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<div class="header">
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<a href="#pub-methods">Public Member Functions</a> &#124;
<a href="#pri-static-methods">Static Private Member Functions</a> &#124;
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<a href="../../de/d1e/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p-members.html">List of all members</a> </div>
<div class="headertitle"><div class="title">math::ncr_modulo_p::NCRModuloP Class Reference</div></div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:af3d41271912f9fa50b774c96c51874b9" id="r_af3d41271912f9fa50b774c96c51874b9"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#af3d41271912f9fa50b774c96c51874b9">NCRModuloP</a> (const uint64_t &amp;size, const uint64_t &amp;mod)</td></tr>
<tr class="memdesc:af3d41271912f9fa50b774c96c51874b9"><td class="mdescLeft">&#160;</td><td class="mdescRight">the p from (nCr % p) <br /></td></tr>
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<tr class="memitem:afde201f4687740454302c444f507a926" id="r_afde201f4687740454302c444f507a926"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#afde201f4687740454302c444f507a926">gcdExtended</a> (const uint64_t &amp;a, const uint64_t &amp;b, int64_t *x, int64_t *y)</td></tr>
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<tr class="separator:a6b95277f5f527beacc8d0f3bc91fcd08"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a94b07e7dc61d8d7a1e9c5a28988e72f9" id="r_a94b07e7dc61d8d7a1e9c5a28988e72f9"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a94b07e7dc61d8d7a1e9c5a28988e72f9">NCRModuloP</a> (const int64_t &amp;size, const int64_t &amp;p)</td></tr>
<tr class="memdesc:a94b07e7dc61d8d7a1e9c5a28988e72f9"><td class="mdescLeft">&#160;</td><td class="mdescRight">constructs an <a class="el" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html" title="Class which contains all methods required for calculating nCr mod p.">NCRModuloP</a> object allowing to compute (nCr)p for inputs from 0 to size <br /></td></tr>
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<tr class="memdesc:a499df7a01bcd348345dc5a0ab79bb0e9"><td class="mdescLeft">&#160;</td><td class="mdescRight">computes nCr % p <br /></td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pri-static-methods" name="pri-static-methods"></a>
Static Private Member Functions</h2></td></tr>
<tr class="memitem:ab5744fa589f6a48f9fe7bca13dbe661f" id="r_ab5744fa589f6a48f9fe7bca13dbe661f"><td class="memItemLeft" align="right" valign="top">static <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int64_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ab5744fa589f6a48f9fe7bca13dbe661f">computeFactorialsMod</a> (const int64_t &amp;max_arg_val, const int64_t &amp;mod)</td></tr>
<tr class="memdesc:ab5744fa589f6a48f9fe7bca13dbe661f"><td class="mdescLeft">&#160;</td><td class="mdescRight">stores precomputed factorial(i) % p value <br /></td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pri-attribs" name="pri-attribs"></a>
Private Attributes</h2></td></tr>
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uint64_t&#160;</td><td class="memItemRight" valign="bottom"><b>p</b> = 0</td></tr>
<tr class="memdesc:a57c168cd6eb85718eab97da658a698ad"><td class="mdescLeft">&#160;</td><td class="mdescRight">stores precomputed factorial(i) % p value <br /></td></tr>
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const int64_t&#160;</td><td class="memItemRight" valign="bottom"><b>p</b> = 0</td></tr>
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const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int64_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>fac</b></td></tr>
<tr class="memdesc:a738a5f59bb3560c81cdb7f43bcfe9fec"><td class="mdescLeft">&#160;</td><td class="mdescRight">the p from (nCr % p) <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Class which contains all methods required for calculating nCr mod p. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="af3d41271912f9fa50b774c96c51874b9" name="af3d41271912f9fa50b774c96c51874b9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af3d41271912f9fa50b774c96c51874b9">&#9670;&#160;</a></span>NCRModuloP()</h2>
<a id="a94b07e7dc61d8d7a1e9c5a28988e72f9" name="a94b07e7dc61d8d7a1e9c5a28988e72f9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a94b07e7dc61d8d7a1e9c5a28988e72f9">&#9670;&#160;</a></span>NCRModuloP()</h2>
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@@ -156,12 +161,12 @@ uint64_t&#160;</td><td class="memItemRight" valign="bottom"><b>p</b> = 0</td></t
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<td class="memname">math::ncr_modulo_p::NCRModuloP::NCRModuloP </td>
<td>(</td>
<td class="paramtype">const uint64_t &amp;</td> <td class="paramname"><span class="paramname"><em>size</em></span>, </td>
<td class="paramtype">const int64_t &amp;</td> <td class="paramname"><span class="paramname"><em>size</em></span>, </td>
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<td class="paramtype">const uint64_t &amp;</td> <td class="paramname"><span class="paramname"><em>mod</em></span>&#160;)</td>
<td class="paramtype">const int64_t &amp;</td> <td class="paramname"><span class="paramname"><em>p</em></span>&#160;)</td>
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<p>the p from (nCr % p) </p>
<p>Constructor which precomputes the values of n! % mod from n=0 to size and stores them in vector 'fac' @params[in] the numbers 'size', 'mod' </p>
<div class="fragment"><div class="line"><span class="lineno"> 41</span> {</div>
<div class="line"><span class="lineno"> 42</span> <a class="code hl_variable" href="#a57c168cd6eb85718eab97da658a698ad">p</a> = mod;</div>
<div class="line"><span class="lineno"> 43</span> fac = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(size);</div>
<div class="line"><span class="lineno"> 44</span> fac[0] = 1;</div>
<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= size; i++) {</div>
<div class="line"><span class="lineno"> 46</span> fac[i] = (fac[i - 1] * i) % <a class="code hl_variable" href="#a57c168cd6eb85718eab97da658a698ad">p</a>;</div>
<div class="line"><span class="lineno"> 47</span> }</div>
<div class="line"><span class="lineno"> 48</span> }</div>
<div class="ttc" id="aclassmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p_html_a57c168cd6eb85718eab97da658a698ad"><div class="ttname"><a href="#a57c168cd6eb85718eab97da658a698ad">math::ncr_modulo_p::NCRModuloP::p</a></div><div class="ttdeci">uint64_t p</div><div class="ttdoc">stores precomputed factorial(i) % p value</div><div class="ttdef"><b>Definition</b> ncr_modulo_p.cpp:34</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
<p>constructs an <a class="el" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html" title="Class which contains all methods required for calculating nCr mod p.">NCRModuloP</a> object allowing to compute (nCr)p for inputs from 0 to size </p>
<div class="fragment"><div class="line"><span class="lineno"> 108</span> : p(p), <a class="code hl_variable" href="#a738a5f59bb3560c81cdb7f43bcfe9fec">fac</a>(<a class="code hl_function" href="#ab5744fa589f6a48f9fe7bca13dbe661f">computeFactorialsMod</a>(size, p)) {}</div>
<div class="ttc" id="aclassmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p_html_a738a5f59bb3560c81cdb7f43bcfe9fec"><div class="ttname"><a href="#a738a5f59bb3560c81cdb7f43bcfe9fec">math::ncr_modulo_p::NCRModuloP::fac</a></div><div class="ttdeci">const std::vector&lt; int64_t &gt; fac</div><div class="ttdoc">the p from (nCr % p)</div><div class="ttdef"><b>Definition</b> ncr_modulo_p.cpp:83</div></div>
<div class="ttc" id="aclassmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p_html_ab5744fa589f6a48f9fe7bca13dbe661f"><div class="ttname"><a href="#ab5744fa589f6a48f9fe7bca13dbe661f">math::ncr_modulo_p::NCRModuloP::computeFactorialsMod</a></div><div class="ttdeci">static std::vector&lt; int64_t &gt; computeFactorialsMod(const int64_t &amp;max_arg_val, const int64_t &amp;mod)</div><div class="ttdoc">stores precomputed factorial(i) % p value</div><div class="ttdef"><b>Definition</b> ncr_modulo_p.cpp:92</div></div>
</div><!-- fragment -->
</div>
</div>
<h2 class="groupheader">Member Function Documentation</h2>
<a id="afde201f4687740454302c444f507a926" name="afde201f4687740454302c444f507a926"></a>
<h2 class="memtitle"><span class="permalink"><a href="#afde201f4687740454302c444f507a926">&#9670;&#160;</a></span>gcdExtended()</h2>
<a id="ab5744fa589f6a48f9fe7bca13dbe661f" name="ab5744fa589f6a48f9fe7bca13dbe661f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ab5744fa589f6a48f9fe7bca13dbe661f">&#9670;&#160;</a></span>computeFactorialsMod()</h2>
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@@ -197,106 +194,46 @@ uint64_t&#160;</td><td class="memItemRight" valign="bottom"><b>p</b> = 0</td></t
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">uint64_t math::ncr_modulo_p::NCRModuloP::gcdExtended </td>
<td class="memname">static <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int64_t &gt; math::ncr_modulo_p::NCRModuloP::computeFactorialsMod </td>
<td>(</td>
<td class="paramtype">const uint64_t &amp;</td> <td class="paramname"><span class="paramname"><em>a</em></span>, </td>
<td class="paramtype">const int64_t &amp;</td> <td class="paramname"><span class="paramname"><em>max_arg_val</em></span>, </td>
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<td class="paramtype">const uint64_t &amp;</td> <td class="paramname"><span class="paramname"><em>b</em></span>, </td>
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<td class="paramtype">int64_t *</td> <td class="paramname"><span class="paramname"><em>x</em></span>, </td>
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<td></td>
<td class="paramtype">int64_t *</td> <td class="paramname"><span class="paramname"><em>y</em></span>&#160;)</td>
<td class="paramtype">const int64_t &amp;</td> <td class="paramname"><span class="paramname"><em>mod</em></span>&#160;)</td>
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<span class="mlabels"><span class="mlabel">inline</span></span> </td>
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">static</span><span class="mlabel">private</span></span> </td>
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<p>Finds the value of x, y such that a*x + b*y = gcd(a,b)</p>
<p>@params[in] the numbers 'a', 'b' and address of 'x' and 'y' from above equation </p><dl class="section return"><dt>Returns</dt><dd>the gcd of a and b </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 57</span> {</div>
<div class="line"><span class="lineno"> 58</span> <span class="keywordflow">if</span> (a == 0) {</div>
<div class="line"><span class="lineno"> 59</span> *x = 0, *y = 1;</div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">return</span> b;</div>
<div class="line"><span class="lineno"> 61</span> }</div>
<div class="line"><span class="lineno"> 62</span> </div>
<div class="line"><span class="lineno"> 63</span> int64_t x1 = 0, y1 = 0;</div>
<div class="line"><span class="lineno"> 64</span> uint64_t <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> = <a class="code hl_function" href="#afde201f4687740454302c444f507a926">gcdExtended</a>(b % a, a, &amp;x1, &amp;y1);</div>
<div class="line"><span class="lineno"> 65</span> </div>
<div class="line"><span class="lineno"> 66</span> *x = y1 - (b / a) * x1;</div>
<div class="line"><span class="lineno"> 67</span> *y = x1;</div>
<div class="line"><span class="lineno"> 68</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>;</div>
<div class="line"><span class="lineno"> 69</span> }</div>
<div class="ttc" id="aclassmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p_html_afde201f4687740454302c444f507a926"><div class="ttname"><a href="#afde201f4687740454302c444f507a926">math::ncr_modulo_p::NCRModuloP::gcdExtended</a></div><div class="ttdeci">uint64_t gcdExtended(const uint64_t &amp;a, const uint64_t &amp;b, int64_t *x, int64_t *y)</div><div class="ttdef"><b>Definition</b> ncr_modulo_p.cpp:56</div></div>
<div class="ttc" id="agcd__iterative__euclidean_8cpp_html_ae48807fa2b7000afae599e67f327545e"><div class="ttname"><a href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a></div><div class="ttdeci">int gcd(int num1, int num2)</div><div class="ttdef"><b>Definition</b> gcd_iterative_euclidean.cpp:15</div></div>
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Here is the call graph for this function:</div>
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<p>stores precomputed factorial(i) % p value </p>
<p>computes the array of values of factorials reduced modulo mod </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">max_arg_val</td><td>argument of the last factorial stored in the result </td></tr>
<tr><td class="paramname">mod</td><td>value of the divisor used to reduce factorials </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>vector storing factorials of the numbers 0, ..., max_arg_val reduced modulo mod </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 93</span> {</div>
<div class="line"><span class="lineno"> 94</span> <span class="keyword">auto</span> res = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a>(max_arg_val + 1);</div>
<div class="line"><span class="lineno"> 95</span> res[0] = 1;</div>
<div class="line"><span class="lineno"> 96</span> <span class="keywordflow">for</span> (int64_t i = 1; i &lt;= max_arg_val; i++) {</div>
<div class="line"><span class="lineno"> 97</span> res[i] = (res[i - 1] * i) % mod;</div>
<div class="line"><span class="lineno"> 98</span> }</div>
<div class="line"><span class="lineno"> 99</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><span class="lineno"> 100</span> }</div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0431ec5c876e1154d8e1e5f89e1ab34a">&#9670;&#160;</a></span>modInverse()</h2>
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<td class="memname">int64_t math::ncr_modulo_p::NCRModuloP::modInverse </td>
<td>(</td>
<td class="paramtype">const uint64_t &amp;</td> <td class="paramname"><span class="paramname"><em>a</em></span>, </td>
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<td class="paramtype">const uint64_t &amp;</td> <td class="paramname"><span class="paramname"><em>m</em></span>&#160;)</td>
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<p>Find modular inverse of a with m i.e. a number x such that (a*x)m = 1</p>
<p>@params[in] the numbers 'a' and 'm' from above equation </p><dl class="section return"><dt>Returns</dt><dd>the modular inverse of a </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 76</span> {</div>
<div class="line"><span class="lineno"> 77</span> int64_t x = 0, y = 0;</div>
<div class="line"><span class="lineno"> 78</span> uint64_t <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = <a class="code hl_function" href="#afde201f4687740454302c444f507a926">gcdExtended</a>(a, m, &amp;x, &amp;y);</div>
<div class="line"><span class="lineno"> 79</span> <span class="keywordflow">if</span> (g != 1) { <span class="comment">// modular inverse doesn&#39;t exist</span></div>
<div class="line"><span class="lineno"> 80</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><span class="lineno"> 81</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 82</span> int64_t res = ((x + m) % m);</div>
<div class="line"><span class="lineno"> 83</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><span class="lineno"> 84</span> }</div>
<div class="line"><span class="lineno"> 85</span> }</div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a2f67508d5f392b0321772169342c98ad"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> composite_simpson_rule.cpp:115</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6b95277f5f527beacc8d0f3bc91fcd08">&#9670;&#160;</a></span>ncr()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a499df7a01bcd348345dc5a0ab79bb0e9">&#9670;&#160;</a></span>ncr()</h2>
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<td>(</td>
<td class="paramtype">const uint64_t &amp;</td> <td class="paramname"><span class="paramname"><em>n</em></span>, </td>
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<p>Find nCr % p</p>
<p>@params[in] the numbers 'n', 'r' and 'p' </p><dl class="section return"><dt>Returns</dt><dd>the value nCr % p </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 92</span> {</div>
<div class="line"><span class="lineno"> 93</span> <span class="comment">// Base cases</span></div>
<div class="line"><span class="lineno"> 94</span> <span class="keywordflow">if</span> (r &gt; n) {</div>
<div class="line"><span class="lineno"> 95</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 96</span> }</div>
<div class="line"><span class="lineno"> 97</span> <span class="keywordflow">if</span> (r == 1) {</div>
<div class="line"><span class="lineno"> 98</span> <span class="keywordflow">return</span> n % <a class="code hl_variable" href="#a57c168cd6eb85718eab97da658a698ad">p</a>;</div>
<div class="line"><span class="lineno"> 99</span> }</div>
<div class="line"><span class="lineno"> 100</span> <span class="keywordflow">if</span> (r == 0 || r == n) {</div>
<div class="line"><span class="lineno"> 101</span> <span class="keywordflow">return</span> 1;</div>
<div class="line"><span class="lineno"> 102</span> }</div>
<div class="line"><span class="lineno"> 103</span> <span class="comment">// fac is a global array with fac[r] = (r! % p)</span></div>
<div class="line"><span class="lineno"> 104</span> int64_t denominator = <a class="code hl_function" href="#a0431ec5c876e1154d8e1e5f89e1ab34a">modInverse</a>(fac[r], <a class="code hl_variable" href="#a57c168cd6eb85718eab97da658a698ad">p</a>);</div>
<div class="line"><span class="lineno"> 105</span> <span class="keywordflow">if</span> (denominator &lt; 0) { <span class="comment">// modular inverse doesn&#39;t exist</span></div>
<div class="line"><span class="lineno"> 106</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><span class="lineno"> 107</span> }</div>
<div class="line"><span class="lineno"> 108</span> denominator = (denominator * <a class="code hl_function" href="#a0431ec5c876e1154d8e1e5f89e1ab34a">modInverse</a>(fac[n - r], <a class="code hl_variable" href="#a57c168cd6eb85718eab97da658a698ad">p</a>)) % <a class="code hl_variable" href="#a57c168cd6eb85718eab97da658a698ad">p</a>;</div>
<div class="line"><span class="lineno"> 109</span> <span class="keywordflow">if</span> (denominator &lt; 0) { <span class="comment">// modular inverse doesn&#39;t exist</span></div>
<div class="line"><span class="lineno"> 110</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><span class="lineno"> 111</span> }</div>
<div class="line"><span class="lineno"> 112</span> <span class="keywordflow">return</span> (fac[n] * denominator) % <a class="code hl_variable" href="#a57c168cd6eb85718eab97da658a698ad">p</a>;</div>
<div class="line"><span class="lineno"> 113</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aed5b4a9e4fd57fe23812293d4a0f30c1">&#9670;&#160;</a></span>fac</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;uint64_t&gt; math::ncr_modulo_p::NCRModuloP::fac {}</td>
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<div class="fragment"><div class="line"><span class="lineno"> 33</span>{}; <span class="comment">/// stores precomputed factorial(i) % p value</span></div>
<p>computes nCr % p </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>the number of objects to be chosen </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">r</td><td>the number of objects to choose from </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the value nCr % p </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 116</span> {</div>
<div class="line"><span class="lineno"> 117</span> <span class="comment">// Base cases</span></div>
<div class="line"><span class="lineno"> 118</span> <span class="keywordflow">if</span> (r &gt; n) {</div>
<div class="line"><span class="lineno"> 119</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 120</span> }</div>
<div class="line"><span class="lineno"> 121</span> <span class="keywordflow">if</span> (r == 1) {</div>
<div class="line"><span class="lineno"> 122</span> <span class="keywordflow">return</span> n % p;</div>
<div class="line"><span class="lineno"> 123</span> }</div>
<div class="line"><span class="lineno"> 124</span> <span class="keywordflow">if</span> (r == 0 || r == n) {</div>
<div class="line"><span class="lineno"> 125</span> <span class="keywordflow">return</span> 1;</div>
<div class="line"><span class="lineno"> 126</span> }</div>
<div class="line"><span class="lineno"> 127</span> <span class="comment">// fac is a global array with fac[r] = (r! % p)</span></div>
<div class="line"><span class="lineno"> 128</span> <span class="keyword">const</span> <span class="keyword">auto</span> denominator = (<a class="code hl_variable" href="#a738a5f59bb3560c81cdb7f43bcfe9fec">fac</a>[r] * <a class="code hl_variable" href="#a738a5f59bb3560c81cdb7f43bcfe9fec">fac</a>[n - r]) % p;</div>
<div class="line"><span class="lineno"> 129</span> <span class="keyword">const</span> <span class="keyword">auto</span> denominator_inv = utils::modInverse(denominator, p);</div>
<div class="line"><span class="lineno"> 130</span> <span class="keywordflow">if</span> (denominator_inv &lt; 0) { <span class="comment">// modular inverse doesn&#39;t exist</span></div>
<div class="line"><span class="lineno"> 131</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><span class="lineno"> 132</span> }</div>
<div class="line"><span class="lineno"> 133</span> <span class="keywordflow">return</span> (<a class="code hl_variable" href="#a738a5f59bb3560c81cdb7f43bcfe9fec">fac</a>[n] * denominator_inv) % p;</div>
<div class="line"><span class="lineno"> 134</span> }</div>
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