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<div class="headertitle"><div class="title">kruskals_minimum_spanning_tree.cpp File Reference</div></div>
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<p><a href="https://www.simplilearn.com/tutorials/data-structure-tutorial/kruskal-algorithm" target="_blank">Kruskals Minimum Spanning Tree</a> implementation
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;array&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;limits&gt;</code><br />
<code>#include &lt;cstdint&gt;</code><br />
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Include dependency graph for kruskals_minimum_spanning_tree.cpp:</div>
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<p><a href="../../d8/d7d/kruskals__minimum__spanning__tree_8cpp_source.html">Go to the source code of this file.</a></p>
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<tr class="heading"><td colspan="2"><h2 id="header-namespaces" class="groupheader"><a id="namespaces" name="namespaces"></a>
Namespaces</h2></td></tr>
<tr class="memitem:greedy_5Falgorithms" id="r_greedy_5Falgorithms"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d90/namespacegreedy__algorithms.html">greedy_algorithms</a></td></tr>
<tr class="memdesc:d2/d90/namespacegreedy__algorithms"><td class="mdescLeft">&#160;</td><td class="mdescRight">for string class <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a349e4ab9a97532c3931a2bd2a19c0098" id="r_a349e4ab9a97532c3931a2bd2a19c0098"><td class="memTemplParams" colspan="2">template&lt;typename T, std::size_t N, std::size_t M&gt; </td></tr>
<tr class="memitem:a349e4ab9a97532c3931a2bd2a19c0098 template"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a> (const T &amp;infinity, const std::array&lt; std::array&lt; T, N &gt;, M &gt; &amp;graph)</td></tr>
<tr class="memdesc:a349e4ab9a97532c3931a2bd2a19c0098"><td class="mdescLeft">&#160;</td><td class="mdescRight">Finds the minimum edge of the given 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 implementations. <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>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://www.simplilearn.com/tutorials/data-structure-tutorial/kruskal-algorithm" target="_blank">Kruskals Minimum Spanning Tree</a> implementation </p>
<p><em>Quoted from <a href="https://www.simplilearn.com/tutorials/data-structure-tutorial/kruskal-algorithm" target="_blank">Simplilearn</a>.</em></p>
<p>Kruskals algorithm is the concept that is introduced in the graph theory of discrete mathematics. It is used to discover the shortest path between two points in a connected weighted graph. This algorithm converts a given graph into the forest, considering each node as a separate tree. These trees can only link to each other if the edge connecting them has a low value and doesnt generate a cycle in MST structure.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/coleman2246" target="_blank">coleman2246</a> </dd></dl>
<p class="definition">Definition in file <a class="el" href="../../d8/d7d/kruskals__minimum__spanning__tree_8cpp_source.html">kruskals_minimum_spanning_tree.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="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<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>
<td>(</td>
<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<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/d7d/kruskals__minimum__spanning__tree_8cpp_source.html#l00184">184</a> of file <a class="el" href="../../d8/d7d/kruskals__minimum__spanning__tree_8cpp_source.html">kruskals_minimum_spanning_tree.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 184</span> {</div>
<div class="line"><span class="lineno"> 185</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run Self-test implementation</span></div>
<div class="line"><span class="lineno"> 186</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 187</span>}</div>
<div class="ttc" id="akruskals__minimum__spanning__tree_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> <a href="../../d8/d7d/kruskals__minimum__spanning__tree_8cpp_source.html#l00064">kruskals_minimum_spanning_tree.cpp:64</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 implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p>define a large value for int define a large value for float define a large value for double define a large value for uint32_t</p>
<p class="definition">Definition at line <a class="el" href="../../d8/d7d/kruskals__minimum__spanning__tree_8cpp_source.html#l00064">64</a> of file <a class="el" href="../../d8/d7d/kruskals__minimum__spanning__tree_8cpp_source.html">kruskals_minimum_spanning_tree.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 64</span> {</div>
<div class="line"><span class="lineno"> 71</span> <span class="keyword">constexpr</span> <span class="keywordtype">int</span> INFINITY_INT = std::numeric_limits&lt;int&gt;::max();</div>
<div class="line"><span class="lineno"> 72</span> <span class="keyword">constexpr</span> <span class="keywordtype">float</span> INFINITY_FLOAT = std::numeric_limits&lt;float&gt;::max();</div>
<div class="line"><span class="lineno"> 73</span> <span class="keyword">constexpr</span> <span class="keywordtype">double</span> INFINITY_DOUBLE = std::numeric_limits&lt;double&gt;::max();</div>
<div class="line"><span class="lineno"> 74</span> <span class="keyword">constexpr</span> uint32_t INFINITY_UINT32 = UINT32_MAX;</div>
<div class="line"><span class="lineno"> 75</span> </div>
<div class="line"><span class="lineno"> 76</span> <span class="comment">// Test case with integer values</span></div>
<div class="line"><span class="lineno"> 77</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nTest Case 1 :\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 78</span> std::array&lt;std::array&lt;int, 6&gt;, 6&gt; graph1{</div>
<div class="line"><span class="lineno"> 79</span> 0, 4, 1, 4, INFINITY_INT, INFINITY_INT,</div>
<div class="line"><span class="lineno"> 80</span> 4, 0, 3, 8, 3, INFINITY_INT,</div>
<div class="line"><span class="lineno"> 81</span> 1, 3, 0, INFINITY_INT, 1, INFINITY_INT,</div>
<div class="line"><span class="lineno"> 82</span> 4, 8, INFINITY_INT, 0, 5, 7,</div>
<div class="line"><span class="lineno"> 83</span> INFINITY_INT, 3, 1, 5, 0, INFINITY_INT,</div>
<div class="line"><span class="lineno"> 84</span> INFINITY_INT, INFINITY_INT, INFINITY_INT, 7, INFINITY_INT, 0};</div>
<div class="line"><span class="lineno"> 85</span> <a class="code hl_function" href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a>(INFINITY_INT, graph1);</div>
<div class="line"><span class="lineno"> 86</span> </div>
<div class="line"><span class="lineno"> 87</span> <span class="comment">// Test case with floating values</span></div>
<div class="line"><span class="lineno"> 88</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nTest Case 2 :\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 89</span> std::array&lt;std::array&lt;float, 3&gt;, 3&gt; graph2{</div>
<div class="line"><span class="lineno"> 90</span> 0.0f, 2.5f, INFINITY_FLOAT,</div>
<div class="line"><span class="lineno"> 91</span> 2.5f, 0.0f, 3.2f,</div>
<div class="line"><span class="lineno"> 92</span> INFINITY_FLOAT, 3.2f, 0.0f};</div>
<div class="line"><span class="lineno"> 93</span> <a class="code hl_function" href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a>(INFINITY_FLOAT, graph2);</div>
<div class="line"><span class="lineno"> 94</span> </div>
<div class="line"><span class="lineno"> 95</span> <span class="comment">// Test case with double values</span></div>
<div class="line"><span class="lineno"> 96</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nTest Case 3 :\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 97</span> std::array&lt;std::array&lt;double, 5&gt;, 5&gt; graph3{</div>
<div class="line"><span class="lineno"> 98</span> 0.0, 10.5, INFINITY_DOUBLE, 6.7, 3.3,</div>
<div class="line"><span class="lineno"> 99</span> 10.5, 0.0, 8.1, 15.4, INFINITY_DOUBLE,</div>
<div class="line"><span class="lineno"> 100</span> INFINITY_DOUBLE, 8.1, 0.0, INFINITY_DOUBLE, 7.8,</div>
<div class="line"><span class="lineno"> 101</span> 6.7, 15.4, INFINITY_DOUBLE, 0.0, 9.9,</div>
<div class="line"><span class="lineno"> 102</span> 3.3, INFINITY_DOUBLE, 7.8, 9.9, 0.0};</div>
<div class="line"><span class="lineno"> 103</span> <a class="code hl_function" href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a>(INFINITY_DOUBLE, graph3);</div>
<div class="line"><span class="lineno"> 104</span> </div>
<div class="line"><span class="lineno"> 105</span> <span class="comment">// Test Case with negative weights</span></div>
<div class="line"><span class="lineno"> 106</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nTest Case 4 :\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 107</span> std::array&lt;std::array&lt;int, 3&gt;, 3&gt; graph_neg{</div>
<div class="line"><span class="lineno"> 108</span> 0, -2, 4,</div>
<div class="line"><span class="lineno"> 109</span> -2, 0, 3,</div>
<div class="line"><span class="lineno"> 110</span> 4, 3, 0};</div>
<div class="line"><span class="lineno"> 111</span> <a class="code hl_function" href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a>(INFINITY_INT, graph_neg);</div>
<div class="line"><span class="lineno"> 112</span> </div>
<div class="line"><span class="lineno"> 113</span> <span class="comment">// Test Case with Self-Loops</span></div>
<div class="line"><span class="lineno"> 114</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nTest Case 5 :\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 115</span> std::array&lt;std::array&lt;int, 3&gt;, 3&gt; graph_self_loop{</div>
<div class="line"><span class="lineno"> 116</span> 2, 1, INFINITY_INT,</div>
<div class="line"><span class="lineno"> 117</span> INFINITY_INT, 0, 4,</div>
<div class="line"><span class="lineno"> 118</span> INFINITY_INT, 4, 0};</div>
<div class="line"><span class="lineno"> 119</span> <a class="code hl_function" href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a>(INFINITY_INT, graph_self_loop);</div>
<div class="line"><span class="lineno"> 120</span> </div>
<div class="line"><span class="lineno"> 121</span> <span class="comment">// Test Case with no edges</span></div>
<div class="line"><span class="lineno"> 122</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nTest Case 6 :\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 123</span> std::array&lt;std::array&lt;int, 4&gt;, 4&gt; no_edges{</div>
<div class="line"><span class="lineno"> 124</span> 0, INFINITY_INT, INFINITY_INT, INFINITY_INT,</div>
<div class="line"><span class="lineno"> 125</span> INFINITY_INT, 0, INFINITY_INT, INFINITY_INT,</div>
<div class="line"><span class="lineno"> 126</span> INFINITY_INT, INFINITY_INT, 0, INFINITY_INT,</div>
<div class="line"><span class="lineno"> 127</span> INFINITY_INT, INFINITY_INT, INFINITY_INT, 0};</div>
<div class="line"><span class="lineno"> 128</span> <a class="code hl_function" href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a>(INFINITY_INT, no_edges);</div>
<div class="line"><span class="lineno"> 129</span> </div>
<div class="line"><span class="lineno"> 130</span> <span class="comment">// Test Case with a non-connected graph</span></div>
<div class="line"><span class="lineno"> 131</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nTest Case 7:\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 132</span> std::array&lt;std::array&lt;int, 4&gt;, 4&gt; partial_graph{</div>
<div class="line"><span class="lineno"> 133</span> 0, 2, INFINITY_INT, 6,</div>
<div class="line"><span class="lineno"> 134</span> 2, 0, 3, INFINITY_INT,</div>
<div class="line"><span class="lineno"> 135</span> INFINITY_INT, 3, 0, 4,</div>
<div class="line"><span class="lineno"> 136</span> 6, INFINITY_INT, 4, 0};</div>
<div class="line"><span class="lineno"> 137</span> <a class="code hl_function" href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a>(INFINITY_INT, partial_graph);</div>
<div class="line"><span class="lineno"> 138</span> </div>
<div class="line"><span class="lineno"> 139</span> <span class="comment">// Test Case with Directed weighted graph. The Krushkal algorithm does not give</span></div>
<div class="line"><span class="lineno"> 140</span> <span class="comment">// optimal answer</span></div>
<div class="line"><span class="lineno"> 141</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nTest Case 8:\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 142</span> std::array&lt;std::array&lt;int, 4&gt;, 4&gt; directed_graph{</div>
<div class="line"><span class="lineno"> 143</span> 0, 3, 7, INFINITY_INT, <span class="comment">// Vertex 0 has edges to Vertex 1 and Vertex 2</span></div>
<div class="line"><span class="lineno"> 144</span> INFINITY_INT, 0, 2, 5, <span class="comment">// Vertex 1 has edges to Vertex 2 and Vertex 3</span></div>
<div class="line"><span class="lineno"> 145</span> INFINITY_INT, INFINITY_INT, 0, 1, <span class="comment">// Vertex 2 has an edge to Vertex 3</span></div>
<div class="line"><span class="lineno"> 146</span> INFINITY_INT, INFINITY_INT, INFINITY_INT, 0}; <span class="comment">// Vertex 3 has no outgoing edges</span></div>
<div class="line"><span class="lineno"> 147</span> <a class="code hl_function" href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a>(INFINITY_INT, directed_graph);</div>
<div class="line"><span class="lineno"> 148</span> </div>
<div class="line"><span class="lineno"> 149</span> <span class="comment">// Test case with wrong input passed</span></div>
<div class="line"><span class="lineno"> 150</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nTest Case 9:\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 151</span> std::array&lt;std::array&lt;int, 4&gt;, 3&gt; graph9{</div>
<div class="line"><span class="lineno"> 152</span> 0, 5, 5, 5,</div>
<div class="line"><span class="lineno"> 153</span> 5, 0, 5, 5, </div>
<div class="line"><span class="lineno"> 154</span> 5, 5, 5, 5};</div>
<div class="line"><span class="lineno"> 155</span> <a class="code hl_function" href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a>(INFINITY_INT, graph9);</div>
<div class="line"><span class="lineno"> 156</span> </div>
<div class="line"><span class="lineno"> 157</span> <span class="comment">// Test case with all the same values between every edge</span></div>
<div class="line"><span class="lineno"> 158</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nTest Case 10:\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 159</span> std::array&lt;std::array&lt;int, 5&gt;, 5&gt; graph10{</div>
<div class="line"><span class="lineno"> 160</span> 0, 5, 5, 5, 5,</div>
<div class="line"><span class="lineno"> 161</span> 5, 0, 5, 5, 5,</div>
<div class="line"><span class="lineno"> 162</span> 5, 5, 0, 5, 5,</div>
<div class="line"><span class="lineno"> 163</span> 5, 5, 5, 0, 5,</div>
<div class="line"><span class="lineno"> 164</span> 5, 5, 5, 5, 0};</div>
<div class="line"><span class="lineno"> 165</span> <a class="code hl_function" href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a>(INFINITY_INT, graph10);</div>
<div class="line"><span class="lineno"> 166</span> </div>
<div class="line"><span class="lineno"> 167</span> <span class="comment">// Test Case with uint32_t values</span></div>
<div class="line"><span class="lineno"> 168</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nTest Case 11 :\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 169</span> std::array&lt;std::array&lt;uint32_t, 4&gt;, 4&gt; graph_uint32{</div>
<div class="line"><span class="lineno"> 170</span> 0, 5, INFINITY_UINT32, 9,</div>
<div class="line"><span class="lineno"> 171</span> 5, 0, 2, INFINITY_UINT32,</div>
<div class="line"><span class="lineno"> 172</span> INFINITY_UINT32, 2, 0, 6,</div>
<div class="line"><span class="lineno"> 173</span> 9, INFINITY_UINT32, 6, 0};</div>
<div class="line"><span class="lineno"> 174</span> <a class="code hl_function" href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a>(INFINITY_UINT32, graph_uint32);</div>
<div class="line"><span class="lineno"> 175</span> </div>
<div class="line"><span class="lineno"> 176</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nAll tests have successfully passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 177</span>}</div>
<div class="ttc" id="anamespacegreedy__algorithms_html_a349e4ab9a97532c3931a2bd2a19c0098"><div class="ttname"><a href="../../d2/d90/namespacegreedy__algorithms.html#a349e4ab9a97532c3931a2bd2a19c0098">greedy_algorithms::findMinimumEdge</a></div><div class="ttdeci">void findMinimumEdge(const T &amp;infinity, const std::array&lt; std::array&lt; T, N &gt;, M &gt; &amp;graph)</div><div class="ttdoc">Finds the minimum edge of the given graph.</div><div class="ttdef"><b>Definition</b> <a href="../../d8/d7d/kruskals__minimum__spanning__tree_8cpp_source.html#l00038">kruskals_minimum_spanning_tree.cpp:38</a></div></div>
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