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<div class="title">breadth_first_search.cpp File Reference</div> </div>
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<p><a href="https://en.wikipedia.org/wiki/Breadth-first_search">Breadth First Search Algorithm (Breadth First Search)</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;queue&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for breadth_first_search.cpp:</div>
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<tr class="memitem:df/dce/namespacegraph"><td class="memItemLeft" align="right" valign="top"> &#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>
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Functions</h2></td></tr>
<tr class="memitem:adbe6cd1fd148173ce6a01669925d2d72"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#adbe6cd1fd148173ce6a01669925d2d72">graph::add_directed_edge</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; *graph, int u, int v)</td></tr>
<tr class="memdesc:adbe6cd1fd148173ce6a01669925d2d72"><td class="mdescLeft">&#160;</td><td class="mdescRight">Adds a directed edge from vertex u to vertex v. <a href="../../df/dce/namespacegraph.html#adbe6cd1fd148173ce6a01669925d2d72">More...</a><br /></td></tr>
<tr class="separator:adbe6cd1fd148173ce6a01669925d2d72"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a59b4441a0e447469e9a4f61c87f33102"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a59b4441a0e447469e9a4f61c87f33102">graph::add_undirected_edge</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; *graph, int u, int v)</td></tr>
<tr class="memdesc:a59b4441a0e447469e9a4f61c87f33102"><td class="mdescLeft">&#160;</td><td class="mdescRight">Adds an undirected edge from vertex u to vertex v. Essentially adds too directed edges to the adjacency list reprsentation of the graph. <a href="../../df/dce/namespacegraph.html#a59b4441a0e447469e9a4f61c87f33102">More...</a><br /></td></tr>
<tr class="separator:a59b4441a0e447469e9a4f61c87f33102"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a618dce14b4883c20aace1d743d3a3f60"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a618dce14b4883c20aace1d743d3a3f60">graph::breadth_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; int &gt;&gt; &amp;graph, int start)</td></tr>
<tr class="memdesc:a618dce14b4883c20aace1d743d3a3f60"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function performs the breadth first search algorithm over the graph. <a href="../../df/dce/namespacegraph.html#a618dce14b4883c20aace1d743d3a3f60">More...</a><br /></td></tr>
<tr class="separator:a618dce14b4883c20aace1d743d3a3f60"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a88ec9ad42717780d6caaff9d3d6977f9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d82/breadth__first__search_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a> ()</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d82/breadth__first__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Breadth-first_search">Breadth First Search Algorithm (Breadth First Search)</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="http://github.com/ayaankhan98">Ayaan Khan</a></dd></dl>
<p>Breadth First Search also quoted as BFS is a <a class="el" href="../../da/d9a/class_graph.html">Graph</a> Traversal Algorithm. Time Complexity O(|V| + |E|) where V are the number of vertices and E are the number of edges in the graph.</p>
<p>Applications of Breadth First Search are</p>
<ol type="1">
<li>Finding shortest path between two vertices say u and v, with path length measured by number of edges (an advantage over depth first search algorithm)</li>
<li>Ford-Fulkerson Method for computing the maximum flow in a flow network.</li>
<li>Testing bipartiteness of a graph.</li>
<li>Cheney's Algorithm, Copying garbage collection.</li>
</ol>
<p>And there are many more...</p>
<h4>working</h4>
<p>In the implementation below we first created a graph using the adjacency list representation of graph. Breadth First Search Works as follows it requires a vertex as a start vertex, Start vertex is that vertex from where you want to start traversing the graph. We maintain a bool array or a vector to keep track of the vertices which we have visited so that we do not traverse the visited vertices again and again and eventually fall into an infinite loop. Along with this boolen array we use a <a class="el" href="../../dc/db5/struct_queue.html">Queue</a>.</p>
<ol type="1">
<li>First we mark the start vertex as visited.</li>
<li>Push this visited vertex in the <a class="el" href="../../dc/db5/struct_queue.html">Queue</a>.</li>
<li>while the queue is not empty we repeat the following steps<ol type="a">
<li>Take out an element from the front of queue</li>
<li>Explore the adjacency list of this vertex if element in the adjacency list is not visited then we push that element into the queue and mark this as visited </li>
</ol>
</li>
</ol>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160; {</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160; <a class="code" href="../../df/d82/breadth__first__search_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160; </div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160; <span class="keywordtype">size_t</span> vertices = 0, edges = 0;</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of vertices: &quot;</span>;</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vertices;</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the number of edges: &quot;</span>;</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges;</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160; </div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; <a class="code" href="../../df/dce/namespacegraph.html">graph</a>(vertices);</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160; </div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter space-separated pairs of vertices that form edges: &quot;</span></div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160; &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160; <span class="keywordflow">while</span> (edges--) {</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160; <span class="keywordtype">int</span> u = 0, v = 0;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; u &gt;&gt; v;</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160; <span class="comment">// Decrement the vertex index so that we can read more convenint</span></div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; <span class="comment">// 1-based indexing from the user input.</span></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#adbe6cd1fd148173ce6a01669925d2d72">graph::add_directed_edge</a>(&amp;<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, u - 1, v - 1);</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160; }</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160; </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#a618dce14b4883c20aace1d743d3a3f60">graph::breadth_first_search</a>(<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 0);</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">&#9670;&nbsp;</a></span>tests()</h2>
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<td class="memname">void tests </td>
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<p>Test 1 Begin</p>
<p>Test 2 Begin</p>
<p>Test 3 Begins</p>
<div class="fragment"><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; {<span class="comment"></span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160;<span class="comment"> /// Test 1 Begin</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160;<span class="comment"></span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a>&gt; <a class="code" href="../../df/dce/namespacegraph.html">graph</a>(4, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>());</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#a59b4441a0e447469e9a4f61c87f33102">graph::add_undirected_edge</a>(&amp;<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 0, 1);</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#a59b4441a0e447469e9a4f61c87f33102">graph::add_undirected_edge</a>(&amp;<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 1, 2);</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#a59b4441a0e447469e9a4f61c87f33102">graph::add_undirected_edge</a>(&amp;<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 2, 3);</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; </div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> returned_result = <a class="code" href="../../df/dce/namespacegraph.html#a618dce14b4883c20aace1d743d3a3f60">graph::breadth_first_search</a>(<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 2);</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> correct_result = {<span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span>};</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160; </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(correct_result.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), correct_result.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>(),</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; returned_result.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>()));</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed...&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160;<span class="comment"> /// Test 2 Begin</span></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160;<span class="comment"></span> returned_result = <a class="code" href="../../df/dce/namespacegraph.html#a618dce14b4883c20aace1d743d3a3f60">graph::breadth_first_search</a>(<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 0);</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160; </div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(correct_result.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), correct_result.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>(),</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160; returned_result.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>()));</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed...&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160;<span class="comment"> /// Test 3 Begins</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160;<span class="comment"></span> <a class="code" href="../../df/dce/namespacegraph.html">graph</a>.clear();</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html">graph</a>.resize(6);</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#adbe6cd1fd148173ce6a01669925d2d72">graph::add_directed_edge</a>(&amp;<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 0, 1);</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#adbe6cd1fd148173ce6a01669925d2d72">graph::add_directed_edge</a>(&amp;<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 0, 2);</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#adbe6cd1fd148173ce6a01669925d2d72">graph::add_directed_edge</a>(&amp;<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 1, 3);</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#adbe6cd1fd148173ce6a01669925d2d72">graph::add_directed_edge</a>(&amp;<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 2, 3);</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#adbe6cd1fd148173ce6a01669925d2d72">graph::add_directed_edge</a>(&amp;<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 1, 4);</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160; <a class="code" href="../../df/dce/namespacegraph.html#adbe6cd1fd148173ce6a01669925d2d72">graph::add_directed_edge</a>(&amp;<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 3, 5);</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>&#160; </div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>&#160; returned_result = <a class="code" href="../../df/dce/namespacegraph.html#a618dce14b4883c20aace1d743d3a3f60">graph::breadth_first_search</a>(<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, 2);</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>&#160; correct_result = {<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>};</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160; </div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(correct_result.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), correct_result.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>(),</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160; returned_result.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>()));</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3 Passed...&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160;}</div>
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