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d4/d32/fibonacci__fast_8cpp.html

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<div class="textblock"><p>Faster computation of Fibonacci series. </p>
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<p>An efficient way to calculate nth fibonacci number faster and simpler than \(O(n\log n)\) method of matrix exponentiation This works by using both recursion and dynamic programming. as 93rd fibonacci exceeds 19 digits, which cannot be stored in a single long long variable, we can only use it till 92nd fibonacci we can use it for 10000th fibonacci etc, if we implement bigintegers. This algorithm works with the fact that nth fibonacci can easily found if we have already found n/2th or (n+1)/2th fibonacci It is a property of fibonacci similar to matrix exponentiation.</p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
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<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/de4/fibonacci__large_8cpp.html" title="Computes N^th Fibonacci number given as input argument. Uses custom build arbitrary integers library ...">fibonacci_large.cpp</a>, <a class="el" href="../../d9/d89/fibonacci_8cpp.html" title="Generate fibonacci sequence.">fibonacci.cpp</a>, <a class="el" href="../../de/d47/string__fibonacci_8cpp.html" title="This Programme returns the Nth fibonacci as a string.">string_fibonacci.cpp</a> </dd></dl>
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<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/de4/fibonacci__large_8cpp.html" title="Computes N^th Fibonacci number given as input argument. Uses custom build arbitrary integers library ...">fibonacci_large.cpp</a>, <a class="el" href="../../d9/d89/fibonacci_8cpp.html" title="n-th Fibonacci number.">fibonacci.cpp</a>, <a class="el" href="../../de/d47/string__fibonacci_8cpp.html" title="This Programme returns the Nth fibonacci as a string.">string_fibonacci.cpp</a> </dd></dl>
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</div><h2 class="groupheader">Macro Definition Documentation</h2>
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<a id="a392fb874e547e582e9c66a08a1f23326" name="a392fb874e547e582e9c66a08a1f23326"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a392fb874e547e582e9c66a08a1f23326">&#9670;&#160;</a></span>MAX</h2>

d5/d91/namespacesorting.html

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<tr class="separator:a78cb2f3b97b6db2c062b2a1df05c9ea9"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:a8fe6bac9e03f58abcc2ce26ef3de1b5f" id="r_a8fe6bac9e03f58abcc2ce26ef3de1b5f"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
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<tr class="memitem:a8fe6bac9e03f58abcc2ce26ef3de1b5f"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a8fe6bac9e03f58abcc2ce26ef3de1b5f">insertionSort</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; *arr)</td></tr>
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<tr class="memdesc:a8fe6bac9e03f58abcc2ce26ef3de1b5f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insertion Sort for a vector. <br /></td></tr>
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<tr class="separator:a8fe6bac9e03f58abcc2ce26ef3de1b5f"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:aa26de383227859210f14dcf12201a079" id="r_aa26de383227859210f14dcf12201a079"><td class="memTemplParams" colspan="2">template&lt;class Iterator &gt; </td></tr>
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<tr class="memitem:aa26de383227859210f14dcf12201a079"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#aa26de383227859210f14dcf12201a079">merge</a> (Iterator l, Iterator r, const Iterator e, char b[])</td></tr>
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<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a></p>
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<p>for returning multiple values form a function at once</p>
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<p>Sorting Algorithms.</p>
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<p>for using <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
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<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
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<p>Sorting algorithms.</p>
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<p>for algorithm functions for assert for IO operations</p>
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<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a> for assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a> and io operations</p>
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<p>@breif Sorting algorithms</p>
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<p>Sorting algorithms</p>
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<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a> for assert function in testing for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></p>
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<p>Contains sorting algorithms</p>
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<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a> for std::assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a> for IO operations</p>
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<p>Sorting algorithms</p>
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<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack.html">std::stack</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a> for assert</p>
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</tr>
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<p>Insertion Sort for a vector. </p>
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<p>Insertion Sort Function</p>
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<dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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</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,out]</td><td class="paramname">arr</td><td>pointer to array to be sorted </td></tr>
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<tr><td class="paramdir">[in,out]</td><td class="paramname">arr</td><td>pointer to array to be sorted</td></tr>
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</dd>
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</dl>
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<dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">T</td><td>Type of the vector elements </td></tr>
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</table>
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</dd>
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</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,out]</td><td class="paramname">arr</td><td>Pointer to the vector to be sorted </td></tr>
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</table>
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</dd>
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</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,out]</td><td class="paramname">arr</td><td>Array to be sorted </td></tr>
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<tr><td class="paramdir"></td><td class="paramname">n</td><td>Size of Array </td></tr>
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<tr><td class="paramdir"></td><td class="paramname">n</td><td>Size of Array</td></tr>
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</table>
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</dd>
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</dl>
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<dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">T</td><td>Type of the array elements </td></tr>
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</dd>
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</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,out]</td><td class="paramname">arr</td><td>Array to be sorted </td></tr>
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<tr><td class="paramdir"></td><td class="paramname">n</td><td>Size of the array </td></tr>
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