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<div class="headertitle"><div class="title">ncr_modulo_p.cpp</div></div>
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<a href="../../de/dab/ncr__modulo__p_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include &lt;cassert&gt;</span> </div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &lt;vector&gt;</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/d47/namespacemath.html">math</a> {</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d4/db9/namespacencr__modulo__p.html">ncr_modulo_p</a> {</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d6/d84/namespaceutils.html">utils</a> {</div>
<div class="foldopen" id="foldopen00044" data-start="{" data-end="}">
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"><a class="line" href="../../de/dab/ncr__modulo__p_8cpp.html#a9010ad5669d31449c3bf3271ab5ebc86"> 44</a></span>int64_t <a class="code hl_function" href="../../de/dab/ncr__modulo__p_8cpp.html#a9010ad5669d31449c3bf3271ab5ebc86">gcdExtended</a>(<span class="keyword">const</span> int64_t&amp; a, <span class="keyword">const</span> int64_t&amp; b, int64_t&amp; x,</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> int64_t&amp; y) {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordflow">if</span> (a == 0) {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> x = 0;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> y = 1;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">return</span> b;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> int64_t x1 = 0, y1 = 0;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keyword">const</span> int64_t <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> = <a class="code hl_function" href="../../de/dab/ncr__modulo__p_8cpp.html#a9010ad5669d31449c3bf3271ab5ebc86">gcdExtended</a>(b % a, a, x1, y1);</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> x = y1 - (b / a) * x1;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> y = x1;</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</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"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span>}</div>
</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span></div>
<div class="foldopen" id="foldopen00066" data-start="{" data-end="}">
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"><a class="line" href="../../de/dab/ncr__modulo__p_8cpp.html#a6c7bfe3bdaa086d32261a5c5584d0fa9"> 66</a></span>int64_t <a class="code hl_function" href="../../de/dab/ncr__modulo__p_8cpp.html#a6c7bfe3bdaa086d32261a5c5584d0fa9">modInverse</a>(<span class="keyword">const</span> int64_t&amp; a, <span class="keyword">const</span> int64_t&amp; m) {</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> int64_t x = 0, y = 0;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keyword">const</span> int64_t g = <a class="code hl_function" href="../../de/dab/ncr__modulo__p_8cpp.html#a9010ad5669d31449c3bf3271ab5ebc86">gcdExtended</a>(a, m, x, y);</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">if</span> (g != 1) { <span class="comment">// modular inverse doesn&#39;t exist</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">return</span> ((x + m) % m);</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> }</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span>}</div>
</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span>} <span class="comment">// namespace utils</span></div>
<div class="foldopen" id="foldopen00079" data-start="{" data-end="};">
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"><a class="line" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html"> 79</a></span><span class="keyword">class </span><a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a94b07e7dc61d8d7a1e9c5a28988e72f9">NCRModuloP</a> {</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keyword">private</span>:</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keyword">const</span> int64_t p = 0; </div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keyword">const</span> std::vector&lt;int64_t&gt;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"><a class="line" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a738a5f59bb3560c81cdb7f43bcfe9fec"> 83</a></span> <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a738a5f59bb3560c81cdb7f43bcfe9fec">fac</a>; </div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span></div>
<div class="foldopen" id="foldopen00092" data-start="{" data-end="}">
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"><a class="line" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#ab5744fa589f6a48f9fe7bca13dbe661f"> 92</a></span> <span class="keyword">static</span> std::vector&lt;int64_t&gt; <a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#ab5744fa589f6a48f9fe7bca13dbe661f">computeFactorialsMod</a>(<span class="keyword">const</span> int64_t&amp; max_arg_val,</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keyword">const</span> int64_t&amp; mod) {</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keyword">auto</span> res = std::vector&lt;int64_t&gt;(max_arg_val + 1);</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> res[0] = 1;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">for</span> (int64_t i = 1; i &lt;= max_arg_val; i++) {</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> res[i] = (res[i - 1] * i) % mod;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> }</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> }</div>
</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> </div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keyword">public</span>:</div>
<div class="foldopen" id="foldopen00107" data-start="{" data-end="}">
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"><a class="line" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a94b07e7dc61d8d7a1e9c5a28988e72f9"> 107</a></span> <a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a94b07e7dc61d8d7a1e9c5a28988e72f9">NCRModuloP</a>(<span class="keyword">const</span> int64_t&amp; size, <span class="keyword">const</span> int64_t&amp; p)</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> : p(p), <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a738a5f59bb3560c81cdb7f43bcfe9fec">fac</a>(<a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#ab5744fa589f6a48f9fe7bca13dbe661f">computeFactorialsMod</a>(size, p)) {}</div>
</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span></div>
<div class="foldopen" id="foldopen00116" data-start="{" data-end="}">
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"><a class="line" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a499df7a01bcd348345dc5a0ab79bb0e9"> 116</a></span> int64_t <a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a499df7a01bcd348345dc5a0ab79bb0e9">ncr</a>(<span class="keyword">const</span> int64_t&amp; n, <span class="keyword">const</span> int64_t&amp; r)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// Base cases</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordflow">if</span> (r &gt; n) {</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> }</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keywordflow">if</span> (r == 1) {</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">return</span> n % p;</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> }</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">if</span> (r == 0 || r == n) {</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">return</span> 1;</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> }</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// fac is a global array with fac[r] = (r! % p)</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keyword">const</span> <span class="keyword">auto</span> denominator = (<a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a738a5f59bb3560c81cdb7f43bcfe9fec">fac</a>[r] * <a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a738a5f59bb3560c81cdb7f43bcfe9fec">fac</a>[n - r]) % p;</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keyword">const</span> <span class="keyword">auto</span> denominator_inv = <a class="code hl_function" href="../../de/dab/ncr__modulo__p_8cpp.html#a6c7bfe3bdaa086d32261a5c5584d0fa9">utils::modInverse</a>(denominator, p);</div>
<div class="line"><a id="l00130" name="l00130"></a><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"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> }</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keywordflow">return</span> (<a class="code hl_variable" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a738a5f59bb3560c81cdb7f43bcfe9fec">fac</a>[n] * denominator_inv) % p;</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> }</div>
</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span>};</div>
</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span>} <span class="comment">// namespace ncr_modulo_p</span></div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span>} <span class="comment">// namespace math</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span></div>
<div class="foldopen" id="foldopen00142" data-start="{" data-end="}">
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"><a class="line" href="../../de/dab/ncr__modulo__p_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e"> 142</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../de/dab/ncr__modulo__p_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>() {</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="keyword">struct </span><a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a> {</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keyword">const</span> int64_t size;</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="keyword">const</span> int64_t p;</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keyword">const</span> int64_t n;</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keyword">const</span> int64_t r;</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="keyword">const</span> int64_t expected;</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> </div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(<span class="keyword">const</span> int64_t size, <span class="keyword">const</span> int64_t p, <span class="keyword">const</span> int64_t n,</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keyword">const</span> int64_t r, <span class="keyword">const</span> int64_t expected)</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> : size(size), p(p), n(n), r(r), expected(expected) {}</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> };</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keyword">const</span> std::vector&lt;TestCase&gt; test_cases = {</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(60000, 1000000007, 52323, 26161, 224944353),</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(20, 5, 6, 2, 30 % 5),</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(100, 29, 7, 3, 35 % 29),</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(1000, 13, 10, 3, 120 % 13),</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(20, 17, 1, 10, 0),</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(45, 19, 23, 1, 23 % 19),</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(45, 19, 23, 0, 1),</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(45, 19, 23, 23, 1),</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(20, 9, 10, 2, -1)};</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; tc : test_cases) {</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> assert(<a class="code hl_class" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html">math::ncr_modulo_p::NCRModuloP</a>(tc.size, tc.p).<a class="code hl_function" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a499df7a01bcd348345dc5a0ab79bb0e9">ncr</a>(tc.n, tc.r) ==</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> tc.expected);</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> }</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> </div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\n\nAll tests have successfully passed!\n&quot;</span>;</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span>}</div>
</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span></div>
<div class="foldopen" id="foldopen00175" data-start="{" data-end="}">
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"><a class="line" href="../../de/dab/ncr__modulo__p_8cpp.html#afa2b50f4716fc3b42221a72e676e1422"> 175</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../de/dab/ncr__modulo__p_8cpp.html#afa2b50f4716fc3b42221a72e676e1422">example</a>() {</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="keyword">const</span> int64_t size = 1e6 + 1;</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="keyword">const</span> int64_t p = 1e9 + 7;</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> </div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="comment">// the ncrObj contains the precomputed values of factorials modulo p for</span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="comment">// values from 0 to size</span></div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="keyword">const</span> <span class="keyword">auto</span> ncrObj = <a class="code hl_class" 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 id="l00182" name="l00182"></a><span class="lineno"> 182</span> </div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="comment">// having the ncrObj we can efficiently query the values of (n C r)%p</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="comment">// note that time of the computation does not depend on size</span></div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= 7; i++) {</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> std::cout &lt;&lt; 6 &lt;&lt; <span class="stringliteral">&quot;C&quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; mod &quot;</span> &lt;&lt; p &lt;&lt; <span class="stringliteral">&quot; = &quot;</span> &lt;&lt; ncrObj.ncr(6, i)</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> }</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span>}</div>
</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> </div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <a class="code hl_function" href="../../de/dab/ncr__modulo__p_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>();</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <a class="code hl_function" href="../../de/dab/ncr__modulo__p_8cpp.html#afa2b50f4716fc3b42221a72e676e1422">example</a>();</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span>}</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> <a href="#l00079">ncr_modulo_p.cpp:79</a></div></div>
<div class="ttc" id="aclassmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p_html_a499df7a01bcd348345dc5a0ab79bb0e9"><div class="ttname"><a href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a499df7a01bcd348345dc5a0ab79bb0e9">math::ncr_modulo_p::NCRModuloP::ncr</a></div><div class="ttdeci">int64_t ncr(const int64_t &amp;n, const int64_t &amp;r) const</div><div class="ttdoc">computes nCr % p</div><div class="ttdef"><b>Definition</b> <a href="#l00116">ncr_modulo_p.cpp:116</a></div></div>
<div class="ttc" id="aclassmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p_html_a738a5f59bb3560c81cdb7f43bcfe9fec"><div class="ttname"><a href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#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> <a href="#l00083">ncr_modulo_p.cpp:83</a></div></div>
<div class="ttc" id="aclassmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p_html_a94b07e7dc61d8d7a1e9c5a28988e72f9"><div class="ttname"><a href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#a94b07e7dc61d8d7a1e9c5a28988e72f9">math::ncr_modulo_p::NCRModuloP::NCRModuloP</a></div><div class="ttdeci">NCRModuloP(const int64_t &amp;size, const int64_t &amp;p)</div><div class="ttdoc">constructs an NCRModuloP object allowing to compute (nCr)p for inputs from 0 to size</div><div class="ttdef"><b>Definition</b> <a href="#l00107">ncr_modulo_p.cpp:107</a></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="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html#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> <a href="#l00092">ncr_modulo_p.cpp:92</a></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> <a href="../../d4/da0/gcd__iterative__euclidean_8cpp_source.html#l00015">gcd_iterative_euclidean.cpp:15</a></div></div>
<div class="ttc" id="agenerate__parentheses_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00110">generate_parentheses.cpp:110</a></div></div>
<div class="ttc" id="anamespacemath_html"><div class="ttname"><a href="../../dd/d47/namespacemath.html">math</a></div><div class="ttdoc">for assert</div></div>
<div class="ttc" id="anamespacencr__modulo__p_html"><div class="ttname"><a href="../../d4/db9/namespacencr__modulo__p.html">ncr_modulo_p</a></div><div class="ttdoc">Functions for nCr modulo p implementation.</div></div>
<div class="ttc" id="anamespaceutils_html"><div class="ttname"><a href="../../d6/d84/namespaceutils.html">utils</a></div><div class="ttdoc">this namespace contains the definitions of the functions called from the class math::ncr_modulo_p::NC...</div></div>
<div class="ttc" id="ancr__modulo__p_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="../../de/dab/ncr__modulo__p_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">tests math::ncr_modulo_p::NCRModuloP</div><div class="ttdef"><b>Definition</b> <a href="#l00142">ncr_modulo_p.cpp:142</a></div></div>
<div class="ttc" id="ancr__modulo__p_8cpp_html_a6c7bfe3bdaa086d32261a5c5584d0fa9"><div class="ttname"><a href="../../de/dab/ncr__modulo__p_8cpp.html#a6c7bfe3bdaa086d32261a5c5584d0fa9">math::ncr_modulo_p::utils::modInverse</a></div><div class="ttdeci">int64_t modInverse(const int64_t &amp;a, const int64_t &amp;m)</div><div class="ttdef"><b>Definition</b> <a href="#l00066">ncr_modulo_p.cpp:66</a></div></div>
<div class="ttc" id="ancr__modulo__p_8cpp_html_a9010ad5669d31449c3bf3271ab5ebc86"><div class="ttname"><a href="../../de/dab/ncr__modulo__p_8cpp.html#a9010ad5669d31449c3bf3271ab5ebc86">math::ncr_modulo_p::utils::gcdExtended</a></div><div class="ttdeci">int64_t gcdExtended(const int64_t &amp;a, const int64_t &amp;b, int64_t &amp;x, int64_t &amp;y)</div><div class="ttdoc">finds the values x and y such that a*x + b*y = gcd(a,b)</div><div class="ttdef"><b>Definition</b> <a href="#l00044">ncr_modulo_p.cpp:44</a></div></div>
<div class="ttc" id="ancr__modulo__p_8cpp_html_afa2b50f4716fc3b42221a72e676e1422"><div class="ttname"><a href="../../de/dab/ncr__modulo__p_8cpp.html#afa2b50f4716fc3b42221a72e676e1422">example</a></div><div class="ttdeci">void example()</div><div class="ttdoc">example showing the usage of the math::ncr_modulo_p::NCRModuloP class</div><div class="ttdef"><b>Definition</b> <a href="#l00175">ncr_modulo_p.cpp:175</a></div></div>
<div class="ttc" id="astruct_test_case_html"><div class="ttname"><a href="../../da/d86/struct_test_case.html">TestCase</a></div><div class="ttdoc">represents single example inputs and expected output of the function longest_common_string_length</div><div class="ttdef"><b>Definition</b> <a href="../../da/d0d/longest__common__string_8cpp_source.html#l00054">longest_common_string.cpp:54</a></div></div>
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