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<div id="projectbrief">Set of algorithms implemented in C++.</div>
<div id="projectbrief">All the algorithms implemented in C++</div>
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@@ -122,7 +139,9 @@ Include dependency graph for gcd_of_n_numbers.cpp:</div>
<div class="dyncontent">
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Namespaces</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html">math</a></td></tr>
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<tr class="memitem:a509a35e11ed1e17a9e00dd56320a4181" id="r_a509a35e11ed1e17a9e00dd56320a4181"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a509a35e11ed1e17a9e00dd56320a4181">math::gcd_of_n_numbers::gcd_two</a> (int x, int y)</td></tr>
<tr class="memdesc:a509a35e11ed1e17a9e00dd56320a4181"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to compute GCD of 2 numbers x and y. <br /></td></tr>
<tr class="separator:a509a35e11ed1e17a9e00dd56320a4181"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a71b9357c7a722f8208499d9ba573297a" id="r_a71b9357c7a722f8208499d9ba573297a"><td class="memTemplParams" colspan="2">template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> n&gt; </td></tr>
<tr class="memitem:a71b9357c7a722f8208499d9ba573297a"><td class="memTemplItemLeft" align="right" valign="top">bool&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a71b9357c7a722f8208499d9ba573297a">math::gcd_of_n_numbers::check_all_zeros</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt; &amp;a)</td></tr>
<tr class="memitem:a71b9357c7a722f8208499d9ba573297a" id="r_a71b9357c7a722f8208499d9ba573297a"><td class="memTemplParams" colspan="2">template&lt;std::size_t n&gt; </td></tr>
<tr class="memitem:a71b9357c7a722f8208499d9ba573297a"><td class="memTemplItemLeft" align="right" valign="top">bool&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a71b9357c7a722f8208499d9ba573297a">math::gcd_of_n_numbers::check_all_zeros</a> (const std::array&lt; int, n &gt; &amp;a)</td></tr>
<tr class="memdesc:a71b9357c7a722f8208499d9ba573297a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to check if all elements in the array are 0. <br /></td></tr>
<tr class="separator:a71b9357c7a722f8208499d9ba573297a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1161713c662a14c2d5e33504f4324532" id="r_a1161713c662a14c2d5e33504f4324532"><td class="memTemplParams" colspan="2">template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> n&gt; </td></tr>
<tr class="memitem:a1161713c662a14c2d5e33504f4324532"><td class="memTemplItemLeft" align="right" valign="top">int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a1161713c662a14c2d5e33504f4324532">math::gcd_of_n_numbers::gcd</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt; &amp;a)</td></tr>
<tr class="memitem:a1161713c662a14c2d5e33504f4324532" id="r_a1161713c662a14c2d5e33504f4324532"><td class="memTemplParams" colspan="2">template&lt;std::size_t n&gt; </td></tr>
<tr class="memitem:a1161713c662a14c2d5e33504f4324532"><td class="memTemplItemLeft" align="right" valign="top">int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a1161713c662a14c2d5e33504f4324532">math::gcd_of_n_numbers::gcd</a> (const std::array&lt; int, n &gt; &amp;a)</td></tr>
<tr class="memdesc:a1161713c662a14c2d5e33504f4324532"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main program to compute GCD using the Euclidean algorithm. <br /></td></tr>
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@@ -156,6 +175,8 @@ Functions</h2></td></tr>
<div class="textblock"><p>This program aims at calculating the GCD of n numbers. </p>
<p>The GCD of n numbers can be calculated by repeatedly calculating the GCDs of pairs of numbers i.e. \(\gcd(a, b, c)\) = \(\gcd(\gcd(a, b), c)\) Euclidean algorithm helps calculate the GCD of each pair of numbers efficiently</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html" title="Compute the greatest common denominator of two integers using iterative form of Euclidean algorithm">gcd_iterative_euclidean.cpp</a>, <a class="el" href="../../d4/d45/gcd__recursive__euclidean_8cpp.html" title="Compute the greatest common denominator of two integers using recursive form of Euclidean algorithm">gcd_recursive_euclidean.cpp</a> </dd></dl>
<p class="definition">Definition in file <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html">gcd_of_n_numbers.cpp</a>.</p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a71b9357c7a722f8208499d9ba573297a" name="a71b9357c7a722f8208499d9ba573297a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a71b9357c7a722f8208499d9ba573297a">&#9670;&#160;</a></span>check_all_zeros()</h2>
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<div class="memitem">
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template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> n&gt; </div>
template&lt;std::size_t n&gt; </div>
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<td class="memname">bool math::gcd_of_n_numbers::check_all_zeros </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>a</em></span></td><td>)</td>
<td class="paramtype">const std::array&lt; int, n &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>a</em></span></td><td>)</td>
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@@ -184,17 +205,13 @@ template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/
<dl class="section return"><dt>Returns</dt><dd>'True' if all elements are 0 </dd>
<dd>
'False' if not all elements are 0 </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html#l00053">53</a> of file <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html">gcd_of_n_numbers.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 53</span> {</div>
<div class="line"><span class="lineno"> 54</span> <span class="comment">// Use std::all_of to simplify zero-checking</span></div>
<div class="line"><span class="lineno"> 55</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/all_any_none_of.html">std::all_of</a>(a.begin(), a.end(), [](<span class="keywordtype">int</span> x) { return x == 0; });</div>
<div class="line"><span class="lineno"> 55</span> <span class="keywordflow">return</span> std::all_of(a.begin(), a.end(), [](<span class="keywordtype">int</span> x) { return x == 0; });</div>
<div class="line"><span class="lineno"> 56</span>}</div>
<div class="ttc" id="aall_any_none_of_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/all_any_none_of.html">std::all_of</a></div><div class="ttdeci">T all_of(T... args)</div></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/d11/gcd__of__n__numbers_8cpp_a71b9357c7a722f8208499d9ba573297a_cgraph.svg" width="306" height="76"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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<div class="memitem">
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template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> n&gt; </div>
template&lt;std::size_t n&gt; </div>
<table class="memname">
<tr>
<td class="memname">int math::gcd_of_n_numbers::gcd </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>a</em></span></td><td>)</td>
<td class="paramtype">const std::array&lt; int, n &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>a</em></span></td><td>)</td>
<td></td>
</tr>
</table>
@@ -222,6 +239,8 @@ template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>GCD of the numbers in the array or std::nullopt if undefined </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html#l00064">64</a> of file <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html">gcd_of_n_numbers.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 64</span> {</div>
<div class="line"><span class="lineno"> 65</span> <span class="comment">// GCD is undefined if all elements in the array are 0</span></div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="#a71b9357c7a722f8208499d9ba573297a">check_all_zeros</a>(a)) {</div>
@@ -230,7 +249,7 @@ template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/
<div class="line"><span class="lineno"> 69</span> </div>
<div class="line"><span class="lineno"> 70</span> <span class="comment">// divisors can be negative, we only want the positive value</span></div>
<div class="line"><span class="lineno"> 71</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = std::abs(a[0]);</div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> i = 1; i &lt; n; ++i) {</div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordflow">for</span> (std::size_t i = 1; i &lt; n; ++i) {</div>
<div class="line"><span class="lineno"> 73</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="#a509a35e11ed1e17a9e00dd56320a4181">gcd_two</a>(result, std::abs(a[i]));</div>
<div class="line"><span class="lineno"> 74</span> <span class="keywordflow">if</span> (result == 1) {</div>
<div class="line"><span class="lineno"> 75</span> <span class="keywordflow">break</span>; <span class="comment">// Further computations still result in gcd of 1</span></div>
@@ -238,16 +257,10 @@ template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/
<div class="line"><span class="lineno"> 77</span> }</div>
<div class="line"><span class="lineno"> 78</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><span class="lineno"> 79</span>}</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:77</div></div>
<div class="ttc" id="agcd__of__n__numbers_8cpp_html_a509a35e11ed1e17a9e00dd56320a4181"><div class="ttname"><a href="#a509a35e11ed1e17a9e00dd56320a4181">math::gcd_of_n_numbers::gcd_two</a></div><div class="ttdeci">int gcd_two(int x, int y)</div><div class="ttdoc">Function to compute GCD of 2 numbers x and y.</div><div class="ttdef"><b>Definition</b> gcd_of_n_numbers.cpp:35</div></div>
<div class="ttc" id="agcd__of__n__numbers_8cpp_html_a71b9357c7a722f8208499d9ba573297a"><div class="ttname"><a href="#a71b9357c7a722f8208499d9ba573297a">math::gcd_of_n_numbers::check_all_zeros</a></div><div class="ttdeci">bool check_all_zeros(const std::array&lt; int, n &gt; &amp;a)</div><div class="ttdoc">Function to check if all elements in the array are 0.</div><div class="ttdef"><b>Definition</b> gcd_of_n_numbers.cpp:53</div></div>
<div class="ttc" id="asize_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a></div></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d1/d11/gcd__of__n__numbers_8cpp_a1161713c662a14c2d5e33504f4324532_cgraph.svg" width="551" height="215"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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<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> <a href="../../de/dc3/fibonacci__sum_8cpp_source.html#l00077">fibonacci_sum.cpp:77</a></div></div>
<div class="ttc" id="agcd__of__n__numbers_8cpp_html_a509a35e11ed1e17a9e00dd56320a4181"><div class="ttname"><a href="#a509a35e11ed1e17a9e00dd56320a4181">math::gcd_of_n_numbers::gcd_two</a></div><div class="ttdeci">int gcd_two(int x, int y)</div><div class="ttdoc">Function to compute GCD of 2 numbers x and y.</div><div class="ttdef"><b>Definition</b> <a href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html#l00035">gcd_of_n_numbers.cpp:35</a></div></div>
<div class="ttc" id="agcd__of__n__numbers_8cpp_html_a71b9357c7a722f8208499d9ba573297a"><div class="ttname"><a href="#a71b9357c7a722f8208499d9ba573297a">math::gcd_of_n_numbers::check_all_zeros</a></div><div class="ttdeci">bool check_all_zeros(const std::array&lt; int, n &gt; &amp;a)</div><div class="ttdoc">Function to check if all elements in the array are 0.</div><div class="ttdef"><b>Definition</b> <a href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html#l00053">gcd_of_n_numbers.cpp:53</a></div></div>
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@@ -278,6 +291,8 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>GCD of x and y via recursion </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html#l00035">35</a> of file <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html">gcd_of_n_numbers.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 35</span> {</div>
<div class="line"><span class="lineno"> 36</span> <span class="comment">// base cases</span></div>
<div class="line"><span class="lineno"> 37</span> <span class="keywordflow">if</span> (y == 0) {</div>
@@ -288,12 +303,7 @@ Here is the call graph for this function:</div>
<div class="line"><span class="lineno"> 42</span> }</div>
<div class="line"><span class="lineno"> 43</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#a509a35e11ed1e17a9e00dd56320a4181">gcd_two</a>(y, x % y); <span class="comment">// Euclidean method</span></div>
<div class="line"><span class="lineno"> 44</span>}</div>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html#l00111">111</a> of file <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html">gcd_of_n_numbers.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 111</span> {</div>
<div class="line"><span class="lineno"> 112</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementation</span></div>
<div class="line"><span class="lineno"> 113</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 114</span>}</div>
<div class="ttc" id="agcd__of__n__numbers_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementation.</div><div class="ttdef"><b>Definition</b> gcd_of_n_numbers.cpp:87</div></div>
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<div class="ttc" id="agcd__of__n__numbers_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementation.</div><div class="ttdef"><b>Definition</b> <a href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html#l00087">gcd_of_n_numbers.cpp:87</a></div></div>
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<p>Self-test implementation. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html#l00087">87</a> of file <a class="el" href="../../d1/d11/gcd__of__n__numbers_8cpp_source.html">gcd_of_n_numbers.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 87</span> {</div>
<div class="line"><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, 1&gt;</a> array_1 = {0};</div>
<div class="line"><span class="lineno"> 89</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, 1&gt;</a> array_2 = {1};</div>
<div class="line"><span class="lineno"> 90</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, 2&gt;</a> array_3 = {0, 2};</div>
<div class="line"><span class="lineno"> 91</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, 3&gt;</a> array_4 = {-60, 24, 18};</div>
<div class="line"><span class="lineno"> 92</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, 4&gt;</a> array_5 = {100, -100, -100, 200};</div>
<div class="line"><span class="lineno"> 93</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, 5&gt;</a> array_6 = {0, 0, 0, 0, 0};</div>
<div class="line"><span class="lineno"> 94</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, 7&gt;</a> array_7 = {10350, -24150, 0, 17250, 37950, -127650, 51750};</div>
<div class="line"><span class="lineno"> 95</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, 7&gt;</a> array_8 = {9500000, -12121200, 0, 4444, 0, 0, 123456789};</div>
<div class="line"><span class="lineno"> 88</span> std::array&lt;int, 1&gt; array_1 = {0};</div>
<div class="line"><span class="lineno"> 89</span> std::array&lt;int, 1&gt; array_2 = {1};</div>
<div class="line"><span class="lineno"> 90</span> std::array&lt;int, 2&gt; array_3 = {0, 2};</div>
<div class="line"><span class="lineno"> 91</span> std::array&lt;int, 3&gt; array_4 = {-60, 24, 18};</div>
<div class="line"><span class="lineno"> 92</span> std::array&lt;int, 4&gt; array_5 = {100, -100, -100, 200};</div>
<div class="line"><span class="lineno"> 93</span> std::array&lt;int, 5&gt; array_6 = {0, 0, 0, 0, 0};</div>
<div class="line"><span class="lineno"> 94</span> std::array&lt;int, 7&gt; array_7 = {10350, -24150, 0, 17250, 37950, -127650, 51750};</div>
<div class="line"><span class="lineno"> 95</span> std::array&lt;int, 7&gt; array_8 = {9500000, -12121200, 0, 4444, 0, 0, 123456789};</div>
<div class="line"><span class="lineno"> 96</span> </div>
<div class="line"><span class="lineno"> 97</span> assert(math::gcd_of_n_numbers::gcd(array_1) == -1);</div>
<div class="line"><span class="lineno"> 98</span> assert(math::gcd_of_n_numbers::gcd(array_2) == 1);</div>
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<div class="line"><span class="lineno"> 103</span> assert(math::gcd_of_n_numbers::gcd(array_7) == 3450);</div>
<div class="line"><span class="lineno"> 104</span> assert(math::gcd_of_n_numbers::gcd(array_8) == 1);</div>
<div class="line"><span class="lineno"> 105</span>}</div>
<div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
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