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<p><a href="https://en.wikipedia.org/wiki/Topological_sorting" target="_blank">Topological Sort Algorithm</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;stack&gt;</code><br />
<code>#include &lt;stdexcept&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for topological_sort.cpp:</div>
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<p><a href="../../d8/db9/topological__sort_8cpp_source.html">Go to the source code of this file.</a></p>
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Classes</h2></td></tr>
<tr class="memitem:graph_3A_3Atopological_5Fsort_3A_3AGraph" id="r_graph_3A_3Atopological_5Fsort_3A_3AGraph"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/dec/classgraph_1_1topological__sort_1_1_graph.html">graph::topological_sort::Graph</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Class that represents a directed graph and provides methods for manipulating the graph. <a href="../../d5/dec/classgraph_1_1topological__sort_1_1_graph.html#details">More...</a><br /></td></tr>
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Namespaces</h2></td></tr>
<tr class="memitem:graph" id="r_graph"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html">graph</a></td></tr>
<tr class="memdesc:df/dce/namespacegraph"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> Algorithms. <br /></td></tr>
<tr class="memitem:topological_5Fsort" id="r_topological_5Fsort"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d76/namespacetopological__sort.html">topological_sort</a></td></tr>
<tr class="memdesc:d8/d76/namespacetopological__sort"><td class="mdescLeft">&#160;</td><td class="mdescRight">Topological Sort Algorithm. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:abcbcaa2bb70af0a11d0c090ea1796aea" id="r_abcbcaa2bb70af0a11d0c090ea1796aea"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#abcbcaa2bb70af0a11d0c090ea1796aea">graph::topological_sort::dfs</a> (int v, std::vector&lt; int &gt; &amp;visited, const std::vector&lt; std::vector&lt; int &gt; &gt; &amp;graph, std::stack&lt; int &gt; &amp;s)</td></tr>
<tr class="memdesc:abcbcaa2bb70af0a11d0c090ea1796aea"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to perform Depth First Search on the graph. <br /></td></tr>
<tr class="memitem:a54dc5d7914958dbd24dda2fd862dc41b" id="r_a54dc5d7914958dbd24dda2fd862dc41b"><td class="memItemLeft" align="right" valign="top">std::vector&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a54dc5d7914958dbd24dda2fd862dc41b">graph::topological_sort::topologicalSort</a> (const <a class="el" href="../../d5/dec/classgraph_1_1topological__sort_1_1_graph.html">Graph</a> &amp;g)</td></tr>
<tr class="memdesc:a54dc5d7914958dbd24dda2fd862dc41b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to get the topological sort of the graph. <br /></td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementation. <br /></td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
</table>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Topological_sorting" target="_blank">Topological Sort Algorithm</a> </p>
<p>Topological sorting of a directed graph is a linear ordering or its vertices such that for every directed edge (u,v) from vertex u to vertex v, u comes before v in the oredering.</p>
<p>A topological sort is possible only in a directed acyclic graph (DAG). This file contains code of finding topological sort using Kahn's Algorithm which involves using Depth First Search technique </p>
<p class="definition">Definition in file <a class="el" href="../../d8/db9/topological__sort_8cpp_source.html">topological_sort.cpp</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="abcbcaa2bb70af0a11d0c090ea1796aea" name="abcbcaa2bb70af0a11d0c090ea1796aea"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abcbcaa2bb70af0a11d0c090ea1796aea">&#9670;&#160;</a></span>dfs()</h2>
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<td class="memname">void graph::topological_sort::dfs </td>
<td>(</td>
<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>v</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">std::vector&lt; int &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>visited</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const std::vector&lt; std::vector&lt; int &gt; &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>graph</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">std::stack&lt; int &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>s</em></span>&#160;)</td>
</tr>
</table>
</div><div class="memdoc">
<p>Function to perform Depth First Search on the graph. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">v</td><td>Starting vertex for depth-first search </td></tr>
<tr><td class="paramname">visited</td><td>Array representing whether each node has been visited </td></tr>
<tr><td class="paramname">graph</td><td>Adjacency list of the graph </td></tr>
<tr><td class="paramname">s</td><td>Stack containing the vertices for topological sorting </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="../../d8/db9/topological__sort_8cpp_source.html#l00079">79</a> of file <a class="el" href="../../d8/db9/topological__sort_8cpp_source.html">topological_sort.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 80</span> {</div>
<div class="line"><span class="lineno"> 81</span> visited[v] = 1;</div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> neighbour : <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>[v]) {</div>
<div class="line"><span class="lineno"> 83</span> <span class="keywordflow">if</span> (!visited[neighbour]) {</div>
<div class="line"><span class="lineno"> 84</span> <a class="code hl_function" href="#abcbcaa2bb70af0a11d0c090ea1796aea">dfs</a>(neighbour, visited, <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>, s);</div>
<div class="line"><span class="lineno"> 85</span> }</div>
<div class="line"><span class="lineno"> 86</span> }</div>
<div class="line"><span class="lineno"> 87</span> s.push(v);</div>
<div class="line"><span class="lineno"> 88</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="atopological__sort_8cpp_html_abcbcaa2bb70af0a11d0c090ea1796aea"><div class="ttname"><a href="#abcbcaa2bb70af0a11d0c090ea1796aea">graph::topological_sort::dfs</a></div><div class="ttdeci">void dfs(int v, std::vector&lt; int &gt; &amp;visited, const std::vector&lt; std::vector&lt; int &gt; &gt; &amp;graph, std::stack&lt; int &gt; &amp;s)</div><div class="ttdoc">Function to perform Depth First Search on the graph.</div><div class="ttdef"><b>Definition</b> <a href="../../d8/db9/topological__sort_8cpp_source.html#l00079">topological_sort.cpp:79</a></div></div>
</div><!-- fragment -->
</div>
</div>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
<div class="memitem">
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<table class="memname">
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d8/db9/topological__sort_8cpp_source.html#l00186">186</a> of file <a class="el" href="../../d8/db9/topological__sort_8cpp_source.html">topological_sort.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 186</span> {</div>
<div class="line"><span class="lineno"> 187</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self test implementations</span></div>
<div class="line"><span class="lineno"> 188</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 189</span>}</div>
<div class="ttc" id="atopological__sort_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementation.</div><div class="ttdef"><b>Definition</b> <a href="../../d8/db9/topological__sort_8cpp_source.html#l00126">topological_sort.cpp:126</a></div></div>
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<a id="aa8dca7b867074164d5f45b0f3851269d" name="aa8dca7b867074164d5f45b0f3851269d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">void test </td>
<td>(</td>
<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel static">static</span></span> </td>
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<p>Self-test implementation. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d8/db9/topological__sort_8cpp_source.html#l00126">126</a> of file <a class="el" href="../../d8/db9/topological__sort_8cpp_source.html">topological_sort.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 126</span> {</div>
<div class="line"><span class="lineno"> 127</span> <span class="comment">// Test 1</span></div>
<div class="line"><span class="lineno"> 128</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Testing for graph 1\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 129</span> <span class="keywordtype">int</span> n_1 = 6;</div>
<div class="line"><span class="lineno"> 130</span> <a class="code hl_class" href="../../d5/dec/classgraph_1_1topological__sort_1_1_graph.html">graph::topological_sort::Graph</a> graph1(n_1);</div>
<div class="line"><span class="lineno"> 131</span> graph1.addEdge(4, 0);</div>
<div class="line"><span class="lineno"> 132</span> graph1.addEdge(5, 0);</div>
<div class="line"><span class="lineno"> 133</span> graph1.addEdge(5, 2);</div>
<div class="line"><span class="lineno"> 134</span> graph1.addEdge(2, 3);</div>
<div class="line"><span class="lineno"> 135</span> graph1.addEdge(3, 1);</div>
<div class="line"><span class="lineno"> 136</span> graph1.addEdge(4, 1);</div>
<div class="line"><span class="lineno"> 137</span> std::vector&lt;int&gt; ans_1 = <a class="code hl_function" href="#a54dc5d7914958dbd24dda2fd862dc41b">graph::topological_sort::topologicalSort</a>(graph1);</div>
<div class="line"><span class="lineno"> 138</span> std::vector&lt;int&gt; expected_1 = {5, 4, 2, 3, 1, 0};</div>
<div class="line"><span class="lineno"> 139</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Topological Sorting Order: &quot;</span>;</div>
<div class="line"><span class="lineno"> 140</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i : ans_1) {</div>
<div class="line"><span class="lineno"> 141</span> std::cout &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><span class="lineno"> 142</span> }</div>
<div class="line"><span class="lineno"> 143</span> std::cout &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;</div>
<div class="line"><span class="lineno"> 144</span> assert(ans_1 == expected_1);</div>
<div class="line"><span class="lineno"> 145</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test Passed\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 146</span> </div>
<div class="line"><span class="lineno"> 147</span> <span class="comment">// Test 2</span></div>
<div class="line"><span class="lineno"> 148</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Testing for graph 2\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 149</span> <span class="keywordtype">int</span> n_2 = 5;</div>
<div class="line"><span class="lineno"> 150</span> <a class="code hl_class" href="../../d5/dec/classgraph_1_1topological__sort_1_1_graph.html">graph::topological_sort::Graph</a> graph2(n_2);</div>
<div class="line"><span class="lineno"> 151</span> graph2.addEdge(0, 1);</div>
<div class="line"><span class="lineno"> 152</span> graph2.addEdge(0, 2);</div>
<div class="line"><span class="lineno"> 153</span> graph2.addEdge(1, 2);</div>
<div class="line"><span class="lineno"> 154</span> graph2.addEdge(2, 3);</div>
<div class="line"><span class="lineno"> 155</span> graph2.addEdge(1, 3);</div>
<div class="line"><span class="lineno"> 156</span> graph2.addEdge(2, 4);</div>
<div class="line"><span class="lineno"> 157</span> std::vector&lt;int&gt; ans_2 = <a class="code hl_function" href="#a54dc5d7914958dbd24dda2fd862dc41b">graph::topological_sort::topologicalSort</a>(graph2);</div>
<div class="line"><span class="lineno"> 158</span> std::vector&lt;int&gt; expected_2 = {0, 1, 2, 4, 3};</div>
<div class="line"><span class="lineno"> 159</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Topological Sorting Order: &quot;</span>;</div>
<div class="line"><span class="lineno"> 160</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i : ans_2) {</div>
<div class="line"><span class="lineno"> 161</span> std::cout &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><span class="lineno"> 162</span> }</div>
<div class="line"><span class="lineno"> 163</span> std::cout &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;</div>
<div class="line"><span class="lineno"> 164</span> assert(ans_2 == expected_2);</div>
<div class="line"><span class="lineno"> 165</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test Passed\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 166</span> </div>
<div class="line"><span class="lineno"> 167</span> <span class="comment">// Test 3 - Graph with cycle</span></div>
<div class="line"><span class="lineno"> 168</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Testing for graph 3\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 169</span> <span class="keywordtype">int</span> n_3 = 3;</div>
<div class="line"><span class="lineno"> 170</span> <a class="code hl_class" href="../../d5/dec/classgraph_1_1topological__sort_1_1_graph.html">graph::topological_sort::Graph</a> graph3(n_3);</div>
<div class="line"><span class="lineno"> 171</span> graph3.addEdge(0, 1);</div>
<div class="line"><span class="lineno"> 172</span> graph3.addEdge(1, 2);</div>
<div class="line"><span class="lineno"> 173</span> graph3.addEdge(2, 0);</div>
<div class="line"><span class="lineno"> 174</span> <span class="keywordflow">try</span> {</div>
<div class="line"><span class="lineno"> 175</span> <a class="code hl_function" href="#a54dc5d7914958dbd24dda2fd862dc41b">graph::topological_sort::topologicalSort</a>(graph3);</div>
<div class="line"><span class="lineno"> 176</span> } <span class="keywordflow">catch</span> (std::invalid_argument&amp; err) {</div>
<div class="line"><span class="lineno"> 177</span> assert(std::string(err.what()) == <span class="stringliteral">&quot;cycle detected in graph&quot;</span>);</div>
<div class="line"><span class="lineno"> 178</span> }</div>
<div class="line"><span class="lineno"> 179</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test Passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 180</span>}</div>
<div class="ttc" id="aclassgraph_1_1topological__sort_1_1_graph_html"><div class="ttname"><a href="../../d5/dec/classgraph_1_1topological__sort_1_1_graph.html">graph::topological_sort::Graph</a></div><div class="ttdoc">Class that represents a directed graph and provides methods for manipulating the graph.</div><div class="ttdef"><b>Definition</b> <a href="../../d8/db9/topological__sort_8cpp_source.html#l00038">topological_sort.cpp:38</a></div></div>
<div class="ttc" id="atopological__sort_8cpp_html_a54dc5d7914958dbd24dda2fd862dc41b"><div class="ttname"><a href="#a54dc5d7914958dbd24dda2fd862dc41b">graph::topological_sort::topologicalSort</a></div><div class="ttdeci">std::vector&lt; int &gt; topologicalSort(const Graph &amp;g)</div><div class="ttdoc">Function to get the topological sort of the graph.</div><div class="ttdef"><b>Definition</b> <a href="../../d8/db9/topological__sort_8cpp_source.html#l00095">topological_sort.cpp:95</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a54dc5d7914958dbd24dda2fd862dc41b">&#9670;&#160;</a></span>topologicalSort()</h2>
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<td class="memname">std::vector&lt; int &gt; graph::topological_sort::topologicalSort </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="../../d5/dec/classgraph_1_1topological__sort_1_1_graph.html">Graph</a> &amp;</td> <td class="paramname"><span class="paramname"><em>g</em></span></td><td>)</td>
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<p>Function to get the topological sort of the graph. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">g</td><td><a class="el" href="../../da/d9a/class_graph.html">Graph</a> object </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>A vector containing the topological order of nodes </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d8/db9/topological__sort_8cpp_source.html#l00095">95</a> of file <a class="el" href="../../d8/db9/topological__sort_8cpp_source.html">topological_sort.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 95</span> {</div>
<div class="line"><span class="lineno"> 96</span> <span class="keywordtype">int</span> n = g.getNumNodes();</div>
<div class="line"><span class="lineno"> 97</span> <span class="keyword">const</span> <span class="keyword">auto</span>&amp; adj = g.getAdjacencyList();</div>
<div class="line"><span class="lineno"> 98</span> std::vector&lt;int&gt; visited(n, 0);</div>
<div class="line"><span class="lineno"> 99</span> std::stack&lt;int&gt; s;</div>
<div class="line"><span class="lineno"> 100</span> </div>
<div class="line"><span class="lineno"> 101</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><span class="lineno"> 102</span> <span class="keywordflow">if</span> (!visited[i]) {</div>
<div class="line"><span class="lineno"> 103</span> <a class="code hl_function" href="#abcbcaa2bb70af0a11d0c090ea1796aea">dfs</a>(i, visited, adj, s);</div>
<div class="line"><span class="lineno"> 104</span> }</div>
<div class="line"><span class="lineno"> 105</span> }</div>
<div class="line"><span class="lineno"> 106</span> </div>
<div class="line"><span class="lineno"> 107</span> std::vector&lt;int&gt; ans;</div>
<div class="line"><span class="lineno"> 108</span> <span class="keywordflow">while</span> (!s.empty()) {</div>
<div class="line"><span class="lineno"> 109</span> <span class="keywordtype">int</span> elem = s.top();</div>
<div class="line"><span class="lineno"> 110</span> s.pop();</div>
<div class="line"><span class="lineno"> 111</span> ans.push_back(elem);</div>
<div class="line"><span class="lineno"> 112</span> }</div>
<div class="line"><span class="lineno"> 113</span> </div>
<div class="line"><span class="lineno"> 114</span> <span class="keywordflow">if</span> (ans.size() &lt; n) { <span class="comment">// Cycle detected</span></div>
<div class="line"><span class="lineno"> 115</span> <span class="keywordflow">throw</span> std::invalid_argument(<span class="stringliteral">&quot;cycle detected in graph&quot;</span>);</div>
<div class="line"><span class="lineno"> 116</span> }</div>
<div class="line"><span class="lineno"> 117</span> <span class="keywordflow">return</span> ans;</div>
<div class="line"><span class="lineno"> 118</span>}</div>
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