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<p>Matrix Exponentiation.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for matrix_exponentiation.cpp:</div>
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<p><a href="../../d7/d35/matrix__exponentiation_8cpp_source.html">Go to the source code of this file.</a></p>
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Macros</h2></td></tr>
<tr class="memitem:ae1d1ec9482079231e898236e2b23c9ba" id="r_ae1d1ec9482079231e898236e2b23c9ba"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a>&#160;&#160;&#160;int64_t</td></tr>
<tr class="memitem:a600eaf353befc174637855795f12d258" id="r_a600eaf353befc174637855795f12d258"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a600eaf353befc174637855795f12d258">endl</a>&#160;&#160;&#160;std::endl</td></tr>
<tr class="memitem:a276c5a0e984cf60015b27252fe04fe6b" id="r_a276c5a0e984cf60015b27252fe04fe6b"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a276c5a0e984cf60015b27252fe04fe6b">pb</a>&#160;&#160;&#160;push_back</td></tr>
<tr class="memitem:aca7d5718ab8c38506adb3bef2469b319" id="r_aca7d5718ab8c38506adb3bef2469b319"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aca7d5718ab8c38506adb3bef2469b319">MOD</a>&#160;&#160;&#160;1000000007</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a357cfbebfdc47a237a2862fe146af252" id="r_a357cfbebfdc47a237a2862fe146af252"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a357cfbebfdc47a237a2862fe146af252">multiply</a> (const <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt; &gt; &amp;A, const <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt; &gt; &amp;B)</td></tr>
<tr class="memitem:a702a9fc90e79b05b863cc4efa26ae2ec" id="r_a702a9fc90e79b05b863cc4efa26ae2ec"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a702a9fc90e79b05b863cc4efa26ae2ec">power</a> (const <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt; &gt; &amp;A, <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> p)</td></tr>
<tr class="memitem:ad8389ed58fd0ec66df248014775ad1fa" id="r_ad8389ed58fd0ec66df248014775ad1fa"><td class="memItemLeft" align="right" valign="top"><a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ad8389ed58fd0ec66df248014775ad1fa">ans</a> (<a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> n)</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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Variables</h2></td></tr>
<tr class="memitem:a9977ad12548c4a49dee9dc3f0685aa54" id="r_a9977ad12548c4a49dee9dc3f0685aa54"><td class="memItemLeft" align="right" valign="top"><a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></td></tr>
<tr class="memitem:a35b7c98af53ad2ec18658679ad7d43de" id="r_a35b7c98af53ad2ec18658679ad7d43de"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a></td></tr>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Matrix Exponentiation. </p>
<p>The problem can be solved with DP but constraints are high. <br />
\(a_i = b_i\) (for \(i &lt;= k\)) <br />
\(a_i = c_1 a_{i-1} + c_2 a_{i-2} + ... + c_k a_{i-k}\) (for \(i &gt; k\)) <br />
Taking the example of Fibonacci series, \(k=2\) <br />
\(b_1 = 1,\; b_2=1\) <br />
\(c_1 = 1,\; c_2=1\) <br />
\(a = \begin{bmatrix}0&amp; 1&amp; 1&amp; 2&amp; \ldots\end{bmatrix}\) <br />
This way you can find the \(10^{18}\) fibonacci numberMOD. I have given a general way to use it. The program takes the input of B and C matrix.</p>
<p>Steps for Matrix Expo</p><ol type="1">
<li>Create vector F1 : which is the copy of B.</li>
<li>Create transpose matrix (Learn more about it on the internet)</li>
<li>Perform \(T^{n-1}\) [transpose matrix to the power n-1]</li>
<li>Multiply with F to get the last matrix of size (1 \(\times\)k).</li>
</ol>
<p>The first element of this matrix is the required result. </p>
<p class="definition">Definition in file <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html">matrix_exponentiation.cpp</a>.</p>
</div><a name="doc-define-members" id="doc-define-members"></a><h2 id="header-doc-define-members" class="groupheader">Macro Definition Documentation</h2>
<a id="a600eaf353befc174637855795f12d258" name="a600eaf353befc174637855795f12d258"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a600eaf353befc174637855795f12d258">&#9670;&#160;</a></span>endl</h2>
<div class="memitem">
<div class="memproto">
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<td class="memname">#define endl&#160;&#160;&#160;std::endl</td>
</tr>
</table>
</div><div class="memdoc">
<p>shorthand definition for <span class="tt">std::endl</span> </p>
<p class="definition">Definition at line <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00036">36</a> of file <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html">matrix_exponentiation.cpp</a>.</p>
</div>
</div>
<a id="ae1d1ec9482079231e898236e2b23c9ba" name="ae1d1ec9482079231e898236e2b23c9ba"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae1d1ec9482079231e898236e2b23c9ba">&#9670;&#160;</a></span>ll</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">#define ll&#160;&#160;&#160;int64_t</td>
</tr>
</table>
</div><div class="memdoc">
<p>shorthand definition for <span class="tt">int64_t</span> </p>
<p class="definition">Definition at line <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00033">33</a> of file <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html">matrix_exponentiation.cpp</a>.</p>
</div>
</div>
<a id="aca7d5718ab8c38506adb3bef2469b319" name="aca7d5718ab8c38506adb3bef2469b319"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aca7d5718ab8c38506adb3bef2469b319">&#9670;&#160;</a></span>MOD</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">#define MOD&#160;&#160;&#160;1000000007</td>
</tr>
</table>
</div><div class="memdoc">
<p class="definition">Definition at line <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00040">40</a> of file <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html">matrix_exponentiation.cpp</a>.</p>
</div>
</div>
<a id="a276c5a0e984cf60015b27252fe04fe6b" name="a276c5a0e984cf60015b27252fe04fe6b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a276c5a0e984cf60015b27252fe04fe6b">&#9670;&#160;</a></span>pb</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">#define pb&#160;&#160;&#160;push_back</td>
</tr>
</table>
</div><div class="memdoc">
<p>shorthand definition for <span class="tt">int64_t</span> </p>
<p class="definition">Definition at line <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00039">39</a> of file <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html">matrix_exponentiation.cpp</a>.</p>
</div>
</div>
<a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="ad8389ed58fd0ec66df248014775ad1fa" name="ad8389ed58fd0ec66df248014775ad1fa"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad8389ed58fd0ec66df248014775ad1fa">&#9670;&#160;</a></span>ans()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> ans </td>
<td>(</td>
<td class="paramtype"><a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a></td> <td class="paramname"><span class="paramname"><em>n</em></span></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Wrapper for Fibonacci </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>\(n^\text{th}\) Fibonacci number </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>\(n^\text{th}\) Fibonacci number </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00091">91</a> of file <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html">matrix_exponentiation.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 91</span> {</div>
<div class="line"><span class="lineno"> 92</span> <span class="keywordflow">if</span> (n == 0)</div>
<div class="line"><span class="lineno"> 93</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 94</span> <span class="keywordflow">if</span> (n &lt;= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)</div>
<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>
<div class="line"><span class="lineno"> 96</span> <span class="comment">// F1</span></div>
<div class="line"><span class="lineno"> 97</span> vector&lt;ll&gt; F1(<a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1);</div>
<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 &lt;= <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>
<div class="line"><span class="lineno"> 99</span> </div>
<div class="line"><span class="lineno"> 100</span> <span class="comment">// Transpose matrix</span></div>
<div class="line"><span class="lineno"> 101</span> vector&lt;vector&lt;ll&gt;&gt; T(<a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1, vector&lt;ll&gt;(<a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1));</div>
<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 &lt;= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
<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 &lt;= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++) {</div>
<div class="line"><span class="lineno"> 104</span> <span class="keywordflow">if</span> (i &lt; <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>) {</div>
<div class="line"><span class="lineno"> 105</span> <span class="keywordflow">if</span> (j == i + 1)</div>
<div class="line"><span class="lineno"> 106</span> T[i][j] = 1;</div>
<div class="line"><span class="lineno"> 107</span> <span class="keywordflow">else</span></div>
<div class="line"><span class="lineno"> 108</span> T[i][j] = 0;</div>
<div class="line"><span class="lineno"> 109</span> <span class="keywordflow">continue</span>;</div>
<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="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> - j];</div>
<div class="line"><span class="lineno"> 112</span> }</div>
<div class="line"><span class="lineno"> 113</span> }</div>
<div class="line"><span class="lineno"> 114</span> <span class="comment">// T^n-1</span></div>
<div class="line"><span class="lineno"> 115</span> T = <a class="code hl_function" href="#a702a9fc90e79b05b863cc4efa26ae2ec">power</a>(T, n - 1);</div>
<div class="line"><span class="lineno"> 116</span> </div>
<div class="line"><span class="lineno"> 117</span> <span class="comment">// T*F1</span></div>
<div class="line"><span class="lineno"> 118</span> <a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> res = 0;</div>
<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 &lt;= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
<div class="line"><span class="lineno"> 120</span> res = (res + (T[1][i] * F1[i]) % MOD) % MOD;</div>
<div class="line"><span class="lineno"> 121</span> }</div>
<div class="line"><span class="lineno"> 122</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><span class="lineno"> 123</span>}</div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a35b7c98af53ad2ec18658679ad7d43de"><div class="ttname"><a href="#a35b7c98af53ad2ec18658679ad7d43de">fib_b</a></div><div class="ttdeci">vector&lt; ll &gt; 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>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a702a9fc90e79b05b863cc4efa26ae2ec"><div class="ttname"><a href="#a702a9fc90e79b05b863cc4efa26ae2ec">power</a></div><div class="ttdeci">vector&lt; vector&lt; ll &gt; &gt; power(const vector&lt; vector&lt; ll &gt; &gt; &amp;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>
<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>
<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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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function </p>
<p class="definition">Definition at line <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00126">126</a> of file <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html">matrix_exponentiation.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 126</span> {</div>
<div class="line"><span class="lineno"> 127</span> cin.tie(0);</div>
<div class="line"><span class="lineno"> 128</span> cout.tie(0);</div>
<div class="line"><span class="lineno"> 129</span> <a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> t;</div>
<div class="line"><span class="lineno"> 130</span> cin &gt;&gt; t;</div>
<div class="line"><span class="lineno"> 131</span> <a class="code hl_define" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> i, 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> cin &gt;&gt; <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>;</div>
<div class="line"><span class="lineno"> 134</span> <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
<div class="line"><span class="lineno"> 135</span> cin &gt;&gt; x;</div>
<div class="line"><span class="lineno"> 136</span> <a class="code hl_variable" href="#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 &lt; <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
<div class="line"><span class="lineno"> 139</span> cin &gt;&gt; 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> cin &gt;&gt; x;</div>
<div class="line"><span class="lineno"> 143</span> cout &lt;&lt; <a class="code hl_function" href="#ad8389ed58fd0ec66df248014775ad1fa">ans</a>(x) &lt;&lt; <a class="code hl_define" href="#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><span class="lineno"> 144</span> <a class="code hl_variable" href="#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="amatrix__exponentiation_8cpp_html_a600eaf353befc174637855795f12d258"><div class="ttname"><a href="#a600eaf353befc174637855795f12d258">endl</a></div><div class="ttdeci">#define endl</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00036">matrix_exponentiation.cpp:36</a></div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00091">matrix_exponentiation.cpp:91</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a357cfbebfdc47a237a2862fe146af252">&#9670;&#160;</a></span>multiply()</h2>
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<td class="memname"><a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt; &gt; multiply </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt; &gt; &amp;</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>&lt; <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt; &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>B</em></span>&#160;)</td>
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<p>To multiply 2 matrices </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>matrix 1 of size (m \(\times\)n) </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">B</td><td><code class="param">matrix</code> 2 of size (p \(\times\)q)<br />
</td></tr>
</table>
</dd>
</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>
<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>
<div class="fragment"><div class="line"><span class="lineno"> 58</span> {</div>
<div class="line"><span class="lineno"> 59</span> vector&lt;vector&lt;ll&gt;&gt; C(<a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1, vector&lt;ll&gt;(<a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> + 1));</div>
<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 &lt;= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
<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 &lt;= <a class="code hl_variable" href="#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++) {</div>
<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 &lt;= <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>
<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>
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<h2 class="memtitle"><span class="permalink"><a href="#a702a9fc90e79b05b863cc4efa26ae2ec">&#9670;&#160;</a></span>power()</h2>
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<td class="memname"><a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt; &gt; power </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt; <a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> &gt; &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a></td> <td class="paramname"><span class="paramname"><em>p</em></span>&#160;)</td>
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<p>computing integer power of a matrix using recursive multiplication. </p><dl class="section note"><dt>Note</dt><dd>A must be a square matrix for this algorithm. </dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>base matrix </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">p</td><td>exponent </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>matrix of same dimension as A </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00076">76</a> of file <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html">matrix_exponentiation.cpp</a>.</p>
<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="#a357cfbebfdc47a237a2862fe146af252">multiply</a>(A, <a class="code hl_function" href="#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> vector&lt;vector&lt;ll&gt;&gt; X = <a class="code hl_function" href="#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="#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="#a357cfbebfdc47a237a2862fe146af252">multiply</a></div><div class="ttdeci">vector&lt; vector&lt; ll &gt; &gt; multiply(const vector&lt; vector&lt; ll &gt; &gt; &amp;A, const vector&lt; vector&lt; ll &gt; &gt; &amp;B)</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00057">matrix_exponentiation.cpp:57</a></div></div>
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<a name="doc-var-members" id="doc-var-members"></a><h2 id="header-doc-var-members" class="groupheader">Variable Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a35b7c98af53ad2ec18658679ad7d43de">&#9670;&#160;</a></span>fib_b</h2>
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<td class="memname"><a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt;<a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a>&gt; fib_b</td>
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<p>global vector variables used in the <a class="el" href="#ad8389ed58fd0ec66df248014775ad1fa">ans</a> function. </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000008">Todo</a></b></dt><dd>@stepfencurryxiao add documetnation </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00050">50</a> of file <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html">matrix_exponentiation.cpp</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a0cbd1162483ef7eccd5b947b2e01b1ab">&#9670;&#160;</a></span>fib_c</h2>
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<td class="memname"><a class="el" href="../../d7/dfc/classvector.html">vector</a>&lt;<a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a>&gt; fib_c</td>
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<p class="definition">Definition at line <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00050">50</a> of file <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html">matrix_exponentiation.cpp</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a9977ad12548c4a49dee9dc3f0685aa54">&#9670;&#160;</a></span>mat_size</h2>
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<td class="memname"><a class="el" href="#ae1d1ec9482079231e898236e2b23c9ba">ll</a> mat_size</td>
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<p>global variable mat_size </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000007">Todo</a></b></dt><dd>@stepfencurryxiao add documetnation </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00045">45</a> of file <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp_source.html">matrix_exponentiation.cpp</a>.</p>
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