backup/C-Plus-Plus
1
0
Fork 0
mirror of https://github.com/TheAlgorithms/C-Plus-Plus.git synced 2026-10-29 03:44:39 +08:00
Code Issues Projects Releases Wiki Activity
Files
gh-pages
C-Plus-Plus/d5/d83/lcm__sum_8cpp.html
realstealthninja cc04e74d11 Documentation for af6e2c8991
2026-09-21 04:13:18 +00:00

281 lines
16 KiB
HTML
Raw Permalink 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 1.18.0"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>TheAlgorithms/C++: math/lcm_sum.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 1.18.0 -->
<script type="text/javascript">
let searchBox = new SearchBox("searchBox", "../../search/",'.html');
</script>
<script type="text/javascript">
document.addEventListener('DOMContentLoaded', codefold.init);
</script>
<script type="application/json" id="doxygen-config">
{
"relPath": "../../",
"generateTreeView": true,
"searchEngine": true,
"serverBasedSearch": false,
"disableIndex": false,
"dynamicMenus": true,
"fullSidebar": false
}
</script>
<script type="text/javascript" src="../../menudata.js"></script>
<script type="text/javascript" src="../../menu.js"></script>
<div id="main-nav-mobile">
<div class="sm sm-dox"><input id="main-menu-state" type="checkbox"/>
<label class="main-menu-btn" for="main-menu-state">
<span class="main-menu-btn-icon"></span> Toggle main menu visibility</label>
<span id="searchBoxPos1"></span>
</div>
</div><!-- main-nav-mobile -->
<div id="main-nav">
<ul class="sm sm-dox" id="main-menu">
<li id="searchBoxPos2">
<div id="MSearchBox" class="MSearchBoxInactive">
<span class="left">
<span id="MSearchSelect" class="search-icon"><span class="search-icon-dropdown"></span></span>
<input type="text" id="MSearchField" value="" placeholder="Search" accesskey="S"/>
</span><span class="right">
<a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><div id="MSearchCloseImg" class="close-icon"></div></a>
</span>
</div>
</li>
</ul>
</div><!-- main-nav -->
</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" class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
document.addEventListener('DOMContentLoaded',() => { initNavTree('d5/d83/lcm__sum_8cpp.html','../../',''); });
</script>
<div id="container">
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow">
</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">lcm_sum.cpp File Reference</div></div>
</div><!--header-->
<div class="contents">
<p>An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) +
\mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\).
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cstdint&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 lcm_sum.cpp:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" loading="lazy" frameborder="0" src="../../d1/d52/lcm__sum_8cpp__incl.svg" width="336" height="111"><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="../../d5/d83/lcm__sum_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:math" id="r_math"><td class="memItemLeft">namespace &#160;</td><td class="memItemRight"><a class="el" href="../../dd/d47/namespacemath.html">math</a></td></tr>
<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for assert <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:a04065193d190d605e1f0d0d93a87e244" id="r_a04065193d190d605e1f0d0d93a87e244"><td class="memItemLeft">uint64_t&#160;</td><td class="memItemRight"><a class="el" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a> (const uint16_t &amp;num)</td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft">static void&#160;</td><td class="memItemRight"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft">int&#160;</td><td class="memItemRight"><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>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) +
\mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\). </p>
<p>An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) +
\mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\) where \(\mathrm{LCM}(i,n)\) denotes the Least Common Multiple of the integers i and n. For n greater than or equal to 1. The value of the sum is calculated by formula: </p><p class="formulaDsp">
\[ \sum\mathrm{LCM}(i, n) = \frac{1}{2} \left[\left(\sum (d *
\mathrm{ETF}(d)) + 1\right) * n\right] \]
</p>
<p> where \mathrm{ETF}(i) represents Euler totient function of i. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/chestamittal" target="_blank">Chesta Mittal</a> </dd></dl>
<p class="definition">Definition in file <a class="el" href="../../d5/d83/lcm__sum_8cpp_source.html">lcm_sum.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="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="../../d5/d83/lcm__sum_8cpp_source.html#l00097">97</a> of file <a class="el" href="../../d5/d83/lcm__sum_8cpp_source.html">lcm_sum.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 97</span> {</div>
<div class="line"><span class="lineno"> 98</span> <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><span class="lineno"> 99</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 100</span>}</div>
<div class="ttc" id="acaesar__cipher_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition</b> <a href="../../d6/d2c/caesar__cipher_8cpp_source.html#l00100">caesar_cipher.cpp:100</a></div></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>Function for testing lcmSum function. test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><span class="tt">void</span> </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d5/d83/lcm__sum_8cpp_source.html#l00066">66</a> of file <a class="el" href="../../d5/d83/lcm__sum_8cpp_source.html">lcm_sum.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 66</span> {</div>
<div class="line"><span class="lineno"> 67</span> uint64_t n = 2;</div>
<div class="line"><span class="lineno"> 68</span> uint64_t test_1 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
<div class="line"><span class="lineno"> 69</span> assert(test_1 == 4);</div>
<div class="line"><span class="lineno"> 70</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 1!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> n = 5;</div>
<div class="line"><span class="lineno"> 73</span> uint64_t test_2 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
<div class="line"><span class="lineno"> 74</span> assert(test_2 == 55);</div>
<div class="line"><span class="lineno"> 75</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 2!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 76</span> </div>
<div class="line"><span class="lineno"> 77</span> n = 10;</div>
<div class="line"><span class="lineno"> 78</span> uint64_t test_3 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
<div class="line"><span class="lineno"> 79</span> assert(test_3 == 320);</div>
<div class="line"><span class="lineno"> 80</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 3!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 81</span> </div>
<div class="line"><span class="lineno"> 82</span> n = 11;</div>
<div class="line"><span class="lineno"> 83</span> uint64_t test_4 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
<div class="line"><span class="lineno"> 84</span> assert(test_4 == 616);</div>
<div class="line"><span class="lineno"> 85</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 4!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 86</span> </div>
<div class="line"><span class="lineno"> 87</span> n = 15;</div>
<div class="line"><span class="lineno"> 88</span> uint64_t test_5 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a>(n);</div>
<div class="line"><span class="lineno"> 89</span> assert(test_5 == 1110);</div>
<div class="line"><span class="lineno"> 90</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 5!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 91</span>}</div>
<div class="ttc" id="anamespacemath_html_a04065193d190d605e1f0d0d93a87e244"><div class="ttname"><a href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">math::lcmSum</a></div><div class="ttdeci">uint64_t lcmSum(const uint16_t &amp;num)</div><div class="ttdef"><b>Definition</b> <a href="../../d5/d83/lcm__sum_8cpp_source.html#l00030">lcm_sum.cpp:30</a></div></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_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a href="../../d5/d83/lcm__sum_8cpp.html">lcm_sum.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> 1.18.0 </li>
</ul>
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink