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<title>TheAlgorithms/C++: others/matrix_exponentiation.cpp File Reference</title>
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@@ -154,9 +154,9 @@ Macros</h2></td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a357cfbebfdc47a237a2862fe146af252" id="r_a357cfbebfdc47a237a2862fe146af252"><td class="memItemLeft" align="right" valign="top">vector< vector< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a357cfbebfdc47a237a2862fe146af252">multiply</a> (const vector< vector< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &A, const vector< vector< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &B)</td></tr>
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<tr class="memitem:a357cfbebfdc47a237a2862fe146af252" id="r_a357cfbebfdc47a237a2862fe146af252"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a357cfbebfdc47a237a2862fe146af252">multiply</a> (const <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &A, const <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &B)</td></tr>
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<tr class="separator:a357cfbebfdc47a237a2862fe146af252"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a702a9fc90e79b05b863cc4efa26ae2ec" id="r_a702a9fc90e79b05b863cc4efa26ae2ec"><td class="memItemLeft" align="right" valign="top">vector< vector< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a702a9fc90e79b05b863cc4efa26ae2ec">power</a> (const vector< vector< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &A, <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> p)</td></tr>
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<tr class="memitem:a702a9fc90e79b05b863cc4efa26ae2ec" id="r_a702a9fc90e79b05b863cc4efa26ae2ec"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a702a9fc90e79b05b863cc4efa26ae2ec">power</a> (const <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &A, <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> p)</td></tr>
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<tr class="memitem:ad8389ed58fd0ec66df248014775ad1fa" id="r_ad8389ed58fd0ec66df248014775ad1fa"><td class="memItemLeft" align="right" valign="top"><a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="#ad8389ed58fd0ec66df248014775ad1fa">ans</a> (<a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> n)</td></tr>
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Variables</h2></td></tr>
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<tr class="memitem:a9977ad12548c4a49dee9dc3f0685aa54" id="r_a9977ad12548c4a49dee9dc3f0685aa54"><td class="memItemLeft" align="right" valign="top"><a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></td></tr>
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<tr class="memitem:a35b7c98af53ad2ec18658679ad7d43de" id="r_a35b7c98af53ad2ec18658679ad7d43de"><td class="memItemLeft" align="right" valign="top">vector< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a></td></tr>
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<tr class="memitem:a35b7c98af53ad2ec18658679ad7d43de" id="r_a35b7c98af53ad2ec18658679ad7d43de"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a></td></tr>
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<tr class="separator:a35b7c98af53ad2ec18658679ad7d43de"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a0cbd1162483ef7eccd5b947b2e01b1ab" id="r_a0cbd1162483ef7eccd5b947b2e01b1ab"><td class="memItemLeft" align="right" valign="top">vector< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a0cbd1162483ef7eccd5b947b2e01b1ab">fib_c</a></td></tr>
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<tr class="memitem:a0cbd1162483ef7eccd5b947b2e01b1ab" id="r_a0cbd1162483ef7eccd5b947b2e01b1ab"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a0cbd1162483ef7eccd5b947b2e01b1ab">fib_c</a></td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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@@ -290,12 +290,12 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
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<div class="line"><span class="lineno"> 95</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="#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> vector<ll> F1(<a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1);</div>
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<div class="line"><span class="lineno"> 98</span> <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) F1[i] = <a class="code hl_variable" href="#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a>[i - 1];</div>
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<div class="line"><span class="lineno"> 98</span> <span class="keywordflow">for</span> (<a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> i = 1; i <= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) F1[i] = <a class="code hl_variable" href="#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> vector<vector<ll>> T(<a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1, vector<ll>(<a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1));</div>
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<div class="line"><span class="lineno"> 102</span> <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code hl_variable" href="#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="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++) {</div>
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<div class="line"><span class="lineno"> 102</span> <span class="keywordflow">for</span> (<a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> i = 1; i <= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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<div class="line"><span class="lineno"> 103</span> <span class="keywordflow">for</span> (<a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> j = 1; j <= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++) {</div>
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<div class="line"><span class="lineno"> 104</span> <span class="keywordflow">if</span> (i < <a class="code hl_variable" href="#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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@@ -310,8 +310,8 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
|
||||
<div class="line"><span class="lineno"> 115</span> T = <a class="code hl_function" href="#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="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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<div class="line"><span class="lineno"> 118</span> <a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> res = 0;</div>
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<div class="line"><span class="lineno"> 119</span> <span class="keywordflow">for</span> (<a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> i = 1; i <= <a class="code hl_variable" href="#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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@@ -319,6 +319,7 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
|
||||
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a35b7c98af53ad2ec18658679ad7d43de"><div class="ttname"><a href="#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a></div><div class="ttdeci">vector< ll > fib_b</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00050">matrix_exponentiation.cpp:50</a></div></div>
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<div class="ttc" id="amatrix__exponentiation_8cpp_html_a702a9fc90e79b05b863cc4efa26ae2ec"><div class="ttname"><a href="#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> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00076">matrix_exponentiation.cpp:76</a></div></div>
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<div class="ttc" id="amatrix__exponentiation_8cpp_html_a9977ad12548c4a49dee9dc3f0685aa54"><div class="ttname"><a href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></div><div class="ttdeci">ll mat_size</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00045">matrix_exponentiation.cpp:45</a></div></div>
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||||
<div class="ttc" id="amatrix__exponentiation_8cpp_html_ae1d1ec9482079231e898236e2b23c9ba"><div class="ttname"><a href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a></div><div class="ttdeci">#define ll</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00033">matrix_exponentiation.cpp:33</a></div></div>
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</div><!-- fragment -->
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</div>
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</div>
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@@ -342,9 +343,9 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
|
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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> cin.tie(0);</div>
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<div class="line"><span class="lineno"> 128</span> cout.tie(0);</div>
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<div class="line"><span class="lineno"> 129</span> ll t;</div>
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<div class="line"><span class="lineno"> 129</span> <a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> t;</div>
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<div class="line"><span class="lineno"> 130</span> cin >> t;</div>
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<div class="line"><span class="lineno"> 131</span> ll i, j, x;</div>
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<div class="line"><span class="lineno"> 131</span> <a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> i, j, x;</div>
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<div class="line"><span class="lineno"> 132</span> <span class="keywordflow">while</span> (t--) {</div>
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<div class="line"><span class="lineno"> 133</span> cin >> <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>;</div>
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<div class="line"><span class="lineno"> 134</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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@@ -373,21 +374,21 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
|
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">vector< vector< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > multiply </td>
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||||
<td class="memname"><a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > multiply </td>
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<td>(</td>
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<td class="paramtype">const vector< vector< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </td>
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||||
<td class="paramtype">const <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const vector< vector< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &</td> <td class="paramname"><span class="paramname"><em>B</em></span> )</td>
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||||
<td class="paramtype">const <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &</td> <td class="paramname"><span class="paramname"><em>B</em></span> )</td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>To multiply 2 matrices </p><dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>matrix 1 of size (m \(\times\)n) </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">B</td><td><code>matrix</code> 2 of size (p \(\times\)q)<br />
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<tr><td class="paramdir">[in]</td><td class="paramname">B</td><td><code class="param">matrix</code> 2 of size (p \(\times\)q)<br />
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</td></tr>
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</table>
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</dd>
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@@ -398,9 +399,9 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
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<p class="definition">Definition at line <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00057">57</a> of file <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html">matrix_exponentiation.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 58</span> {</div>
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<div class="line"><span class="lineno"> 59</span> vector<vector<ll>> C(<a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1, vector<ll>(<a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1));</div>
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<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">for</span> (ll j = 1; j <= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++) {</div>
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<div class="line"><span class="lineno"> 62</span> <span class="keywordflow">for</span> (ll z = 1; z <= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; z++) {</div>
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<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">for</span> (<a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> i = 1; i <= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">for</span> (<a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> j = 1; j <= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++) {</div>
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||||
<div class="line"><span class="lineno"> 62</span> <span class="keywordflow">for</span> (<a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> z = 1; z <= <a class="code hl_variable" href="#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>
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<div class="line"><span class="lineno"> 65</span> }</div>
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@@ -417,9 +418,9 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
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<div class="memproto">
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<table class="memname">
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||||
<tr>
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<td class="memname">vector< vector< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > power </td>
|
||||
<td class="memname"><a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > power </td>
|
||||
<td>(</td>
|
||||
<td class="paramtype">const vector< vector< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </td>
|
||||
<td class="paramtype">const <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="../../d7/dfc/classvector.html">vector</a>< <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </td>
|
||||
</tr>
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||||
<tr>
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||||
<td class="paramkey"></td>
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||||
@@ -461,7 +462,7 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
|
||||
<div class="memproto">
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||||
<table class="memname">
|
||||
<tr>
|
||||
<td class="memname">vector<<a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a>> fib_b</td>
|
||||
<td class="memname"><a class="el" href="../../d7/dfc/classvector.html">vector</a><<a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a>> fib_b</td>
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||||
</tr>
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||||
</table>
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||||
</div><div class="memdoc">
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||||
@@ -478,7 +479,7 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
|
||||
<div class="memproto">
|
||||
<table class="memname">
|
||||
<tr>
|
||||
<td class="memname">vector<<a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a>> fib_c</td>
|
||||
<td class="memname"><a class="el" href="../../d7/dfc/classvector.html">vector</a><<a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a>> fib_c</td>
|
||||
</tr>
|
||||
</table>
|
||||
</div><div class="memdoc">
|
||||
@@ -510,7 +511,7 @@ This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a genera
|
||||
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