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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="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"></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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Functions</h2></td></tr>
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<tr class="memitem:a8bcf0bfddddfd7f6d0848703632d795d"><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#a8bcf0bfddddfd7f6d0848703632d795d">ab</a> (<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> x)</td></tr>
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<tr class="separator:a8bcf0bfddddfd7f6d0848703632d795d"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ac62a499b83c7895dd0aa69da1b64c904"><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#ac62a499b83c7895dd0aa69da1b64c904">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:ac62a499b83c7895dd0aa69da1b64c904"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a5769b745458157ef2679949155684f3b"><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#a5769b745458157ef2679949155684f3b">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:a5769b745458157ef2679949155684f3b"><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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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="var-members"></a>
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Variables</h2></td></tr>
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<tr class="memitem:afcf0d19607cd0edd8ae333d2b9c220c0"><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#afcf0d19607cd0edd8ae333d2b9c220c0">k</a></td></tr>
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<tr class="separator:afcf0d19607cd0edd8ae333d2b9c220c0"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a9ecd98ce0064e2f7f97bb6a92f58ee72"><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#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a></td></tr>
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<tr class="separator:a9ecd98ce0064e2f7f97bb6a92f58ee72"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:acf41e44dfa1536fb48606ff20770f92f"><td class="memItemLeft" align="right" valign="top"><a id="acf41e44dfa1536fb48606ff20770f92f"></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>b</b></td></tr>
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<tr class="separator:acf41e44dfa1536fb48606ff20770f92f"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ad54b52a703d277babd3f30d20d9d416d"><td class="memItemLeft" align="right" valign="top"><a id="ad54b52a703d277babd3f30d20d9d416d"></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>c</b></td></tr>
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<tr class="separator:ad54b52a703d277babd3f30d20d9d416d"><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"></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"></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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</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"></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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<td class="memname">#define pb   push_back</td>
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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="a8bcf0bfddddfd7f6d0848703632d795d"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a8bcf0bfddddfd7f6d0848703632d795d">◆ </a></span>ab()</h2>
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<div class="memitem">
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<td class="memname"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> ab </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>x</em></td><td>)</td>
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<td></td>
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<td class="mlabels-right">
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<span class="mlabels"><span class="mlabel">inline</span></span> </td>
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</div><div class="memdoc">
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<p>returns absolute value </p>
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<div class="fragment"><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> { <span class="keywordflow">return</span> x > 0LL ? x : -x; }</div>
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</div><!-- fragment -->
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<a id="ad8389ed58fd0ec66df248014775ad1fa"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ad8389ed58fd0ec66df248014775ad1fa">◆ </a></span>ans()</h2>
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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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</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"><a name="l00094"></a><span class="lineno"> 94</span>  {</div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">if</span> (n == 0)</div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">if</span> (n <= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>)</div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">return</span> b[n - 1];</div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="comment">// F1</span></div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<ll></a> F1(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> + 1);</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; i++) F1[i] = b[i - 1];</div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  </div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="comment">// Transpose matrix</span></div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<vector<ll></a>> T(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> + 1, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<ll></a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> + 1));</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; i++) {</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">for</span> (ll j = 1; j <= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; j++) {</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keywordflow">if</span> (i < <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>) {</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordflow">if</span> (j == i + 1)</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  T[i][j] = 1;</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordflow">else</span></div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  T[i][j] = 0;</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  }</div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  T[i][j] = c[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> - j];</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  }</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  }</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">// T^n-1</span></div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  T = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a5769b745458157ef2679949155684f3b">power</a>(T, n - 1);</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  </div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// T*F1</span></div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  ll res = 0;</div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; i++) {</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  res = (res + (T[1][i] * F1[i]) % MOD) % MOD;</div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  }</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordflow">return</span> res;</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<td class="memname">int main </td>
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<td>(</td>
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<p>Main function </p>
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<div class="fragment"><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  {</div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a>.tie(0);</div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a>.tie(0);</div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  ll t;</div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> t;</div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  ll i, j, x;</div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">while</span> (t--) {</div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>;</div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordflow">for</span> (i = 0; i < <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; i++) {</div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> x;</div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  b.pb(x);</div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  }</div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordflow">for</span> (i = 0; i < <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; i++) {</div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> x;</div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  c.pb(x);</div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  }</div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">cin</a> >> x;</div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> << <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>(x) << <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  b.clear();</div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  c.clear();</div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  }</div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ac62a499b83c7895dd0aa69da1b64c904">◆ </a></span>multiply()</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>> > 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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<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>
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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"><a name="l00061"></a><span class="lineno"> 61</span>  {</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<vector<ll></a>> C(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> + 1, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<ll></a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> + 1));</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">for</span> (ll i = 1; i <= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; i++) {</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keywordflow">for</span> (ll j = 1; j <= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; j++) {</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">for</span> (ll z = 1; z <= <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>; z++) {</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  C[i][j] = (C[i][j] + (A[i][z] * B[z][j]) % MOD) % MOD;</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  }</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  }</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  }</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">return</span> C;</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a5769b745458157ef2679949155684f3b">◆ </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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<td class="paramtype"><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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<table class="params">
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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"><a name="l00079"></a><span class="lineno"> 79</span>  {</div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">if</span> (p == 1)</div>
|
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordflow">return</span> A;</div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keywordflow">if</span> (p % 2 == 1) {</div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">return</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ac62a499b83c7895dd0aa69da1b64c904">multiply</a>(A, <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a5769b745458157ef2679949155684f3b">power</a>(A, p - 1));</div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector<vector<ll></a>> X = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a5769b745458157ef2679949155684f3b">power</a>(A, p / 2);</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">return</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ac62a499b83c7895dd0aa69da1b64c904">multiply</a>(X, X);</div>
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<h2 class="groupheader">Variable Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a9ecd98ce0064e2f7f97bb6a92f58ee72">◆ </a></span>a</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>> a</td>
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<p>global vector variables </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000005">Todo:</a></b></dt><dd>@stepfencurryxiao add documetnation </dd></dl>
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<h2 class="memtitle"><span class="permalink"><a href="#afcf0d19607cd0edd8ae333d2b9c220c0">◆ </a></span>k</h2>
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<td class="memname"><a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">ll</a> k</td>
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<p>global variable k </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000004">Todo:</a></b></dt><dd>@stepfencurryxiao add documetnation </dd></dl>
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<div class="ttc" id="amatrix__exponentiation_8cpp_html_ac62a499b83c7895dd0aa69da1b64c904"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ac62a499b83c7895dd0aa69da1b64c904">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:60</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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<div class="ttc" id="amatrix__exponentiation_8cpp_html_a5769b745458157ef2679949155684f3b"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a5769b745458157ef2679949155684f3b">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:79</div></div>
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