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<p>Faster computation of Fibonacci series.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cinttypes&gt;</code><br />
<code>#include &lt;cstdio&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
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Include dependency graph for fibonacci_fast.cpp:</div>
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Functions</h2></td></tr>
<tr class="memitem:a5712edca101204eca8accdb1e096707f"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a> (uint64_t n)</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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Variables</h2></td></tr>
<tr class="memitem:a692ac7187ee88621a9f78fca78ec498d"><td class="memItemLeft" align="right" valign="top">const uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a692ac7187ee88621a9f78fca78ec498d">MAX</a> = 93</td></tr>
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<tr class="memitem:a3ba232425d45f9e9c0b87a8cf7ab69d9"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a> [<a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a692ac7187ee88621a9f78fca78ec498d">MAX</a>] = {0}</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Faster computation of Fibonacci series. </p>
<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>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
<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>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a5712edca101204eca8accdb1e096707f">&#9670;&nbsp;</a></span>fib()</h2>
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<td class="memname">uint64_t fib </td>
<td>(</td>
<td class="paramtype">uint64_t&#160;</td>
<td class="paramname"><em>n</em></td><td>)</td>
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<p>Algorithm </p>
<div class="fragment"><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; {</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordflow">if</span> (n == 0)</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordflow">if</span> (n == 1 || n == 2)</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keywordflow">return</span> (<a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a>[n] = 1);</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; </div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a>[n])</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a>[n];</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; </div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; uint64_t <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = (n % 2 != 0) ? (n + 1) / 2 : n / 2;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; </div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a>[n] = (n % 2 != 0) ? (<a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>) * <a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>) + <a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> - 1) * <a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> - 1))</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; : (2 * <a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> - 1) + <a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>)) * <a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>);</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a>[n];</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; {</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="comment">// Main Function</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="keywordflow">for</span> (uint64_t i = 1; i &lt; 93; i++) {</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; th fibonacci number is &quot;</span> &lt;&lt; <a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a>(i) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; }</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160;}</div>
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<h2 class="groupheader">Variable Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a3ba232425d45f9e9c0b87a8cf7ab69d9">&#9670;&nbsp;</a></span>f</h2>
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<td class="memname">uint64_t f[<a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a692ac7187ee88621a9f78fca78ec498d">MAX</a>] = {0}</td>
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<p>Array of computed fibonacci numbers </p>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a692ac7187ee88621a9f78fca78ec498d">&#9670;&nbsp;</a></span>MAX</h2>
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<td class="memname">const uint64_t MAX = 93</td>
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<p>maximum number that can be computed - The result after 93 cannot be stored in a <code>uint64_t</code> data type. </p>
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<div class="ttc" id="afibonacci__fast_8cpp_html_a3ba232425d45f9e9c0b87a8cf7ab69d9"><div class="ttname"><a href="../../d4/d32/fibonacci__fast_8cpp.html#a3ba232425d45f9e9c0b87a8cf7ab69d9">f</a></div><div class="ttdeci">uint64_t f[MAX]</div><div class="ttdef"><b>Definition:</b> fibonacci_fast.cpp:27</div></div>
<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>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_afcf0d19607cd0edd8ae333d2b9c220c0"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a></div><div class="ttdeci">ll k</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:48</div></div>
<div class="ttc" id="afibonacci__fast_8cpp_html_a5712edca101204eca8accdb1e096707f"><div class="ttname"><a href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a></div><div class="ttdeci">uint64_t fib(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_fast.cpp:30</div></div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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