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<tr class="memdesc:a80825a4fd4c41860b689d253dd2c8e93"><td class="mdescLeft">&#160;</td><td class="mdescRight">Stores the tree and precomputs "up lifts". <br /></td></tr>
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<tr class="memitem:a60151e19512b48cc0b14ea121df00488" id="r_a60151e19512b48cc0b14ea121df00488"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a60151e19512b48cc0b14ea121df00488">lowest_common_ancestor</a> (int u, int v) const</td></tr>
<tr class="memdesc:a60151e19512b48cc0b14ea121df00488"><td class="mdescLeft">&#160;</td><td class="mdescRight">Query the structure to find the lowest common ancestor. Assumes that the provided numbers are valid indices of vertices. Iterativelly modifies ("lifts") u an v until it finnds their lowest common ancestor. <br /></td></tr>
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const <a class="el" href="../../d0/d58/classgraph_1_1_rooted_tree.html">RootedTree</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><b>tree</b></td></tr>
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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>up</b></td></tr>
<tr class="memdesc:a46d10f669791e3da9a4809bd8ff8d3ad"><td class="mdescLeft">&#160;</td><td class="mdescRight">for every vertex stores a list of its ancestors by powers of two For each vertex, the first element of the corresponding list contains the index of its parent. The i-th element of the list is an index of the (2^i)-th ancestor of the vertex. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>A structure that holds a rooted tree and allow for effecient queries of the lowest common ancestor of two given vertices in the tree. </p>
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<h2 class="memtitle"><span class="permalink"><a href="#a80825a4fd4c41860b689d253dd2c8e93">&#9670;&#160;</a></span>LowestCommonAncestor()</h2>
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<td class="memname">graph::LowestCommonAncestor::LowestCommonAncestor </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="../../d0/d58/classgraph_1_1_rooted_tree.html">RootedTree</a> &amp;</td> <td class="paramname"><span class="paramname"><em>tree_</em></span></td><td>)</td>
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<p>Stores the tree and precomputs "up lifts". </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">tree_</td><td>rooted tree. </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 151</span> : tree(tree_) {</div>
<div class="line"><span class="lineno"> 152</span> <a class="code hl_function" href="#a42589cc39d6bbff6c997152f1b96e356">populate_up</a>();</div>
<div class="line"><span class="lineno"> 153</span> }</div>
<div class="ttc" id="aclassgraph_1_1_lowest_common_ancestor_html_a42589cc39d6bbff6c997152f1b96e356"><div class="ttname"><a href="#a42589cc39d6bbff6c997152f1b96e356">graph::LowestCommonAncestor::populate_up</a></div><div class="ttdeci">void populate_up()</div><div class="ttdef"><b>Definition</b> lowest_common_ancestor.cpp:212</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a60151e19512b48cc0b14ea121df00488">&#9670;&#160;</a></span>lowest_common_ancestor()</h2>
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<td class="memname">int graph::LowestCommonAncestor::lowest_common_ancestor </td>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>u</em></span>, </td>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>v</em></span>&#160;) const</td>
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<p>Query the structure to find the lowest common ancestor. Assumes that the provided numbers are valid indices of vertices. Iterativelly modifies ("lifts") u an v until it finnds their lowest common ancestor. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">u</td><td>index of one of the queried vertex </td></tr>
<tr><td class="paramname">v</td><td>index of the other queried vertex </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>index of the vertex which is the lowet common ancestor of u and v </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 164</span> {</div>
<div class="line"><span class="lineno"> 165</span> <span class="comment">// Ensure u is the deeper (higher level) of the two vertices</span></div>
<div class="line"><span class="lineno"> 166</span> <span class="keywordflow">if</span> (tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[v] &gt; tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[u]) {</div>
<div class="line"><span class="lineno"> 167</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(u, v);</div>
<div class="line"><span class="lineno"> 168</span> }</div>
<div class="line"><span class="lineno"> 169</span> </div>
<div class="line"><span class="lineno"> 170</span> <span class="comment">// &quot;Lift&quot; u to the same level as v.</span></div>
<div class="line"><span class="lineno"> 171</span> <span class="keywordtype">int</span> level_diff = tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[u] - tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[v];</div>
<div class="line"><span class="lineno"> 172</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; (1 &lt;&lt; i) &lt;= level_diff; ++i) {</div>
<div class="line"><span class="lineno"> 173</span> <span class="keywordflow">if</span> (level_diff &amp; (1 &lt;&lt; i)) {</div>
<div class="line"><span class="lineno"> 174</span> u = <a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][i];</div>
<div class="line"><span class="lineno"> 175</span> }</div>
<div class="line"><span class="lineno"> 176</span> }</div>
<div class="line"><span class="lineno"> 177</span> assert(tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[u] == tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">level</a>[v]);</div>
<div class="line"><span class="lineno"> 178</span> </div>
<div class="line"><span class="lineno"> 179</span> <span class="keywordflow">if</span> (u == v) {</div>
<div class="line"><span class="lineno"> 180</span> <span class="keywordflow">return</span> u;</div>
<div class="line"><span class="lineno"> 181</span> }</div>
<div class="line"><span class="lineno"> 182</span> </div>
<div class="line"><span class="lineno"> 183</span> <span class="comment">// &quot;Lift&quot; u and v to their 2^i th ancestor if they are different</span></div>
<div class="line"><span class="lineno"> 184</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u].size()) - 1; i &gt;= 0; --i) {</div>
<div class="line"><span class="lineno"> 185</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][i] != <a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[v][i]) {</div>
<div class="line"><span class="lineno"> 186</span> u = <a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][i];</div>
<div class="line"><span class="lineno"> 187</span> v = <a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[v][i];</div>
<div class="line"><span class="lineno"> 188</span> }</div>
<div class="line"><span class="lineno"> 189</span> }</div>
<div class="line"><span class="lineno"> 190</span> </div>
<div class="line"><span class="lineno"> 191</span> <span class="comment">// As we regressed u an v such that they cannot further be lifted so</span></div>
<div class="line"><span class="lineno"> 192</span> <span class="comment">// that their ancestor would be different, the only logical</span></div>
<div class="line"><span class="lineno"> 193</span> <span class="comment">// consequence is that their parent is the sought answer.</span></div>
<div class="line"><span class="lineno"> 194</span> assert(<a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][0] == <a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[v][0]);</div>
<div class="line"><span class="lineno"> 195</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[u][0];</div>
<div class="line"><span class="lineno"> 196</span> }</div>
<div class="ttc" id="aclassgraph_1_1_lowest_common_ancestor_html_a46d10f669791e3da9a4809bd8ff8d3ad"><div class="ttname"><a href="#a46d10f669791e3da9a4809bd8ff8d3ad">graph::LowestCommonAncestor::up</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; int &gt; &gt; up</div><div class="ttdoc">for every vertex stores a list of its ancestors by powers of two For each vertex, the first element o...</div><div class="ttdef"><b>Definition</b> lowest_common_ancestor.cpp:206</div></div>
<div class="ttc" id="aclassgraph_1_1_rooted_tree_html_a2ee3ad1161ac2532da30c3e22c265ad3"><div class="ttname"><a href="../../d0/d58/classgraph_1_1_rooted_tree.html#a2ee3ad1161ac2532da30c3e22c265ad3">graph::RootedTree::level</a></div><div class="ttdeci">std::vector&lt; int &gt; level</div><div class="ttdoc">Stores the distance from the root.</div><div class="ttdef"><b>Definition</b> lowest_common_ancestor.cpp:106</div></div>
<div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a42589cc39d6bbff6c997152f1b96e356">&#9670;&#160;</a></span>populate_up()</h2>
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<td class="memname">void graph::LowestCommonAncestor::populate_up </td>
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<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p>Populate the "up" structure. See above. </p>
<div class="fragment"><div class="line"><span class="lineno"> 212</span> {</div>
<div class="line"><span class="lineno"> 213</span> <a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/resize.html">resize</a>(tree.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a8930d1470d132b19e430d1c71f94c904">number_of_vertices</a>());</div>
<div class="line"><span class="lineno"> 214</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> vertex = 0; vertex &lt; tree.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a8930d1470d132b19e430d1c71f94c904">number_of_vertices</a>(); ++vertex) {</div>
<div class="line"><span class="lineno"> 215</span> <a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[vertex].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(tree.<a class="code hl_variable" href="../../d0/d58/classgraph_1_1_rooted_tree.html#a3831583a91914988897a4cc8748fda43">parent</a>[vertex]);</div>
<div class="line"><span class="lineno"> 216</span> }</div>
<div class="line"><span class="lineno"> 217</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> level = 0; (1 &lt;&lt; level) &lt; tree.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a8930d1470d132b19e430d1c71f94c904">number_of_vertices</a>(); ++level) {</div>
<div class="line"><span class="lineno"> 218</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> vertex = 0; vertex &lt; tree.<a class="code hl_function" href="../../dc/d61/classgraph_1_1_graph.html#a8930d1470d132b19e430d1c71f94c904">number_of_vertices</a>(); ++vertex) {</div>
<div class="line"><span class="lineno"> 219</span> <span class="comment">// up[vertex][level + 1] = 2^(level + 1) th ancestor of vertex =</span></div>
<div class="line"><span class="lineno"> 220</span> <span class="comment">// = 2^level th ancestor of 2^level th ancestor of vertex =</span></div>
<div class="line"><span class="lineno"> 221</span> <span class="comment">// = 2^level th ancestor of up[vertex][level]</span></div>
<div class="line"><span class="lineno"> 222</span> <a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[vertex].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[<a class="code hl_variable" href="#a46d10f669791e3da9a4809bd8ff8d3ad">up</a>[vertex][level]][level]);</div>
<div class="line"><span class="lineno"> 223</span> }</div>
<div class="line"><span class="lineno"> 224</span> }</div>
<div class="line"><span class="lineno"> 225</span> }</div>
<div class="ttc" id="aclassgraph_1_1_graph_html_a8930d1470d132b19e430d1c71f94c904"><div class="ttname"><a href="../../dc/d61/classgraph_1_1_graph.html#a8930d1470d132b19e430d1c71f94c904">graph::Graph::number_of_vertices</a></div><div class="ttdeci">int number_of_vertices() const</div><div class="ttdef"><b>Definition</b> lowest_common_ancestor.cpp:74</div></div>
<div class="ttc" id="aclassgraph_1_1_rooted_tree_html_a3831583a91914988897a4cc8748fda43"><div class="ttname"><a href="../../d0/d58/classgraph_1_1_rooted_tree.html#a3831583a91914988897a4cc8748fda43">graph::RootedTree::parent</a></div><div class="ttdeci">std::vector&lt; int &gt; parent</div><div class="ttdoc">Stores parent of every vertex and for root its own index. The root is technically not its own parent,...</div><div class="ttdef"><b>Definition</b> lowest_common_ancestor.cpp:104</div></div>
<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
<div class="ttc" id="aresize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/resize.html">std::vector::resize</a></div><div class="ttdeci">T resize(T... args)</div></div>
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