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<p>Struct representation of the treap.
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<tr class="memdesc:ab2db3ad3aecc240011e0c8b8604d2c69"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the KTH largest value (External method) <br /></td></tr>
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<tr class="memdesc:ac94e9d69305940f6d8804031455af039"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the rank of specified element (External method) <br /></td></tr>
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</table><table class="memberdecls">
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Public Attributes</h2></td></tr>
<tr class="memitem:a3081969b2714a8101f7df28b1ce5ed2c" id="r_a3081969b2714a8101f7df28b1ce5ed2c"><td class="memItemLeft" align="right" valign="top"><a id="a3081969b2714a8101f7df28b1ce5ed2c" name="a3081969b2714a8101f7df28b1ce5ed2c"></a>
int&#160;</td><td class="memItemRight" valign="bottom"><b>root</b> = 0</td></tr>
<tr class="memdesc:a3081969b2714a8101f7df28b1ce5ed2c"><td class="mdescLeft">&#160;</td><td class="mdescRight">root of the treap <br /></td></tr>
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<tr class="memitem:a1ab082fe0aa95a238bbbc68ab6a72425" id="r_a1ab082fe0aa95a238bbbc68ab6a72425"><td class="memItemLeft" align="right" valign="top"><a id="a1ab082fe0aa95a238bbbc68ab6a72425" name="a1ab082fe0aa95a238bbbc68ab6a72425"></a>
int&#160;</td><td class="memItemRight" valign="bottom"><b>treapCnt</b> = 0</td></tr>
<tr class="memdesc:a1ab082fe0aa95a238bbbc68ab6a72425"><td class="mdescLeft">&#160;</td><td class="mdescRight">Total number of current nodes in the treap. <br /></td></tr>
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<tr class="memitem:a32db3ba3b2630943faacd27b2ecd1b04" id="r_a32db3ba3b2630943faacd27b2ecd1b04"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, <a class="el" href="../../dd/d2e/namespacedata__structures_1_1treap.html#ad939ec178d0069aeea14b7d6d7d12099">maxNode</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a> = {}</td></tr>
<tr class="memdesc:a32db3ba3b2630943faacd27b2ecd1b04"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a class="el" href="../../d9/d49/structdata__structures_1_1_node.html">Node</a> identifier. <br /></td></tr>
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<tr class="memitem:a8be70f0a25e53e870e97d8d23968d723" id="r_a8be70f0a25e53e870e97d8d23968d723"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, <a class="el" href="../../dd/d2e/namespacedata__structures_1_1treap.html#ad939ec178d0069aeea14b7d6d7d12099">maxNode</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a8be70f0a25e53e870e97d8d23968d723">priority</a> = {}</td></tr>
<tr class="memdesc:a8be70f0a25e53e870e97d8d23968d723"><td class="mdescLeft">&#160;</td><td class="mdescRight">Random priority. <br /></td></tr>
<tr class="separator:a8be70f0a25e53e870e97d8d23968d723"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab99f68b79e1c4ff0f1cd6f2f0b6a545f" id="r_ab99f68b79e1c4ff0f1cd6f2f0b6a545f"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, 2 &gt;, <a class="el" href="../../dd/d2e/namespacedata__structures_1_1treap.html#ad939ec178d0069aeea14b7d6d7d12099">maxNode</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a></td></tr>
<tr class="separator:ab99f68b79e1c4ff0f1cd6f2f0b6a545f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af7e6c6620ab32bc96633d101245fa919" id="r_af7e6c6620ab32bc96633d101245fa919"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, <a class="el" href="../../dd/d2e/namespacedata__structures_1_1treap.html#ad939ec178d0069aeea14b7d6d7d12099">maxNode</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#af7e6c6620ab32bc96633d101245fa919">cnt</a></td></tr>
<tr class="memdesc:af7e6c6620ab32bc96633d101245fa919"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maintains the subtree size for ranking query. <br /></td></tr>
<tr class="separator:af7e6c6620ab32bc96633d101245fa919"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af5f0b8263339485989f8a02ae026114c" id="r_af5f0b8263339485989f8a02ae026114c"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, <a class="el" href="../../dd/d2e/namespacedata__structures_1_1treap.html#ad939ec178d0069aeea14b7d6d7d12099">maxNode</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#af5f0b8263339485989f8a02ae026114c">size</a> = {}</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Struct representation of the treap. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="a5d200493aeaa02a269f6b6deda39a683" name="a5d200493aeaa02a269f6b6deda39a683"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a5d200493aeaa02a269f6b6deda39a683">&#9670;&#160;</a></span>Treap()</h2>
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<td class="memname">data_structures::treap::Treap::Treap </td>
<td>(</td>
<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p>Initialization. </p>
<div class="fragment"><div class="line"><span class="lineno"> 54</span> : <a class="code hl_variable" href="#a1ab082fe0aa95a238bbbc68ab6a72425">treapCnt</a>(1) {</div>
<div class="line"><span class="lineno"> 55</span> <a class="code hl_variable" href="#a8be70f0a25e53e870e97d8d23968d723">priority</a>[0] = INT32_MAX;</div>
<div class="line"><span class="lineno"> 56</span> <a class="code hl_variable" href="#af5f0b8263339485989f8a02ae026114c">size</a>[0] = 0;</div>
<div class="line"><span class="lineno"> 57</span> }</div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_a1ab082fe0aa95a238bbbc68ab6a72425"><div class="ttname"><a href="#a1ab082fe0aa95a238bbbc68ab6a72425">data_structures::treap::Treap::treapCnt</a></div><div class="ttdeci">int treapCnt</div><div class="ttdoc">Total number of current nodes in the treap.</div><div class="ttdef"><b>Definition</b> treap.cpp:41</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_a8be70f0a25e53e870e97d8d23968d723"><div class="ttname"><a href="#a8be70f0a25e53e870e97d8d23968d723">data_structures::treap::Treap::priority</a></div><div class="ttdeci">std::array&lt; int, maxNode &gt; priority</div><div class="ttdoc">Random priority.</div><div class="ttdef"><b>Definition</b> treap.cpp:43</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_af5f0b8263339485989f8a02ae026114c"><div class="ttname"><a href="#af5f0b8263339485989f8a02ae026114c">data_structures::treap::Treap::size</a></div><div class="ttdeci">std::array&lt; int, maxNode &gt; size</div><div class="ttdoc">The number of copies per node.</div><div class="ttdef"><b>Definition</b> treap.cpp:50</div></div>
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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#aeb4bb0db68c7c04ef9498c88c3777887">&#9670;&#160;</a></span>_erase()</h2>
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<td class="memname">void data_structures::treap::Treap::_erase </td>
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<td class="paramtype">int &amp;</td> <td class="paramname"><span class="paramname"><em>x</em></span>, </td>
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<p>Erase a value from the specified subtree (internal method) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>Erase from the subtree of node x (Usually x=root) </td></tr>
<tr><td class="paramname">k</td><td>Key to erase </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 111</span> {</div>
<div class="line"><span class="lineno"> 112</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a>[x] == k) {</div>
<div class="line"><span class="lineno"> 113</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#af7e6c6620ab32bc96633d101245fa919">cnt</a>[x] &gt; 1) {</div>
<div class="line"><span class="lineno"> 114</span> <a class="code hl_variable" href="#af7e6c6620ab32bc96633d101245fa919">cnt</a>[x]--;</div>
<div class="line"><span class="lineno"> 115</span> } <span class="comment">// If the node has more than one copy, the number of copies --</span></div>
<div class="line"><span class="lineno"> 116</span> <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 117</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][0] == 0 &amp;&amp; <a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][1] == 0) {</div>
<div class="line"><span class="lineno"> 118</span> x = 0;</div>
<div class="line"><span class="lineno"> 119</span> <span class="keywordflow">return</span>;</div>
<div class="line"><span class="lineno"> 120</span> } <span class="comment">// If there are no children, delete and return</span></div>
<div class="line"><span class="lineno"> 121</span> <span class="comment">// Otherwise, we need to rotate the sons and delete them</span></div>
<div class="line"><span class="lineno"> 122</span> <span class="comment">// recursively</span></div>
<div class="line"><span class="lineno"> 123</span> <span class="keywordtype">int</span> t = (<a class="code hl_variable" href="#a8be70f0a25e53e870e97d8d23968d723">priority</a>[<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][0]] &gt; <a class="code hl_variable" href="#a8be70f0a25e53e870e97d8d23968d723">priority</a>[<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][1]]);</div>
<div class="line"><span class="lineno"> 124</span> <a class="code hl_function" href="#a75a48584a6560de20484fbba6229fd29">rotate</a>(x, t);</div>
<div class="line"><span class="lineno"> 125</span> <a class="code hl_function" href="#aeb4bb0db68c7c04ef9498c88c3777887">_erase</a>(x, k);</div>
<div class="line"><span class="lineno"> 126</span> }</div>
<div class="line"><span class="lineno"> 127</span> } <span class="keywordflow">else</span> { <span class="comment">// Find the target value based on BST properties</span></div>
<div class="line"><span class="lineno"> 128</span> <a class="code hl_function" href="#aeb4bb0db68c7c04ef9498c88c3777887">_erase</a>(<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][<a class="code hl_variable" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a>[x] &lt; k], k);</div>
<div class="line"><span class="lineno"> 129</span> }</div>
<div class="line"><span class="lineno"> 130</span> <a class="code hl_function" href="#aae9facaede462ad924856c4d707646d7">update</a>(x);</div>
<div class="line"><span class="lineno"> 131</span> }</div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_a32db3ba3b2630943faacd27b2ecd1b04"><div class="ttname"><a href="#a32db3ba3b2630943faacd27b2ecd1b04">data_structures::treap::Treap::key</a></div><div class="ttdeci">std::array&lt; int, maxNode &gt; key</div><div class="ttdoc">Node identifier.</div><div class="ttdef"><b>Definition</b> treap.cpp:42</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_a75a48584a6560de20484fbba6229fd29"><div class="ttname"><a href="#a75a48584a6560de20484fbba6229fd29">data_structures::treap::Treap::rotate</a></div><div class="ttdeci">void rotate(int &amp;x, int t)</div><div class="ttdoc">Rotate without breaking the property of BST.</div><div class="ttdef"><b>Definition</b> treap.cpp:70</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_aae9facaede462ad924856c4d707646d7"><div class="ttname"><a href="#aae9facaede462ad924856c4d707646d7">data_structures::treap::Treap::update</a></div><div class="ttdeci">void update(int x)</div><div class="ttdoc">Update the subtree size of the node.</div><div class="ttdef"><b>Definition</b> treap.cpp:62</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_ab99f68b79e1c4ff0f1cd6f2f0b6a545f"><div class="ttname"><a href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">data_structures::treap::Treap::childs</a></div><div class="ttdeci">std::array&lt; std::array&lt; int, 2 &gt;, maxNode &gt; childs</div><div class="ttdef"><b>Definition</b> treap.cpp:44</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_aeb4bb0db68c7c04ef9498c88c3777887"><div class="ttname"><a href="#aeb4bb0db68c7c04ef9498c88c3777887">data_structures::treap::Treap::_erase</a></div><div class="ttdeci">void _erase(int &amp;x, int k)</div><div class="ttdoc">Erase a value from the specified subtree (internal method)</div><div class="ttdef"><b>Definition</b> treap.cpp:111</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_af7e6c6620ab32bc96633d101245fa919"><div class="ttname"><a href="#af7e6c6620ab32bc96633d101245fa919">data_structures::treap::Treap::cnt</a></div><div class="ttdeci">std::array&lt; int, maxNode &gt; cnt</div><div class="ttdoc">Maintains the subtree size for ranking query.</div><div class="ttdef"><b>Definition</b> treap.cpp:48</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ad08520c0617eb8dcfcbfa90d258aa6b2">&#9670;&#160;</a></span>_get_k_th()</h2>
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<td class="memname">int data_structures::treap::Treap::_get_k_th </td>
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<td class="paramtype">int &amp;</td> <td class="paramname"><span class="paramname"><em>x</em></span>, </td>
</tr>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>k</em></span>&#160;)</td>
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<p>Find the KTH largest value (internal method) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>Query the subtree of node x (Usually x=root) </td></tr>
<tr><td class="paramname">k</td><td>The queried rank </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>The element ranked number k </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 138</span> {</div>
<div class="line"><span class="lineno"> 139</span> <span class="keywordflow">if</span> (k &lt;= <a class="code hl_variable" href="#af5f0b8263339485989f8a02ae026114c">size</a>[<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][0]]) {</div>
<div class="line"><span class="lineno"> 140</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#ad08520c0617eb8dcfcbfa90d258aa6b2">_get_k_th</a>(<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][0], k);</div>
<div class="line"><span class="lineno"> 141</span> }</div>
<div class="line"><span class="lineno"> 142</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> -= <a class="code hl_variable" href="#af5f0b8263339485989f8a02ae026114c">size</a>[<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][0]] + <a class="code hl_variable" href="#af7e6c6620ab32bc96633d101245fa919">cnt</a>[x];</div>
<div class="line"><span class="lineno"> 143</span> <span class="keywordflow">if</span> (k &lt;= 0) {</div>
<div class="line"><span class="lineno"> 144</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a>[x];</div>
<div class="line"><span class="lineno"> 145</span> }</div>
<div class="line"><span class="lineno"> 146</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#ad08520c0617eb8dcfcbfa90d258aa6b2">_get_k_th</a>(<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][1], k);</div>
<div class="line"><span class="lineno"> 147</span> }</div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> composite_simpson_rule.cpp:117</div></div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_ad08520c0617eb8dcfcbfa90d258aa6b2"><div class="ttname"><a href="#ad08520c0617eb8dcfcbfa90d258aa6b2">data_structures::treap::Treap::_get_k_th</a></div><div class="ttdeci">int _get_k_th(int &amp;x, int k)</div><div class="ttdoc">Find the KTH largest value (internal method)</div><div class="ttdef"><b>Definition</b> treap.cpp:138</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9a77d22f97add119123108211c6655ec">&#9670;&#160;</a></span>_get_rank()</h2>
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<td class="memname">int data_structures::treap::Treap::_get_rank </td>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>x</em></span>, </td>
</tr>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>k</em></span>&#160;)</td>
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<p>Query the rank of specified element (internal method) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>Query the subtree of node x (Usually x=root) </td></tr>
<tr><td class="paramname">k</td><td>The queried element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>The rank of element k </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 154</span> {</div>
<div class="line"><span class="lineno"> 155</span> <span class="keywordflow">if</span> (!x) {</div>
<div class="line"><span class="lineno"> 156</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 157</span> }</div>
<div class="line"><span class="lineno"> 158</span> <span class="keywordflow">if</span> (k == <a class="code hl_variable" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a>[x]) {</div>
<div class="line"><span class="lineno"> 159</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="#af5f0b8263339485989f8a02ae026114c">size</a>[<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][0]] + 1;</div>
<div class="line"><span class="lineno"> 160</span> }</div>
<div class="line"><span class="lineno"> 161</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (k &lt; <a class="code hl_variable" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a>[x]) {</div>
<div class="line"><span class="lineno"> 162</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#a9a77d22f97add119123108211c6655ec">_get_rank</a>(<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][0], k);</div>
<div class="line"><span class="lineno"> 163</span> }</div>
<div class="line"><span class="lineno"> 164</span> <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 165</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="#af5f0b8263339485989f8a02ae026114c">size</a>[<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][0]] + <a class="code hl_variable" href="#af7e6c6620ab32bc96633d101245fa919">cnt</a>[x] + <a class="code hl_function" href="#a9a77d22f97add119123108211c6655ec">_get_rank</a>(<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][1], k);</div>
<div class="line"><span class="lineno"> 166</span> }</div>
<div class="line"><span class="lineno"> 167</span> }</div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_a9a77d22f97add119123108211c6655ec"><div class="ttname"><a href="#a9a77d22f97add119123108211c6655ec">data_structures::treap::Treap::_get_rank</a></div><div class="ttdeci">int _get_rank(int x, int k)</div><div class="ttdoc">Query the rank of specified element (internal method)</div><div class="ttdef"><b>Definition</b> treap.cpp:154</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6a023a4f0c42fb8ed5b3368fba1a5f2c">&#9670;&#160;</a></span>_insert()</h2>
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<td class="memname">void data_structures::treap::Treap::_insert </td>
<td>(</td>
<td class="paramtype">int &amp;</td> <td class="paramname"><span class="paramname"><em>x</em></span>, </td>
</tr>
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<td class="paramkey"></td>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>k</em></span>&#160;)</td>
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<p>Insert a value into the specified subtree (internal method) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>Insert into the subtree of node x (Usually x=root) </td></tr>
<tr><td class="paramname">k</td><td>Key to insert </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 84</span> {</div>
<div class="line"><span class="lineno"> 85</span> <span class="keywordflow">if</span> (x) {</div>
<div class="line"><span class="lineno"> 86</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a>[x] == k) {</div>
<div class="line"><span class="lineno"> 87</span> <a class="code hl_variable" href="#af7e6c6620ab32bc96633d101245fa919">cnt</a>[x]++;</div>
<div class="line"><span class="lineno"> 88</span> } <span class="comment">// If the node already exists, the number of copies is ++</span></div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 90</span> <span class="keywordtype">int</span> t = (<a class="code hl_variable" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a>[x] &lt; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>); <span class="comment">// Insert according to BST properties</span></div>
<div class="line"><span class="lineno"> 91</span> <a class="code hl_function" href="#a6a023a4f0c42fb8ed5b3368fba1a5f2c">_insert</a>(<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][t], k);</div>
<div class="line"><span class="lineno"> 92</span> <span class="comment">// After insertion, the heap properties are retained by rotation</span></div>
<div class="line"><span class="lineno"> 93</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#a8be70f0a25e53e870e97d8d23968d723">priority</a>[<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][t]] &lt; <a class="code hl_variable" href="#a8be70f0a25e53e870e97d8d23968d723">priority</a>[x]) {</div>
<div class="line"><span class="lineno"> 94</span> <a class="code hl_function" href="#a75a48584a6560de20484fbba6229fd29">rotate</a>(x, t);</div>
<div class="line"><span class="lineno"> 95</span> }</div>
<div class="line"><span class="lineno"> 96</span> }</div>
<div class="line"><span class="lineno"> 97</span> } <span class="keywordflow">else</span> { <span class="comment">// Create a new node</span></div>
<div class="line"><span class="lineno"> 98</span> x = <a class="code hl_variable" href="#a1ab082fe0aa95a238bbbc68ab6a72425">treapCnt</a>++;</div>
<div class="line"><span class="lineno"> 99</span> <a class="code hl_variable" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a>[x] = <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>;</div>
<div class="line"><span class="lineno"> 100</span> <a class="code hl_variable" href="#af7e6c6620ab32bc96633d101245fa919">cnt</a>[x] = 1;</div>
<div class="line"><span class="lineno"> 101</span> <a class="code hl_variable" href="#a8be70f0a25e53e870e97d8d23968d723">priority</a>[x] = rand(); <span class="comment">// Random priority</span></div>
<div class="line"><span class="lineno"> 102</span> <a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][0] = <a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][1] = 0;</div>
<div class="line"><span class="lineno"> 103</span> }</div>
<div class="line"><span class="lineno"> 104</span> <a class="code hl_function" href="#aae9facaede462ad924856c4d707646d7">update</a>(x);</div>
<div class="line"><span class="lineno"> 105</span> }</div>
<div class="ttc" id="astructdata__structures_1_1treap_1_1_treap_html_a6a023a4f0c42fb8ed5b3368fba1a5f2c"><div class="ttname"><a href="#a6a023a4f0c42fb8ed5b3368fba1a5f2c">data_structures::treap::Treap::_insert</a></div><div class="ttdeci">void _insert(int &amp;x, int k)</div><div class="ttdoc">Insert a value into the specified subtree (internal method)</div><div class="ttdef"><b>Definition</b> treap.cpp:84</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9ea2becd904e2e7d22f23a001b444469">&#9670;&#160;</a></span>erase()</h2>
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<td class="memname">void data_structures::treap::Treap::erase </td>
<td>(</td>
<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>k</em></span></td><td>)</td>
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<p>Erase element (External method) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">k</td><td>Key to erase </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 209</span>{ <a class="code hl_function" href="#aeb4bb0db68c7c04ef9498c88c3777887">_erase</a>(<a class="code hl_variable" href="#a3081969b2714a8101f7df28b1ce5ed2c">root</a>, k); }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ab2db3ad3aecc240011e0c8b8604d2c69">&#9670;&#160;</a></span>get_k_th()</h2>
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<td class="memname">int data_structures::treap::Treap::get_k_th </td>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>k</em></span></td><td>)</td>
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<p>Get the KTH largest value (External method) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">k</td><td>The queried rank </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>The element ranked number x </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 215</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="#ad08520c0617eb8dcfcbfa90d258aa6b2">_get_k_th</a>(<a class="code hl_variable" href="#a3081969b2714a8101f7df28b1ce5ed2c">root</a>, k); }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a767b28f9911fc32b8462862be058a4a4">&#9670;&#160;</a></span>get_next()</h2>
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<td class="memname">int data_structures::treap::Treap::get_next </td>
<td>(</td>
<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>k</em></span></td><td>)</td>
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<p>Get the successor node of element k. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">k</td><td>The queried element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>The successor </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 189</span> {</div>
<div class="line"><span class="lineno"> 190</span> <span class="keywordtype">int</span> x = <a class="code hl_variable" href="#a3081969b2714a8101f7df28b1ce5ed2c">root</a>, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = -1;</div>
<div class="line"><span class="lineno"> 191</span> <span class="keywordflow">while</span> (x) {</div>
<div class="line"><span class="lineno"> 192</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a>[x] &gt; k) {</div>
<div class="line"><span class="lineno"> 193</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = <a class="code hl_variable" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a>[x], x = <a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][0];</div>
<div class="line"><span class="lineno"> 194</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 195</span> x = <a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][1];</div>
<div class="line"><span class="lineno"> 196</span> }</div>
<div class="line"><span class="lineno"> 197</span> }</div>
<div class="line"><span class="lineno"> 198</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a>;</div>
<div class="line"><span class="lineno"> 199</span> }</div>
<div class="ttc" id="anext_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/next.html">std::next</a></div><div class="ttdeci">T next(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ab8b9899f22070cfa01db5bf874296126">&#9670;&#160;</a></span>get_predecessor()</h2>
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<td class="memname">int data_structures::treap::Treap::get_predecessor </td>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>k</em></span></td><td>)</td>
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<p>Get the predecessor node of element k. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">k</td><td>The queried element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>The predecessor </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 173</span> {</div>
<div class="line"><span class="lineno"> 174</span> <span class="keywordtype">int</span> x = <a class="code hl_variable" href="#a3081969b2714a8101f7df28b1ce5ed2c">root</a>, pre = -1;</div>
<div class="line"><span class="lineno"> 175</span> <span class="keywordflow">while</span> (x) {</div>
<div class="line"><span class="lineno"> 176</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a>[x] &lt; k) {</div>
<div class="line"><span class="lineno"> 177</span> pre = <a class="code hl_variable" href="#a32db3ba3b2630943faacd27b2ecd1b04">key</a>[x], x = <a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][1];</div>
<div class="line"><span class="lineno"> 178</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 179</span> x = <a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][0];</div>
<div class="line"><span class="lineno"> 180</span> }</div>
<div class="line"><span class="lineno"> 181</span> }</div>
<div class="line"><span class="lineno"> 182</span> <span class="keywordflow">return</span> pre;</div>
<div class="line"><span class="lineno"> 183</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ac94e9d69305940f6d8804031455af039">&#9670;&#160;</a></span>get_rank()</h2>
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<td class="memname">int data_structures::treap::Treap::get_rank </td>
<td>(</td>
<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>k</em></span></td><td>)</td>
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<p>Get the rank of specified element (External method) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">k</td><td>The queried element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>The rank of element k </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 221</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="#a9a77d22f97add119123108211c6655ec">_get_rank</a>(<a class="code hl_variable" href="#a3081969b2714a8101f7df28b1ce5ed2c">root</a>, k); }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a5e884d2686aff501ef589b0d1185492f">&#9670;&#160;</a></span>insert()</h2>
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<td class="memname">void data_structures::treap::Treap::insert </td>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>k</em></span></td><td>)</td>
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<p>Insert element (External method) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">k</td><td>Key to insert </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 204</span>{ <a class="code hl_function" href="#a6a023a4f0c42fb8ed5b3368fba1a5f2c">_insert</a>(<a class="code hl_variable" href="#a3081969b2714a8101f7df28b1ce5ed2c">root</a>, k); }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a75a48584a6560de20484fbba6229fd29">&#9670;&#160;</a></span>rotate()</h2>
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<td class="memname">void data_structures::treap::Treap::rotate </td>
<td>(</td>
<td class="paramtype">int &amp;</td> <td class="paramname"><span class="paramname"><em>x</em></span>, </td>
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<p>Rotate without breaking the property of BST. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>The node to rotate </td></tr>
<tr><td class="paramname">t</td><td>0 represent left hand, while 1 right hand </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 70</span> {</div>
<div class="line"><span class="lineno"> 71</span> <span class="keywordtype">int</span> y = <a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][t];</div>
<div class="line"><span class="lineno"> 72</span> <a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][t] = <a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[y][1 - t];</div>
<div class="line"><span class="lineno"> 73</span> <a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[y][1 - t] = x;</div>
<div class="line"><span class="lineno"> 74</span> <span class="comment">// The rotation will only change itself and its son nodes</span></div>
<div class="line"><span class="lineno"> 75</span> <a class="code hl_function" href="#aae9facaede462ad924856c4d707646d7">update</a>(x);</div>
<div class="line"><span class="lineno"> 76</span> <a class="code hl_function" href="#aae9facaede462ad924856c4d707646d7">update</a>(y);</div>
<div class="line"><span class="lineno"> 77</span> x = y;</div>
<div class="line"><span class="lineno"> 78</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aae9facaede462ad924856c4d707646d7">&#9670;&#160;</a></span>update()</h2>
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<td class="memname">void data_structures::treap::Treap::update </td>
<td>(</td>
<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>x</em></span></td><td>)</td>
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<p>Update the subtree size of the node. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>The node to update </td></tr>
</table>
</dd>
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<div class="fragment"><div class="line"><span class="lineno"> 62</span> {</div>
<div class="line"><span class="lineno"> 63</span> <a class="code hl_variable" href="#af5f0b8263339485989f8a02ae026114c">size</a>[x] = <a class="code hl_variable" href="#af5f0b8263339485989f8a02ae026114c">size</a>[<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][0]] + <a class="code hl_variable" href="#af7e6c6620ab32bc96633d101245fa919">cnt</a>[x] + <a class="code hl_variable" href="#af5f0b8263339485989f8a02ae026114c">size</a>[<a class="code hl_variable" href="#ab99f68b79e1c4ff0f1cd6f2f0b6a545f">childs</a>[x][1]];</div>
<div class="line"><span class="lineno"> 64</span> }</div>
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<h2 class="groupheader">Member Data Documentation</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int, 2&gt;, <a class="el" href="../../dd/d2e/namespacedata__structures_1_1treap.html#ad939ec178d0069aeea14b7d6d7d12099">maxNode</a>&gt; data_structures::treap::Treap::childs</td>
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<b>Initial value:</b><div class="fragment"><div class="line">= {</div>
<div class="line"> {}}</div>
</div><!-- fragment --><p>[i][0] represents the left child of node i, and [i][1] represents the right </p>
<div class="fragment"><div class="line"><span class="lineno"> 44</span> {</div>
<div class="line"><span class="lineno"> 45</span> {}}; <span class="comment">///&lt; [i][0] represents the</span></div>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int, <a class="el" href="../../dd/d2e/namespacedata__structures_1_1treap.html#ad939ec178d0069aeea14b7d6d7d12099">maxNode</a>&gt; data_structures::treap::Treap::cnt</td>
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<b>Initial value:</b><div class="fragment"><div class="line">=</div>
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<p>Maintains the subtree size for ranking query. </p>
<div class="fragment"><div class="line"><span class="lineno"> 49</span> {}; <span class="comment">///&lt; Maintains the subtree size for ranking query</span></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a32db3ba3b2630943faacd27b2ecd1b04">&#9670;&#160;</a></span>key</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int, <a class="el" href="../../dd/d2e/namespacedata__structures_1_1treap.html#ad939ec178d0069aeea14b7d6d7d12099">maxNode</a>&gt; data_structures::treap::Treap::key = {}</td>
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<p><a class="el" href="../../d9/d49/structdata__structures_1_1_node.html">Node</a> identifier. </p>
<div class="fragment"><div class="line"><span class="lineno"> 42</span>{}; <span class="comment">///&lt; Node identifier</span></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a8be70f0a25e53e870e97d8d23968d723">&#9670;&#160;</a></span>priority</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int, <a class="el" href="../../dd/d2e/namespacedata__structures_1_1treap.html#ad939ec178d0069aeea14b7d6d7d12099">maxNode</a>&gt; data_structures::treap::Treap::priority = {}</td>
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<p>Random priority. </p>
<div class="fragment"><div class="line"><span class="lineno"> 43</span>{}; <span class="comment">///&lt; Random priority</span></div>
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<h2 class="memtitle"><span class="permalink"><a href="#af5f0b8263339485989f8a02ae026114c">&#9670;&#160;</a></span>size</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;int, <a class="el" href="../../dd/d2e/namespacedata__structures_1_1treap.html#ad939ec178d0069aeea14b7d6d7d12099">maxNode</a>&gt; data_structures::treap::Treap::size = {}</td>
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<p>The number of copies per node. </p>
<div class="fragment"><div class="line"><span class="lineno"> 50</span>{}; <span class="comment">///&lt; The number of copies per node</span></div>
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<hr/>The documentation for this struct was generated from the following file:<ul>
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