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realstealthninja
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<title>TheAlgorithms/C++: math/linear_recurrence_matrix.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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var searchBox = new SearchBox("searchBox", "../../search/",'.html');
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@@ -124,12 +124,12 @@ $(function(){initNavTree('dc/d52/linear__recurrence__matrix_8cpp_source.html','.
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<div class="headertitle"><div class="title">linear_recurrence_matrix.cpp</div></div>
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</div><!--header-->
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<div class="contents">
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<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
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<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="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include <cassert></span> </div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include <cstdint></span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include <iostream></span> </div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include <vector></span> </div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> </div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</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="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d9/dd1/namespacelinear__recurrence__matrix.html">linear_recurrence_matrix</a> {</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="keyword">template</span> <<span class="keyword">typename</span> T = <span class="keywordtype">int</span>64_t></div>
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@@ -142,10 +142,10 @@ $(function(){initNavTree('dc/d52/linear__recurrence__matrix_8cpp_source.html','.
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> std::vector<T>(_mat_b[0].size(), 0));</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">for</span> (uint32_t i = 0; i < _mat_a.size(); ++i) {</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">for</span> (uint32_t j = 0; j < _mat_b[0].size(); ++j) {</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">for</span> (uint32_t k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> < _mat_b.size(); ++<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>) {</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">for</span> (uint32_t k = 0; k < _mat_b.size(); ++k) {</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> _mat_c[i][j] =</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> (_mat_c[i][j] % mod +</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> (_mat_a[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] % mod * _mat_b[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j] % mod) % mod) %</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> (_mat_a[i][k] % mod * _mat_b[k][j] % mod) % mod) %</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> mod;</div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> }</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> }</div>
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@@ -163,10 +163,10 @@ $(function(){initNavTree('dc/d52/linear__recurrence__matrix_8cpp_source.html','.
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span>}</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> </div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="keyword">template</span> <<span class="keyword">typename</span> T = <span class="keywordtype">int</span>64_t></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span>std::vector<std::vector<T>> matrix_exponentiation(</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> std::vector<std::vector<T>> _mat, uint64_t <a class="code hl_function" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">power</a>,</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> std::vector<std::vector<T>> _mat, uint64_t <a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a>,</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keyword">const</span> int64_t mod = 1000000007) {</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordflow">if</span> (is_zero_matrix(_mat)) {</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keywordflow">return</span> _mat;</div>
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@@ -179,31 +179,32 @@ $(function(){initNavTree('dc/d52/linear__recurrence__matrix_8cpp_source.html','.
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> _mat_answer[i][i] = 1;</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> }</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="comment">// exponentiation algorithm here.</span></div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordflow">while</span> (<a class="code hl_function" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">power</a> > 0) {</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">power</a> & 1) {</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordflow">while</span> (<a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a> > 0) {</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a> & 1) {</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> _mat_answer = matrix_multiplication(_mat_answer, _mat, mod);</div>
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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> <a class="code hl_function" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">power</a> >>= 1;</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a> >>= 1;</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> _mat = matrix_multiplication(_mat, _mat, mod);</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> }</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</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> _mat_answer;</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span>}</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> </div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span></div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span><span class="keyword">template</span> <<span class="keyword">typename</span> T = <span class="keywordtype">int</span>64_t></div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span>T get_nth_term_of_recurrence_series(</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keyword">const</span> std::vector<std::vector<T>>& _mat,</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keyword">const</span> std::vector<std::vector<T>>& _base_cases, uint64_t nth_term,</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keywordtype">bool</span> constant_or_sum_included = <span class="keyword">false</span>) {</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> assert(_mat.size() == _base_cases.back().size());</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> </div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span></div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> </div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="keywordflow">if</span> (nth_term < _base_cases.back().size() - constant_or_sum_included) {</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="keywordflow">return</span> _base_cases.back()[nth_term - constant_or_sum_included];</div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> std::vector<std::vector<T>> _res_matrix =</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> matrix_exponentiation(_mat, nth_term - _base_cases.back().size() +</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> 1 + constant_or_sum_included);</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> </div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span></div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> std::vector<std::vector<T>> _res =</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> matrix_multiplication(_base_cases, _res_matrix);</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> </div>
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@@ -212,8 +213,8 @@ $(function(){initNavTree('dc/d52/linear__recurrence__matrix_8cpp_source.html','.
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span>}</div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span>} <span class="comment">// namespace linear_recurrence_matrix</span></div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span>} <span class="comment">// namespace math</span></div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> </div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>() {</div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span></div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="comment">/*</span></div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span><span class="comment"> * Example 1: [Fibonacci</span></div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span><span class="comment"> * series](https://en.wikipedia.org/wiki/Fibonacci_number);</span></div>
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@@ -385,24 +386,23 @@ $(function(){initNavTree('dc/d52/linear__recurrence__matrix_8cpp_source.html','.
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> assert(math::linear_recurrence_matrix::get_nth_term_of_recurrence_series(</div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> tribonacci_sum, trib_sum_base_case, 19, 1) == 42762LL);</div>
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<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span>}</div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> </div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span></div>
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<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>(); <span class="comment">// run self-test implementations</span></div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
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<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span>}</div>
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<div class="ttc" id="acaesar__cipher_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition</b> <a href="../../d6/d2c/caesar__cipher_8cpp_source.html#l00100">caesar_cipher.cpp:100</a></div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00117">composite_simpson_rule.cpp:117</a></div></div>
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||||
<div class="ttc" id="agenerate__parentheses_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00082">generate_parentheses.cpp:82</a></div></div>
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||||
<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>
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<div class="ttc" id="anamespacelinear__recurrence__matrix_html"><div class="ttname"><a href="../../d9/dd1/namespacelinear__recurrence__matrix.html">linear_recurrence_matrix</a></div><div class="ttdoc">Functions for Linear Recurrence Matrix implementation.</div></div>
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<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>
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<div class="ttc" id="anamespacemath_html_afcd07701d73ed65cd616bcba02737f3d"><div class="ttname"><a href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">math::power</a></div><div class="ttdeci">uint64_t power(uint64_t a, uint64_t b, uint64_t c)</div><div class="ttdoc">This function calculates a raised to exponent b under modulo c using modular exponentiation.</div><div class="ttdef"><b>Definition</b> <a href="../../d0/d6d/modular__exponentiation_8cpp_source.html#l00035">modular_exponentiation.cpp:35</a></div></div>
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