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<p><a href="https://en.wikipedia.org/wiki/Disjoint-set-data_structure" target="_blank">DSU (Disjoint sets)</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;vector&gt;</code><br />
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Include dependency graph for dsu_path_compression.cpp:</div>
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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>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Disjoint sets union data structure, class based representation. <a href="../../dd/d1f/classdsu.html#details">More...</a><br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:ae7880ce913f3058a35ff106d5be9e243"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/dae/dsu__path__compression_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a> ()</td></tr>
<tr class="memdesc:ae7880ce913f3058a35ff106d5be9e243"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations, 1st test. <a href="../../d3/dae/dsu__path__compression_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">More...</a><br /></td></tr>
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<tr class="memitem:a45d94ead4cf4e1ff9f87c38bc99f59ae"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/dae/dsu__path__compression_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a> ()</td></tr>
<tr class="memdesc:a45d94ead4cf4e1ff9f87c38bc99f59ae"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-implementations, 2nd test. <a href="../../d3/dae/dsu__path__compression_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">More...</a><br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/dae/dsu__path__compression_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d3/dae/dsu__path__compression_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Disjoint-set-data_structure" target="_blank">DSU (Disjoint sets)</a> </p>
<p >It is a very powerful data structure that 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) get_max(i),get_min(i) : returns the maximum and minimum Below is the class-based approach which uses the heuristic of path compression. Using path compression in findSet(i),we are able to get to the representative of i in O(1) time. </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="../../df/d28/dsu__union__rank_8cpp.html" title="DSU (Disjoint sets)">dsu_union_rank.cpp</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p >&lt; number of items</p>
<p >&lt; object of class disjoint sets</p>
<div class="fragment"><div class="line"><span class="lineno"> 205</span> {</div>
<div class="line"><span class="lineno"> 206</span> uint64_t n = 10; <span class="comment">///&lt; number of items</span></div>
<div class="line"><span class="lineno"> 207</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"> 208</span> </div>
<div class="line"><span class="lineno"> 209</span> <a class="code hl_function" href="../../d3/dae/dsu__path__compression_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>(); <span class="comment">// run 1st test case</span></div>
<div class="line"><span class="lineno"> 210</span> <a class="code hl_function" href="../../d3/dae/dsu__path__compression_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>(); <span class="comment">// run 2nd test case</span></div>
<div class="line"><span class="lineno"> 211</span> </div>
<div class="line"><span class="lineno"> 212</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 213</span>}</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="adsu__path__compression_8cpp_html_a45d94ead4cf4e1ff9f87c38bc99f59ae"><div class="ttname"><a href="../../d3/dae/dsu__path__compression_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_path_compression.cpp:186</div></div>
<div class="ttc" id="adsu__path__compression_8cpp_html_ae7880ce913f3058a35ff106d5be9e243"><div class="ttname"><a href="../../d3/dae/dsu__path__compression_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a></div><div class="ttdeci">static void test1()</div><div class="ttdoc">Self-test implementations, 1st test.</div><div class="ttdef"><b>Definition:</b> dsu_path_compression.cpp:169</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae7880ce913f3058a35ff106d5be9e243">&#9670;&nbsp;</a></span>test1()</h2>
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<p>Self-test implementations, 1st test. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p >&lt; number of items</p>
<p >&lt; object of class disjoint sets</p>
<div class="fragment"><div class="line"><span class="lineno"> 169</span> {</div>
<div class="line"><span class="lineno"> 170</span> <span class="comment">// the minimum, maximum, and size of the set</span></div>
<div class="line"><span class="lineno"> 171</span> uint64_t n = 10; <span class="comment">///&lt; number of items</span></div>
<div class="line"><span class="lineno"> 172</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"> 173</span> <span class="comment">// set 1</span></div>
<div class="line"><span class="lineno"> 174</span> d.UnionSet(1, 2); <span class="comment">// performs union operation on 1 and 2</span></div>
<div class="line"><span class="lineno"> 175</span> d.UnionSet(1, 4); <span class="comment">// performs union operation on 1 and 4</span></div>
<div class="line"><span class="lineno"> 176</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> = {1, 4, 3};</div>
<div class="line"><span class="lineno"> 177</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"> 178</span> assert(d.get(4).at(i) == <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"> 179</span> }</div>
<div class="line"><span class="lineno"> 180</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"> 181</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="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="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</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="#a45d94ead4cf4e1ff9f87c38bc99f59ae">&#9670;&nbsp;</a></span>test2()</h2>
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<p>Self-implementations, 2nd test. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p >&lt; number of items</p>
<p >&lt; object of class disjoint sets</p>
<div class="fragment"><div class="line"><span class="lineno"> 186</span> {</div>
<div class="line"><span class="lineno"> 187</span> <span class="comment">// the minimum, maximum, and size of the set</span></div>
<div class="line"><span class="lineno"> 188</span> uint64_t n = 10; <span class="comment">///&lt; number of items</span></div>
<div class="line"><span class="lineno"> 189</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"> 190</span> <span class="comment">// set 1</span></div>
<div class="line"><span class="lineno"> 191</span> d.UnionSet(3, 5);</div>
<div class="line"><span class="lineno"> 192</span> d.UnionSet(5, 6);</div>
<div class="line"><span class="lineno"> 193</span> d.UnionSet(5, 7);</div>
<div class="line"><span class="lineno"> 194</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> = {3, 7, 4};</div>
<div class="line"><span class="lineno"> 195</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"> 196</span> assert(d.get(3).at(i) == <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"> 197</span> }</div>
<div class="line"><span class="lineno"> 198</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"> 199</span>}</div>
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