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<p><a href="https://en.wikipedia.org/wiki/Prefix_sum" target="_blank">Prefix Sum Array</a> data structure implementation.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for prefix_sum_array.cpp:</div>
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Namespaces</h2></td></tr>
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<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:d7/d88/namespaceprefix__sum__array"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d88/namespaceprefix__sum__array.html">prefix_sum_array</a></td></tr>
<tr class="memdesc:d7/d88/namespaceprefix__sum__array"><td class="mdescLeft">&#160;</td><td class="mdescRight">Range sum queries using prefix-sum-array. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:ab36151479ad37d53ef9fcb60a274b1d9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/d9e/prefix__sum__array_8cpp.html#ab36151479ad37d53ef9fcb60a274b1d9">range_queries::prefix_sum_array::build</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int64_t &gt; original_array)</td></tr>
<tr class="memdesc:ab36151479ad37d53ef9fcb60a274b1d9"><td class="mdescLeft">&#160;</td><td class="mdescRight">function that builds the PSA <br /></td></tr>
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<tr class="memitem:a7c8fd967c36dbba5fdf9c71faed604cf"><td class="memItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/d9e/prefix__sum__array_8cpp.html#a7c8fd967c36dbba5fdf9c71faed604cf">range_queries::prefix_sum_array::query</a> (int64_t beg, int64_t end)</td></tr>
<tr class="memdesc:a7c8fd967c36dbba5fdf9c71faed604cf"><td class="mdescLeft">&#160;</td><td class="mdescRight">query function <br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/d9e/prefix__sum__array_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</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="../../d1/d9e/prefix__sum__array_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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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int64_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>range_queries::prefix_sum_array::PSA</b> (1, 0)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Prefix_sum" target="_blank">Prefix Sum Array</a> data structure implementation. </p>
<p>Prefix Sum Array is a data structure, that allows answering sum in some range queries. It can answer most sum range queries in O(1), with a build time complexity of O(N). But it hasn't an update querie.</p>
<ul>
<li>Running Time Complexity <br />
</li>
<li>Build : O(N) <br />
</li>
<li>Range Query : O(1) <br />
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/PauloVLB" target="_blank">Paulo Vitor Lima Borges</a> </dd></dl>
</li>
</ul>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ab36151479ad37d53ef9fcb60a274b1d9" name="ab36151479ad37d53ef9fcb60a274b1d9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ab36151479ad37d53ef9fcb60a274b1d9">&#9670;&#160;</a></span>build()</h2>
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<td class="memname">void range_queries::prefix_sum_array::build </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int64_t &gt;&#160;</td>
<td class="paramname"><em>original_array</em></td><td>)</td>
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<p>function that builds the PSA </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">original_array</td><td>original array of values </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 41</span> {</div>
<div class="line"><span class="lineno"> 42</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= static_cast&lt;int&gt;(original_array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()); i++) {</div>
<div class="line"><span class="lineno"> 43</span> PSA.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(PSA[i - 1] + original_array[i]);</div>
<div class="line"><span class="lineno"> 44</span> }</div>
<div class="line"><span class="lineno"> 45</span>}</div>
<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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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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<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</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"> 80</span> {</div>
<div class="line"><span class="lineno"> 81</span> <a class="code hl_function" href="../../d1/d9e/prefix__sum__array_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 83</span>}</div>
<div class="ttc" id="aprefix__sum__array_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d1/d9e/prefix__sum__array_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> prefix_sum_array.cpp:61</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a7c8fd967c36dbba5fdf9c71faed604cf">&#9670;&#160;</a></span>query()</h2>
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<td class="memname">int64_t range_queries::prefix_sum_array::query </td>
<td>(</td>
<td class="paramtype">int64_t&#160;</td>
<td class="paramname"><em>beg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int64_t&#160;</td>
<td class="paramname"><em>end</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
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<p>query function </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">beg</td><td>begin of the interval to sum </td></tr>
<tr><td class="paramname">end</td><td>end of the interval to sum </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>sum of the range [beg, end] </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 52</span>{ <span class="keywordflow">return</span> PSA[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>] - PSA[beg - 1]; }</div>
<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a></div><div class="ttdeci">T end(T... args)</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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<td class="paramname"></td><td>)</td>
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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"> 61</span> {</div>
<div class="line"><span class="lineno"> 62</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> values{0, 123, 0, 2, -2, 5,</div>
<div class="line"><span class="lineno"> 63</span> 24, 0, 23, -1, -1}; <span class="comment">// original array</span></div>
<div class="line"><span class="lineno"> 64</span> </div>
<div class="line"><span class="lineno"> 65</span> <a class="code hl_function" href="../../d1/d9e/prefix__sum__array_8cpp.html#ab36151479ad37d53ef9fcb60a274b1d9">range_queries::prefix_sum_array::build</a>(values);</div>
<div class="line"><span class="lineno"> 66</span> <span class="comment">// queries are of the type: sum of the range [a, b] = psa[b] - psa[a-1]</span></div>
<div class="line"><span class="lineno"> 67</span> </div>
<div class="line"><span class="lineno"> 68</span> assert(range_queries::prefix_sum_array::query(1, 10) ==</div>
<div class="line"><span class="lineno"> 69</span> 173); <span class="comment">// sum of the entire array</span></div>
<div class="line"><span class="lineno"> 70</span> assert(range_queries::prefix_sum_array::query(4, 6) ==</div>
<div class="line"><span class="lineno"> 71</span> 27); <span class="comment">// the sum of the interval [4, 6]</span></div>
<div class="line"><span class="lineno"> 72</span> assert(range_queries::prefix_sum_array::query(5, 9) ==</div>
<div class="line"><span class="lineno"> 73</span> 51); <span class="comment">// the sum of the interval [5, 9]</span></div>
<div class="line"><span class="lineno"> 74</span>}</div>
<div class="ttc" id="aprefix__sum__array_8cpp_html_ab36151479ad37d53ef9fcb60a274b1d9"><div class="ttname"><a href="../../d1/d9e/prefix__sum__array_8cpp.html#ab36151479ad37d53ef9fcb60a274b1d9">range_queries::prefix_sum_array::build</a></div><div class="ttdeci">void build(std::vector&lt; int64_t &gt; original_array)</div><div class="ttdoc">function that builds the PSA</div><div class="ttdef"><b>Definition:</b> prefix_sum_array.cpp:41</div></div>
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