ae58274187a3346" id="r_ab7706341d006e20d1ae58274187a3346"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ab7706341d006e20d1ae58274187a3346">TravellingSalesmanProblem</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; uint32_t &gt; &gt; *cities, int32_t src, uint32_t V)</td></tr>
<tr class="memitem:ab7706341d006e20d1ae58274187a3346" id="r_ab7706341d006e20d1ae58274187a3346"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ab7706341d006e20d1ae58274187a3346">TravellingSalesmanProblem</a> (std::vector&lt; std::vector&lt; uint32_t &gt; &gt; *cities, int32_t src, uint32_t V)</td></tr>
<tr class="memdesc:ab7706341d006e20d1ae58274187a3346"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function calculates the minimum path distance that will cover all the cities starting from the source. <br /></td></tr>
<tr class="separator:ab7706341d006e20d1ae58274187a3346"><td class="memSeparator" colspan="2">&#160;</td></tr>
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@@ -166,14 +183,14 @@ Functions</h2></td></tr>
<div class="textblock"><p><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> Algorithms. </p>
<p>for assert</p>
<p>Check whether a given graph is bipartite or not.</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p>for std::vector</p>
<p><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> algorithms.</p>
<p>for IO operations for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/set.html">std::set</a></p>
<p>for IO operations for std::set</p>
<p><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> Algorithms</p>
<p>A bipartite graph is the one whose nodes can be divided into two disjoint sets in such a way that the nodes in a set are not connected to each other at all, i.e. no intra-set connections. The only connections that exist are that of inter-set, i.e. the nodes from one set are connected to a subset of nodes in the other set. In this implementation, using a graph in the form of adjacency list, check whether the given graph is a bipartite or not.</p>
<p>References used: <a href="https://www.geeksforgeeks.org/bipartite-graph/" target="_blank">GeeksForGeeks</a> </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/tushar2407" target="_blank">tushar2407</a> for assert for IO operations for queue data structure for vector data structure</dd></dl>
<p>Graphical algorithms</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a> for IO operations for limits of integral types for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p>for std::min for IO operations for limits of integral types for std::vector</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="a9125ceb66bfbec3093bba64c2c1e99e2" name="a9125ceb66bfbec3093bba64c2c1e99e2"></a>
@@ -185,7 +202,7 @@ Functions</h2></td></tr>
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<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; *</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
<td class="paramtype">std::vector&lt; std::vector&lt; int &gt; &gt; *</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
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<p class="definition">Definition at line <a class="el" href="../../df/ddd/connected__components_8cpp_source.html#l00046">46</a> of file <a class="el" href="../../df/ddd/connected__components_8cpp_source.html">connected_components.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 46</span> {</div>
<div class="line"><span class="lineno"> 47</span> (*adj)[u - 1].push_back(v - 1);</div>
<div class="line"><span class="lineno"> 48</span> (*adj)[v - 1].push_back(u - 1);</div>
@@ -225,7 +244,7 @@ Functions</h2></td></tr>
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<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; *</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
<td class="paramtype">std::vector&lt; std::vector&lt; size_t &gt; &gt; *</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
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<p class="definition">Definition at line <a class="el" href="../../da/d8d/depth__first__search_8cpp_source.html#l00056">56</a> of file <a class="el" href="../../da/d8d/depth__first__search_8cpp_source.html">depth_first_search.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 56</span> {</div>
<div class="line"><span class="lineno"> 57</span> <span class="comment">/*</span></div>
<div class="line"><span class="lineno"> 58</span><span class="comment"> *</span></div>
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<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; *</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
<td class="paramtype">std::vector&lt; std::vector&lt; std::pair&lt; int, int &gt; &gt; &gt; *</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
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@@ -300,17 +321,13 @@ Functions</h2></td></tr>
</table>
</dd>
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<p class="definition">Definition at line <a class="el" href="../../d8/d68/dijkstra_8cpp_source.html#l00048">48</a> of file <a class="el" href="../../d8/d68/dijkstra_8cpp_source.html">dijkstra.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 49</span> {</div>
<div class="line"><span class="lineno"> 50</span> (*adj)[u - 1].push_back(<a class="code hl_functionRef" 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"><span class="lineno"> 50</span> (*adj)[u - 1].push_back(std::make_pair(v - 1, w));</div>
<div class="line"><span class="lineno"> 51</span> <span class="comment">// (*adj)[v - 1].push_back(std::make_pair(u - 1, w));</span></div>
<div class="line"><span class="lineno"> 52</span>}</div>
<div class="ttc" id="amake_pair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a></div><div class="ttdeci">T make_pair(T... args)</div></div>
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<td class="memname">bool graph::checkBipartite </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; int64_t &gt; &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>graph</em></span>, </td>
<td class="paramtype">const std::vector&lt; std::vector&lt; int64_t &gt; &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>graph</em></span>, </td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int64_t &gt; *</td> <td class="paramname"><span class="paramname"><em>visited</em></span>&#160;)</td>
<td class="paramtype">std::vector&lt; int64_t &gt; *</td> <td class="paramname"><span class="paramname"><em>visited</em></span>&#160;)</td>
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@@ -356,40 +373,35 @@ Here is the call graph for this function:</div>
<p>insert the neighbouring node into the queue</p>
<p>if both the current node and its neighbour has the same state then it is not a bipartite graph</p>
<p>return true when all the connected nodes of the current nodes are travelled and satisify all the above conditions</p>
<p class="definition">Definition at line <a class="el" href="../../dd/dc3/is__graph__bipartite2_8cpp_source.html#l00037">37</a> of file <a class="el" href="../../dd/dc3/is__graph__bipartite2_8cpp_source.html">is_graph_bipartite2.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 38</span> {</div>
<div class="line"><span class="lineno"> 39</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue&lt;int64_t&gt;</a> q; <span class="comment">///&lt; stores the neighbouring node indexes in squence</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 40</span><span class="comment"> /// of being reached</span></div>
<div class="line"><span class="lineno"> 41</span><span class="comment"></span> q.push(index); <span class="comment">/// insert the current node into the queue</span></div>
<div class="line"><span class="lineno"> 42</span> (*visited)[index] = 1; <span class="comment">/// mark the current node as travelled</span></div>
<div class="line"><span class="lineno"> 39</span> std::queue&lt;int64_t&gt; q; </div>
<div class="line"><span class="lineno"> 41</span> q.push(index); </div>
<div class="line"><span class="lineno"> 42</span> (*visited)[index] = 1; </div>
<div class="line"><span class="lineno"> 43</span> <span class="keywordflow">while</span> (q.size()) {</div>
<div class="line"><span class="lineno"> 44</span> int64_t u = q.front();</div>
<div class="line"><span class="lineno"> 45</span> q.pop();</div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[u].size(); i++) {</div>
<div class="line"><span class="lineno"> 47</span> int64_t v =</div>
<div class="line"><span class="lineno"> 48</span> <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[u][i]; <span class="comment">///&lt; stores the neighbour of the current node</span></div>
<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">if</span> (!(*visited)[v]) <span class="comment">/// check whether the neighbour node is</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 50</span><span class="comment"> /// travelled already or not</span></div>
<div class="line"><span class="lineno"> 51</span><span class="comment"></span> {</div>
<div class="line"><span class="lineno"> 48</span> <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[u][i]; </div>
<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">if</span> (!(*visited)[v]) </div>
<div class="line"><span class="lineno"> 51</span> {</div>
<div class="line"><span class="lineno"> 52</span> (*visited)[v] =</div>
<div class="line"><span class="lineno"> 53</span> ((*visited)[u] == 1)</div>
<div class="line"><span class="lineno"> 54</span> ? -1</div>
<div class="line"><span class="lineno"> 55</span> : 1; <span class="comment">/// colour the neighbouring node with</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 56</span><span class="comment"> /// different colour than the current node</span></div>
<div class="line"><span class="lineno"> 57</span><span class="comment"></span> q.push(v); <span class="comment">/// insert the neighbouring node into the queue</span></div>
<div class="line"><span class="lineno"> 55</span> : 1; </div>
<div class="line"><span class="lineno"> 57</span> q.push(v); </div>
<div class="line"><span class="lineno"> 58</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> ((*visited)[v] ==</div>
<div class="line"><span class="lineno"> 59</span> (*visited)[u]) <span class="comment">/// if both the current node and its</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 60</span><span class="comment"> /// neighbour has the same state then it</span></div>
<div class="line"><span class="lineno"> 61</span><span class="comment"> /// is not a bipartite graph</span></div>
<div class="line"><span class="lineno"> 62</span><span class="comment"></span> {</div>
<div class="line"><span class="lineno"> 59</span> (*visited)[u]) </div>
<div class="line"><span class="lineno"> 62</span> {</div>
<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 64</span> }</div>
<div class="line"><span class="lineno"> 65</span> }</div>
<div class="line"><span class="lineno"> 66</span> }</div>
<div class="line"><span class="lineno"> 67</span> <span class="keywordflow">return</span> <span class="keyword">true</span>; <span class="comment">/// return true when all the connected nodes of the current</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 68</span><span class="comment"> /// nodes are travelled and satisify all the above conditions</span></div>
<div class="line"><span class="lineno"> 69</span><span class="comment"></span>}</div>
<div class="line"><span class="lineno"> 67</span> <span class="keywordflow">return</span> <span class="keyword">true</span>; </div>
<div class="line"><span class="lineno"> 69</span>}</div>
<div class="ttc" id="anamespacegraph_html"><div class="ttname"><a href="../../df/dce/namespacegraph.html">graph</a></div><div class="ttdoc">Graph Algorithms.</div></div>
<div class="ttc" id="aqueue_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue</a></div></div>
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<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;</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
<td class="paramtype">const std::vector&lt; std::vector&lt; size_t &gt; &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
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</table>
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<p class="definition">Definition at line <a class="el" href="../../da/d8d/depth__first__search_8cpp_source.html#l00099">99</a> of file <a class="el" href="../../da/d8d/depth__first__search_8cpp_source.html">depth_first_search.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 100</span> {</div>
<div class="line"><span class="lineno"> 101</span> <span class="keywordtype">size_t</span> vertices = adj.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 101</span> <span class="keywordtype">size_t</span> vertices = adj.size();</div>
<div class="line"><span class="lineno"> 102</span> </div>
<div class="line"><span class="lineno"> 103</span> <a class="code hl_classRef" 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"><span class="lineno"> 103</span> std::vector&lt;bool&gt; visited(vertices, <span class="keyword">false</span>);</div>
<div class="line"><span class="lineno"> 104</span> <a class="code hl_function" href="#a3ae80bc4c6a79d041b4f3a6589eb7fb8">explore</a>(adj, start, &amp;visited);</div>
<div class="line"><span class="lineno"> 105</span>}</div>
<div class="ttc" id="anamespacegraph_html_a3ae80bc4c6a79d041b4f3a6589eb7fb8"><div class="ttname"><a href="#a3ae80bc4c6a79d041b4f3a6589eb7fb8">graph::explore</a></div><div class="ttdeci">void explore(const std::vector&lt; std::vector&lt; int &gt; &gt; *adj, int u, std::vector&lt; bool &gt; *visited)</div><div class="ttdoc">Utility function for depth first seach algorithm this function explores the vertex which is passed in...</div><div class="ttdef"><b>Definition</b> connected_components.cpp:59</div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
<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>
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<div class="ttc" id="anamespacegraph_html_a3ae80bc4c6a79d041b4f3a6589eb7fb8"><div class="ttname"><a href="#a3ae80bc4c6a79d041b4f3a6589eb7fb8">graph::explore</a></div><div class="ttdeci">void explore(const std::vector&lt; std::vector&lt; int &gt; &gt; *adj, int u, std::vector&lt; bool &gt; *visited)</div><div class="ttdoc">Utility function for depth first seach algorithm this function explores the vertex which is passed in...</div><div class="ttdef"><b>Definition</b> <a href="../../df/ddd/connected__components_8cpp_source.html#l00059">connected_components.cpp:59</a></div></div>
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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; *</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
<td class="paramtype">std::vector&lt; std::vector&lt; std::pair&lt; int, int &gt; &gt; &gt; *</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
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<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"><span class="lineno"> 66</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 67</span><span class="comment"> /// n denotes the number of vertices in graph</span></div>
<div class="line"><span class="lineno"> 68</span><span class="comment"></span> <span class="keywordtype">int</span> n = adj-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 69</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 70</span><span class="comment"> /// setting all the distances initially to INF</span></div>
<div class="line"><span class="lineno"> 71</span><span class="comment"></span> <a class="code hl_classRef" 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"><span class="lineno"> 72</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 73</span><span class="comment"> /// creating a min heap using priority queue</span></div>
<div class="line"><span class="lineno"> 74</span><span class="comment"> /// first element of pair contains the distance</span></div>
<div class="line"><span class="lineno"> 75</span><span class="comment"> /// second element of pair contains the vertex</span></div>
<div class="line"><span class="lineno"> 76</span><span class="comment"></span> <a class="code hl_classRef" 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="code hl_classRef" 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"><span class="lineno"> 77</span> <a class="code hl_classRef" 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>
<p class="definition">Definition at line <a class="el" href="../../d8/d68/dijkstra_8cpp_source.html#l00066">66</a> of file <a class="el" href="../../d8/d68/dijkstra_8cpp_source.html">dijkstra.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 66</span> {</div>
<div class="line"><span class="lineno"> 68</span> <span class="keywordtype">int</span> n = adj-&gt;size();</div>
<div class="line"><span class="lineno"> 69</span> </div>
<div class="line"><span class="lineno"> 71</span> std::vector&lt;int64_t&gt; dist(n, INF);</div>
<div class="line"><span class="lineno"> 72</span> </div>
<div class="line"><span class="lineno"> 76</span> std::priority_queue&lt;std::pair&lt;int, int&gt;, std::vector&lt;std::pair&lt;int, int&gt;&gt;,</div>
<div class="line"><span class="lineno"> 77</span> std::greater&lt;std::pair&lt;int, int&gt;&gt;&gt;</div>
<div class="line"><span class="lineno"> 78</span> pq;</div>
<div class="line"><span class="lineno"> 79</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 80</span><span class="comment"> /// pushing the source vertex &#39;s&#39; with 0 distance in min heap</span></div>
<div class="line"><span class="lineno"> 81</span><span class="comment"></span> pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/push.html">push</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(0, s));</div>
<div class="line"><span class="lineno"> 82</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 83</span><span class="comment"> /// marking the distance of source as 0</span></div>
<div class="line"><span class="lineno"> 84</span><span class="comment"></span> dist[s] = 0;</div>
<div class="line"><span class="lineno"> 79</span> </div>
<div class="line"><span class="lineno"> 81</span> pq.push(std::make_pair(0, s));</div>
<div class="line"><span class="lineno"> 82</span> </div>
<div class="line"><span class="lineno"> 84</span> dist[s] = 0;</div>
<div class="line"><span class="lineno"> 85</span> </div>
<div class="line"><span class="lineno"> 86</span> <span class="keywordflow">while</span> (!pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/empty.html">empty</a>()) {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 87</span><span class="comment"> /// second element of pair denotes the node / vertex</span></div>
<div class="line"><span class="lineno"> 88</span><span class="comment"></span> <span class="keywordtype">int</span> currentNode = pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/top.html">top</a>().second;</div>
<div class="line"><span class="lineno"> 89</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 90</span><span class="comment"> /// first element of pair denotes the distance</span></div>
<div class="line"><span class="lineno"> 91</span><span class="comment"></span> <span class="keywordtype">int</span> currentDist = pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/top.html">top</a>().first;</div>
<div class="line"><span class="lineno"> 86</span> <span class="keywordflow">while</span> (!pq.empty()) {</div>
<div class="line"><span class="lineno"> 88</span> <span class="keywordtype">int</span> currentNode = pq.top().second;</div>
<div class="line"><span class="lineno"> 89</span> </div>
<div class="line"><span class="lineno"> 91</span> <span class="keywordtype">int</span> currentDist = pq.top().first;</div>
<div class="line"><span class="lineno"> 92</span> </div>
<div class="line"><span class="lineno"> 93</span> pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/pop.html">pop</a>();</div>
<div class="line"><span class="lineno"> 94</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 95</span><span class="comment"> /// for all the reachable vertex from the currently exploring vertex</span></div>
<div class="line"><span class="lineno"> 96</span><span class="comment"> /// we will try to minimize the distance</span></div>
<div class="line"><span class="lineno"> 97</span><span class="comment"></span> <span class="keywordflow">for</span> (<a class="code hl_classRef" 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"><span class="lineno"> 98</span><span class="comment"> /// minimizing distances</span></div>
<div class="line"><span class="lineno"> 99</span><span class="comment"></span> <span class="keywordflow">if</span> (currentDist + edge.second &lt; dist[edge.first]) {</div>
<div class="line"><span class="lineno"> 93</span> pq.pop();</div>
<div class="line"><span class="lineno"> 94</span> </div>
<div class="line"><span class="lineno"> 97</span> <span class="keywordflow">for</span> (std::pair&lt;int, int&gt; edge : (*adj)[currentNode]) {</div>
<div class="line"><span class="lineno"> 99</span> <span class="keywordflow">if</span> (currentDist + edge.second &lt; dist[edge.first]) {</div>
<div class="line"><span class="lineno"> 100</span> dist[edge.first] = currentDist + edge.second;</div>
<div class="line"><span class="lineno"> 101</span> pq.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue/push.html">push</a>(<a class="code hl_functionRef" 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"><span class="lineno"> 101</span> pq.push(std::make_pair(dist[edge.first], edge.first));</div>
<div class="line"><span class="lineno"> 102</span> }</div>
<div class="line"><span class="lineno"> 103</span> }</div>
<div class="line"><span class="lineno"> 104</span> }</div>
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<div class="line"><span class="lineno"> 107</span> }</div>
<div class="line"><span class="lineno"> 108</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><span class="lineno"> 109</span>}</div>
<div class="ttc" id="aempty_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/priority_queue/empty.html">std::priority_queue::empty</a></div><div class="ttdeci">T empty(T... args)</div></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; int &gt; &gt; *</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
<td class="paramtype">const std::vector&lt; std::vector&lt; int &gt; &gt; *</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
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<td class="paramtype">std::vector&lt; bool &gt; *</td> <td class="paramname"><span class="paramname"><em>visited</em></span>&#160;)</td>
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<p class="definition">Definition at line <a class="el" href="../../df/ddd/connected__components_8cpp_source.html#l00059">59</a> of file <a class="el" href="../../df/ddd/connected__components_8cpp_source.html">connected_components.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 60</span> {</div>
<div class="line"><span class="lineno"> 61</span> (*visited)[u] = <span class="keyword">true</span>;</div>
<div class="line"><span class="lineno"> 62</span> <span class="keywordflow">for</span> (<span class="keyword">auto</span> v : (*adj)[u]) {</div>
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<div class="line"><span class="lineno"> 65</span> }</div>
<div class="line"><span class="lineno"> 66</span> }</div>
<div class="line"><span class="lineno"> 67</span>}</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;</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
<td class="paramtype">const std::vector&lt; std::vector&lt; size_t &gt; &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>adj</em></span>, </td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt; *</td> <td class="paramname"><span class="paramname"><em>visited</em></span>&#160;)</td>
<td class="paramtype">std::vector&lt; bool &gt; *</td> <td class="paramname"><span class="paramname"><em>visited</em></span>&#160;)</td>
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</table>
</dd>
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<p class="definition">Definition at line <a class="el" href="../../da/d8d/depth__first__search_8cpp_source.html#l00080">80</a> of file <a class="el" href="../../da/d8d/depth__first__search_8cpp_source.html">depth_first_search.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 81</span> {</div>
<div class="line"><span class="lineno"> 82</span> <a class="code hl_classRef" 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"><span class="lineno"> 82</span> std::cout &lt;&lt; v + 1 &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><span class="lineno"> 83</span> (*visited)[v] = <span class="keyword">true</span>;</div>
<div class="line"><span class="lineno"> 84</span> <span class="keywordflow">for</span> (<span class="keyword">auto</span> x : adj[v]) {</div>
<div class="line"><span class="lineno"> 85</span> <span class="keywordflow">if</span> (!(*visited)[x]) {</div>
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<div class="line"><span class="lineno"> 87</span> }</div>
<div class="line"><span class="lineno"> 88</span> }</div>
<div class="line"><span class="lineno"> 89</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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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; *</td> <td class="paramname"><span class="paramname"><em>adj</em></span></td><td>)</td>
<td class="paramtype">const std::vector&lt; std::vector&lt; int &gt; &gt; *</td> <td class="paramname"><span class="paramname"><em>adj</em></span></td><td>)</td>
<td></td>
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<dl class="section return"><dt>Returns</dt><dd>connected_components number of connected components in graph. </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../df/ddd/connected__components_8cpp_source.html#l00077">77</a> of file <a class="el" href="../../df/ddd/connected__components_8cpp_source.html">connected_components.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 77</span> {</div>
<div class="line"><span class="lineno"> 78</span> <span class="keywordtype">int</span> n = adj-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 78</span> <span class="keywordtype">int</span> n = adj-&gt;size();</div>
<div class="line"><span class="lineno"> 79</span> <span class="keywordtype">int</span> connected_components = 0;</div>
<div class="line"><span class="lineno"> 80</span> <a class="code hl_classRef" 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"><span class="lineno"> 80</span> std::vector&lt;bool&gt; visited(n, <span class="keyword">false</span>);</div>
<div class="line"><span class="lineno"> 81</span> </div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><span class="lineno"> 83</span> <span class="keywordflow">if</span> (!visited[i]) {</div>
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<div class="line"><span class="lineno"> 87</span> }</div>
<div class="line"><span class="lineno"> 88</span> <span class="keywordflow">return</span> connected_components;</div>
<div class="line"><span class="lineno"> 89</span>}</div>
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<td class="memname">bool graph::isBipartite </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; int64_t &gt; &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>graph</em></span></td><td>)</td>
<td class="paramtype">const std::vector&lt; std::vector&lt; int64_t &gt; &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>graph</em></span></td><td>)</td>
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<dl class="section return"><dt>Returns</dt><dd>booleans </dd></dl>
<p>&lt; stores boolean values which signify whether that node had been visited or not</p>
<p>if the current node is not visited then check whether the sub-graph of that node is a bipartite or not</p>
<p class="definition">Definition at line <a class="el" href="../../dd/dc3/is__graph__bipartite2_8cpp_source.html#l00076">76</a> of file <a class="el" href="../../dd/dc3/is__graph__bipartite2_8cpp_source.html">is_graph_bipartite2.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 76</span> {</div>
<div class="line"><span class="lineno"> 77</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> visited(</div>
<div class="line"><span class="lineno"> 78</span> <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size()); <span class="comment">///&lt; stores boolean values</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 79</span><span class="comment"> /// which signify whether that node had been visited or</span></div>
<div class="line"><span class="lineno"> 80</span><span class="comment"> /// not</span></div>
<div class="line"><span class="lineno"> 81</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 77</span> std::vector&lt;int64_t&gt; visited(</div>
<div class="line"><span class="lineno"> 78</span> <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size()); </div>
<div class="line"><span class="lineno"> 81</span> </div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size(); i++) {</div>
<div class="line"><span class="lineno"> 83</span> <span class="keywordflow">if</span> (!visited[i]) <span class="comment">/// if the current node is not visited then check</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 84</span><span class="comment"> /// whether the sub-graph of that node is a bipartite</span></div>
<div class="line"><span class="lineno"> 85</span><span class="comment"> /// or not</span></div>
<div class="line"><span class="lineno"> 86</span><span class="comment"></span> {</div>
<div class="line"><span class="lineno"> 83</span> <span class="keywordflow">if</span> (!visited[i]) </div>
<div class="line"><span class="lineno"> 86</span> {</div>
<div class="line"><span class="lineno"> 87</span> <span class="keywordflow">if</span> (!<a class="code hl_function" href="#a8e1b547cd407c0774e63f0dc95cda9e7">checkBipartite</a>(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, i, &amp;visited)) {</div>
<div class="line"><span class="lineno"> 88</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 89</span> }</div>
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<div class="line"><span class="lineno"> 91</span> }</div>
<div class="line"><span class="lineno"> 92</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><span class="lineno"> 93</span>}</div>
<div class="ttc" id="anamespacegraph_html_a8e1b547cd407c0774e63f0dc95cda9e7"><div class="ttname"><a href="#a8e1b547cd407c0774e63f0dc95cda9e7">graph::checkBipartite</a></div><div class="ttdeci">bool checkBipartite(const std::vector&lt; std::vector&lt; int64_t &gt; &gt; &amp;graph, int64_t index, std::vector&lt; int64_t &gt; *visited)</div><div class="ttdoc">function to check whether the passed graph is bipartite or not</div><div class="ttdef"><b>Definition</b> is_graph_bipartite2.cpp:37</div></div>
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<div class="ttc" id="anamespacegraph_html_a8e1b547cd407c0774e63f0dc95cda9e7"><div class="ttname"><a href="#a8e1b547cd407c0774e63f0dc95cda9e7">graph::checkBipartite</a></div><div class="ttdeci">bool checkBipartite(const std::vector&lt; std::vector&lt; int64_t &gt; &gt; &amp;graph, int64_t index, std::vector&lt; int64_t &gt; *visited)</div><div class="ttdoc">function to check whether the passed graph is bipartite or not</div><div class="ttdef"><b>Definition</b> <a href="../../dd/dc3/is__graph__bipartite2_8cpp_source.html#l00037">is_graph_bipartite2.cpp:37</a></div></div>
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<td class="memname">int graph::TravellingSalesmanProblem </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; uint32_t &gt; &gt; *</td> <td class="paramname"><span class="paramname"><em>cities</em></span>, </td>
<td class="paramtype">std::vector&lt; std::vector&lt; uint32_t &gt; &gt; *</td> <td class="paramname"><span class="paramname"><em>cities</em></span>, </td>
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<td class="paramkey"></td>
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<div class="fragment"><div class="line"><span class="lineno"> 42</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 43</span><span class="comment"> //// vtx stores the vertexs of the graph</span></div>
<div class="line"><span class="lineno"> 44</span><span class="comment"></span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> vtx;</div>
<p class="definition">Definition at line <a class="el" href="../../de/d88/travelling__salesman__problem_8cpp_source.html#l00041">41</a> of file <a class="el" href="../../de/d88/travelling__salesman__problem_8cpp_source.html">travelling_salesman_problem.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 42</span> {</div>
<div class="line"><span class="lineno"> 44</span> std::vector&lt;uint32_t&gt; vtx;</div>
<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">for</span> (uint32_t i = 0; i &lt; V; i++) {</div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">if</span> (i != src) {</div>
<div class="line"><span class="lineno"> 47</span> vtx.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(i);</div>
<div class="line"><span class="lineno"> 47</span> vtx.push_back(i);</div>
<div class="line"><span class="lineno"> 48</span> }</div>
<div class="line"><span class="lineno"> 49</span> }</div>
<div class="line"><span class="lineno"> 50</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 51</span><span class="comment"> //// store minimum weight Hamiltonian Cycle.</span></div>
<div class="line"><span class="lineno"> 52</span><span class="comment"></span> int32_t min_path = 2147483647;</div>
<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">do</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 54</span><span class="comment"> //// store current Path weight(cost)</span></div>
<div class="line"><span class="lineno"> 55</span><span class="comment"></span> int32_t curr_weight = 0;</div>
<div class="line"><span class="lineno"> 56</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 57</span><span class="comment"> //// compute current path weight</span></div>
<div class="line"><span class="lineno"> 58</span><span class="comment"></span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = src;</div>
<div class="line"><span class="lineno"> 50</span> </div>
<div class="line"><span class="lineno"> 52</span> int32_t min_path = 2147483647;</div>
<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">do</span> {</div>
<div class="line"><span class="lineno"> 55</span> int32_t curr_weight = 0;</div>
<div class="line"><span class="lineno"> 56</span> </div>
<div class="line"><span class="lineno"> 58</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = src;</div>
<div class="line"><span class="lineno"> 59</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i : vtx) {</div>
<div class="line"><span class="lineno"> 60</span> curr_weight += (*cities)[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][i];</div>
<div class="line"><span class="lineno"> 61</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = i;</div>
<div class="line"><span class="lineno"> 62</span> }</div>
<div class="line"><span class="lineno"> 63</span> curr_weight += (*cities)[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][src];</div>
<div class="line"><span class="lineno"> 64</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 65</span><span class="comment"> //// update minimum</span></div>
<div class="line"><span class="lineno"> 66</span><span class="comment"></span> min_path = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(min_path, curr_weight);</div>
<div class="line"><span class="lineno"> 64</span> </div>
<div class="line"><span class="lineno"> 66</span> min_path = std::min(min_path, curr_weight);</div>
<div class="line"><span class="lineno"> 67</span> </div>
<div class="line"><span class="lineno"> 68</span> } <span class="keywordflow">while</span> (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/next_permutation.html">next_permutation</a>(vtx.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), vtx.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>()));</div>
<div class="line"><span class="lineno"> 68</span> } <span class="keywordflow">while</span> (next_permutation(vtx.begin(), vtx.end()));</div>
<div class="line"><span class="lineno"> 69</span> </div>
<div class="line"><span class="lineno"> 70</span> <span class="keywordflow">return</span> min_path;</div>
<div class="line"><span class="lineno"> 71</span>}</div>
<div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/begin.html">std::vector::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> composite_simpson_rule.cpp:117</div></div>
<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/end.html">std::vector::end</a></div><div class="ttdeci">T end(T... args)</div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00117">composite_simpson_rule.cpp:117</a></div></div>
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