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Documentation for a283f2a96f
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@@ -109,12 +109,17 @@ Functions</h2></td></tr>
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<tr class="memitem:afcd07701d73ed65cd616bcba02737f3d"><td class="memItemLeft" align="right" valign="top">uint64_t </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>
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<tr class="memdesc:afcd07701d73ed65cd616bcba02737f3d"><td class="mdescLeft"> </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>
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<tr class="separator:afcd07701d73ed65cd616bcba02737f3d"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a6e2dff75c5de70455b90c799d6ad6967"><td class="memTemplParams" colspan="2">template<class T > </td></tr>
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<tr class="memitem:a6e2dff75c5de70455b90c799d6ad6967"><td class="memTemplItemLeft" align="right" valign="top">T </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>
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<tr class="memdesc:a6e2dff75c5de70455b90c799d6ad6967"><td class="mdescLeft"> </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>
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<tr class="separator:a6e2dff75c5de70455b90c799d6ad6967"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae1ca505751f5a6d3977b86372cfe75ea"><td class="memItemLeft" align="right" valign="top">uint64_t </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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<tr class="separator:ae1ca505751f5a6d3977b86372cfe75ea"><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>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html" title="STL class.">std::vector</a> </p>
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<p>for assert</p>
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<p>Mathematical algorithms.</p>
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<p>for io operations</p>
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<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>
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<p>Mathematical algorithms</p>
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@@ -122,6 +127,7 @@ Functions</h2></td></tr>
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<p>Mathematical algorithms</p>
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<p>for assert</p>
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<p>Mathematical algorithms</p>
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<p>for io operations for assert</p>
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<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>
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<p>Mathematical algorithms </p>
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</div><h2 class="groupheader">Function Documentation</h2>
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@@ -245,6 +251,68 @@ Functions</h2></td></tr>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  }</div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> }</div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="a6e2dff75c5de70455b90c799d6ad6967"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a6e2dff75c5de70455b90c799d6ad6967">◆ </a></span>n_choose_r()</h2>
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<div class="memitem">
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template<class T > </div>
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<tr>
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<td class="memname">T math::n_choose_r </td>
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<td>(</td>
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<td class="paramtype">T </td>
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<td class="paramname"><em>n</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">T </td>
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<td class="paramname"><em>r</em> </td>
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<td>)</td>
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</div><div class="memdoc">
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<p>This is the function implementation of \( \binom{n}{r} \). </p>
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<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>
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<table class="tparams">
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<tr><td class="paramname">T</td><td>Only for integer types such as long, int_64 etc </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="paramname">n</td><td>\( n \) in \( \binom{n}{r} \) </td></tr>
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<tr><td class="paramname">r</td><td>\( r \) in \( \binom{n}{r} \) </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>ans \( \binom{n}{r} \) </dd></dl>
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<div class="fragment"><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  {</div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordflow">if</span>(r > n / 2)</div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  r = n - r; <span class="comment">// Because of the fact that nCr(n, r) == nCr(n, n - r)</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  T <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = 1;</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 1; i <= r; i++) {</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> *= n - r + i;</div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> /= i;</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  }</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordflow">return</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> }</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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