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<div class="headertitle"><div class="title">gcd_of_n_numbers.cpp</div></div>
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<div class="contents">
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<a href="../../d1/d11/gcd__of__n__numbers_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include <algorithm></span> </div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include <array></span> </div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include <cassert></span> </div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <iostream></span> </div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/d47/namespacemath.html">math</a> {</div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d2/ddb/namespacegcd__of__n__numbers.html">gcd_of_n_numbers</a> {</div>
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<div class="foldopen" id="foldopen00035" data-start="{" data-end="}">
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"><a class="line" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a509a35e11ed1e17a9e00dd56320a4181"> 35</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a509a35e11ed1e17a9e00dd56320a4181">gcd_two</a>(<span class="keywordtype">int</span> x, <span class="keywordtype">int</span> y) {</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// base cases</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">if</span> (y == 0) {</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">return</span> x;</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> }</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">if</span> (x == 0) {</div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordflow">return</span> y;</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> }</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a509a35e11ed1e17a9e00dd56320a4181">gcd_two</a>(y, x % y); <span class="comment">// Euclidean method</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span>}</div>
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</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="keyword">template</span> <std::<span class="keywordtype">size_t</span> n></div>
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<div class="foldopen" id="foldopen00053" data-start="{" data-end="}">
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"><a class="line" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a71b9357c7a722f8208499d9ba573297a"> 53</a></span><span class="keywordtype">bool</span> <a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a71b9357c7a722f8208499d9ba573297a">check_all_zeros</a>(<span class="keyword">const</span> std::array<int, n> &a) {</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// Use std::all_of to simplify zero-checking</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><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>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span>}</div>
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</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="keyword">template</span> <std::<span class="keywordtype">size_t</span> n></div>
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<div class="foldopen" id="foldopen00064" data-start="{" data-end="}">
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"><a class="line" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a1161713c662a14c2d5e33504f4324532"> 64</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a1161713c662a14c2d5e33504f4324532">gcd</a>(<span class="keyword">const</span> std::array<int, n> &a) {</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// GCD is undefined if all elements in the array are 0</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a71b9357c7a722f8208499d9ba573297a">check_all_zeros</a>(a)) {</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">return</span> -1; <span class="comment">// Use std::optional to represent undefined GCD</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> }</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// divisors can be negative, we only want the positive value</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordtype">int</span> result = std::abs(a[0]);</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">for</span> (std::size_t i = 1; i < n; ++i) {</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> result = <a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a509a35e11ed1e17a9e00dd56320a4181">gcd_two</a>(result, std::abs(a[i]));</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">if</span> (result == 1) {</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordflow">break</span>; <span class="comment">// Further computations still result in gcd of 1</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> }</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> }</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">return</span> result;</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span>}</div>
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</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span>} <span class="comment">// namespace gcd_of_n_numbers</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span>} <span class="comment">// namespace math</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span></div>
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<div class="foldopen" id="foldopen00087" data-start="{" data-end="}">
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"><a class="line" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 87</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> std::array<int, 1> array_1 = {0};</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> std::array<int, 1> array_2 = {1};</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> std::array<int, 2> array_3 = {0, 2};</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> std::array<int, 3> array_4 = {-60, 24, 18};</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> std::array<int, 4> array_5 = {100, -100, -100, 200};</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> std::array<int, 5> array_6 = {0, 0, 0, 0, 0};</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> std::array<int, 7> array_7 = {10350, -24150, 0, 17250, 37950, -127650, 51750};</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> std::array<int, 7> array_8 = {9500000, -12121200, 0, 4444, 0, 0, 123456789};</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> </div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> assert(<a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a1161713c662a14c2d5e33504f4324532">math::gcd_of_n_numbers::gcd</a>(array_1) == -1);</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> assert(<a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a1161713c662a14c2d5e33504f4324532">math::gcd_of_n_numbers::gcd</a>(array_2) == 1);</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> assert(<a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a1161713c662a14c2d5e33504f4324532">math::gcd_of_n_numbers::gcd</a>(array_3) == 2);</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> assert(<a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a1161713c662a14c2d5e33504f4324532">math::gcd_of_n_numbers::gcd</a>(array_4) == 6);</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> assert(<a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a1161713c662a14c2d5e33504f4324532">math::gcd_of_n_numbers::gcd</a>(array_5) == 100);</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> assert(<a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a1161713c662a14c2d5e33504f4324532">math::gcd_of_n_numbers::gcd</a>(array_6) == -1);</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> assert(<a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a1161713c662a14c2d5e33504f4324532">math::gcd_of_n_numbers::gcd</a>(array_7) == 3450);</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> assert(<a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a1161713c662a14c2d5e33504f4324532">math::gcd_of_n_numbers::gcd</a>(array_8) == 1);</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span>}</div>
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</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span></div>
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<div class="foldopen" id="foldopen00111" data-start="{" data-end="}">
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"><a class="line" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 111</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <a class="code hl_function" href="../../d1/d11/gcd__of__n__numbers_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementation</span></div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span>}</div>
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</div>
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<div class="ttc" id="agcd__of__n__numbers_8cpp_html_a1161713c662a14c2d5e33504f4324532"><div class="ttname"><a href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a1161713c662a14c2d5e33504f4324532">math::gcd_of_n_numbers::gcd</a></div><div class="ttdeci">int gcd(const std::array< int, n > &a)</div><div class="ttdoc">Main program to compute GCD using the Euclidean algorithm.</div><div class="ttdef"><b>Definition</b> <a href="#l00064">gcd_of_n_numbers.cpp:64</a></div></div>
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<div class="ttc" id="agcd__of__n__numbers_8cpp_html_a509a35e11ed1e17a9e00dd56320a4181"><div class="ttname"><a href="../../d1/d11/gcd__of__n__numbers_8cpp.html#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="#l00035">gcd_of_n_numbers.cpp:35</a></div></div>
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<div class="ttc" id="agcd__of__n__numbers_8cpp_html_a71b9357c7a722f8208499d9ba573297a"><div class="ttname"><a href="../../d1/d11/gcd__of__n__numbers_8cpp.html#a71b9357c7a722f8208499d9ba573297a">math::gcd_of_n_numbers::check_all_zeros</a></div><div class="ttdeci">bool check_all_zeros(const std::array< int, n > &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="#l00053">gcd_of_n_numbers.cpp:53</a></div></div>
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<div class="ttc" id="agcd__of__n__numbers_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d1/d11/gcd__of__n__numbers_8cpp.html#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="#l00087">gcd_of_n_numbers.cpp:87</a></div></div>
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<div class="ttc" id="agcd__of__n__numbers_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d1/d11/gcd__of__n__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00111">gcd_of_n_numbers.cpp:111</a></div></div>
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<div class="ttc" id="anamespacegcd__of__n__numbers_html"><div class="ttname"><a href="../../d2/ddb/namespacegcd__of__n__numbers.html">gcd_of_n_numbers</a></div><div class="ttdoc">Compute GCD of numbers in an array.</div></div>
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<div class="ttc" id="anamespacemath_html"><div class="ttname"><a href="../../dd/d47/namespacemath.html">math</a></div><div class="ttdoc">for assert</div></div>
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