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 <span id="projectnumber">1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C.</div>
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<a href="#func-members">Functions</a> </div>
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<div class="title">sol1.c File Reference</div> </div>
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<div class="contents">
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<p><a href="https://projecteuler.net/problem=15">Problem 15</a> solution
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <stdint.h></code><br />
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<code>#include <stdio.h></code><br />
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<code>#include <stdlib.h></code><br />
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Include dependency graph for sol1.c:</div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a4650d1d3897633d84253f93433f601d6"><td class="memItemLeft" align="right" valign="top">unsigned long long </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>
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<tr class="memdesc:a4650d1d3897633d84253f93433f601d6"><td class="mdescLeft"> </td><td class="mdescRight">At every node, there are 2 possible ways to move -> down or right. <a href="../../d7/d91/problem__15_2sol1_8c.html#a4650d1d3897633d84253f93433f601d6">More...</a><br /></td></tr>
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<tr class="separator:a4650d1d3897633d84253f93433f601d6"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top"><a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
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int </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>
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<tr class="memdesc:a3c04138a5bfe5d72780bb7e82a18e627"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <br /></td></tr>
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<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p><a href="https://projecteuler.net/problem=15">Problem 15</a> solution </p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a4650d1d3897633d84253f93433f601d6"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a4650d1d3897633d84253f93433f601d6">◆ </a></span>number_of_paths()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">unsigned long long number_of_paths </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>N</em></td><td>)</td>
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<td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>At every node, there are 2 possible ways to move -> down or right. </p>
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<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>
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<div class="fragment"><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> {</div>
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<div class="line"><a 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>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < N; i++)</div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  {</div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  path *= (N << 1) - i;</div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  path /= i + 1;</div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  }</div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  </div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="keywordflow">return</span> path;</div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> }</div>
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<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>
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