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<p>This program aims at calculating <a href="https://cp-algorithms.com/combinatorics/binomial-coefficients.html">nCr modulo p</a>.
<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 ncr_modulo_p.cpp:</div>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html">math::ncr_modulo_p::NCRModuloP</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Class which contains all methods required for calculating nCr mod p. <a href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#details">More...</a><br /></td></tr>
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<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html" title="STL class.">std::vector</a> <br /></td></tr>
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<tr class="memitem:d4/db9/namespacencr__modulo__p"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/db9/namespacencr__modulo__p.html">ncr_modulo_p</a></td></tr>
<tr class="memdesc:d4/db9/namespacencr__modulo__p"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://cp-algorithms.com/combinatorics/binomial-coefficients.html">nCr modulo p</a> implementation. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:af0a3e6827f41c151e47451f5ff98b1f1"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dab/ncr__modulo__p_8cpp.html#af0a3e6827f41c151e47451f5ff98b1f1">tests</a> (<a class="el" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html">math::ncr_modulo_p::NCRModuloP</a> ncrObj)</td></tr>
<tr class="memdesc:af0a3e6827f41c151e47451f5ff98b1f1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test implementations. <a href="../../de/dab/ncr__modulo__p_8cpp.html#af0a3e6827f41c151e47451f5ff98b1f1">More...</a><br /></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="../../de/dab/ncr__modulo__p_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../de/dab/ncr__modulo__p_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>This program aims at calculating <a href="https://cp-algorithms.com/combinatorics/binomial-coefficients.html">nCr modulo p</a>. </p>
<p>nCr is defined as n! / (r! * (n-r)!) where n! represents factorial of n. In many cases, the value of nCr is too large to fit in a 64 bit integer. Hence, in competitive programming, there are many problems or subproblems to compute nCr modulo p where p is a given number. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/KaustubhDamania">Kaustubh Damania</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </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"><a name="l00137"></a><span class="lineno"> 137</span>&#160; {</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160; <span class="comment">// populate the fac array</span></div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160; <span class="keyword">const</span> uint64_t size = 1e6 + 1;</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160; <span class="keyword">const</span> uint64_t p = 1e9 + 7;</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160; <a class="code" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html">math::ncr_modulo_p::NCRModuloP</a> ncrObj =</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160; <a class="code" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html">math::ncr_modulo_p::NCRModuloP</a>(size, p);</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160; <span class="comment">// test 6Ci for i=0 to 7</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= 7; i++) {</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; 6 &lt;&lt; <span class="stringliteral">&quot;C&quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; = &quot;</span> &lt;&lt; ncrObj.<a class="code" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a6b95277f5f527beacc8d0f3bc91fcd08">ncr</a>(6, i, p) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160; }</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160; <a class="code" href="../../de/dab/ncr__modulo__p_8cpp.html#af0a3e6827f41c151e47451f5ff98b1f1">tests</a>(ncrObj); <span class="comment">// execute the tests</span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Assertions passed\n&quot;</span>;</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#af0a3e6827f41c151e47451f5ff98b1f1">&#9670;&nbsp;</a></span>tests()</h2>
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<td class="memname">static void tests </td>
<td>(</td>
<td class="paramtype"><a class="el" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html">math::ncr_modulo_p::NCRModuloP</a>&#160;</td>
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<p>Test implementations. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">ncrObj</td><td>object which contains the precomputed factorial values and ncr function </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; {</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; <span class="comment">// (52323 C 26161) % (1e9 + 7) = 224944353</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; assert(ncrObj.<a class="code" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a6b95277f5f527beacc8d0f3bc91fcd08">ncr</a>(52323, 26161, 1000000007) == 224944353);</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; <span class="comment">// 6 C 2 = 30, 30%5 = 0</span></div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; assert(ncrObj.<a class="code" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a6b95277f5f527beacc8d0f3bc91fcd08">ncr</a>(6, 2, 5) == 0);</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; <span class="comment">// 7C3 = 35, 35 % 29 = 8</span></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; assert(ncrObj.<a class="code" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a6b95277f5f527beacc8d0f3bc91fcd08">ncr</a>(7, 3, 29) == 6);</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160;}</div>
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<div class="ttc" id="ancr__modulo__p_8cpp_html_af0a3e6827f41c151e47451f5ff98b1f1"><div class="ttname"><a href="../../de/dab/ncr__modulo__p_8cpp.html#af0a3e6827f41c151e47451f5ff98b1f1">tests</a></div><div class="ttdeci">static void tests(math::ncr_modulo_p::NCRModuloP ncrObj)</div><div class="ttdoc">Test implementations.</div><div class="ttdef"><b>Definition:</b> ncr_modulo_p.cpp:124</div></div>
<div class="ttc" id="aclassmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p_html"><div class="ttname"><a href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html">math::ncr_modulo_p::NCRModuloP</a></div><div class="ttdoc">Class which contains all methods required for calculating nCr mod p.</div><div class="ttdef"><b>Definition:</b> ncr_modulo_p.cpp:31</div></div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="aclassmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p_html_a6b95277f5f527beacc8d0f3bc91fcd08"><div class="ttname"><a href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a6b95277f5f527beacc8d0f3bc91fcd08">math::ncr_modulo_p::NCRModuloP::ncr</a></div><div class="ttdeci">int64_t ncr(const uint64_t &amp;n, const uint64_t &amp;r, const uint64_t &amp;p)</div><div class="ttdef"><b>Definition:</b> ncr_modulo_p.cpp:92</div></div>
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