OpenSoure_Repos/TheAlgorithms-C
1
0
Fork 0
mirror of https://github.moeyy.xyz/https://github.com/TheAlgorithms/C.git synced 2023-10-11 15:56:24 +08:00
Code Issues Packages Projects Releases Wiki Activity
b81cf7e70d
TheAlgorithms-C/d7/d91/problem__15_2sol1_8c.html
github-actions ec104fadad Documentation for 37534f4d8c
2021-12-09 17:57:52 +00:00

214 lines
12 KiB
HTML
Raw Blame History

<!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">
<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 1.9.2"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Algorithms_in_C: project_euler/problem_15/sol1.c File Reference</title>
<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>
<link href="../../navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../resize.js"></script>
<script type="text/javascript" src="../../navtreedata.js"></script>
<script type="text/javascript" src="../../navtree.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/x-mathjax-config">
MathJax.Hub.Config({
extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
jax: ["input/TeX","output/HTML-CSS"],
});
</script>
<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
<link href="../../doxygen.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 style="height: 56px;">
<td id="projectalign" style="padding-left: 0.5em;">
<div id="projectname">Algorithms_in_C<span id="projectnumber">&#160;1.0.0</span>
</div>
<div id="projectbrief">Set of algorithms implemented in C.</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.9.2 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
var searchBox = new SearchBox("searchBox", "../../search",'Search','.html');
/* @license-end */
</script>
<script type="text/javascript" src="../../menudata.js"></script>
<script type="text/javascript" src="../../menu.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(function() {
initMenu('../../',true,false,'search.php','Search');
$(document).ready(function() { init_search(); });
});
/* @license-end */
</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">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(document).ready(function(){initNavTree('d7/d91/problem__15_2sol1_8c.html','../../'); initResizable(); });
/* @license-end */
</script>
<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">
<iframe src="javascript:void(0)" frameborder="0"
name="MSearchResults" id="MSearchResults">
</iframe>
</div>
<div class="header">
<div class="summary">
<a href="#func-members">Functions</a> </div>
<div class="headertitle"><div class="title">sol1.c File Reference</div></div>
</div><!--header-->
<div class="contents">
<p><a href="https://projecteuler.net/problem=15" target="_blank">Problem 15</a> solution
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;stdint.h&gt;</code><br />
<code>#include &lt;stdio.h&gt;</code><br />
<code>#include &lt;stdlib.h&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for sol1.c:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d75/problem__15_2sol1_8c__incl.svg" width="251" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
</div>
</div>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a4650d1d3897633d84253f93433f601d6"><td class="memItemLeft" align="right" valign="top">unsigned long long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d91/problem__15_2sol1_8c.html#a4650d1d3897633d84253f93433f601d6">number_of_paths</a> (int N)</td></tr>
<tr class="memdesc:a4650d1d3897633d84253f93433f601d6"><td class="mdescLeft">&#160;</td><td class="mdescRight">At every node, there are 2 possible ways to move -&gt; down or right. <a href="../../d7/d91/problem__15_2sol1_8c.html#a4650d1d3897633d84253f93433f601d6">More...</a><br /></td></tr>
<tr class="separator:a4650d1d3897633d84253f93433f601d6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d91/problem__15_2sol1_8c.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
<tr class="memdesc:a3c04138a5bfe5d72780bb7e82a18e627"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d7/d91/problem__15_2sol1_8c.html#a3c04138a5bfe5d72780bb7e82a18e627">More...</a><br /></td></tr>
<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p ><a href="https://projecteuler.net/problem=15" target="_blank">Problem 15</a> solution </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a3c04138a5bfe5d72780bb7e82a18e627" name="a3c04138a5bfe5d72780bb7e82a18e627"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&nbsp;</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">int&#160;</td>
<td class="paramname"><em>argc</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">char **&#160;</td>
<td class="paramname"><em>argv</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Main function. </p>
<div class="fragment"><div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span>{</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keywordtype">int</span> N = 20;</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">if</span> (argc == 2)</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> N = atoi(argv[1]);</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> printf(<span class="stringliteral">&quot;Number of ways to traverse diagonal of %dx%d grid = %llu\n&quot;</span>, N, N,</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <a class="code hl_function" href="../../d7/d91/problem__15_2sol1_8c.html#a4650d1d3897633d84253f93433f601d6">number_of_paths</a>(N));</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span>}</div>
<div class="ttc" id="aproblem__15_2sol1_8c_html_a4650d1d3897633d84253f93433f601d6"><div class="ttname"><a href="../../d7/d91/problem__15_2sol1_8c.html#a4650d1d3897633d84253f93433f601d6">number_of_paths</a></div><div class="ttdeci">unsigned long long number_of_paths(int N)</div><div class="ttdoc">At every node, there are 2 possible ways to move -&gt; down or right.</div><div class="ttdef"><b>Definition:</b> sol1.c:17</div></div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../d7/d91/problem__15_2sol1_8c_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="232" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
</div>
</div>
</div>
</div>
<a id="a4650d1d3897633d84253f93433f601d6" name="a4650d1d3897633d84253f93433f601d6"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a4650d1d3897633d84253f93433f601d6">&#9670;&nbsp;</a></span>number_of_paths()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">unsigned long long number_of_paths </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>N</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>At every node, there are 2 possible ways to move -&gt; down or right. </p>
<p >Since it is a square grid, there are in all, 2N steps with N down and N right options, without preference for order. Hence, the path can be be traced in N out of 2N number of ways. This is the same as binomial coeeficient. </p>
<div class="fragment"><div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span>{</div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> <span class="keywordtype">long</span> path = 1;</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++)</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> {</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> path *= (N &lt;&lt; 1) - i;</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> path /= i + 1;</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> }</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> </div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <span class="keywordflow">return</span> path;</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span>}</div>
</div><!-- fragment -->
</div>
</div>
</div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_b3d331eabd4234f247030c297aaf021c.html">project_euler</a></li><li class="navelem"><a class="el" href="../../dir_2b14f32f14b51065d3a322bea21da3c0.html">problem_15</a></li><li class="navelem"><a class="el" href="../../d7/d91/problem__15_2sol1_8c.html">sol1.c</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> 1.9.2 </li>
</ul>
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink