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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>
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Functions</h2></td></tr>
<tr class="memitem:afa39ec943a4836c878e1614fd89b146f"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">largestPower</a> (uint32_t n, const uint16_t &amp;p)</td></tr>
<tr class="memdesc:afa39ec943a4836c878e1614fd89b146f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to calculate largest power. <a href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">More...</a><br /></td></tr>
<tr class="separator:afa39ec943a4836c878e1614fd89b146f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a04065193d190d605e1f0d0d93a87e244"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">lcmSum</a> (const uint16_t &amp;num)</td></tr>
<tr class="separator:a04065193d190d605e1f0d0d93a87e244"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8d8e81a7cd59644b311ef9adb268f5f0"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a8d8e81a7cd59644b311ef9adb268f5f0">magic_number</a> (const uint64_t &amp;n)</td></tr>
<tr class="separator:a8d8e81a7cd59644b311ef9adb268f5f0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afcd07701d73ed65cd616bcba02737f3d"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">power</a> (uint64_t a, uint64_t b, uint64_t c)</td></tr>
<tr class="memdesc:afcd07701d73ed65cd616bcba02737f3d"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function calculates a raised to exponent b under modulo c using modular exponentiation. <a href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">More...</a><br /></td></tr>
<tr class="separator:afcd07701d73ed65cd616bcba02737f3d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6e2dff75c5de70455b90c799d6ad6967"><td class="memTemplParams" colspan="2">template&lt;class T &gt; </td></tr>
<tr class="memitem:a6e2dff75c5de70455b90c799d6ad6967"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a6e2dff75c5de70455b90c799d6ad6967">n_choose_r</a> (T n, T r)</td></tr>
<tr class="memdesc:a6e2dff75c5de70455b90c799d6ad6967"><td class="mdescLeft">&#160;</td><td class="mdescRight">This is the function implementation of \( \binom{n}{r} \). <a href="../../dd/d47/namespacemath.html#a6e2dff75c5de70455b90c799d6ad6967">More...</a><br /></td></tr>
<tr class="separator:a6e2dff75c5de70455b90c799d6ad6967"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a89ab7d6c3e3ee72a8cbaa85127986185"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a89ab7d6c3e3ee72a8cbaa85127986185">power_of_two</a> (int n)</td></tr>
<tr class="memdesc:a89ab7d6c3e3ee72a8cbaa85127986185"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to test above algorithm. <a href="../../dd/d47/namespacemath.html#a89ab7d6c3e3ee72a8cbaa85127986185">More...</a><br /></td></tr>
<tr class="separator:a89ab7d6c3e3ee72a8cbaa85127986185"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae1ca505751f5a6d3977b86372cfe75ea"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ae1ca505751f5a6d3977b86372cfe75ea">binomialCoeffSum</a> (uint64_t n)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> </p>
<p>Math algorithms.</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
<p>for IO operations</p>
<p>for io operations</p>
<p>for assert</p>
<p>for assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
<p>Mathematical algorithms</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
<p>Mathematical algorithms</p>
<p>for assert</p>
<p>Mathematical algorithms</p>
<p>for assert for io operations</p>
<p>Mathematical algorithms</p>
<p>Mathematical algorithms </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae1ca505751f5a6d3977b86372cfe75ea"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae1ca505751f5a6d3977b86372cfe75ea">&#9670;&nbsp;</a></span>binomialCoeffSum()</h2>
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<td class="memname">uint64_t math::binomialCoeffSum </td>
<td>(</td>
<td class="paramtype">uint64_t&#160;</td>
<td class="paramname"><em>n</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Function to calculate sum of binomial coefficients </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>number </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>Sum of binomial coefficients of number </dd></dl>
<div class="fragment"><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; {</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <span class="comment">// Calculating 2^n</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; <span class="keywordflow">return</span> (1 &lt;&lt; n);</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160;}</div>
</div><!-- fragment -->
</div>
</div>
<a id="afa39ec943a4836c878e1614fd89b146f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#afa39ec943a4836c878e1614fd89b146f">&#9670;&nbsp;</a></span>largestPower()</h2>
<div class="memitem">
<div class="memproto">
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<td class="memname">uint64_t math::largestPower </td>
<td>(</td>
<td class="paramtype">uint32_t&#160;</td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const uint16_t &amp;&#160;</td>
<td class="paramname"><em>p</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Function to calculate largest power. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>number </td></tr>
<tr><td class="paramname">p</td><td>prime number </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>largest power </dd></dl>
<div class="fragment"><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; { </div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; <span class="comment">// Initialize result </span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keywordtype">int</span> x = 0; </div>
<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="comment">// Calculate result </span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="keywordflow">while</span> (n) </div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; { </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; n /= p; </div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; x += n; </div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; } </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordflow">return</span> x; </div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; }</div>
</div><!-- fragment -->
</div>
</div>
<a id="a04065193d190d605e1f0d0d93a87e244"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a04065193d190d605e1f0d0d93a87e244">&#9670;&nbsp;</a></span>lcmSum()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
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<td class="memname">uint64_t math::lcmSum </td>
<td>(</td>
<td class="paramtype">const uint16_t &amp;&#160;</td>
<td class="paramname"><em>num</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Function to compute sum of euler totients in sumOfEulerTotient vector </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">num</td><td>input number </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>int Sum of LCMs, i.e. ∑LCM(i, num) from i = 1 to num </dd></dl>
<div class="fragment"><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; {</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; uint64_t i = 0, j = 0;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> eulerTotient(num + 1);</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> sumOfEulerTotient(num + 1);</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="comment">// storing initial values in eulerTotient vector</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <span class="keywordflow">for</span> (i = 1; i &lt;= num; i++) {</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; eulerTotient[i] = i;</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; }</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; <span class="comment">// applying totient sieve</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">for</span> (i = 2; i &lt;= num; i++) {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="keywordflow">if</span> (eulerTotient[i] == i) {</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordflow">for</span> (j = i; j &lt;= num; j += i) {</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; eulerTotient[j] = eulerTotient[j] / i;</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; eulerTotient[j] = eulerTotient[j] * (i - 1);</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; }</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; }</div>
<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; </div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="comment">// computing sum of euler totients</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="keywordflow">for</span> (i = 1; i &lt;= num; i++) {</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="keywordflow">for</span> (j = i; j &lt;= num; j += i) {</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; sumOfEulerTotient[j] += eulerTotient[i] * i;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; }</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordflow">return</span> ((sumOfEulerTotient[num] + 1) * num) / 2;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160;}</div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; uint64_t &gt;</a></div></div>
</div><!-- fragment -->
</div>
</div>
<a id="a8d8e81a7cd59644b311ef9adb268f5f0"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8d8e81a7cd59644b311ef9adb268f5f0">&#9670;&nbsp;</a></span>magic_number()</h2>
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<td class="memname">bool math::magic_number </td>
<td>(</td>
<td class="paramtype">const uint64_t &amp;&#160;</td>
<td class="paramname"><em>n</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Function to check if the given number is magic number or not. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>number to be checked. </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>if number is a magic number, returns true, else false. </dd></dl>
<div class="fragment"><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; {</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordflow">if</span> (n &lt;= 0) {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</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="comment">// result stores the modulus of @param n with 9</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; uint64_t <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = n % 9;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <span class="comment">// if result is 1 then the number is a magic number else not</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordflow">if</span> (result == 1) {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; }</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160;}</div>
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6e2dff75c5de70455b90c799d6ad6967">&#9670;&nbsp;</a></span>n_choose_r()</h2>
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template&lt;class T &gt; </div>
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<tr>
<td class="memname">T math::n_choose_r </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>r</em>&#160;</td>
</tr>
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<td></td>
<td>)</td>
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<p>This is the function implementation of \( \binom{n}{r} \). </p>
<p>We are calculating the ans with iterations instead of calculating three different factorials. Also, we are using the fact that \( \frac{n!}{r! (n-r)!} = \frac{(n - r + 1) \times \cdots \times n}{1 \times \cdots \times r} \) </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Only for integer types such as long, int_64 etc </td></tr>
</table>
</dd>
</dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>\( n \) in \( \binom{n}{r} \) </td></tr>
<tr><td class="paramname">r</td><td>\( r \) in \( \binom{n}{r} \) </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>ans \( \binom{n}{r} \) </dd></dl>
<div class="fragment"><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> (r &gt; n / 2) {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; r = n - r; <span class="comment">// Because of the fact that nCr(n, r) == nCr(n, n - r)</span></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; T <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = 1;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= r; i++) {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> *= n - r + i;</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> /= i;</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; }</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160;}</div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#afcd07701d73ed65cd616bcba02737f3d">&#9670;&nbsp;</a></span>power()</h2>
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<td class="memname">uint64_t math::power </td>
<td>(</td>
<td class="paramtype">uint64_t&#160;</td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint64_t&#160;</td>
<td class="paramname"><em>b</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint64_t&#160;</td>
<td class="paramname"><em>c</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>This function calculates a raised to exponent b under modulo c using modular exponentiation. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>integer base </td></tr>
<tr><td class="paramname">b</td><td>unsigned integer exponent </td></tr>
<tr><td class="paramname">c</td><td>integer modulo </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>a raised to power b modulo c </dd></dl>
<p>Initialize the answer to be returned</p>
<p>Update a if it is more than or equal to c</p>
<p>In case a is divisible by c;</p>
<p>If b is odd, multiply a with answer</p>
<p>b must be even now</p>
<p>b = b/2</p>
<div class="fragment"><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; uint64_t <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = 1; <span class="comment">/// Initialize the answer to be returned</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; a = a % c; <span class="comment">/// Update a if it is more than or equal to c</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <span class="keywordflow">if</span> (a == 0) {</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordflow">return</span> 0; <span class="comment">/// In case a is divisible by c;</span></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; <span class="keywordflow">while</span> (b &gt; 0) {<span class="comment"></span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160;<span class="comment"> /// If b is odd, multiply a with answer</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160;<span class="comment"></span> <span class="keywordflow">if</span> (b &amp; 1) {</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = ((<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> % c) * (a % c)) % c;</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; }<span class="comment"></span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160;<span class="comment"> /// b must be even now</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160;<span class="comment"></span> b = b &gt;&gt; 1; <span class="comment">/// b = b/2</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; a = ((a % c) * (a % c)) % c;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; }</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a89ab7d6c3e3ee72a8cbaa85127986185">&#9670;&nbsp;</a></span>power_of_two()</h2>
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<td class="memname">void math::power_of_two </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Function to test above algorithm. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>description </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p>This function finds whether a number is power of 2 or not </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>value for which we want to check prints the result, as "Yes, the number n is a power of 2" or "No, the number is not a power of 2" without quotes</td></tr>
</table>
</dd>
</dl>
<p>result stores the bitwise and of n and n-1</p>
<div class="fragment"><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; {<span class="comment"></span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160;<span class="comment"> /**</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160;<span class="comment"> * This function finds whether a number is power of 2 or not</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160;<span class="comment"> * @param n value for which we want to check</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160;<span class="comment"> * prints the result, as &quot;Yes, the number n is a power of 2&quot; or</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160;<span class="comment"> * &quot;No, the number is not a power of 2&quot; without quotes</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160;<span class="comment"> */</span><span class="comment"></span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160;<span class="comment"> /// result stores the</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160;<span class="comment"> /// bitwise and of n and n-1</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160;<span class="comment"></span> <span class="keywordtype">int</span> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = n &amp; (n - 1);</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="keywordflow">if</span> (result == 0) {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Yes, the number &quot;</span> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; is a power of 2&quot;</span>;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;No, the number &quot;</span> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; is not a power of 2&quot;</span>;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; }</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160;}</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>
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