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<div class="headertitle"><div class="title">fenwick_tree.cpp</div></div>
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<div class="contents">
<a href="../../d6/d2e/fenwick__tree_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include &lt;cassert&gt;</span> </div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include &lt;vector&gt;</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span></div>
<div class="foldopen" id="foldopen00028" data-start="{" data-end="}">
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"><a class="line" href="../../dd/d69/namespacerange__queries.html"> 28</a></span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/d69/namespacerange__queries.html">range_queries</a> {</div>
<div class="foldopen" id="foldopen00032" data-start="{" data-end="};">
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"><a class="line" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html"> 32</a></span><span class="keyword">class </span><a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a5ea37183524553bbf2234a36a44a4b9a">fenwick_tree</a> {</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"><a class="line" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af9f543aa5976b8cc5422490b3d6250c6"> 33</a></span> <span class="keywordtype">size_t</span> <a class="code hl_variable" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af9f543aa5976b8cc5422490b3d6250c6">n</a> = 0; </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"><a class="line" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af7b7a8c1c5724ed8683d7e28bef526e6"> 34</a></span> std::vector&lt;int&gt; <a class="code hl_variable" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af7b7a8c1c5724ed8683d7e28bef526e6">bit</a>{}; </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"><a class="line" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#ab492ebf07cab0e3c32d277ad986de801"> 41</a></span> <span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#ab492ebf07cab0e3c32d277ad986de801">offset</a>(<span class="keywordtype">int</span> x) { <span class="keywordflow">return</span> (x &amp; (-x)); }</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="foldopen" id="foldopen00050" data-start="{" data-end="}">
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"><a class="line" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a5ea37183524553bbf2234a36a44a4b9a"> 50</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a5ea37183524553bbf2234a36a44a4b9a">fenwick_tree</a>(<span class="keyword">const</span> std::vector&lt;T&gt;&amp; arr) : <a class="code hl_variable" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af9f543aa5976b8cc5422490b3d6250c6">n</a>(arr.size()) {</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <a class="code hl_variable" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af7b7a8c1c5724ed8683d7e28bef526e6">bit</a>.assign(<a class="code hl_variable" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af9f543aa5976b8cc5422490b3d6250c6">n</a> + 1, 0);</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_variable" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af9f543aa5976b8cc5422490b3d6250c6">n</a>; ++i) {</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a19dea5e88bbd7683a719030623315de9">update</a>(i, arr[i]);</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> }</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"><a class="line" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#aef7ba885b91af093e9e514358fa0f36c"> 64</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#aef7ba885b91af093e9e514358fa0f36c">fenwick_tree</a>(T x) : <a class="code hl_variable" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af9f543aa5976b8cc5422490b3d6250c6">n</a>(x) { <a class="code hl_variable" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af7b7a8c1c5724ed8683d7e28bef526e6">bit</a>.assign(<a class="code hl_variable" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af9f543aa5976b8cc5422490b3d6250c6">n</a> + 1, 0); }</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="foldopen" id="foldopen00075" data-start="{" data-end="}">
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"><a class="line" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a19dea5e88bbd7683a719030623315de9"> 75</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a19dea5e88bbd7683a719030623315de9">update</a>(T <span class="keywordtype">id</span>, T val) {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordtype">id</span>++;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">while</span> (<span class="keywordtype">id</span> &lt;= <a class="code hl_variable" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af9f543aa5976b8cc5422490b3d6250c6">n</a>) {</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <a class="code hl_variable" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af7b7a8c1c5724ed8683d7e28bef526e6">bit</a>[id] += val;</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordtype">id</span> += <a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#ab492ebf07cab0e3c32d277ad986de801">offset</a>(<span class="keywordtype">id</span>);</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> }</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> }</div>
</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="foldopen" id="foldopen00090" data-start="{" data-end="}">
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"><a class="line" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a1fa0559d987fde0044761b17b35f5abd"> 90</a></span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a1fa0559d987fde0044761b17b35f5abd">sum</a>(T <span class="keywordtype">id</span>) {</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordtype">id</span>++;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> T res = 0;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">while</span> (<span class="keywordtype">id</span> &gt; 0) {</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> res += <a class="code hl_variable" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af7b7a8c1c5724ed8683d7e28bef526e6">bit</a>[id];</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordtype">id</span> -= <a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#ab492ebf07cab0e3c32d277ad986de801">offset</a>(<span class="keywordtype">id</span>);</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> }</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> }</div>
</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"><a class="line" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a0914a4b1401a7c427de91c92885724fe"> 106</a></span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a0914a4b1401a7c427de91c92885724fe">sum_range</a>(<span class="keywordtype">int</span> l, <span class="keywordtype">int</span> r) { <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a1fa0559d987fde0044761b17b35f5abd">sum</a>(r) - <a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a1fa0559d987fde0044761b17b35f5abd">sum</a>(l - 1); }</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span>};</div>
</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span>} <span class="comment">// namespace range_queries</span></div>
</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span></div>
<div class="foldopen" id="foldopen00114" data-start="{" data-end="}">
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"><a class="line" href="../../d6/d2e/fenwick__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e"> 114</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d6/d2e/fenwick__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>() {</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> std::vector&lt;int&gt; arr = {1, 2, 3, 4, 5};</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <a class="code hl_class" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html">range_queries::fenwick_tree</a> fenwick_tree(arr);</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> </div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> assert(fenwick_tree.<a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a0914a4b1401a7c427de91c92885724fe">sum_range</a>(0, 0) == 1);</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> assert(fenwick_tree.<a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a0914a4b1401a7c427de91c92885724fe">sum_range</a>(0, 1) == 3);</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> assert(fenwick_tree.<a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a0914a4b1401a7c427de91c92885724fe">sum_range</a>(0, 2) == 6);</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> assert(fenwick_tree.<a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a0914a4b1401a7c427de91c92885724fe">sum_range</a>(0, 3) == 10);</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> assert(fenwick_tree.<a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a0914a4b1401a7c427de91c92885724fe">sum_range</a>(0, 4) == 15);</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> </div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> fenwick_tree.<a class="code hl_function" href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a19dea5e88bbd7683a719030623315de9">update</a>(0, 6);</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> std::cout &lt;&lt; <span class="stringliteral">&quot;All tests have successfully passed!\n&quot;</span>;</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span>}</div>
</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span></div>
<div class="foldopen" id="foldopen00132" data-start="{" data-end="}">
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"><a class="line" href="../../d6/d2e/fenwick__tree_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 132</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d6/d2e/fenwick__tree_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <a class="code hl_function" href="../../d6/d2e/fenwick__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span>}</div>
</div>
<div class="ttc" id="aclassrange__queries_1_1fenwick__tree_html"><div class="ttname"><a href="../../de/d0d/classrange__queries_1_1fenwick__tree.html">range_queries::fenwick_tree</a></div><div class="ttdoc">The class that initializes the Fenwick Tree.</div><div class="ttdef"><b>Definition</b> <a href="#l00032">fenwick_tree.cpp:32</a></div></div>
<div class="ttc" id="aclassrange__queries_1_1fenwick__tree_html_a0914a4b1401a7c427de91c92885724fe"><div class="ttname"><a href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a0914a4b1401a7c427de91c92885724fe">range_queries::fenwick_tree::sum_range</a></div><div class="ttdeci">int sum_range(int l, int r)</div><div class="ttdoc">Returns the prefix sum in range from L to R.</div><div class="ttdef"><b>Definition</b> <a href="#l00106">fenwick_tree.cpp:106</a></div></div>
<div class="ttc" id="aclassrange__queries_1_1fenwick__tree_html_a19dea5e88bbd7683a719030623315de9"><div class="ttname"><a href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a19dea5e88bbd7683a719030623315de9">range_queries::fenwick_tree::update</a></div><div class="ttdeci">void update(T id, T val)</div><div class="ttdoc">Updates the value of an element in original array and accordingly updates the values in BIT array.</div><div class="ttdef"><b>Definition</b> <a href="#l00075">fenwick_tree.cpp:75</a></div></div>
<div class="ttc" id="aclassrange__queries_1_1fenwick__tree_html_a1fa0559d987fde0044761b17b35f5abd"><div class="ttname"><a href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a1fa0559d987fde0044761b17b35f5abd">range_queries::fenwick_tree::sum</a></div><div class="ttdeci">int sum(T id)</div><div class="ttdoc">Returns the sum of elements in range from 0 to ID.</div><div class="ttdef"><b>Definition</b> <a href="#l00090">fenwick_tree.cpp:90</a></div></div>
<div class="ttc" id="aclassrange__queries_1_1fenwick__tree_html_a5ea37183524553bbf2234a36a44a4b9a"><div class="ttname"><a href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#a5ea37183524553bbf2234a36a44a4b9a">range_queries::fenwick_tree::fenwick_tree</a></div><div class="ttdeci">fenwick_tree(const std::vector&lt; T &gt; &amp;arr)</div><div class="ttdoc">Class Constructor.</div><div class="ttdef"><b>Definition</b> <a href="#l00050">fenwick_tree.cpp:50</a></div></div>
<div class="ttc" id="aclassrange__queries_1_1fenwick__tree_html_ab492ebf07cab0e3c32d277ad986de801"><div class="ttname"><a href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#ab492ebf07cab0e3c32d277ad986de801">range_queries::fenwick_tree::offset</a></div><div class="ttdeci">int offset(int x)</div><div class="ttdoc">Returns the highest power of two which is not more than x.</div><div class="ttdef"><b>Definition</b> <a href="#l00041">fenwick_tree.cpp:41</a></div></div>
<div class="ttc" id="aclassrange__queries_1_1fenwick__tree_html_aef7ba885b91af093e9e514358fa0f36c"><div class="ttname"><a href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#aef7ba885b91af093e9e514358fa0f36c">range_queries::fenwick_tree::fenwick_tree</a></div><div class="ttdeci">fenwick_tree(T x)</div><div class="ttdoc">Class Constructor.</div><div class="ttdef"><b>Definition</b> <a href="#l00064">fenwick_tree.cpp:64</a></div></div>
<div class="ttc" id="aclassrange__queries_1_1fenwick__tree_html_af7b7a8c1c5724ed8683d7e28bef526e6"><div class="ttname"><a href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af7b7a8c1c5724ed8683d7e28bef526e6">range_queries::fenwick_tree::bit</a></div><div class="ttdeci">std::vector&lt; int &gt; bit</div><div class="ttdoc">Array that represents Binary Indexed Tree.</div><div class="ttdef"><b>Definition</b> <a href="#l00034">fenwick_tree.cpp:34</a></div></div>
<div class="ttc" id="aclassrange__queries_1_1fenwick__tree_html_af9f543aa5976b8cc5422490b3d6250c6"><div class="ttname"><a href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#af9f543aa5976b8cc5422490b3d6250c6">range_queries::fenwick_tree::n</a></div><div class="ttdeci">size_t n</div><div class="ttdoc">No. of elements present in input array.</div><div class="ttdef"><b>Definition</b> <a href="#l00033">fenwick_tree.cpp:33</a></div></div>
<div class="ttc" id="afenwick__tree_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="../../d6/d2e/fenwick__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="#l00114">fenwick_tree.cpp:114</a></div></div>
<div class="ttc" id="afenwick__tree_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d6/d2e/fenwick__tree_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00132">fenwick_tree.cpp:132</a></div></div>
<div class="ttc" id="anamespacerange__queries_html"><div class="ttname"><a href="../../dd/d69/namespacerange__queries.html">range_queries</a></div><div class="ttdoc">for std::vector</div><div class="ttdef"><b>Definition</b> <a href="#l00028">fenwick_tree.cpp:28</a></div></div>
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