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@@ -122,50 +122,50 @@ Classes</h2></td></tr>
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a9125ceb66bfbec3093bba64c2c1e99e2"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">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:a9125ceb66bfbec3093bba64c2c1e99e2"><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#a9125ceb66bfbec3093bba64c2c1e99e2">More...</a><br /></td></tr>
<tr class="memdesc:a9125ceb66bfbec3093bba64c2c1e99e2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function that add edge between two nodes or vertices of graph. <br /></td></tr>
<tr class="separator:a9125ceb66bfbec3093bba64c2c1e99e2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3ae80bc4c6a79d041b4f3a6589eb7fb8"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a3ae80bc4c6a79d041b4f3a6589eb7fb8">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: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. <a href="../../df/dce/namespacegraph.html#a3ae80bc4c6a79d041b4f3a6589eb7fb8">More...</a><br /></td></tr>
<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>
<tr class="separator:a3ae80bc4c6a79d041b4f3a6589eb7fb8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a83ab16e96cec644109a58dfc9329bc2b"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a83ab16e96cec644109a58dfc9329bc2b">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:a83ab16e96cec644109a58dfc9329bc2b"><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#a83ab16e96cec644109a58dfc9329bc2b">More...</a><br /></td></tr>
<tr class="memdesc:a83ab16e96cec644109a58dfc9329bc2b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function that perfoms depth first search algorithm on graph and calculated the number of connected components. <br /></td></tr>
<tr class="separator:a83ab16e96cec644109a58dfc9329bc2b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad4016cfc80485a43748895a2c26c7d08"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#ad4016cfc80485a43748895a2c26c7d08">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:ad4016cfc80485a43748895a2c26c7d08"><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#ad4016cfc80485a43748895a2c26c7d08">More...</a><br /></td></tr>
<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>
<tr class="separator:ad4016cfc80485a43748895a2c26c7d08"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a64c1db5aad7502c6f08e4652f6edd463"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a64c1db5aad7502c6f08e4652f6edd463">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: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. <a href="../../df/dce/namespacegraph.html#a64c1db5aad7502c6f08e4652f6edd463">More...</a><br /></td></tr>
<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>
<tr class="separator:a64c1db5aad7502c6f08e4652f6edd463"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab5428a3519267a28bba4b4310cfbb6ae"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#ab5428a3519267a28bba4b4310cfbb6ae">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:ab5428a3519267a28bba4b4310cfbb6ae"><td class="mdescLeft">&#160;</td><td class="mdescRight">initiates depth first search algorithm. <a href="../../df/dce/namespacegraph.html#ab5428a3519267a28bba4b4310cfbb6ae">More...</a><br /></td></tr>
<tr class="memdesc:ab5428a3519267a28bba4b4310cfbb6ae"><td class="mdescLeft">&#160;</td><td class="mdescRight">initiates depth first search algorithm. <br /></td></tr>
<tr class="separator:ab5428a3519267a28bba4b4310cfbb6ae"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0e30e0dca68cb6e4f671440819b35b6a"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a0e30e0dca68cb6e4f671440819b35b6a">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:a0e30e0dca68cb6e4f671440819b35b6a"><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#a0e30e0dca68cb6e4f671440819b35b6a">More...</a><br /></td></tr>
<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>
<tr class="separator:a0e30e0dca68cb6e4f671440819b35b6a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:adc68cbc8ba09eb1142265935c0d45b84"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84">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:adc68cbc8ba09eb1142265935c0d45b84"><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#adc68cbc8ba09eb1142265935c0d45b84">More...</a><br /></td></tr>
<tr class="memdesc:adc68cbc8ba09eb1142265935c0d45b84"><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. <br /></td></tr>
<tr class="separator:adc68cbc8ba09eb1142265935c0d45b84"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8e1b547cd407c0774e63f0dc95cda9e7"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a8e1b547cd407c0774e63f0dc95cda9e7">checkBipartite</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; int64_t &gt; &gt; &amp;graph, int64_t index, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int64_t &gt; *visited)</td></tr>
<tr class="memdesc:a8e1b547cd407c0774e63f0dc95cda9e7"><td class="mdescLeft">&#160;</td><td class="mdescRight">function to check whether the passed graph is bipartite or not <a href="../../df/dce/namespacegraph.html#a8e1b547cd407c0774e63f0dc95cda9e7">More...</a><br /></td></tr>
<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>
<tr class="separator:a8e1b547cd407c0774e63f0dc95cda9e7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a84b0551489c613a681cc83b34450da4b"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a84b0551489c613a681cc83b34450da4b">isBipartite</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; int64_t &gt; &gt; &amp;graph)</td></tr>
<tr class="memdesc:a84b0551489c613a681cc83b34450da4b"><td class="mdescLeft">&#160;</td><td class="mdescRight">returns true if the given graph is bipartite else returns false <a href="../../df/dce/namespacegraph.html#a84b0551489c613a681cc83b34450da4b">More...</a><br /></td></tr>
<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>
<tr class="separator:a84b0551489c613a681cc83b34450da4b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab7706341d006e20d1ae58274187a3346"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#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="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. <a href="../../df/dce/namespacegraph.html#ab7706341d006e20d1ae58274187a3346">More...</a><br /></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>
</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 >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 ><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 ><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>
<div class="textblock"><p><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> Algorithms. </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><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><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 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>
<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>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a9125ceb66bfbec3093bba64c2c1e99e2" name="a9125ceb66bfbec3093bba64c2c1e99e2"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a9125ceb66bfbec3093bba64c2c1e99e2">&#9670;&#160;</a></span>addEdge() <span class="overload">[1/3]</span></h2>
@@ -372,15 +372,15 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>boolean </dd></dl>
<p >&lt; stores the neighbouring node indexes in squence of being reached</p>
<p >insert the current node into the queue</p>
<p >mark the current node as travelled</p>
<p >&lt; stores the neighbour of the current node</p>
<p >check whether the neighbour node is travelled already or not</p>
<p >colour the neighbouring node with different colour than the current node</p>
<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>&lt; stores the neighbouring node indexes in squence of being reached</p>
<p>insert the current node into the queue</p>
<p>mark the current node as travelled</p>
<p>&lt; stores the neighbour of the current node</p>
<p>check whether the neighbour node is travelled already or not</p>
<p>colour the neighbouring node with different colour than the current node</p>
<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>
<div class="fragment"><div class="line"><span class="lineno"> 37</span> {</div>
<div class="line"><span class="lineno"> 38</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"> 39</span><span class="comment"> /// of being reached</span></div>
@@ -512,15 +512,15 @@ Here is the call graph for this function:</div>
</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>
<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"><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>
@@ -769,8 +769,8 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<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>&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>
<div class="fragment"><div class="line"><span class="lineno"> 75</span> {</div>
<div class="line"><span class="lineno"> 76</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"> 77</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>
@@ -891,7 +891,7 @@ Here is the call graph for this function:</div>
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