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<p>Data structure for finding the lowest common ancestor of two vertices in a rooted tree using binary lifting.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;utility&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
<code>#include &lt;queue&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
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<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dde/lowest__common__ancestor_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Data structure for finding the lowest common ancestor of two vertices in a rooted tree using binary lifting. </p>
<p>Algorithm: <a href="https://cp-algorithms.com/graph/lca_binary_lifting.html">https://cp-algorithms.com/graph/lca_binary_lifting.html</a></p>
<p>Complexity:</p><ul>
<li>Precomputation: \(O(N \log N)\) where \(N\) is the number of vertices in the tree</li>
<li>Query: \(O(\log N)\)</li>
<li>Space: \(O(N \log N)\)</li>
</ul>
<p>Example: <br />
Tree: </p><pre>
_ 3 _
/ | \
1 6 4
/ | / \ \
7 5 2 8 0
|
9
</pre><p><br />
lowest_common_ancestor(7, 4) = 3 <br />
lowest_common_ancestor(9, 6) = 6 <br />
lowest_common_ancestor(0, 0) = 0 <br />
lowest_common_ancestor(8, 2) = 6</p>
<p>The query is symmetrical, therefore lowest_common_ancestor(x, y) = lowest_common_ancestor(y, x) </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main function </p>
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<p>Unit tests @rerturns none </p>
<pre class="fragment"> _ 3 _
/ | \
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</pre><p> / | / \ \ 7 5 2 8 0 | 9</p>
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