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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;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;queue&gt;</code><br />
<code>#include &lt;utility&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for lowest_common_ancestor.cpp:</div>
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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>
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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>
<div class="fragment"><div class="line"><span class="lineno"> 255</span> {</div>
<div class="line"><span class="lineno"> 256</span> <a class="code hl_function" href="../../de/dde/lowest__common__ancestor_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>();</div>
<div class="line"><span class="lineno"> 257</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 258</span>}</div>
<div class="ttc" id="alowest__common__ancestor_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="../../de/dde/lowest__common__ancestor_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdef"><b>Definition:</b> lowest_common_ancestor.cpp:234</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">&#9670;&nbsp;</a></span>tests()</h2>
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<p >Unit tests </p><dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
<pre class="fragment"> _ 3 _
/ | \
1 6 4
</pre><p> / | / \ \ 7 5 2 8 0 | 9</p>
<div class="fragment"><div class="line"><span class="lineno"> 234</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 235</span><span class="comment"> /**</span></div>
<div class="line"><span class="lineno"> 236</span><span class="comment"> * _ 3 _</span></div>
<div class="line"><span class="lineno"> 237</span><span class="comment"> * / | \</span></div>
<div class="line"><span class="lineno"> 238</span><span class="comment"> * 1 6 4</span></div>
<div class="line"><span class="lineno"> 239</span><span class="comment"> * / | / \ \</span></div>
<div class="line"><span class="lineno"> 240</span><span class="comment"> * 7 5 2 8 0</span></div>
<div class="line"><span class="lineno"> 241</span><span class="comment"> * |</span></div>
<div class="line"><span class="lineno"> 242</span><span class="comment"> * 9</span></div>
<div class="line"><span class="lineno"> 243</span><span class="comment"> */</span></div>
<div class="line"><span class="lineno"> 244</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::pair&lt;int, int&gt;</a> &gt; edges = {</div>
<div class="line"><span class="lineno"> 245</span> {7, 1}, {1, 5}, {1, 3}, {3, 6}, {6, 2}, {2, 9}, {6, 8}, {4, 3}, {0, 4}};</div>
<div class="line"><span class="lineno"> 246</span> <a class="code hl_class" href="../../d0/d58/classgraph_1_1_rooted_tree.html">graph::RootedTree</a> t(edges, 3);</div>
<div class="line"><span class="lineno"> 247</span> <a class="code hl_class" href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html">graph::LowestCommonAncestor</a> lca(t);</div>
<div class="line"><span class="lineno"> 248</span> assert(lca.lowest_common_ancestor(7, 4) == 3);</div>
<div class="line"><span class="lineno"> 249</span> assert(lca.lowest_common_ancestor(9, 6) == 6);</div>
<div class="line"><span class="lineno"> 250</span> assert(lca.lowest_common_ancestor(0, 0) == 0);</div>
<div class="line"><span class="lineno"> 251</span> assert(lca.lowest_common_ancestor(8, 2) == 6);</div>
<div class="line"><span class="lineno"> 252</span>}</div>
<div class="ttc" id="aclassgraph_1_1_lowest_common_ancestor_html"><div class="ttname"><a href="../../d9/d23/classgraph_1_1_lowest_common_ancestor.html">graph::LowestCommonAncestor</a></div><div class="ttdef"><b>Definition:</b> lowest_common_ancestor.cpp:145</div></div>
<div class="ttc" id="aclassgraph_1_1_rooted_tree_html"><div class="ttname"><a href="../../d0/d58/classgraph_1_1_rooted_tree.html">graph::RootedTree</a></div><div class="ttdef"><b>Definition:</b> lowest_common_ancestor.cpp:84</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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