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<p>Fenwick tree.
<p><a href="https://en.wikipedia.org/wiki/Fenwick_tree" target="_blank">Fenwick Tree</a> algorithm implementation
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d91/class_fenwick_tree.html">FenwickTree</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">The class that initializes the Fenwick Tree. <a href="../../de/d0d/classrange__queries_1_1fenwick__tree.html#details">More...</a><br /></td></tr>
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<tr class="memitem:dd/d69/namespacerange__queries"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d69/namespacerange__queries.html">range_queries</a></td></tr>
<tr class="memdesc:dd/d69/namespacerange__queries"><td class="mdescLeft">&#160;</td><td class="mdescRight">Algorithms and Data Structures that support range queries and updates. <br /></td></tr>
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<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d2e/fenwick__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
<tr class="memdesc:a483bb8ccf42aaf7375a83e91490eda1e"><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="../../d6/d2e/fenwick__tree_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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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Fenwick tree. </p>
<p>A Fenwick tree or binary indexed tree is a data structure that can efficiently update elements and calculate prefix sums in a table of numbers. </p>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Fenwick_tree" target="_blank">Fenwick Tree</a> algorithm implementation </p>
<p><em>From Wikipedia, the free encyclopedia.</em></p>
<p>A Fenwick tree or binary indexed tree (BIT) is a clever implementation of a datastructure called bionomal tree. It can update values and solve range queries with operations that is; commulative, associative and has an inverse for this type of element. It can also solve immutable range queries (min/max), when operations only are associative over this type of element. Some of these restrictions can be removed, by storing redunant information; like in max/min range queries.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/mateusz-grzegorzek" target="_blank">Mateusz Grzegorzek</a> </dd>
<dd>
<a href="https://github.com/Panquesito7" target="_blank">David Leal</a> </dd></dl>
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<p>Main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 69</span> {</div>
<div class="line"><span class="lineno"> 70</span> <span class="keywordtype">int</span> n = 5;</div>
<div class="line"><span class="lineno"> 71</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> arr = {1, 2, 3, 4, 5};</div>
<div class="line"><span class="lineno"> 72</span> <a class="code hl_class" href="../../dd/d91/class_fenwick_tree.html">FenwickTree</a> fenwick_tree(arr);</div>
<div class="line"><span class="lineno"> 73</span> </div>
<div class="line"><span class="lineno"> 74</span> assert(fenwick_tree.sum_range(0, 0) == 1);</div>
<div class="line"><span class="lineno"> 75</span> assert(fenwick_tree.sum_range(0, 1) == 3);</div>
<div class="line"><span class="lineno"> 76</span> assert(fenwick_tree.sum_range(0, 2) == 6);</div>
<div class="line"><span class="lineno"> 77</span> fenwick_tree.update(0, 6);</div>
<div class="line"><span class="lineno"> 78</span> assert(fenwick_tree.sum_range(0, 0) == 6);</div>
<div class="line"><span class="lineno"> 79</span> assert(fenwick_tree.sum_range(0, 1) == 8);</div>
<div class="line"><span class="lineno"> 80</span> assert(fenwick_tree.sum_range(0, 2) == 11);</div>
<div class="line"><span class="lineno"> 81</span> <span class="keywordflow">return</span> 0;</div>
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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"> 132</span> {</div>
<div class="line"><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"><span class="lineno"> 134</span> <span class="keywordflow">return</span> 0;</div>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 114</span> {</div>
<div class="line"><span class="lineno"> 115</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> arr = {1, 2, 3, 4, 5};</div>
<div class="line"><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"><span class="lineno"> 117</span> </div>
<div class="line"><span class="lineno"> 118</span> assert(fenwick_tree.sum_range(0, 0) == 1);</div>
<div class="line"><span class="lineno"> 119</span> assert(fenwick_tree.sum_range(0, 1) == 3);</div>
<div class="line"><span class="lineno"> 120</span> assert(fenwick_tree.sum_range(0, 2) == 6);</div>
<div class="line"><span class="lineno"> 121</span> assert(fenwick_tree.sum_range(0, 3) == 10);</div>
<div class="line"><span class="lineno"> 122</span> assert(fenwick_tree.sum_range(0, 4) == 15);</div>
<div class="line"><span class="lineno"> 123</span> </div>
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<div class="line"><span class="lineno"> 125</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"> 126</span>}</div>
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