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Documentation for 8a6f2052e2
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@@ -156,7 +156,7 @@ Functions</h2></td></tr>
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<p >for IO operations for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/set.html">std::set</a></p>
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<p ><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> Algorithms</p>
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<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>
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<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 IO operations for queue data structure for vector data structure for assert</dd></dl>
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<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>
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<p>Graphical algorithms</p>
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<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a> for assert 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>
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</div><h2 class="groupheader">Function Documentation</h2>
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@@ -374,34 +374,37 @@ Here is the call graph for this function:</div>
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<p >insert the neighbouring node into the queue</p>
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<p >if both the current node and its neighbour has the same state then it is not a bipartite graph</p>
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<p >return true when all the connected nodes of the current nodes are travelled and satisify all the above conditions</p>
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<div class="fragment"><div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span>{</div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue<int64_t></a> q; <span class="comment">///< stores the neighbouring node indexes in squence </span><span class="comment"></span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment"> /// of being reached</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment"></span> q.push(index); <span class="comment">/// insert the current node into the queue</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> (*visited)[index] = 1; <span class="comment">/// mark the current node as travelled</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">while</span>(q.size())</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> {</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> int64_t u = q.front();</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> q.pop();</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">for</span>(uint64_t i=0;i<<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[u].size();i++)</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> {</div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> int64_t v = <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[u][i]; <span class="comment">///< stores the neighbour of the current node</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">if</span>(!(*visited)[v]) <span class="comment">/// check whether the neighbour node is </span><span class="comment"></span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment"> /// travelled already or not</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment"></span> {</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> (*visited)[v] = ((*visited)[u]==1)?-1:1; <span class="comment">/// colour the neighbouring node with </span><span class="comment"></span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment"> /// different colour than the current node</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment"></span> q.push(v); <span class="comment">/// insert the neighbouring node into the queue</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> }</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span>((*visited)[v] == (*visited)[u]) <span class="comment">/// if both the current node and its neighbour</span><span class="comment"></span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment"> /// has the same state then it is not a bipartite graph</span></div>
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<div class="fragment"><div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> {</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue<int64_t></a> q; <span class="comment">///< stores the neighbouring node indexes in squence</span><span class="comment"></span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment"> /// of being reached</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment"></span> q.push(index); <span class="comment">/// insert the current node into the queue</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> (*visited)[index] = 1; <span class="comment">/// mark the current node as travelled</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">while</span> (q.size()) {</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> int64_t u = q.front();</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> q.pop();</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">for</span> (uint64_t i = 0; i < <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[u].size(); i++) {</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> int64_t v =</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[u][i]; <span class="comment">///< stores the neighbour of the current node</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordflow">if</span> (!(*visited)[v]) <span class="comment">/// check whether the neighbour node is</span><span class="comment"></span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment"> /// travelled already or not</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment"></span> {</div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> (*visited)[v] =</div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> ((*visited)[u] == 1)</div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> ? -1</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> : 1; <span class="comment">/// colour the neighbouring node with</span><span class="comment"></span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment"> /// different colour than the current node</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment"></span> q.push(v); <span class="comment">/// insert the neighbouring node into the queue</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> ((*visited)[v] ==</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> (*visited)[u]) <span class="comment">/// if both the current node and its</span><span class="comment"></span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment"> /// neighbour has the same state then it</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment"> /// is not a bipartite graph</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment"></span> {</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> }</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> }</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> }</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</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>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment"> /// nodes are travelled and satisify all the above conditions</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</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>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment"> /// nodes are travelled and satisify all the above conditions</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="comment"></span>}</div>
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<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>
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<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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@@ -755,24 +758,25 @@ Here is the call graph for this function:</div>
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<dl class="section return"><dt>Returns</dt><dd>booleans </dd></dl>
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<p >< stores boolean values which signify whether that node had been visited or not</p>
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<p >if the current node is not visited then check whether the sub-graph of that node is a bipartite or not</p>
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<div class="fragment"><div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span>{</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int64_t></a> visited(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size()); <span class="comment">///< stores boolean values </span><span class="comment"></span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="comment"> /// which signify whether that node had been visited or not</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="comment"></span> </div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keywordflow">for</span>(uint64_t i=0;i<<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size();i++)</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> { </div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</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>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="comment"> /// whether the sub-graph of that node is a bipartite or not</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span><span class="comment"></span> {</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keywordflow">if</span>(!<a class="code hl_function" href="../../df/dce/namespacegraph.html#a8e1b547cd407c0774e63f0dc95cda9e7">checkBipartite</a>(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, i, &visited))</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> {</div>
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<div class="fragment"><div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> {</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int64_t></a> visited(</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size()); <span class="comment">///< stores boolean values</span><span class="comment"></span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="comment"> /// which signify whether that node had been visited or</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="comment"> /// not</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="comment"></span> </div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordflow">for</span> (uint64_t i = 0; i < <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size(); i++) {</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</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>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="comment"> /// whether the sub-graph of that node is a bipartite</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span><span class="comment"> /// or not</span></div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="comment"></span> {</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../df/dce/namespacegraph.html#a8e1b547cd407c0774e63f0dc95cda9e7">checkBipartite</a>(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, i, &visited)) {</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> }</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> }</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span>}</div>
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<div class="ttc" id="anamespacegraph_html_a8e1b547cd407c0774e63f0dc95cda9e7"><div class="ttname"><a href="../../df/dce/namespacegraph.html#a8e1b547cd407c0774e63f0dc95cda9e7">graph::checkBipartite</a></div><div class="ttdeci">bool checkBipartite(const std::vector< std::vector< int64_t > > &graph, int64_t index, std::vector< int64_t > *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:35</div></div>
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<div class="ttc" id="anamespacegraph_html_a8e1b547cd407c0774e63f0dc95cda9e7"><div class="ttname"><a href="../../df/dce/namespacegraph.html#a8e1b547cd407c0774e63f0dc95cda9e7">graph::checkBipartite</a></div><div class="ttdeci">bool checkBipartite(const std::vector< std::vector< int64_t > > &graph, int64_t index, std::vector< int64_t > *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:36</div></div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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@@ -839,12 +843,12 @@ Here is the call graph for this function:</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment"></span> int32_t curr_weight = 0;</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment"></span> </div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment"> //// compute current path weight</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment"></span> <span class="keywordtype">int</span> k = src;</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment"></span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#ae9f66040f8e0ba73c1c741261c22a52a">k</a> = src;</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i : vtx) {</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> curr_weight += (*cities)[k][i];</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> k = i;</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> curr_weight += (*cities)[<a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#ae9f66040f8e0ba73c1c741261c22a52a">k</a>][i];</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#ae9f66040f8e0ba73c1c741261c22a52a">k</a> = i;</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> }</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> curr_weight += (*cities)[k][src];</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> curr_weight += (*cities)[<a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#ae9f66040f8e0ba73c1c741261c22a52a">k</a>][src];</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="comment"></span> </div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="comment"> //// update minimum</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</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>
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@@ -855,6 +859,7 @@ Here is the call graph for this function:</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span>}</div>
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<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>
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<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="amidpoint__integral__method_8cpp_html_ae9f66040f8e0ba73c1c741261c22a52a"><div class="ttname"><a href="../../df/d11/midpoint__integral__method_8cpp.html#ae9f66040f8e0ba73c1c741261c22a52a">numerical_methods::midpoint_rule::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">A function k(x) that will be used to test the method.</div><div class="ttdef"><b>Definition:</b> midpoint_integral_method.cpp:103</div></div>
|
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<div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
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<div class="ttc" id="anext_permutation_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/next_permutation.html">std::next_permutation</a></div><div class="ttdeci">T next_permutation(T... args)</div></div>
|
||||
<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
|
||||
|
||||
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