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<title>Algorithms_in_C++: data_structures/dsu_path_compression.cpp File Reference</title>
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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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@@ -129,7 +129,8 @@ Functions</h2></td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Disjoint-set-data_structure" target="_blank">DSU (Disjoint sets)</a> </p>
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<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>
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<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
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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>
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<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>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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@@ -152,15 +153,15 @@ Functions</h2></td></tr>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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<p >< number of items</p>
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<p >< object of class disjoint sets</p>
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<div class="fragment"><div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> {</div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> uint64_t n = 10; <span class="comment">///< number of items</span></div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); <span class="comment">///< object of class disjoint sets</span></div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> </div>
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<div class="line"><a id="l00209" name="l00209"></a><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>
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<div class="line"><a id="l00210" name="l00210"></a><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>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> </div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 205</span> {</div>
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<div class="line"><span class="lineno"> 206</span> uint64_t n = 10; <span class="comment">///< number of items</span></div>
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<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">///< object of class disjoint sets</span></div>
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<div class="line"><span class="lineno"> 208</span> </div>
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<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>
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<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>
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<div class="line"><span class="lineno"> 211</span> </div>
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<div class="line"><span class="lineno"> 212</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 213</span>}</div>
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<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>
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<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>
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<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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@@ -200,19 +201,19 @@ Here is the call graph for this function:</div>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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<p >< number of items</p>
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<p >< object of class disjoint sets</p>
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<div class="fragment"><div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> {</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="comment">// the minimum, maximum, and size of the set</span></div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> uint64_t n = 10; <span class="comment">///< number of items</span></div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); <span class="comment">///< object of class disjoint sets</span></div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="comment">// set 1</span></div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> d.UnionSet(1, 2); <span class="comment">// performs union operation on 1 and 2</span></div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> d.UnionSet(1, 4); <span class="comment">// performs union operation on 1 and 4</span></div>
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<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/container/vector.html">vector<uint64_t></a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {1, 4, 3};</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="keywordflow">for</span> (uint64_t i = 0; i < <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
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<div class="line"><a id="l00178" name="l00178"></a><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>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> }</div>
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<div class="line"><a id="l00180" name="l00180"></a><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> << <span class="stringliteral">"1st test passed!"</span> << <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 169</span> {</div>
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<div class="line"><span class="lineno"> 170</span> <span class="comment">// the minimum, maximum, and size of the set</span></div>
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<div class="line"><span class="lineno"> 171</span> uint64_t n = 10; <span class="comment">///< number of items</span></div>
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<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">///< object of class disjoint sets</span></div>
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<div class="line"><span class="lineno"> 173</span> <span class="comment">// set 1</span></div>
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<div class="line"><span class="lineno"> 174</span> d.UnionSet(1, 2); <span class="comment">// performs union operation on 1 and 2</span></div>
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<div class="line"><span class="lineno"> 175</span> d.UnionSet(1, 4); <span class="comment">// performs union operation on 1 and 4</span></div>
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<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<uint64_t></a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {1, 4, 3};</div>
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<div class="line"><span class="lineno"> 177</span> <span class="keywordflow">for</span> (uint64_t i = 0; i < <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
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<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>
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<div class="line"><span class="lineno"> 179</span> }</div>
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<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> << <span class="stringliteral">"1st test passed!"</span> << <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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<div class="line"><span class="lineno"> 181</span>}</div>
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<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>
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<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>
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<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>
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@@ -253,20 +254,20 @@ Here is the call graph for this function:</div>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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<p >< number of items</p>
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<p >< object of class disjoint sets</p>
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<div class="fragment"><div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> {</div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="comment">// the minimum, maximum, and size of the set</span></div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> uint64_t n = 10; <span class="comment">///< number of items</span></div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); <span class="comment">///< object of class disjoint sets</span></div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="comment">// set 1</span></div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> d.UnionSet(3, 5);</div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> d.UnionSet(5, 6);</div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> d.UnionSet(5, 7);</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<uint64_t></a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {3, 7, 4};</div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="keywordflow">for</span> (uint64_t i = 0; i < <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
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<div class="line"><a id="l00196" name="l00196"></a><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>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> }</div>
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<div class="line"><a id="l00198" name="l00198"></a><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> << <span class="stringliteral">"2nd test passed!"</span> << <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 186</span> {</div>
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<div class="line"><span class="lineno"> 187</span> <span class="comment">// the minimum, maximum, and size of the set</span></div>
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<div class="line"><span class="lineno"> 188</span> uint64_t n = 10; <span class="comment">///< number of items</span></div>
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<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">///< object of class disjoint sets</span></div>
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<div class="line"><span class="lineno"> 190</span> <span class="comment">// set 1</span></div>
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<div class="line"><span class="lineno"> 191</span> d.UnionSet(3, 5);</div>
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<div class="line"><span class="lineno"> 192</span> d.UnionSet(5, 6);</div>
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<div class="line"><span class="lineno"> 193</span> d.UnionSet(5, 7);</div>
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<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<uint64_t></a> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = {3, 7, 4};</div>
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<div class="line"><span class="lineno"> 195</span> <span class="keywordflow">for</span> (uint64_t i = 0; i < <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>.size(); i++) {</div>
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<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>
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<div class="line"><span class="lineno"> 197</span> }</div>
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<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> << <span class="stringliteral">"2nd test passed!"</span> << <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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<div class="line"><span class="lineno"> 199</span>}</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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@@ -282,7 +283,7 @@ Here is the call graph for this function:</div>
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<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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<ul>
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<li class="navelem"><a class="el" href="../../dir_2e746e9d06bf2d8ff842208bcc6ebcfc.html">data_structures</a></li><li class="navelem"><a class="el" href="../../d3/dae/dsu__path__compression_8cpp.html">dsu_path_compression.cpp</a></li>
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<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
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