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<a href="#namespaces">Namespaces</a> &#124;
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<a href="#var-members">Variables</a> </div>
<div class="headertitle"><div class="title">dijkstra.cpp File Reference</div></div>
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<p>[<a class="el" href="../../da/d9a/class_graph.html">Graph</a> Dijkstras Shortest Path Algorithm (Dijkstra's Shortest Path)] (<a href="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm">https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm</a>)
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;limits&gt;</code><br />
<code>#include &lt;memory&gt;</code><br />
<code>#include &lt;queue&gt;</code><br />
<code>#include &lt;utility&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for dijkstra.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:"><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>
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Functions</h2></td></tr>
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<tr class="memdesc:a0e30e0dca68cb6e4f671440819b35b6a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function that add edge between two nodes or vertices of graph. <br /></td></tr>
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<tr class="memdesc: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>
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Variables</h2></td></tr>
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constexpr int64_t&#160;</td><td class="memItemRight" valign="bottom"><b>INF</b> = <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits</a>&lt;int64_t&gt;::max()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>[<a class="el" href="../../da/d9a/class_graph.html">Graph</a> Dijkstras Shortest Path Algorithm (Dijkstra's Shortest Path)] (<a href="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm">https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm</a>) </p>
<dl class="section author"><dt>Author</dt><dd><a href="http://github.com/ayaankhan98" target="_blank">Ayaan Khan</a></dd></dl>
<p>Dijkstra's Algorithm is used to find the shortest path from a source vertex to all other reachable vertex in the graph. The algorithm initially assumes all the nodes are unreachable from the given source vertex so we mark the distances of all vertices as INF (infinity) from source vertex (INF / infinity denotes unable to reach).</p>
<p>in similar fashion with BFS we assume the distance of source vertex as 0 and pushes the vertex in a priority queue with it's distance. we maintain the priority queue as a min heap so that we can get the minimum element at the top of heap</p>
<p>Basically what we do in this algorithm is that we try to minimize the distances of all the reachable vertices from the current vertex, look at the code below to understand in better way. </p>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</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"><span class="lineno"> 152</span> {</div>
<div class="line"><span class="lineno"> 153</span> <span class="comment">// running predefined tests</span></div>
<div class="line"><span class="lineno"> 154</span> <a class="code hl_function" href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
<div class="line"><span class="lineno"> 155</span> </div>
<div class="line"><span class="lineno"> 156</span> <span class="keywordtype">int</span> vertices = int(), edges = int();</div>
<div class="line"><span class="lineno"> 157</span> <a class="code hl_classRef" 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"><span class="lineno"> 158</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; vertices;</div>
<div class="line"><span class="lineno"> 159</span> <a class="code hl_classRef" 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"><span class="lineno"> 160</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges;</div>
<div class="line"><span class="lineno"> 161</span> </div>
<div class="line"><span class="lineno"> 162</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;int, int&gt;</a>&gt;&gt; adj(</div>
<div class="line"><span class="lineno"> 163</span> vertices, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a>&gt;());</div>
<div class="line"><span class="lineno"> 164</span> </div>
<div class="line"><span class="lineno"> 165</span> <span class="keywordtype">int</span> u = int(), v = int(), w = int();</div>
<div class="line"><span class="lineno"> 166</span> <span class="keywordflow">while</span> (edges--) {</div>
<div class="line"><span class="lineno"> 167</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; u &gt;&gt; v &gt;&gt; w;</div>
<div class="line"><span class="lineno"> 168</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj, u, v, w);</div>
<div class="line"><span class="lineno"> 169</span> }</div>
<div class="line"><span class="lineno"> 170</span> </div>
<div class="line"><span class="lineno"> 171</span> <span class="keywordtype">int</span> s = int(), t = int();</div>
<div class="line"><span class="lineno"> 172</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; s &gt;&gt; t;</div>
<div class="line"><span class="lineno"> 173</span> <span class="keywordtype">int</span> dist = <a class="code hl_function" href="../../df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84">graph::dijkstra</a>(&amp;adj, s - 1, t - 1);</div>
<div class="line"><span class="lineno"> 174</span> <span class="keywordflow">if</span> (dist == -1) {</div>
<div class="line"><span class="lineno"> 175</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Target not reachable from source&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 176</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 177</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Shortest Path Distance : &quot;</span> &lt;&lt; dist &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 178</span> }</div>
<div class="line"><span class="lineno"> 179</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 180</span>}</div>
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="adijkstra_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition</b> dijkstra.cpp:113</div></div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
<div class="ttc" id="anamespacegraph_html_a9125ceb66bfbec3093bba64c2c1e99e2"><div class="ttname"><a href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a></div><div class="ttdeci">void addEdge(std::vector&lt; std::vector&lt; int &gt; &gt; *adj, int u, int v)</div><div class="ttdoc">Function that add edge between two nodes or vertices of graph.</div><div class="ttdef"><b>Definition</b> connected_components.cpp:46</div></div>
<div class="ttc" id="anamespacegraph_html_adc68cbc8ba09eb1142265935c0d45b84"><div class="ttname"><a href="../../df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84">graph::dijkstra</a></div><div class="ttdeci">int dijkstra(std::vector&lt; std::vector&lt; std::pair&lt; int, int &gt; &gt; &gt; *adj, int s, int t)</div><div class="ttdoc">Function runs the dijkstra algorithm for some source vertex and target vertex in the graph and return...</div><div class="ttdef"><b>Definition</b> dijkstra.cpp:66</div></div>
<div class="ttc" id="apair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a></div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">&#9670;&#160;</a></span>tests()</h2>
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<td class="memname">void tests </td>
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<p>Function to test the Algorithm </p>
<div class="fragment"><div class="line"><span class="lineno"> 113</span> {</div>
<div class="line"><span class="lineno"> 114</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiatinig Predefined Tests...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 115</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 1...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 116</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;int, int&gt;</a>&gt;&gt; adj1(</div>
<div class="line"><span class="lineno"> 117</span> 4, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a>&gt;());</div>
<div class="line"><span class="lineno"> 118</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 1, 2, 1);</div>
<div class="line"><span class="lineno"> 119</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 4, 1, 2);</div>
<div class="line"><span class="lineno"> 120</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 2, 3, 2);</div>
<div class="line"><span class="lineno"> 121</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj1, 1, 3, 5);</div>
<div class="line"><span class="lineno"> 122</span> </div>
<div class="line"><span class="lineno"> 123</span> <span class="keywordtype">int</span> s = 1, t = 3;</div>
<div class="line"><span class="lineno"> 124</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84">graph::dijkstra</a>(&amp;adj1, s - 1, t - 1) == 3);</div>
<div class="line"><span class="lineno"> 125</span> <a class="code hl_classRef" 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="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 126</span> </div>
<div class="line"><span class="lineno"> 127</span> s = 4, t = 3;</div>
<div class="line"><span class="lineno"> 128</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 2...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 129</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84">graph::dijkstra</a>(&amp;adj1, s - 1, t - 1) == 5);</div>
<div class="line"><span class="lineno"> 130</span> <a class="code hl_classRef" 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="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 131</span> </div>
<div class="line"><span class="lineno"> 132</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;std::pair&lt;int, int&gt;</a>&gt;&gt; adj2(</div>
<div class="line"><span class="lineno"> 133</span> 5, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair&lt;int, int&gt;</a>&gt;());</div>
<div class="line"><span class="lineno"> 134</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 1, 2, 4);</div>
<div class="line"><span class="lineno"> 135</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 1, 3, 2);</div>
<div class="line"><span class="lineno"> 136</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 2, 3, 2);</div>
<div class="line"><span class="lineno"> 137</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 3, 2, 1);</div>
<div class="line"><span class="lineno"> 138</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 2, 4, 2);</div>
<div class="line"><span class="lineno"> 139</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 3, 5, 4);</div>
<div class="line"><span class="lineno"> 140</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 5, 4, 1);</div>
<div class="line"><span class="lineno"> 141</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 2, 5, 3);</div>
<div class="line"><span class="lineno"> 142</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2">graph::addEdge</a>(&amp;adj2, 3, 4, 4);</div>
<div class="line"><span class="lineno"> 143</span> </div>
<div class="line"><span class="lineno"> 144</span> s = 1, t = 5;</div>
<div class="line"><span class="lineno"> 145</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Initiating Test 3...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 146</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84">graph::dijkstra</a>(&amp;adj2, s - 1, t - 1) == 6);</div>
<div class="line"><span class="lineno"> 147</span> <a class="code hl_classRef" 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="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 148</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All Test Passed...&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 149</span>}</div>
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<p>Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> for <code>min()</code> function.
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<div class="textblock"><code>#include &lt;array&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
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Include dependency graph for sparse_table.cpp:</div>
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<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
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<tr class="memdesc:a0ddf1224851353fc92bfbff6f499fa97"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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Variables</h2></td></tr>
<tr class="memitem:a10f3ffb3f6f7e1b83d556b9c8de89a5d" id="r_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><td class="memItemLeft" align="right" valign="top">constexpr uint32_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a> = 12345</td></tr>
<tr class="memdesc:a10f3ffb3f6f7e1b83d556b9c8de89a5d"><td class="mdescLeft">&#160;</td><td class="mdescRight">A struct to represent sparse table for <code>min()</code> as their invariant function, for the given array <code>A</code>. The answer to queries are stored in the array ST. <br /></td></tr>
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constexpr uint8_t&#160;</td><td class="memItemRight" valign="bottom"><b>data_structures::sparse_table::M</b> = 14</td></tr>
<tr class="memdesc:af7db62f21983565c64d5d42d2a49888e"><td class="mdescLeft">&#160;</td><td class="mdescRight">ceil(log2(N)). <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> for <code>min()</code> function. </p>
<p>Implementation of <a href="https://en.wikipedia.org/wiki/Range_minimum_query" target="_blank">Sparse Table</a> data structure.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/manncodes" target="_blank">Mann Patel</a></dd></dl>
<p>Sparse Table is a data structure, that allows answering range queries. It can answer most range queries in O(logn), but its true power is answering range minimum queries (or equivalent range maximum queries). For those queries it can compute the answer in O(1) time. The only drawback of this data structure is, that it can only be used on immutable arrays. This means, that the array cannot be changed between two queries.</p>
<p>If any element in the array changes, the complete data structure has to be recomputed.</p>
<dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000004">Todo</a></b></dt><dd>make stress tests.</dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>This sparse table is made for <code>min(a1,a2,...an)</code> duplicate invariant function. This implementation can be changed to other functions like <code><a class="el" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd()</a></code>, <code><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm()</a></code>, and <code>max()</code> by changing a few lines of code.</dd></dl>
<p>Sparse Table is a data structure, that allows answering range queries. It can answer most range queries in O(logn), but its true power is answering range minimum queries or equivalent range maximum queries). For those queries it can compute the answer in O(1) time.</p>
<ul>
<li>Running Time Complexity <br />
</li>
<li>Build : O(NlogN) <br />
</li>
<li>Range Query : O(1) <br />
</li>
</ul>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>argc</em></span>, </td>
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<p>Main function. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">argc</td><td>commandline argument count (ignored) </td></tr>
<tr><td class="paramname">argv</td><td>commandline array of arguments (ignored) </td></tr>
</table>
</dd>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 162</span> {</div>
<div class="line"><span class="lineno"> 163</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"> 164</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 165</span>}</div>
<div class="ttc" id="asparse__table_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> sparse_table.cpp:129</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">static void test </td>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p>&lt; array on which RMQ will be performed.</p>
<p>&lt; size of self test's array</p>
<p>&lt; declaring sparse tree</p>
<p>&lt; copying array to the struct</p>
<p>&lt; passing the array's size to the struct</p>
<p>&lt; precomputing sparse tree</p>
<p>&lt; as 1 is smallest from 1..9</p>
<p>&lt; as 2 is smallest from 2..6</p>
<p>&lt; as 3 is smallest from 3..8</p>
<div class="fragment"><div class="line"><span class="lineno"> 129</span> {</div>
<div class="line"><span class="lineno"> 130</span> <span class="comment">/* We take an array as an input on which we need to perform the ranged</span></div>
<div class="line"><span class="lineno"> 131</span><span class="comment"> * minimum queries[RMQ](https://en.wikipedia.org/wiki/Range_minimum_query).</span></div>
<div class="line"><span class="lineno"> 132</span><span class="comment"> */</span></div>
<div class="line"><span class="lineno"> 133</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, 10&gt;</a> testcase = {</div>
<div class="line"><span class="lineno"> 134</span> 1, 2, 3, 4, 5,</div>
<div class="line"><span class="lineno"> 135</span> 6, 7, 8, 9, 10}; <span class="comment">///&lt; array on which RMQ will be performed.</span></div>
<div class="line"><span class="lineno"> 136</span> <span class="keywordtype">size_t</span> testcase_size =</div>
<div class="line"><span class="lineno"> 137</span> <span class="keyword">sizeof</span>(testcase) / <span class="keyword">sizeof</span>(testcase[0]); <span class="comment">///&lt; size of self test&#39;s array</span></div>
<div class="line"><span class="lineno"> 138</span> </div>
<div class="line"><span class="lineno"> 139</span> <a class="code hl_struct" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html">data_structures::sparse_table::Sparse_table</a></div>
<div class="line"><span class="lineno"> 140</span> st{}; <span class="comment">///&lt; declaring sparse tree</span></div>
<div class="line"><span class="lineno"> 141</span> </div>
<div class="line"><span class="lineno"> 142</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/copy.html">std::copy</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(testcase), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(testcase),</div>
<div class="line"><span class="lineno"> 143</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(st.A)); <span class="comment">///&lt; copying array to the struct</span></div>
<div class="line"><span class="lineno"> 144</span> st.n = testcase_size; <span class="comment">///&lt; passing the array&#39;s size to the struct</span></div>
<div class="line"><span class="lineno"> 145</span> </div>
<div class="line"><span class="lineno"> 146</span> st.buildST(); <span class="comment">///&lt; precomputing sparse tree</span></div>
<div class="line"><span class="lineno"> 147</span> </div>
<div class="line"><span class="lineno"> 148</span> <span class="comment">// pass queries of the form: [l,r]</span></div>
<div class="line"><span class="lineno"> 149</span> assert(st.query(1, 9) == 1); <span class="comment">///&lt; as 1 is smallest from 1..9</span></div>
<div class="line"><span class="lineno"> 150</span> assert(st.query(2, 6) == 2); <span class="comment">///&lt; as 2 is smallest from 2..6</span></div>
<div class="line"><span class="lineno"> 151</span> assert(st.query(3, 8) == 3); <span class="comment">///&lt; as 3 is smallest from 3..8</span></div>
<div class="line"><span class="lineno"> 152</span> </div>
<div class="line"><span class="lineno"> 153</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Self-test implementations passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 154</span>}</div>
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<div class="ttc" id="astructdata__structures_1_1sparse__table_1_1_sparse__table_html"><div class="ttname"><a href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html">data_structures::sparse_table::Sparse_table</a></div><div class="ttdef"><b>Definition</b> sparse_table.cpp:51</div></div>
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<h2 class="groupheader">Variable Documentation</h2>
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<td class="memname">uint32_t data_structures::sparse_table::N = 12345</td>
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<p>A struct to represent sparse table for <code>min()</code> as their invariant function, for the given array <code>A</code>. The answer to queries are stored in the array ST. </p>
<p>the maximum size of the array. </p>
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@@ -212,7 +212,7 @@ Here is the call graph for this function:</div>
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<div class="fragment"><div class="line"><span class="lineno"> 65</span> {</div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">for</span> (uint32_t i = 2; i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">for</span> (uint32_t i = 2; i &lt;= <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><span class="lineno"> 67</span> <span class="keywordflow">if</span> (is_prime[i]) {</div>
<div class="line"><span class="lineno"> 68</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="charliteral">&#39; &#39;</span>;</div>
<div class="line"><span class="lineno"> 69</span> }</div>
@@ -220,8 +220,8 @@ Here is the call graph for this function:</div>
<div class="line"><span class="lineno"> 71</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 72</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition</b> sparse_table.cpp:48</div></div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
<div class="ttc" id="asparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition</b> sparse_table.cpp:48</div></div>
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Here is the call graph for this function:</div>
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@@ -258,9 +258,9 @@ Here is the call graph for this function:</div>
<div class="line"><span class="lineno"> 46</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>(N + 1, <span class="keyword">true</span>); <span class="comment">// Initialize all as prime numbers</span></div>
<div class="line"><span class="lineno"> 47</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[0] = <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[1] = <span class="keyword">false</span>; <span class="comment">// 0 and 1 are not prime numbers</span></div>
<div class="line"><span class="lineno"> 48</span> </div>
<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">for</span> (uint32_t i = 2; i * i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">for</span> (uint32_t i = 2; i * i &lt;= <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">if</span> (is_prime[i]) {</div>
<div class="line"><span class="lineno"> 51</span> <span class="keywordflow">for</span> (uint32_t j = i * i; j &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j += i) {</div>
<div class="line"><span class="lineno"> 51</span> <span class="keywordflow">for</span> (uint32_t j = i * i; j &lt;= <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j += i) {</div>
<div class="line"><span class="lineno"> 52</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[j] = <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 53</span> }</div>
<div class="line"><span class="lineno"> 54</span> }</div>