backup/C-Plus-Plus
1
0
Fork 0
mirror of https://github.com/TheAlgorithms/C-Plus-Plus.git synced 2026-03-21 04:18:34 +08:00
Code Issues Projects Releases Wiki Activity
Files
534053f7c48fee934362034b46366bd30f7ad2ad
C-Plus-Plus/d1/d9e/prefix__sum__array_8cpp.html
realstealthninja 534053f7c4 Documentation for 93c64b558a
2025-08-17 10:14:39 +00:00

349 lines
20 KiB
HTML
Raw Blame History

<!-- HTML header for doxygen 1.12.0-->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en-US">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=11"/>
<meta name="generator" content="Doxygen 1.14.0"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>TheAlgorithms/C++: range_queries/prefix_sum_array.cpp File Reference</title>
<link rel="icon" href="../../favicon.svg" type="image/x-icon" />
<link href="../../tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../jquery.js"></script>
<script type="text/javascript" src="../../dynsections.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/@xpack-3rd-party/doxygen-awesome-css@2.2.0-1/doxygen-awesome-darkmode-toggle.js"></script>
<script type="text/javascript">
DoxygenAwesomeDarkModeToggle.init()
</script>
<script type="text/javascript" src="../../clipboard.js"></script>
<link href="../../navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../navtreedata.js"></script>
<script type="text/javascript" src="../../navtree.js"></script>
<script type="text/javascript" src="../../cookie.js"></script>
<link href="../../search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../search/searchdata.js"></script>
<script type="text/javascript" src="../../search/search.js"></script>
<script type="text/javascript">
window.MathJax = {
options: {
ignoreHtmlClass: 'tex2jax_ignore',
processHtmlClass: 'tex2jax_process'
},
loader: {
load: ['[tex]/ams']
},
tex: {
macros: {},
packages: ['base','configmacros','ams']
}
};
</script>
<script type="text/javascript" id="MathJax-script" async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>
<link href="../../doxygen.css" rel="stylesheet" type="text/css" />
<link href="../../doxygen-awesome.css" rel="stylesheet" type="text/css"/>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr id="projectrow">
<td id="projectlogo"><img alt="Logo" src="../../project_logo.png"/></td>
<td id="projectalign">
<div id="projectname">TheAlgorithms/C++<span id="projectnumber">&#160;1.0.0</span>
</div>
<div id="projectbrief">All the algorithms implemented in C++</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.14.0 -->
<script type="text/javascript">
var searchBox = new SearchBox("searchBox", "../../search/",'.html');
</script>
<script type="text/javascript">
$(function() { codefold.init(); });
</script>
<script type="text/javascript" src="../../menudata.js"></script>
<script type="text/javascript" src="../../menu.js"></script>
<script type="text/javascript">
$(function() {
initMenu('../../',true,false,'search.php','Search',true);
$(function() { init_search(); });
});
</script>
<div id="main-nav"></div>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;"
class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
$(function(){initNavTree('d1/d9e/prefix__sum__array_8cpp.html','../../',''); });
</script>
<div id="container">
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<div id="MSearchResults">
<div class="SRPage">
<div id="SRIndex">
<div id="SRResults"></div>
<div class="SRStatus" id="Loading">Loading...</div>
<div class="SRStatus" id="Searching">Searching...</div>
<div class="SRStatus" id="NoMatches">No Matches</div>
</div>
</div>
</div>
</div>
<div class="header">
<div class="headertitle"><div class="title">prefix_sum_array.cpp File Reference</div></div>
</div><!--header-->
<div class="contents">
<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 />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for prefix_sum_array.cpp:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" loading="lazy" frameborder="0" src="../../d2/d76/prefix__sum__array_8cpp__incl.svg" width="252" height="126"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
</div>
</div>
<p><a href="../../d1/d9e/prefix__sum__array_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-namespaces" class="groupheader"><a id="namespaces" name="namespaces"></a>
Namespaces</h2></td></tr>
<tr class="memitem:range_5Fqueries" id="r_range_5Fqueries"><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">for std::vector <br /></td></tr>
<tr class="memitem:prefix_5Fsum_5Farray" id="r_prefix_5Fsum_5Farray"><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>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a98e118ed64ba95a8198e1a915459c177" id="r_a98e118ed64ba95a8198e1a915459c177"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a98e118ed64ba95a8198e1a915459c177">range_queries::prefix_sum_array::build</a> (const std::vector&lt; int64_t &gt; &amp;original_array)</td></tr>
<tr class="memdesc:a98e118ed64ba95a8198e1a915459c177"><td class="mdescLeft">&#160;</td><td class="mdescRight">function that builds the PSA <br /></td></tr>
<tr class="memitem:a7c8fd967c36dbba5fdf9c71faed604cf" id="r_a7c8fd967c36dbba5fdf9c71faed604cf"><td class="memItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#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>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-var-members" class="groupheader"><a id="var-members" name="var-members"></a>
Variables</h2></td></tr>
<tr class="memitem:a4051fe9652babad269ce08239eb493f1" id="r_a4051fe9652babad269ce08239eb493f1"><td class="memItemLeft" align="right" valign="top">std::vector&lt; int64_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a4051fe9652babad269ce08239eb493f1">range_queries::prefix_sum_array::PSA</a> {}</td></tr>
</table>
<a name="details" id="details"></a><h2 id="header-details" 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>
<p class="definition">Definition in file <a class="el" href="../../d1/d9e/prefix__sum__array_8cpp_source.html">prefix_sum_array.cpp</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="a98e118ed64ba95a8198e1a915459c177" name="a98e118ed64ba95a8198e1a915459c177"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a98e118ed64ba95a8198e1a915459c177">&#9670;&#160;</a></span>build()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void range_queries::prefix_sum_array::build </td>
<td>(</td>
<td class="paramtype">const std::vector&lt; int64_t &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>original_array</em></span></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<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>
<p class="definition">Definition at line <a class="el" href="../../d1/d9e/prefix__sum__array_8cpp_source.html#l00041">41</a> of file <a class="el" href="../../d1/d9e/prefix__sum__array_8cpp_source.html">prefix_sum_array.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 41</span> {</div>
<div class="line"><span class="lineno"> 42</span> PSA.clear();</div>
<div class="line"><span class="lineno"> 43</span> PSA.push_back(0);</div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">for</span> (std::size_t i = 1; i &lt; original_array.size(); ++i) {</div>
<div class="line"><span class="lineno"> 45</span> PSA.push_back(PSA.back() + original_array[i]);</div>
<div class="line"><span class="lineno"> 46</span> }</div>
<div class="line"><span class="lineno"> 47</span>}</div>
</div><!-- fragment -->
</div>
</div>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d1/d9e/prefix__sum__array_8cpp_source.html#l00082">82</a> of file <a class="el" href="../../d1/d9e/prefix__sum__array_8cpp_source.html">prefix_sum_array.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 82</span> {</div>
<div class="line"><span class="lineno"> 83</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 84</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 85</span>}</div>
<div class="ttc" id="aprefix__sum__array_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../d1/d9e/prefix__sum__array_8cpp_source.html#l00063">prefix_sum_array.cpp:63</a></div></div>
</div><!-- fragment -->
</div>
</div>
<a id="a7c8fd967c36dbba5fdf9c71faed604cf" name="a7c8fd967c36dbba5fdf9c71faed604cf"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7c8fd967c36dbba5fdf9c71faed604cf">&#9670;&#160;</a></span>query()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int64_t range_queries::prefix_sum_array::query </td>
<td>(</td>
<td class="paramtype">int64_t</td> <td class="paramname"><span class="paramname"><em>beg</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int64_t</td> <td class="paramname"><span class="paramname"><em>end</em></span>&#160;)</td>
</tr>
</table>
</div><div class="memdoc">
<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>
<p class="definition">Definition at line <a class="el" href="../../d1/d9e/prefix__sum__array_8cpp_source.html#l00054">54</a> of file <a class="el" href="../../d1/d9e/prefix__sum__array_8cpp_source.html">prefix_sum_array.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 54</span>{ <span class="keywordflow">return</span> PSA[end] - PSA[beg - 1]; }</div>
</div><!-- fragment -->
</div>
</div>
<a id="aa8dca7b867074164d5f45b0f3851269d" name="aa8dca7b867074164d5f45b0f3851269d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
<div class="memitem">
<div class="memproto">
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">void test </td>
<td>(</td>
<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel static">static</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d1/d9e/prefix__sum__array_8cpp_source.html#l00063">63</a> of file <a class="el" href="../../d1/d9e/prefix__sum__array_8cpp_source.html">prefix_sum_array.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 63</span> {</div>
<div class="line"><span class="lineno"> 64</span> std::vector&lt;int64_t&gt; values{0, 123, 0, 2, -2, 5,</div>
<div class="line"><span class="lineno"> 65</span> 24, 0, 23, -1, -1}; <span class="comment">// original array</span></div>
<div class="line"><span class="lineno"> 66</span> </div>
<div class="line"><span class="lineno"> 67</span> <a class="code hl_function" href="#a98e118ed64ba95a8198e1a915459c177">range_queries::prefix_sum_array::build</a>(values);</div>
<div class="line"><span class="lineno"> 68</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"> 69</span> </div>
<div class="line"><span class="lineno"> 70</span> assert(<a class="code hl_function" href="#a7c8fd967c36dbba5fdf9c71faed604cf">range_queries::prefix_sum_array::query</a>(1, 10) ==</div>
<div class="line"><span class="lineno"> 71</span> 173); <span class="comment">// sum of the entire array</span></div>
<div class="line"><span class="lineno"> 72</span> assert(<a class="code hl_function" href="#a7c8fd967c36dbba5fdf9c71faed604cf">range_queries::prefix_sum_array::query</a>(4, 6) ==</div>
<div class="line"><span class="lineno"> 73</span> 27); <span class="comment">// the sum of the interval [4, 6]</span></div>
<div class="line"><span class="lineno"> 74</span> assert(<a class="code hl_function" href="#a7c8fd967c36dbba5fdf9c71faed604cf">range_queries::prefix_sum_array::query</a>(5, 9) ==</div>
<div class="line"><span class="lineno"> 75</span> 51); <span class="comment">// the sum of the interval [5, 9]</span></div>
<div class="line"><span class="lineno"> 76</span>}</div>
<div class="ttc" id="aprefix__sum__array_8cpp_html_a7c8fd967c36dbba5fdf9c71faed604cf"><div class="ttname"><a href="#a7c8fd967c36dbba5fdf9c71faed604cf">range_queries::prefix_sum_array::query</a></div><div class="ttdeci">int64_t query(int64_t beg, int64_t end)</div><div class="ttdoc">query function</div><div class="ttdef"><b>Definition</b> <a href="../../d1/d9e/prefix__sum__array_8cpp_source.html#l00054">prefix_sum_array.cpp:54</a></div></div>
<div class="ttc" id="aprefix__sum__array_8cpp_html_a98e118ed64ba95a8198e1a915459c177"><div class="ttname"><a href="#a98e118ed64ba95a8198e1a915459c177">range_queries::prefix_sum_array::build</a></div><div class="ttdeci">void build(const std::vector&lt; int64_t &gt; &amp;original_array)</div><div class="ttdoc">function that builds the PSA</div><div class="ttdef"><b>Definition</b> <a href="../../d1/d9e/prefix__sum__array_8cpp_source.html#l00041">prefix_sum_array.cpp:41</a></div></div>
</div><!-- fragment -->
</div>
</div>
<a name="doc-var-members" id="doc-var-members"></a><h2 id="header-doc-var-members" class="groupheader">Variable Documentation</h2>
<a id="a4051fe9652babad269ce08239eb493f1" name="a4051fe9652babad269ce08239eb493f1"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a4051fe9652babad269ce08239eb493f1">&#9670;&#160;</a></span>PSA</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">std::vector&lt;int64_t&gt; range_queries::prefix_sum_array::PSA {}</td>
</tr>
</table>
</div><div class="memdoc">
<p class="definition">Definition at line <a class="el" href="../../d1/d9e/prefix__sum__array_8cpp_source.html#l00034">34</a> of file <a class="el" href="../../d1/d9e/prefix__sum__array_8cpp_source.html">prefix_sum_array.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 34</span>{};</div>
</div><!-- fragment -->
</div>
</div>
</div><!-- contents -->
</div><!-- doc-content -->
<div id="page-nav" class="page-nav-panel">
<div id="page-nav-resize-handle"></div>
<div id="page-nav-tree">
<div id="page-nav-contents">
</div><!-- page-nav-contents -->
</div><!-- page-nav-tree -->
</div><!-- page-nav -->
</div><!-- container -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a href="../../dir_074119ce3a874b57120c49a0cc4bb5ad.html">range_queries</a></li><li class="navelem"><a href="../../d1/d9e/prefix__sum__array_8cpp.html">prefix_sum_array.cpp</a></li>
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.14.0 </li>
</ul>
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink