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df/d28/dsu__union__rank_8cpp.html
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<title>Algorithms_in_C++: data_structures/dsu_union_rank.cpp File Reference</title>
<title>TheAlgorithms/C++: data_structures/dsu_union_rank.cpp File Reference</title>
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<div id="projectname">TheAlgorithms/C++<span id="projectnumber">&#160;1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
<div id="projectbrief">All the algorithms implemented in C++</div>
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@@ -122,7 +139,9 @@ Include dependency graph for dsu_union_rank.cpp:</div>
<div class="dyncontent">
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<p><a href="../../df/d28/dsu__union__rank_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="nested-classes" name="nested-classes"></a>
Classes</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d1f/classdsu.html">dsu</a></td></tr>
@@ -146,6 +165,8 @@ Functions</h2></td></tr>
<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>
<p class="definition">Definition in file <a class="el" href="../../df/d28/dsu__union__rank_8cpp_source.html">dsu_union_rank.cpp</a>.</p>
</div><h2 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>
@@ -164,20 +185,17 @@ element). Disjoint sets uses cases : for finding connected components in a graph
<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="../../df/d28/dsu__union__rank_8cpp_source.html#l00183">183</a> of file <a class="el" href="../../df/d28/dsu__union__rank_8cpp_source.html">dsu_union_rank.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 183</span> {</div>
<div class="line"><span class="lineno"> 184</span> <a class="code hl_function" href="#ae7880ce913f3058a35ff106d5be9e243">test1</a>(); <span class="comment">// run 1st test case</span></div>
<div class="line"><span class="lineno"> 185</span> <a class="code hl_function" href="#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>(); <span class="comment">// run 2nd test case</span></div>
<div class="line"><span class="lineno"> 186</span> </div>
<div class="line"><span class="lineno"> 187</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 188</span>}</div>
<div class="ttc" id="adsu__union__rank_8cpp_html_a45d94ead4cf4e1ff9f87c38bc99f59ae"><div class="ttname"><a href="#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:158</div></div>
<div class="ttc" id="adsu__union__rank_8cpp_html_ae7880ce913f3058a35ff106d5be9e243"><div class="ttname"><a href="#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:134</div></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d28/dsu__union__rank_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="602" height="138"><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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<div class="ttc" id="adsu__union__rank_8cpp_html_a45d94ead4cf4e1ff9f87c38bc99f59ae"><div class="ttname"><a href="#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> <a href="../../df/d28/dsu__union__rank_8cpp_source.html#l00158">dsu_union_rank.cpp:158</a></div></div>
<div class="ttc" id="adsu__union__rank_8cpp_html_ae7880ce913f3058a35ff106d5be9e243"><div class="ttname"><a href="#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> <a href="../../df/d28/dsu__union__rank_8cpp_source.html#l00134">dsu_union_rank.cpp:134</a></div></div>
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@@ -208,11 +226,13 @@ 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>
<p class="definition">Definition at line <a class="el" href="../../df/d28/dsu__union__rank_8cpp_source.html#l00134">134</a> of file <a class="el" href="../../df/d28/dsu__union__rank_8cpp_source.html">dsu_union_rank.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 134</span> {</div>
<div class="line"><span class="lineno"> 135</span> <span class="comment">/* checks the parents in the resultant structures */</span></div>
<div class="line"><span class="lineno"> 136</span> uint64_t n = 10; <span class="comment">///&lt; number of elements</span></div>
<div class="line"><span class="lineno"> 137</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"> 138</span> d.unionSet(2, 1); <span class="comment">///&lt; performs union operation on 1 and 2</span></div>
<div class="line"><span class="lineno"> 136</span> uint64_t n = 10; </div>
<div class="line"><span class="lineno"> 137</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); </div>
<div class="line"><span class="lineno"> 138</span> d.unionSet(2, 1); </div>
<div class="line"><span class="lineno"> 139</span> d.unionSet(1, 4);</div>
<div class="line"><span class="lineno"> 140</span> d.unionSet(8, 1);</div>
<div class="line"><span class="lineno"> 141</span> d.unionSet(3, 5);</div>
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<div class="line"><span class="lineno"> 144</span> d.unionSet(9, 10);</div>
<div class="line"><span class="lineno"> 145</span> d.unionSet(2, 10);</div>
<div class="line"><span class="lineno"> 146</span> <span class="comment">// keeping track of the changes using parent pointers</span></div>
<div class="line"><span class="lineno"> 147</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;uint64_t&gt;</a> ans = {7, 5};</div>
<div class="line"><span class="lineno"> 147</span> vector&lt;uint64_t&gt; ans = {7, 5};</div>
<div class="line"><span class="lineno"> 148</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; ans.size(); i++) {</div>
<div class="line"><span class="lineno"> 149</span> assert(d.getParents(7).at(i) ==</div>
<div class="line"><span class="lineno"> 150</span> ans[i]); <span class="comment">// makes sure algorithm works fine</span></div>
<div class="line"><span class="lineno"> 151</span> }</div>
<div class="line"><span class="lineno"> 152</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> cout &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"> 153</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:34</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>
<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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<div class="center"><iframe scrolling="no" frameborder="0" src="../../df/d28/dsu__union__rank_8cpp_ae7880ce913f3058a35ff106d5be9e243_cgraph.svg" width="504" height="135"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></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> <a href="../../d3/dae/dsu__path__compression_8cpp_source.html#l00034">dsu_path_compression.cpp:34</a></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> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00036">matrix_exponentiation.cpp:36</a></div></div>
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@@ -270,11 +283,13 @@ 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>
<p class="definition">Definition at line <a class="el" href="../../df/d28/dsu__union__rank_8cpp_source.html#l00158">158</a> of file <a class="el" href="../../df/d28/dsu__union__rank_8cpp_source.html">dsu_union_rank.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 158</span> {</div>
<div class="line"><span class="lineno"> 159</span> <span class="comment">// checks the parents in the resultant structures</span></div>
<div class="line"><span class="lineno"> 160</span> uint64_t n = 10; <span class="comment">///&lt; number of elements</span></div>
<div class="line"><span class="lineno"> 161</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"> 162</span> d.unionSet(2, 1); <span class="comment">/// performs union operation on 1 and 2</span></div>
<div class="line"><span class="lineno"> 160</span> uint64_t n = 10; </div>
<div class="line"><span class="lineno"> 161</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); </div>
<div class="line"><span class="lineno"> 162</span> d.unionSet(2, 1); </div>
<div class="line"><span class="lineno"> 163</span> d.unionSet(1, 4);</div>
<div class="line"><span class="lineno"> 164</span> d.unionSet(8, 1);</div>
<div class="line"><span class="lineno"> 165</span> d.unionSet(3, 5);</div>
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<div class="line"><span class="lineno"> 167</span> d.unionSet(5, 7);</div>
<div class="line"><span class="lineno"> 168</span> d.unionSet(9, 10);</div>
<div class="line"><span class="lineno"> 169</span> d.unionSet(2, 10);</div>
<div class="line"><span class="lineno"> 170</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 171</span><span class="comment"> /// keeping track of the changes using parent pointers</span></div>
<div class="line"><span class="lineno"> 172</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> ans = {2, 1, 10};</div>
<div class="line"><span class="lineno"> 170</span> </div>
<div class="line"><span class="lineno"> 172</span> vector&lt;uint64_t&gt; ans = {2, 1, 10};</div>
<div class="line"><span class="lineno"> 173</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; ans.size(); i++) {</div>
<div class="line"><span class="lineno"> 174</span> assert(d.getParents(2).at(i) ==</div>
<div class="line"><span class="lineno"> 175</span> ans[i]); <span class="comment">/// makes sure algorithm works fine</span></div>
<div class="line"><span class="lineno"> 175</span> ans[i]); </div>
<div class="line"><span class="lineno"> 176</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">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"><span class="lineno"> 177</span> cout &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"><span class="lineno"> 178</span>}</div>
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<div class="headertitle"><div class="title">dsu_union_rank.cpp</div></div>
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<a href="../../df/d28/dsu__union__rank_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include &lt;cassert&gt;</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include &lt;vector&gt;</span> </div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> </div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="keyword">using </span>std::cout;</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="keyword">using </span>std::endl;</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="keyword">using </span>std::vector;</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="keyword">class </span><a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> {</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keyword">private</span>:</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> vector&lt;uint64_t&gt; <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>; </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> vector&lt;uint64_t&gt; <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>; </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> vector&lt;uint64_t&gt; <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>; </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keyword">public</span>:</div>
<div class="foldopen" id="foldopen00045" data-start="{" data-end="}">
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a126e3002a464e53cd54b07ba56482a72"> 45</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="../../dd/d1f/classdsu.html#a126e3002a464e53cd54b07ba56482a72">dsu</a>(uint64_t n) {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>.assign(n, 0);</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>.assign(n, 0);</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>.assign(n, 0);</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] = i;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[i] = 0;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[i] = 1;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> }</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
</div>
<div class="foldopen" id="foldopen00062" data-start="{" data-end="}">
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c"> 62</a></span> uint64_t <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(uint64_t i) {</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">while</span> (i != <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i]) {</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> i = <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i];</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> }</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">return</span> i;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> }</div>
</div>
<div class="foldopen" id="foldopen00076" data-start="{" data-end="}">
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f"> 76</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(uint64_t i, uint64_t j) {</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303">isSame</a>(i, j)) {</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> }</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> uint64_t x = <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i);</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> uint64_t y = <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(j);</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[x] &gt; <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[y]) {</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> std::swap(x, y);</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[x] = y;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[x] == <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[y]) {</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[y]++;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> }</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[y] += <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[x];</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> }</div>
</div>
<div class="foldopen" id="foldopen00108" data-start="{" data-end="}">
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303"> 108</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303">isSame</a>(uint64_t i, uint64_t j) {</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i) == <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(j)) {</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> }</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> }</div>
</div>
<div class="foldopen" id="foldopen00120" data-start="{" data-end="}">
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#ab8ee27083a3c2e2df80755165a2ec280"> 120</a></span> vector&lt;uint64_t&gt; <a class="code hl_function" href="../../dd/d1f/classdsu.html#ab8ee27083a3c2e2df80755165a2ec280">getParents</a>(uint64_t i) {</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> vector&lt;uint64_t&gt; ans;</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">while</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] != i) {</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> ans.push_back(i);</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> i = <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i];</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> }</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> ans.push_back(i);</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keywordflow">return</span> ans;</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> }</div>
</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span>};</div>
<div class="foldopen" id="foldopen00134" data-start="{" data-end="}">
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"><a class="line" href="../../df/d28/dsu__union__rank_8cpp.html#ae7880ce913f3058a35ff106d5be9e243"> 134</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../df/d28/dsu__union__rank_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>() {</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="comment">/* checks the parents in the resultant structures */</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> uint64_t n = 10; </div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); </div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(2, 1); </div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(1, 4);</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(8, 1);</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(3, 5);</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(5, 6);</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(5, 7);</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(9, 10);</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(2, 10);</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="comment">// keeping track of the changes using parent pointers</span></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> vector&lt;uint64_t&gt; ans = {7, 5};</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; ans.size(); i++) {</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> assert(d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#ab8ee27083a3c2e2df80755165a2ec280">getParents</a>(7).at(i) ==</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> ans[i]); <span class="comment">// makes sure algorithm works fine</span></div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> }</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> cout &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="l00153" name="l00153"></a><span class="lineno"> 153</span>}</div>
</div>
<div class="foldopen" id="foldopen00158" data-start="{" data-end="}">
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"><a class="line" href="../../df/d28/dsu__union__rank_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae"> 158</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../df/d28/dsu__union__rank_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>() {</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="comment">// checks the parents in the resultant structures</span></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> uint64_t n = 10; </div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); </div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(2, 1); </div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(1, 4);</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(8, 1);</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(3, 5);</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(5, 6);</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(5, 7);</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(9, 10);</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">unionSet</a>(2, 10);</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> </div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> vector&lt;uint64_t&gt; ans = {2, 1, 10};</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; ans.size(); i++) {</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> assert(d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#ab8ee27083a3c2e2df80755165a2ec280">getParents</a>(2).at(i) ==</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> ans[i]); </div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> }</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> cout &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="l00178" name="l00178"></a><span class="lineno"> 178</span>}</div>
</div>
<div class="foldopen" id="foldopen00183" data-start="{" data-end="}">
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"><a class="line" href="../../df/d28/dsu__union__rank_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 183</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../df/d28/dsu__union__rank_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</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#ae7880ce913f3058a35ff106d5be9e243">test1</a>(); <span class="comment">// run 1st test case</span></div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</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="l00186" name="l00186"></a><span class="lineno"> 186</span> </div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span>}</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> <a href="../../d3/dae/dsu__path__compression_8cpp_source.html#l00034">dsu_path_compression.cpp:34</a></div></div>
<div class="ttc" id="aclassdsu_html_a126e3002a464e53cd54b07ba56482a72"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a126e3002a464e53cd54b07ba56482a72">dsu::dsu</a></div><div class="ttdeci">dsu(uint64_t n)</div><div class="ttdoc">constructor for initialising all data members</div><div class="ttdef"><b>Definition</b> <a href="#l00045">dsu_union_rank.cpp:45</a></div></div>
<div class="ttc" id="aclassdsu_html_a16851f78fe390fc1430905c83d6a2f1c"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">dsu::findSet</a></div><div class="ttdeci">uint64_t findSet(uint64_t i)</div><div class="ttdoc">Method to find the representative of the set to which i belongs to, T(n) = O(logN)</div><div class="ttdef"><b>Definition</b> <a href="#l00062">dsu_union_rank.cpp:62</a></div></div>
<div class="ttc" id="aclassdsu_html_a1ef0b0462a0dda63514f641cbb7dd8cb"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">dsu::p</a></div><div class="ttdeci">vector&lt; uint64_t &gt; p</div><div class="ttdoc">keeps track of the parent of ith element</div><div class="ttdef"><b>Definition</b> <a href="../../d3/dae/dsu__path__compression_8cpp_source.html#l00036">dsu_path_compression.cpp:36</a></div></div>
<div class="ttc" id="aclassdsu_html_a4bf54d33fba178998dbbe4c57f2e9429"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">dsu::depth</a></div><div class="ttdeci">vector&lt; uint64_t &gt; depth</div><div class="ttdoc">tracks the depth(rank) of i in the tree</div><div class="ttdef"><b>Definition</b> <a href="../../d3/dae/dsu__path__compression_8cpp_source.html#l00037">dsu_path_compression.cpp:37</a></div></div>
<div class="ttc" id="aclassdsu_html_a64d25c5986742f7c234ed449b2ff7303"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303">dsu::isSame</a></div><div class="ttdeci">bool isSame(uint64_t i, uint64_t j)</div><div class="ttdoc">A utility function which check whether i and j belongs to same set or not.</div><div class="ttdef"><b>Definition</b> <a href="../../d3/dae/dsu__path__compression_8cpp_source.html#l00124">dsu_path_compression.cpp:124</a></div></div>
<div class="ttc" id="aclassdsu_html_a81897528bdb53fd5e796d75d7dbc430f"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a81897528bdb53fd5e796d75d7dbc430f">dsu::unionSet</a></div><div class="ttdeci">void unionSet(uint64_t i, uint64_t j)</div><div class="ttdoc">Method that combines two disjoint sets to which i and j belongs to and make a single set having a com...</div><div class="ttdef"><b>Definition</b> <a href="#l00076">dsu_union_rank.cpp:76</a></div></div>
<div class="ttc" id="aclassdsu_html_ab8ee27083a3c2e2df80755165a2ec280"><div class="ttname"><a href="../../dd/d1f/classdsu.html#ab8ee27083a3c2e2df80755165a2ec280">dsu::getParents</a></div><div class="ttdeci">vector&lt; uint64_t &gt; getParents(uint64_t i)</div><div class="ttdoc">Method to print all the parents of i, or the path from i to representative.</div><div class="ttdef"><b>Definition</b> <a href="#l00120">dsu_union_rank.cpp:120</a></div></div>
<div class="ttc" id="aclassdsu_html_ac0dc3e17e49fe19b159b4ea4096d7b55"><div class="ttname"><a href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">dsu::setSize</a></div><div class="ttdeci">vector&lt; uint64_t &gt; setSize</div><div class="ttdoc">size of each chunk(set)</div><div class="ttdef"><b>Definition</b> <a href="../../d3/dae/dsu__path__compression_8cpp_source.html#l00038">dsu_path_compression.cpp:38</a></div></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> <a href="#l00158">dsu_union_rank.cpp:158</a></div></div>
<div class="ttc" id="adsu__union__rank_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../df/d28/dsu__union__rank_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00183">dsu_union_rank.cpp:183</a></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> <a href="#l00134">dsu_union_rank.cpp:134</a></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> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00036">matrix_exponentiation.cpp:36</a></div></div>
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