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<p>A balanced binary search tree (BST) on the basis of binary search tree and heap: the <a href="https://en.wikipedia.org/wiki/Treap" target="_blank">Treap</a> algorithm implementation.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;array&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
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Include dependency graph for treap.cpp:</div>
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<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Struct representation of the treap. <a href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#details">More...</a><br /></td></tr>
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Namespaces</h2></td></tr>
<tr class="memitem:d5/d3c/namespacedata__structures"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d3c/namespacedata__structures.html">data_structures</a></td></tr>
<tr class="memdesc:d5/d3c/namespacedata__structures"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/dd2/treap_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <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="../../d0/dd2/treap_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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Variables</h2></td></tr>
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const int&#160;</td><td class="memItemRight" valign="bottom"><b>data_structures::treap::maxNode</b> = 1e5 + 5</td></tr>
<tr class="memdesc:ad939ec178d0069aeea14b7d6d7d12099"><td class="mdescLeft">&#160;</td><td class="mdescRight">maximum number of nodes <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>A balanced binary search tree (BST) on the basis of binary search tree and heap: the <a href="https://en.wikipedia.org/wiki/Treap" target="_blank">Treap</a> algorithm implementation. </p>
<p>Implementation of the treap data structre</p>
<p>Support operations including insert, erase, and query (the rank of specified element or the element ranked x) as the same as BST</p>
<p>But these operations take O(log N) time, since treap keeps property of heap using rotate operation, and the desired depth of the tree is O(log N). There's very little chance that it will degenerate into a chain like BST</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/fgmn" target="_blank">Kairao ZHENG</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 256</span> {</div>
<div class="line"><span class="lineno"> 257</span> <a class="code hl_function" href="../../d0/dd2/treap_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 258</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 259</span>}</div>
<div class="ttc" id="atreap_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d0/dd2/treap_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> treap.cpp:230</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">static void test </td>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p>&lt; Treap object instance</p>
<div class="fragment"><div class="line"><span class="lineno"> 230</span> {</div>
<div class="line"><span class="lineno"> 231</span> <a class="code hl_struct" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html">data_structures::treap::Treap</a> mTreap; <span class="comment">///&lt; Treap object instance</span></div>
<div class="line"><span class="lineno"> 232</span> </div>
<div class="line"><span class="lineno"> 233</span> mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a5e884d2686aff501ef589b0d1185492f">insert</a>(1);</div>
<div class="line"><span class="lineno"> 234</span> mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a5e884d2686aff501ef589b0d1185492f">insert</a>(2);</div>
<div class="line"><span class="lineno"> 235</span> mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a5e884d2686aff501ef589b0d1185492f">insert</a>(3);</div>
<div class="line"><span class="lineno"> 236</span> assert(mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#ab2db3ad3aecc240011e0c8b8604d2c69">get_k_th</a>(2) == 2);</div>
<div class="line"><span class="lineno"> 237</span> mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a5e884d2686aff501ef589b0d1185492f">insert</a>(4);</div>
<div class="line"><span class="lineno"> 238</span> mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a5e884d2686aff501ef589b0d1185492f">insert</a>(5);</div>
<div class="line"><span class="lineno"> 239</span> mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a5e884d2686aff501ef589b0d1185492f">insert</a>(6);</div>
<div class="line"><span class="lineno"> 240</span> assert(mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a767b28f9911fc32b8462862be058a4a4">get_next</a>(4) == 5);</div>
<div class="line"><span class="lineno"> 241</span> mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a5e884d2686aff501ef589b0d1185492f">insert</a>(7);</div>
<div class="line"><span class="lineno"> 242</span> assert(mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#ab8b9899f22070cfa01db5bf874296126">get_predecessor</a>(7) == 6);</div>
<div class="line"><span class="lineno"> 243</span> mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a9ea2becd904e2e7d22f23a001b444469">erase</a>(4);</div>
<div class="line"><span class="lineno"> 244</span> assert(mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#ab2db3ad3aecc240011e0c8b8604d2c69">get_k_th</a>(4) == 5);</div>
<div class="line"><span class="lineno"> 245</span> assert(mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#ac94e9d69305940f6d8804031455af039">get_rank</a>(5) == 4);</div>
<div class="line"><span class="lineno"> 246</span> mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a5e884d2686aff501ef589b0d1185492f">insert</a>(10);</div>
<div class="line"><span class="lineno"> 247</span> assert(mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#ac94e9d69305940f6d8804031455af039">get_rank</a>(10) == 7);</div>
<div class="line"><span class="lineno"> 248</span> assert(mTreap.<a class="code hl_function" href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#ab8b9899f22070cfa01db5bf874296126">get_predecessor</a>(10) == 7);</div>
<div class="line"><span class="lineno"> 249</span> </div>
<div class="line"><span class="lineno"> 250</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests have successfully passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 251</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="astructdata__structures_1_1treap_1_1_treap_html"><div class="ttname"><a href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html">data_structures::treap::Treap</a></div><div class="ttdoc">Struct representation of the treap.</div><div class="ttdef"><b>Definition</b> treap.cpp:39</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_a5e884d2686aff501ef589b0d1185492f"><div class="ttname"><a href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a5e884d2686aff501ef589b0d1185492f">data_structures::treap::Treap::insert</a></div><div class="ttdeci">void insert(int k)</div><div class="ttdoc">Insert element (External method)</div><div class="ttdef"><b>Definition</b> treap.cpp:204</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_a767b28f9911fc32b8462862be058a4a4"><div class="ttname"><a href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a767b28f9911fc32b8462862be058a4a4">data_structures::treap::Treap::get_next</a></div><div class="ttdeci">int get_next(int k)</div><div class="ttdoc">Get the successor node of element k.</div><div class="ttdef"><b>Definition</b> treap.cpp:189</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_a9ea2becd904e2e7d22f23a001b444469"><div class="ttname"><a href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#a9ea2becd904e2e7d22f23a001b444469">data_structures::treap::Treap::erase</a></div><div class="ttdeci">void erase(int k)</div><div class="ttdoc">Erase element (External method)</div><div class="ttdef"><b>Definition</b> treap.cpp:209</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_ab2db3ad3aecc240011e0c8b8604d2c69"><div class="ttname"><a href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#ab2db3ad3aecc240011e0c8b8604d2c69">data_structures::treap::Treap::get_k_th</a></div><div class="ttdeci">int get_k_th(int k)</div><div class="ttdoc">Get the KTH largest value (External method)</div><div class="ttdef"><b>Definition</b> treap.cpp:215</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_ab8b9899f22070cfa01db5bf874296126"><div class="ttname"><a href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#ab8b9899f22070cfa01db5bf874296126">data_structures::treap::Treap::get_predecessor</a></div><div class="ttdeci">int get_predecessor(int k)</div><div class="ttdoc">Get the predecessor node of element k.</div><div class="ttdef"><b>Definition</b> treap.cpp:173</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_ac94e9d69305940f6d8804031455af039"><div class="ttname"><a href="../../d5/d95/structdata__structures_1_1treap_1_1_treap.html#ac94e9d69305940f6d8804031455af039">data_structures::treap::Treap::get_rank</a></div><div class="ttdeci">int get_rank(int k)</div><div class="ttdoc">Get the rank of specified element (External method)</div><div class="ttdef"><b>Definition</b> treap.cpp:221</div></div>
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