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realstealthninja
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<title>TheAlgorithms/C++: math/ncr_modulo_p.cpp Source File</title>
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@@ -60,7 +60,7 @@ window.MathJax = {
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/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
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@@ -124,14 +124,15 @@ $(function(){initNavTree('de/dab/ncr__modulo__p_8cpp_source.html','../../'); ini
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<div class="headertitle"><div class="title">ncr_modulo_p.cpp</div></div>
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</div><!--header-->
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<div class="contents">
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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>
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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>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span> </div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include <cassert></span> </div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include <iostream></span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include <vector></span> </div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span></div>
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<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>
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<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>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span></div>
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<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>
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<div class="foldopen" id="foldopen00044" data-start="{" data-end="}">
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<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& a, <span class="keyword">const</span> int64_t& b, int64_t& x,</div>
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@@ -150,7 +151,7 @@ $(function(){initNavTree('de/dab/ncr__modulo__p_8cpp_source.html','../../'); ini
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<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>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span>}</div>
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</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span></div>
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<div class="foldopen" id="foldopen00066" data-start="{" data-end="}">
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<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& a, <span class="keyword">const</span> int64_t& m) {</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> int64_t x = 0, y = 0;</div>
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@@ -164,12 +165,12 @@ $(function(){initNavTree('de/dab/ncr__modulo__p_8cpp_source.html','../../'); ini
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</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span>} <span class="comment">// namespace utils</span></div>
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<div class="foldopen" id="foldopen00079" data-start="{" data-end="};">
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<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_class" href="../../d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html">NCRModuloP</a> {</div>
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<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>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keyword">const</span> int64_t p = 0; </div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keyword">const</span> std::vector<int64_t></div>
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<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>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span></div>
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<div class="foldopen" id="foldopen00092" data-start="{" data-end="}">
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<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<int64_t> <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& max_arg_val,</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keyword">const</span> int64_t& mod) {</div>
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@@ -187,7 +188,7 @@ $(function(){initNavTree('de/dab/ncr__modulo__p_8cpp_source.html','../../'); ini
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<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& size, <span class="keyword">const</span> int64_t& p)</div>
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<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>
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</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> </div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span></div>
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<div class="foldopen" id="foldopen00116" data-start="{" data-end="}">
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<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& n, <span class="keyword">const</span> int64_t& r)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// Base cases</span></div>
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@@ -202,7 +203,7 @@ $(function(){initNavTree('de/dab/ncr__modulo__p_8cpp_source.html','../../'); ini
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> }</div>
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<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>
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<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>
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<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 = utils::modInverse(denominator, p);</div>
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<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>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="keywordflow">if</span> (denominator_inv < 0) { <span class="comment">// modular inverse doesn't exist</span></div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keywordflow">return</span> -1;</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> }</div>
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@@ -213,7 +214,7 @@ $(function(){initNavTree('de/dab/ncr__modulo__p_8cpp_source.html','../../'); ini
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</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span>} <span class="comment">// namespace ncr_modulo_p</span></div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span>} <span class="comment">// namespace math</span></div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> </div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span></div>
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<div class="foldopen" id="foldopen00142" data-start="{" data-end="}">
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<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>
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<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>
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@@ -245,7 +246,7 @@ $(function(){initNavTree('de/dab/ncr__modulo__p_8cpp_source.html','../../'); ini
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> std::cout << <span class="stringliteral">"\n\nAll tests have successfully passed!\n"</span>;</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span>}</div>
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</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> </div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span></div>
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<div class="foldopen" id="foldopen00175" data-start="{" data-end="}">
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<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>
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<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>
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@@ -290,7 +291,7 @@ $(function(){initNavTree('de/dab/ncr__modulo__p_8cpp_source.html','../../'); ini
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<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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<ul>
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<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../de/dab/ncr__modulo__p_8cpp.html">ncr_modulo_p.cpp</a></li>
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<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> 1.12.0 </li>
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