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<p>Matrix Exponentiation.
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <iostream></code><br />
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<code>#include <vector></code><br />
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Include dependency graph for matrix_exponentiation.cpp:</div>
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Macros</h2></td></tr>
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<tr class="memitem:ae1d1ec9482079231e898236e2b23c9ba"><td class="memItemLeft" align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a>   int64_t</td></tr>
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<tr class="separator:ae1d1ec9482079231e898236e2b23c9ba"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a600eaf353befc174637855795f12d258"><td class="memItemLeft" align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>   std::endl</td></tr>
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<tr class="memitem:a276c5a0e984cf60015b27252fe04fe6b"><td class="memItemLeft" align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a276c5a0e984cf60015b27252fe04fe6b">pb</a>   push_back</td></tr>
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<tr class="memitem:aca7d5718ab8c38506adb3bef2469b319"><td class="memItemLeft" align="right" valign="top"><a id="aca7d5718ab8c38506adb3bef2469b319" name="aca7d5718ab8c38506adb3bef2469b319"></a>
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#define </td><td class="memItemRight" valign="bottom"><b>MOD</b>   1000000007</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"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a357cfbebfdc47a237a2862fe146af252">multiply</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &A, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#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"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a702a9fc90e79b05b863cc4efa26ae2ec">power</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > &A, <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> p)</td></tr>
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<tr class="separator:a702a9fc90e79b05b863cc4efa26ae2ec"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ad8389ed58fd0ec66df248014775ad1fa"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> (<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> n)</td></tr>
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<tr class="separator:ad8389ed58fd0ec66df248014775ad1fa"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2"> </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="var-members" name="var-members"></a>
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Variables</h2></td></tr>
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<tr class="memitem:a9977ad12548c4a49dee9dc3f0685aa54"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></td></tr>
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<tr class="separator:a9977ad12548c4a49dee9dc3f0685aa54"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a35b7c98af53ad2ec18658679ad7d43de"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#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"><td class="memItemLeft" align="right" valign="top"><a id="a0cbd1162483ef7eccd5b947b2e01b1ab" name="a0cbd1162483ef7eccd5b947b2e01b1ab"></a>
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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > </td><td class="memItemRight" valign="bottom"><b>fib_c</b></td></tr>
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<tr class="separator:a0cbd1162483ef7eccd5b947b2e01b1ab"><td class="memSeparator" colspan="2"> </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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<div class="textblock"><p>Matrix Exponentiation. </p>
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<p>The problem can be solved with DP but constraints are high. <br />
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\(a_i = b_i\) (for \(i <= k\)) <br />
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\(a_i = c_1 a_{i-1} + c_2 a_{i-2} + ... + c_k a_{i-k}\) (for \(i > k\)) <br />
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Taking the example of Fibonacci series, \(k=2\) <br />
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\(b_1 = 1,\; b_2=1\) <br />
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\(c_1 = 1,\; c_2=1\) <br />
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\(a = \begin{bmatrix}0& 1& 1& 2& \ldots\end{bmatrix}\) <br />
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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>
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<p>Steps for Matrix Expo</p><ol type="1">
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<li>Create vector F1 : which is the copy of B.</li>
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<li>Create transpose matrix (Learn more about it on the internet)</li>
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<li>Perform \(T^{n-1}\) [transpose matrix to the power n-1]</li>
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<li>Multiply with F to get the last matrix of size (1 \(\times\)k).</li>
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</ol>
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<p>The first element of this matrix is the required result. </p>
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</div><h2 class="groupheader">Macro Definition Documentation</h2>
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<a id="a600eaf353befc174637855795f12d258" name="a600eaf353befc174637855795f12d258"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a600eaf353befc174637855795f12d258">◆ </a></span>endl</h2>
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<div class="memitem">
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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">#define endl   std::endl</td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>shorthand definition for <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></code> </p>
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</div>
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</div>
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<a id="ae1d1ec9482079231e898236e2b23c9ba" name="ae1d1ec9482079231e898236e2b23c9ba"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae1d1ec9482079231e898236e2b23c9ba">◆ </a></span>ll</h2>
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<div class="memitem">
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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">#define ll   int64_t</td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>shorthand definition for <code>int64_t</code> </p>
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</div>
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</div>
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<a id="a276c5a0e984cf60015b27252fe04fe6b" name="a276c5a0e984cf60015b27252fe04fe6b"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a276c5a0e984cf60015b27252fe04fe6b">◆ </a></span>pb</h2>
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<div class="memitem">
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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">#define pb   push_back</td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>shorthand definition for <code>int64_t</code> </p>
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</div>
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</div>
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<h2 class="groupheader">Function Documentation</h2>
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<a id="ad8389ed58fd0ec66df248014775ad1fa" name="ad8389ed58fd0ec66df248014775ad1fa"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ad8389ed58fd0ec66df248014775ad1fa">◆ </a></span>ans()</h2>
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<div class="memitem">
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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"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> ans </td>
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<td>(</td>
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<td class="paramtype"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> </td>
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<td class="paramname"><em>n</em></td><td>)</td>
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<td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Wrapper for Fibonacci </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">n</td><td>\(n^\text{th}\) Fibonacci number </td></tr>
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</table>
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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"><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>
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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="../../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>
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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="../../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>
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<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>
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<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>
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<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>
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<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>
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<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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<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d7/d35/matrix__exponentiation_8cpp_ad8389ed58fd0ec66df248014775ad1fa_cgraph.svg" width="272" height="60"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<div class="memitem">
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">void </td>
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<td class="paramname"></td><td>)</td>
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<td></td>
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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"><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>
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<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>
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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"> 132</span> <span class="keywordflow">while</span> (t--) {</div>
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<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>
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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="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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<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>
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<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>
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<div class="line"><span class="lineno"> 137</span> }</div>
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<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>
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<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>
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<div class="line"><span class="lineno"> 140</span> fib_c.pb(x);</div>
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<div class="line"><span class="lineno"> 141</span> }</div>
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<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>
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<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> << ans(x) << <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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<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>
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<div class="line"><span class="lineno"> 145</span> fib_c.clear();</div>
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<div class="line"><span class="lineno"> 146</span> }</div>
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<div class="line"><span class="lineno"> 147</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 148</span>}</div>
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<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>
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<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>
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<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>
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<a id="a357cfbebfdc47a237a2862fe146af252" name="a357cfbebfdc47a237a2862fe146af252"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a357cfbebfdc47a237a2862fe146af252">◆ </a></span>multiply()</h2>
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<div class="memitem">
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > multiply </td>
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<td>(</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > & </td>
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<td class="paramname"><em>A</em>, </td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > & </td>
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<td class="paramname"><em>B</em> </td>
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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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</td></tr>
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<dl class="section note"><dt>Note</dt><dd>\(p=n\) </dd></dl>
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<dl class="section return"><dt>Returns</dt><dd>matrix of dimension (m \(\times\)q) </dd></dl>
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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> <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>
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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="../../d7/d35/matrix__exponentiation_8cpp.html#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="../../d7/d35/matrix__exponentiation_8cpp.html#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="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; z++) {</div>
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<div class="line"><span class="lineno"> 63</span> C[i][j] = (C[i][j] + (A[i][z] * B[z][j]) % MOD) % MOD;</div>
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<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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<div class="line"><span class="lineno"> 66</span> }</div>
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<div class="line"><span class="lineno"> 67</span> <span class="keywordflow">return</span> C;</div>
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<div class="line"><span class="lineno"> 68</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a702a9fc90e79b05b863cc4efa26ae2ec">◆ </a></span>power()</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > power </td>
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<td>(</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>< <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> > > & </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>
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>base matrix </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">p</td><td>exponent </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>matrix of same dimension as A </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 76</span> {</div>
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<div class="line"><span class="lineno"> 77</span> <span class="keywordflow">if</span> (p == 1)</div>
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<div class="line"><span class="lineno"> 78</span> <span class="keywordflow">return</span> A;</div>
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<div class="line"><span class="lineno"> 79</span> <span class="keywordflow">if</span> (p % 2 == 1) {</div>
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<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>
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<div class="line"><span class="lineno"> 81</span> } <span class="keywordflow">else</span> {</div>
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<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>
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<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>
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<div class="line"><span class="lineno"> 84</span> }</div>
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<div class="line"><span class="lineno"> 85</span>}</div>
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<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>
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<h2 class="groupheader">Variable Documentation</h2>
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<a id="a35b7c98af53ad2ec18658679ad7d43de" name="a35b7c98af53ad2ec18658679ad7d43de"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a35b7c98af53ad2ec18658679ad7d43de">◆ </a></span>fib_b</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a><<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a>> fib_b</td>
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<p>global vector variables used in the <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#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>
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<a id="a9977ad12548c4a49dee9dc3f0685aa54" name="a9977ad12548c4a49dee9dc3f0685aa54"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a9977ad12548c4a49dee9dc3f0685aa54">◆ </a></span>mat_size</h2>
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<td class="memname"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#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>
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