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<title>Algorithms_in_C++: others/matrix_exponentiation.cpp File Reference</title>
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@@ -30,8 +30,8 @@ MathJax.Hub.Config({
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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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</div>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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@@ -228,39 +228,39 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>\(n^\text{th}\) Fibonacci number </dd></dl>
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<div class="fragment"><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> <span class="keywordflow">if</span> (n == 0)</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">if</span> (n <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)</div>
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||||
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>[n - 1];</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// F1</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<ll></a> F1(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1);</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) F1[i] = <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>[i - 1];</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> </div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="comment">// Transpose matrix</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<vector<ll></a>> T(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<ll></a>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1));</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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||||
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordflow">for</span> (ll j = 1; j <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++) {</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordflow">if</span> (i < <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>) {</div>
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||||
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordflow">if</span> (j == i + 1)</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> T[i][j] = 1;</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keywordflow">else</span></div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> T[i][j] = 0;</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> }</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> T[i][j] = fib_c[<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> - j];</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> }</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> }</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="comment">// T^n-1</span></div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> T = <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#a702a9fc90e79b05b863cc4efa26ae2ec">power</a>(T, n - 1);</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> </div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// T*F1</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> ll res = 0;</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> res = (res + (T[1][i] * F1[i]) % MOD) % MOD;</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="keywordflow">return</span> res;</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 91</span> {</div>
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<div class="line"><span class="lineno"> 92</span> <span class="keywordflow">if</span> (n == 0)</div>
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<div class="line"><span class="lineno"> 93</span> <span class="keywordflow">return</span> 0;</div>
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||||
<div class="line"><span class="lineno"> 94</span> <span class="keywordflow">if</span> (n <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)</div>
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||||
<div class="line"><span class="lineno"> 95</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>[n - 1];</div>
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<div class="line"><span class="lineno"> 96</span> <span class="comment">// F1</span></div>
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<div class="line"><span class="lineno"> 97</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<ll></a> F1(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1);</div>
|
||||
<div class="line"><span class="lineno"> 98</span> <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) F1[i] = <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>[i - 1];</div>
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||||
<div class="line"><span class="lineno"> 99</span> </div>
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||||
<div class="line"><span class="lineno"> 100</span> <span class="comment">// Transpose matrix</span></div>
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||||
<div class="line"><span class="lineno"> 101</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<vector<ll></a>> T(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<ll></a>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1));</div>
|
||||
<div class="line"><span class="lineno"> 102</span> <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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||||
<div class="line"><span class="lineno"> 103</span> <span class="keywordflow">for</span> (ll j = 1; j <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++) {</div>
|
||||
<div class="line"><span class="lineno"> 104</span> <span class="keywordflow">if</span> (i < <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>) {</div>
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||||
<div class="line"><span class="lineno"> 105</span> <span class="keywordflow">if</span> (j == i + 1)</div>
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||||
<div class="line"><span class="lineno"> 106</span> T[i][j] = 1;</div>
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||||
<div class="line"><span class="lineno"> 107</span> <span class="keywordflow">else</span></div>
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||||
<div class="line"><span class="lineno"> 108</span> T[i][j] = 0;</div>
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||||
<div class="line"><span class="lineno"> 109</span> <span class="keywordflow">continue</span>;</div>
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||||
<div class="line"><span class="lineno"> 110</span> }</div>
|
||||
<div class="line"><span class="lineno"> 111</span> T[i][j] = fib_c[<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> - j];</div>
|
||||
<div class="line"><span class="lineno"> 112</span> }</div>
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||||
<div class="line"><span class="lineno"> 113</span> }</div>
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<div class="line"><span class="lineno"> 114</span> <span class="comment">// T^n-1</span></div>
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||||
<div class="line"><span class="lineno"> 115</span> T = <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#a702a9fc90e79b05b863cc4efa26ae2ec">power</a>(T, n - 1);</div>
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||||
<div class="line"><span class="lineno"> 116</span> </div>
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<div class="line"><span class="lineno"> 117</span> <span class="comment">// T*F1</span></div>
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<div class="line"><span class="lineno"> 118</span> ll res = 0;</div>
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||||
<div class="line"><span class="lineno"> 119</span> <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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||||
<div class="line"><span class="lineno"> 120</span> res = (res + (T[1][i] * F1[i]) % MOD) % MOD;</div>
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<div class="line"><span class="lineno"> 121</span> }</div>
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<div class="line"><span class="lineno"> 122</span> <span class="keywordflow">return</span> res;</div>
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<div class="line"><span class="lineno"> 123</span>}</div>
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||||
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a35b7c98af53ad2ec18658679ad7d43de"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a></div><div class="ttdeci">vector< ll > fib_b</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:50</div></div>
|
||||
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a702a9fc90e79b05b863cc4efa26ae2ec"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a702a9fc90e79b05b863cc4efa26ae2ec">power</a></div><div class="ttdeci">vector< vector< ll > > power(const vector< vector< ll > > &A, ll p)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:76</div></div>
|
||||
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a9977ad12548c4a49dee9dc3f0685aa54"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></div><div class="ttdeci">ll mat_size</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:45</div></div>
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||||
@@ -284,29 +284,29 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
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||||
</table>
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||||
</div><div class="memdoc">
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||||
<p >Main function </p>
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||||
<div class="fragment"><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_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a>.tie(0);</div>
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||||
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a>.tie(0);</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> ll t;</div>
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||||
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> t;</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> ll i, j, x;</div>
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||||
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keywordflow">while</span> (t--) {</div>
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||||
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>;</div>
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||||
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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||||
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> x;</div>
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||||
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>.pb(x);</div>
|
||||
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> }</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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||||
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> x;</div>
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||||
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> fib_c.pb(x);</div>
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||||
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> }</div>
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||||
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> x;</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> << <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>(x) << <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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||||
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>.clear();</div>
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||||
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> fib_c.clear();</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> }</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span>}</div>
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||||
<div class="fragment"><div class="line"><span class="lineno"> 126</span> {</div>
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<div class="line"><span class="lineno"> 127</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a>.tie(0);</div>
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||||
<div class="line"><span class="lineno"> 128</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a>.tie(0);</div>
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<div class="line"><span class="lineno"> 129</span> ll t;</div>
|
||||
<div class="line"><span class="lineno"> 130</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> t;</div>
|
||||
<div class="line"><span class="lineno"> 131</span> ll i, j, x;</div>
|
||||
<div class="line"><span class="lineno"> 132</span> <span class="keywordflow">while</span> (t--) {</div>
|
||||
<div class="line"><span class="lineno"> 133</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>;</div>
|
||||
<div class="line"><span class="lineno"> 134</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
|
||||
<div class="line"><span class="lineno"> 135</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> x;</div>
|
||||
<div class="line"><span class="lineno"> 136</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>.pb(x);</div>
|
||||
<div class="line"><span class="lineno"> 137</span> }</div>
|
||||
<div class="line"><span class="lineno"> 138</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
|
||||
<div class="line"><span class="lineno"> 139</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> x;</div>
|
||||
<div class="line"><span class="lineno"> 140</span> fib_c.pb(x);</div>
|
||||
<div class="line"><span class="lineno"> 141</span> }</div>
|
||||
<div class="line"><span class="lineno"> 142</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> x;</div>
|
||||
<div class="line"><span class="lineno"> 143</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> << <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>(x) << <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
|
||||
<div class="line"><span class="lineno"> 144</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>.clear();</div>
|
||||
<div class="line"><span class="lineno"> 145</span> fib_c.clear();</div>
|
||||
<div class="line"><span class="lineno"> 146</span> }</div>
|
||||
<div class="line"><span class="lineno"> 147</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 148</span>}</div>
|
||||
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
|
||||
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
|
||||
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a600eaf353befc174637855795f12d258"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a></div><div class="ttdeci">#define endl</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:36</div></div>
|
||||
@@ -349,17 +349,17 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
|
||||
</dl>
|
||||
<dl class="section note"><dt>Note</dt><dd>\(p=n\) </dd></dl>
|
||||
<dl class="section return"><dt>Returns</dt><dd>matrix of dimension (m \(\times\)q) </dd></dl>
|
||||
<div class="fragment"><div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> {</div>
|
||||
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<vector<ll></a>> C(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<ll></a>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1));</div>
|
||||
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
|
||||
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">for</span> (ll j = 1; j <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++) {</div>
|
||||
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">for</span> (ll z = 1; z <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; z++) {</div>
|
||||
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> C[i][j] = (C[i][j] + (A[i][z] * B[z][j]) % MOD) % MOD;</div>
|
||||
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> }</div>
|
||||
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> }</div>
|
||||
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> }</div>
|
||||
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">return</span> C;</div>
|
||||
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 58</span> {</div>
|
||||
<div class="line"><span class="lineno"> 59</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<vector<ll></a>> C(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<ll></a>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1));</div>
|
||||
<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
|
||||
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">for</span> (ll j = 1; j <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++) {</div>
|
||||
<div class="line"><span class="lineno"> 62</span> <span class="keywordflow">for</span> (ll z = 1; z <= <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; z++) {</div>
|
||||
<div class="line"><span class="lineno"> 63</span> C[i][j] = (C[i][j] + (A[i][z] * B[z][j]) % MOD) % MOD;</div>
|
||||
<div class="line"><span class="lineno"> 64</span> }</div>
|
||||
<div class="line"><span class="lineno"> 65</span> }</div>
|
||||
<div class="line"><span class="lineno"> 66</span> }</div>
|
||||
<div class="line"><span class="lineno"> 67</span> <span class="keywordflow">return</span> C;</div>
|
||||
<div class="line"><span class="lineno"> 68</span>}</div>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
|
||||
@@ -397,16 +397,16 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
|
||||
</dd>
|
||||
</dl>
|
||||
<dl class="section return"><dt>Returns</dt><dd>matrix of same dimension as A </dd></dl>
|
||||
<div class="fragment"><div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> {</div>
|
||||
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">if</span> (p == 1)</div>
|
||||
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">return</span> A;</div>
|
||||
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordflow">if</span> (p % 2 == 1) {</div>
|
||||
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#a357cfbebfdc47a237a2862fe146af252">multiply</a>(A, <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#a702a9fc90e79b05b863cc4efa26ae2ec">power</a>(A, p - 1));</div>
|
||||
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> } <span class="keywordflow">else</span> {</div>
|
||||
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<vector<ll></a>> X = <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#a702a9fc90e79b05b863cc4efa26ae2ec">power</a>(A, p / 2);</div>
|
||||
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#a357cfbebfdc47a237a2862fe146af252">multiply</a>(X, X);</div>
|
||||
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> }</div>
|
||||
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 76</span> {</div>
|
||||
<div class="line"><span class="lineno"> 77</span> <span class="keywordflow">if</span> (p == 1)</div>
|
||||
<div class="line"><span class="lineno"> 78</span> <span class="keywordflow">return</span> A;</div>
|
||||
<div class="line"><span class="lineno"> 79</span> <span class="keywordflow">if</span> (p % 2 == 1) {</div>
|
||||
<div class="line"><span class="lineno"> 80</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#a357cfbebfdc47a237a2862fe146af252">multiply</a>(A, <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#a702a9fc90e79b05b863cc4efa26ae2ec">power</a>(A, p - 1));</div>
|
||||
<div class="line"><span class="lineno"> 81</span> } <span class="keywordflow">else</span> {</div>
|
||||
<div class="line"><span class="lineno"> 82</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<vector<ll></a>> X = <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#a702a9fc90e79b05b863cc4efa26ae2ec">power</a>(A, p / 2);</div>
|
||||
<div class="line"><span class="lineno"> 83</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#a357cfbebfdc47a237a2862fe146af252">multiply</a>(X, X);</div>
|
||||
<div class="line"><span class="lineno"> 84</span> }</div>
|
||||
<div class="line"><span class="lineno"> 85</span>}</div>
|
||||
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a357cfbebfdc47a237a2862fe146af252"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a357cfbebfdc47a237a2862fe146af252">multiply</a></div><div class="ttdeci">vector< vector< ll > > multiply(const vector< vector< ll > > &A, const vector< vector< ll > > &B)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:57</div></div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
@@ -454,7 +454,7 @@ Here is the call graph for this function:</div>
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