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<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Gnome_sort">gnome sort</a> algorithm. </p>
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<a href="https://github.com/kvedala">Krishna Vedala</a> Gnome sort algorithm is not the best one but it is widely used. The algorithm iteratively checks the order of pairs in the array. If they are on right order it moves to the next successive pair, otherwise it swaps elements. This operation is repeated until no more swaps are made thus indicating the values to be in ascending order.</dd></dl>
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<p>Gnome sort algorithm is not the best one but it is widely used. The algorithm iteratively checks the order of pairs in the array. If they are on right order it moves to the next successive pair, otherwise it swaps elements. This operation is repeated until no more swaps are made thus indicating the values to be in ascending order.</p>
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<p>two elements a[i] and a[j] form an inversion if <code>a[i]</code> &gt; <code>a[j]</code> and i &lt; j</p>
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<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_a1fda852e6e522707fd97f61cdb0a2591"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a1fda852e6e522707fd97f61cdb0a2591">range_queries::heavy_light_decomposition::SG::query</a></div><div class="ttdeci">X query(int l, int r)</div><div class="ttdoc">Make a range query from node label l to node label r.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:305</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_a41c733f5f5e262b308f7cb95c88c1e74"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a41c733f5f5e262b308f7cb95c88c1e74">range_queries::heavy_light_decomposition::SG::combine</a></div><div class="ttdeci">X combine(X lhs, X rhs)</div><div class="ttdoc">Function that specifies the type of operation involved when segments are combined.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:274</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_aa7f93971a9f891e0bbb7023081f379d5"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#aa7f93971a9f891e0bbb7023081f379d5">range_queries::heavy_light_decomposition::SG::sret_init</a></div><div class="ttdeci">X sret_init</div><div class="ttdoc">inital query return value</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:264</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_a0efd0b9c564092f443ca97030d866ef1"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a0efd0b9c564092f443ca97030d866ef1">range_queries::heavy_light_decomposition::Tree::t_depth</a></div><div class="ttdeci">std::vector&lt; int &gt; t_depth</div><div class="ttdoc">a vector to store the depth of a node,</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:88</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_a350157a5fb79f76fceae33fc84171203"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a350157a5fb79f76fceae33fc84171203">range_queries::heavy_light_decomposition::Tree::t_par</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; int &gt; &gt; t_par</div><div class="ttdoc">a matrix to store every node's 2^kth parent</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:87</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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@@ -377,6 +393,9 @@ template&lt;typename X &gt; </div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>&#160; }</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>&#160; <a class="code" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a84424f180f12b514eaab57a6aa20b104">h_heavychlid</a>[u] = hc_id;</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>&#160; }</div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_af64848d6630c39d0f09ce2359cc7c4f8"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#af64848d6630c39d0f09ce2359cc7c4f8">range_queries::heavy_light_decomposition::HLD::dfs_hc</a></div><div class="ttdeci">void dfs_hc(int u, int p=-1)</div><div class="ttdoc">Utility function to assign heavy child to each node (-1 for a leaf node)</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:350</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ab1aeaefa1bd97b867c652ba916fbdb43"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ab1aeaefa1bd97b867c652ba916fbdb43">range_queries::heavy_light_decomposition::Tree::t_adj</a></div><div class="ttdeci">std::vector&lt; std::list&lt; int &gt; &gt; t_adj</div><div class="ttdoc">an adjacency list to stores the tree edges</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:83</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ada1494fccbc7f1f07b2f9be9f7e07ad5"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">range_queries::heavy_light_decomposition::Tree::t_size</a></div><div class="ttdeci">std::vector&lt; int &gt; t_size</div><div class="ttdoc">a vector to store the subtree size rooted at node</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:89</div></div>
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@@ -436,6 +455,7 @@ template&lt;typename X &gt; </div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>&#160; }</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>&#160; }</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>&#160; }</div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_a0579062b384e54b611b80c6337c7f2c8"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a0579062b384e54b611b80c6337c7f2c8">range_queries::heavy_light_decomposition::HLD::dfs_labels</a></div><div class="ttdeci">void dfs_labels(int u, int p=-1)</div><div class="ttdoc">Utility function to lable the nodes so that heavy chains have a contigous lable.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:390</div></div>
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@@ -495,6 +515,7 @@ template&lt;typename X &gt; </div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>&#160; }</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>&#160; }</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>&#160; }</div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_a2dfbda148aad0bfaba2ebfda9ebc915a"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a2dfbda148aad0bfaba2ebfda9ebc915a">range_queries::heavy_light_decomposition::HLD::dfs_par</a></div><div class="ttdeci">void dfs_par(int u, int p=-1)</div><div class="ttdoc">Utility function to assign highest parent that can be reached though heavy chains.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:371</div></div>
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@@ -543,6 +564,10 @@ template&lt;typename X &gt; </div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>&#160; <a class="code" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a41c733f5f5e262b308f7cb95c88c1e74">SG&lt;X&gt;::combine</a>(<a class="code" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#afbf8a9cb9449d5ca844f4e141a801e6a">SG&lt;X&gt;::s_tree</a>[i &lt;&lt; 1], <a class="code" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#afbf8a9cb9449d5ca844f4e141a801e6a">SG&lt;X&gt;::s_tree</a>[i &lt;&lt; 1 | 1]);</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>&#160; }</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>&#160; }</div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_afbf8a9cb9449d5ca844f4e141a801e6a"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#afbf8a9cb9449d5ca844f4e141a801e6a">range_queries::heavy_light_decomposition::SG::s_tree</a></div><div class="ttdeci">std::vector&lt; X &gt; s_tree</div><div class="ttdoc">Everything here is private, and can only be accessed through the methods, in the derived class (HLD)</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:262</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_a135b7952593c9b1aae38fcaf1cc1abf7"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">range_queries::heavy_light_decomposition::Tree::t_val</a></div><div class="ttdeci">std::vector&lt; X &gt; t_val</div><div class="ttdoc">values of nodes</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:92</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_aa6c37e840355b9fb2105181c578694e8"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">range_queries::heavy_light_decomposition::Tree::t_root</a></div><div class="ttdeci">int t_root</div><div class="ttdoc">the root of the tree</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:91</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ad22d760a5a33545a70e7ea5e1786c8dc"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ad22d760a5a33545a70e7ea5e1786c8dc">range_queries::heavy_light_decomposition::Tree::init</a></div><div class="ttdeci">void init()</div><div class="ttdoc">This function must be called after the tree adjacency list and node values are populated The function...</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:186</div></div>
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@@ -605,10 +630,12 @@ template&lt;typename X &gt; </div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>&#160; ret += <a class="code" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a7d5b40c076347a6aabfb37a0590f2f24">chain_query</a>(b, lc);</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>&#160; <span class="keywordflow">return</span> ret - <a class="code" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">Tree&lt;X&gt;::t_val</a>[lc];</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>&#160; }</div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_a7d5b40c076347a6aabfb37a0590f2f24"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a7d5b40c076347a6aabfb37a0590f2f24">range_queries::heavy_light_decomposition::HLD::chain_query</a></div><div class="ttdeci">X chain_query(int a, int b)</div><div class="ttdoc">Utility function to break down a path query into two chain queries.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:409</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ae2b407e64aaf9878fbee7ee6efe9c7d4"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae2b407e64aaf9878fbee7ee6efe9c7d4">range_queries::heavy_light_decomposition::Tree::lca</a></div><div class="ttdeci">int lca(int a, int b)</div><div class="ttdoc">The function returns the least common ancestor of two nodes.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:229</div></div>
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@@ -664,6 +691,9 @@ template&lt;typename X &gt; </div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>&#160; <a class="code" href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a3c75bf5770790f8eba8cc92227b5400c">SG&lt;X&gt;::update</a>(<a class="code" href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#aa86a91ae0cd7898990a8170a2f2c9cda">h_label</a>[<a class="code" href="../../d5/da1/structnode.html">node</a>], diff);</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>&#160; <a class="code" href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#a135b7952593c9b1aae38fcaf1cc1abf7">Tree&lt;X&gt;::t_val</a>[<a class="code" href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a>] = val;</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>&#160; }</div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_a3c75bf5770790f8eba8cc92227b5400c"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a3c75bf5770790f8eba8cc92227b5400c">range_queries::heavy_light_decomposition::SG::update</a></div><div class="ttdeci">void update(int p, X v)</div><div class="ttdoc">Update the value at a node.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:293</div></div>
<div class="ttc" id="ahash__search_8cpp_html_a8ca8dcb494104d273679e219e53d0555"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a></div><div class="ttdeci">struct list node</div></div>
<div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
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@@ -678,41 +708,11 @@ Here is the call graph for this function:</div>
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<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>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_h_l_d_html_a7d5b40c076347a6aabfb37a0590f2f24"><div class="ttname"><a href="../../d2/d8a/classrange__queries_1_1heavy__light__decomposition_1_1_h_l_d.html#a7d5b40c076347a6aabfb37a0590f2f24">range_queries::heavy_light_decomposition::HLD::chain_query</a></div><div class="ttdeci">X chain_query(int a, int b)</div><div class="ttdoc">Utility function to break down a path query into two chain queries.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:409</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ada1494fccbc7f1f07b2f9be9f7e07ad5"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ada1494fccbc7f1f07b2f9be9f7e07ad5">range_queries::heavy_light_decomposition::Tree::t_size</a></div><div class="ttdeci">std::vector&lt; int &gt; t_size</div><div class="ttdoc">a vector to store the subtree size rooted at node</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:89</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_aa6c37e840355b9fb2105181c578694e8"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#aa6c37e840355b9fb2105181c578694e8">range_queries::heavy_light_decomposition::Tree::t_root</a></div><div class="ttdeci">int t_root</div><div class="ttdoc">the root of the tree</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:91</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ae2b407e64aaf9878fbee7ee6efe9c7d4"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae2b407e64aaf9878fbee7ee6efe9c7d4">range_queries::heavy_light_decomposition::Tree::lca</a></div><div class="ttdeci">int lca(int a, int b)</div><div class="ttdoc">The function returns the least common ancestor of two nodes.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:229</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ad22d760a5a33545a70e7ea5e1786c8dc"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ad22d760a5a33545a70e7ea5e1786c8dc">range_queries::heavy_light_decomposition::Tree::init</a></div><div class="ttdeci">void init()</div><div class="ttdoc">This function must be called after the tree adjacency list and node values are populated The function...</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:186</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_a3c75bf5770790f8eba8cc92227b5400c"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a3c75bf5770790f8eba8cc92227b5400c">range_queries::heavy_light_decomposition::SG::update</a></div><div class="ttdeci">void update(int p, X v)</div><div class="ttdoc">Update the value at a node.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:293</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_aa7f93971a9f891e0bbb7023081f379d5"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#aa7f93971a9f891e0bbb7023081f379d5">range_queries::heavy_light_decomposition::SG::sret_init</a></div><div class="ttdeci">X sret_init</div><div class="ttdoc">inital query return value</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:264</div></div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_s_g_html_a41c733f5f5e262b308f7cb95c88c1e74"><div class="ttname"><a href="../../d9/d35/classrange__queries_1_1heavy__light__decomposition_1_1_s_g.html#a41c733f5f5e262b308f7cb95c88c1e74">range_queries::heavy_light_decomposition::SG::combine</a></div><div class="ttdeci">X combine(X lhs, X rhs)</div><div class="ttdoc">Function that specifies the type of operation involved when segments are combined.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:274</div></div>
<div class="ttc" id="astructnode_html"><div class="ttname"><a href="../../d5/da1/structnode.html">node</a></div><div class="ttdef"><b>Definition:</b> avltree.cpp:13</div></div>
<div class="ttc" id="ahash__search_8cpp_html_a8ca8dcb494104d273679e219e53d0555"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a8ca8dcb494104d273679e219e53d0555">node</a></div><div class="ttdeci">struct list node</div></div>
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