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<div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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@@ -129,7 +129,8 @@ Functions</h2></td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Disjoint-set-data_structure" target="_blank">DSU (Disjoint sets)</a> </p>
<p >dsu : It is a very powerful data structure which keeps track of different clusters(sets) of elements, these sets are disjoint(doesnot have a common element). Disjoint sets uses cases : for finding connected components in a graph, used in Kruskal's algorithm for finding <a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> Spanning tree. Operations that can be performed: 1) UnionSet(i,j): add(element i and j to the set) 2) findSet(i): returns the representative of the set to which i belogngs to. 3) getParents(i): prints the parent of i and so on and so forth. Below is the class-based approach which uses the heuristic of union-ranks. Using union-rank in findSet(i),we are able to get to the representative of i in slightly delayed O(logN) time but it allows us to keep tracks of the parent of i. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/AayushVyasKIIT" target="_blank">AayushVyasKIIT</a> </dd></dl>
<p >dsu : It is a very powerful data structure which keeps track of different clusters(sets) of elements, these sets are disjoint(doesnot have a common
element). Disjoint sets uses cases : for finding connected components in a graph, used in Kruskal's algorithm for finding <a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> Spanning tree. Operations that can be performed: 1) UnionSet(i,j): add(element i and j to the set) 2) findSet(i): returns the representative of the set to which i belogngs to. 3) getParents(i): prints the parent of i and so on and so forth. Below is the class-based approach which uses the heuristic of union-ranks. Using union-rank in findSet(i),we are able to get to the representative of i in slightly delayed O(logN) time but it allows us to keep tracks of the parent of i. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/AayushVyasKIIT" target="_blank">AayushVyasKIIT</a> </dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d3/dae/dsu__path__compression_8cpp.html" title="DSU (Disjoint sets)">dsu_path_compression.cpp</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
@@ -150,18 +151,18 @@ Functions</h2></td></tr>
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> {</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <a class="code hl_function" href="../../df/d28/dsu__union__rank_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>(); <span class="comment">// run 1st test case</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <a class="code hl_function" href="../../df/d28/dsu__union__rank_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>(); <span class="comment">// run 2nd test case</span></div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> </div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 182</span> {</div>
<div class="line"><span class="lineno"> 183</span> <a class="code hl_function" href="../../df/d28/dsu__union__rank_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>(); <span class="comment">// run 1st test case</span></div>
<div class="line"><span class="lineno"> 184</span> <a class="code hl_function" href="../../df/d28/dsu__union__rank_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>(); <span class="comment">// run 2nd test case</span></div>
<div class="line"><span class="lineno"> 185</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="adsu__union__rank_8cpp_html_a45d94ead4cf4e1ff9f87c38bc99f59ae"><div class="ttname"><a href="../../df/d28/dsu__union__rank_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a></div><div class="ttdeci">static void test2()</div><div class="ttdoc">Self-implementations, 2nd test.</div><div class="ttdef"><b>Definition:</b> dsu_union_rank.cpp:157</div></div>
<div class="ttc" id="adsu__union__rank_8cpp_html_ae7880ce913f3058a35ff106d5be9e243"><div class="ttname"><a href="../../df/d28/dsu__union__rank_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a></div><div class="ttdeci">static void test1()</div><div class="ttdoc">Self-implementations, 1st test.</div><div class="ttdef"><b>Definition:</b> dsu_union_rank.cpp:133</div></div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d28/dsu__union__rank_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="606" height="207"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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@@ -195,26 +196,26 @@ Here is the call graph for this function:</div>
<p >&lt; number of elements</p>
<p >&lt; object of class disjoint sets</p>
<p >&lt; performs union operation on 1 and 2</p>
<div class="fragment"><div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> {</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="comment">/* checks the parents in the resultant structures */</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> uint64_t n = 10; <span class="comment">///&lt; number of elements</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); <span class="comment">///&lt; object of class disjoint sets</span></div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> d.unionSet(2, 1); <span class="comment">///&lt; performs union operation on 1 and 2</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> d.unionSet(1, 4);</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> d.unionSet(8, 1);</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> d.unionSet(3, 5);</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> d.unionSet(5, 6);</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> d.unionSet(5, 7);</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> d.unionSet(9, 10);</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> d.unionSet(2, 10);</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="comment">// keeping track of the changes using parent pointers</span></div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {7, 5};</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> assert(d.getParents(7).at(i) ==</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[i]); <span class="comment">// makes sure algorithm works fine</span></div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> }</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 133</span> {</div>
<div class="line"><span class="lineno"> 134</span> <span class="comment">/* checks the parents in the resultant structures */</span></div>
<div class="line"><span class="lineno"> 135</span> uint64_t n = 10; <span class="comment">///&lt; number of elements</span></div>
<div class="line"><span class="lineno"> 136</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); <span class="comment">///&lt; object of class disjoint sets</span></div>
<div class="line"><span class="lineno"> 137</span> d.unionSet(2, 1); <span class="comment">///&lt; performs union operation on 1 and 2</span></div>
<div class="line"><span class="lineno"> 138</span> d.unionSet(1, 4);</div>
<div class="line"><span class="lineno"> 139</span> d.unionSet(8, 1);</div>
<div class="line"><span class="lineno"> 140</span> d.unionSet(3, 5);</div>
<div class="line"><span class="lineno"> 141</span> d.unionSet(5, 6);</div>
<div class="line"><span class="lineno"> 142</span> d.unionSet(5, 7);</div>
<div class="line"><span class="lineno"> 143</span> d.unionSet(9, 10);</div>
<div class="line"><span class="lineno"> 144</span> d.unionSet(2, 10);</div>
<div class="line"><span class="lineno"> 145</span> <span class="comment">// keeping track of the changes using parent pointers</span></div>
<div class="line"><span class="lineno"> 146</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {7, 5};</div>
<div class="line"><span class="lineno"> 147</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
<div class="line"><span class="lineno"> 148</span> assert(d.getParents(7).at(i) ==</div>
<div class="line"><span class="lineno"> 149</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[i]); <span class="comment">// makes sure algorithm works fine</span></div>
<div class="line"><span class="lineno"> 150</span> }</div>
<div class="line"><span class="lineno"> 151</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><span class="lineno"> 152</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="aclassdsu_html"><div class="ttname"><a href="../../dd/d1f/classdsu.html">dsu</a></div><div class="ttdoc">Disjoint sets union data structure, class based representation.</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:33</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a600eaf353befc174637855795f12d258"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a></div><div class="ttdeci">#define endl</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:36</div></div>
@@ -223,7 +224,7 @@ Here is the call graph for this function:</div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d28/dsu__union__rank_8cpp_ae7880ce913f3058a35ff106d5be9e243_cgraph.svg" width="507" height="190"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d28/dsu__union__rank_8cpp_ae7880ce913f3058a35ff106d5be9e243_cgraph.svg" width="507" height="215"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
</div>
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@@ -259,31 +260,31 @@ Here is the call graph for this function:</div>
<p >performs union operation on 1 and 2</p>
<p >keeping track of the changes using parent pointers</p>
<p >makes sure algorithm works fine</p>
<div class="fragment"><div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> {</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="comment">// checks the parents in the resultant structures</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> uint64_t n = 10; <span class="comment">///&lt; number of elements</span></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); <span class="comment">///&lt; object of class disjoint sets</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> d.unionSet(2, 1); <span class="comment">/// performs union operation on 1 and 2</span></div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> d.unionSet(1, 4);</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> d.unionSet(8, 1);</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> d.unionSet(3, 5);</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> d.unionSet(5, 6);</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> d.unionSet(5, 7);</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> d.unionSet(9, 10);</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> d.unionSet(2, 10);</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span><span class="comment"></span> </div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span><span class="comment"> /// keeping track of the changes using parent pointers</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span><span class="comment"></span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {2, 1, 10};</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> assert(d.getParents(2).at(i) ==</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[i]); <span class="comment">/// makes sure algorithm works fine</span></div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> }</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 157</span> {</div>
<div class="line"><span class="lineno"> 158</span> <span class="comment">// checks the parents in the resultant structures</span></div>
<div class="line"><span class="lineno"> 159</span> uint64_t n = 10; <span class="comment">///&lt; number of elements</span></div>
<div class="line"><span class="lineno"> 160</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); <span class="comment">///&lt; object of class disjoint sets</span></div>
<div class="line"><span class="lineno"> 161</span> d.unionSet(2, 1); <span class="comment">/// performs union operation on 1 and 2</span></div>
<div class="line"><span class="lineno"> 162</span> d.unionSet(1, 4);</div>
<div class="line"><span class="lineno"> 163</span> d.unionSet(8, 1);</div>
<div class="line"><span class="lineno"> 164</span> d.unionSet(3, 5);</div>
<div class="line"><span class="lineno"> 165</span> d.unionSet(5, 6);</div>
<div class="line"><span class="lineno"> 166</span> d.unionSet(5, 7);</div>
<div class="line"><span class="lineno"> 167</span> d.unionSet(9, 10);</div>
<div class="line"><span class="lineno"> 168</span> d.unionSet(2, 10);</div>
<div class="line"><span class="lineno"> 169</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 170</span><span class="comment"> /// keeping track of the changes using parent pointers</span></div>
<div class="line"><span class="lineno"> 171</span><span class="comment"></span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {2, 1, 10};</div>
<div class="line"><span class="lineno"> 172</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
<div class="line"><span class="lineno"> 173</span> assert(d.getParents(2).at(i) ==</div>
<div class="line"><span class="lineno"> 174</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[i]); <span class="comment">/// makes sure algorithm works fine</span></div>
<div class="line"><span class="lineno"> 175</span> }</div>
<div class="line"><span class="lineno"> 176</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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