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<title>Algorithms_in_C++: math/extended_euclid_algorithm.cpp File Reference</title>
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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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@@ -96,7 +96,7 @@ $(document).ready(function(){initNavTree('d9/d5d/extended__euclid__algorithm_8cp
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</div><!--header-->
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<div class="contents">
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<p>GCD using <a href="https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm" target="_blank">extended Euclid's algorithm</a>
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<p>GCD using [extended Euclid's algorithm] (<a href="https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm">https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm</a>)
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <algorithm></code><br />
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<code>#include <iostream></code><br />
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@@ -123,7 +123,7 @@ Functions</h2></td></tr>
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<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><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 >GCD using <a href="https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm" target="_blank">extended Euclid's algorithm</a> </p>
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<div class="textblock"><p >GCD using [extended Euclid's algorithm] (<a href="https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm">https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm</a>) </p>
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<p >Finding coefficients of a and b ie x and y in Bézout's identity </p><p class="formulaDsp">
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\[\text{gcd}(a, b) = a \times x + b \times y \]
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</p>
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@@ -185,21 +185,21 @@ template<typename T , typename T2 > </div>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> {</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">if</span> (B > A)</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(A, B); <span class="comment">// Ensure that A >= B</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">if</span> (B == 0) {</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> *GCD = A;</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> *x = 1;</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> *y = 0;</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d">extendedEuclid</a>(B, A % B, GCD, x, y);</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> T2 temp = *x;</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> *x = *y;</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> *y = temp - (A / B) * (*y);</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> }</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 70</span> {</div>
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<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">if</span> (B > A)</div>
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<div class="line"><span class="lineno"> 72</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(A, B); <span class="comment">// Ensure that A >= B</span></div>
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<div class="line"><span class="lineno"> 73</span> </div>
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<div class="line"><span class="lineno"> 74</span> <span class="keywordflow">if</span> (B == 0) {</div>
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<div class="line"><span class="lineno"> 75</span> *GCD = A;</div>
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<div class="line"><span class="lineno"> 76</span> *x = 1;</div>
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<div class="line"><span class="lineno"> 77</span> *y = 0;</div>
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<div class="line"><span class="lineno"> 78</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><span class="lineno"> 79</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d">extendedEuclid</a>(B, A % B, GCD, x, y);</div>
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<div class="line"><span class="lineno"> 80</span> T2 temp = *x;</div>
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<div class="line"><span class="lineno"> 81</span> *x = *y;</div>
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<div class="line"><span class="lineno"> 82</span> *y = temp - (A / B) * (*y);</div>
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<div class="line"><span class="lineno"> 83</span> }</div>
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<div class="line"><span class="lineno"> 84</span>}</div>
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<div class="ttc" id="aextended__euclid__algorithm_8cpp_html_acba15ca55b3e7dcb91f3c65d72ba052d"><div class="ttname"><a href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d">extendedEuclid</a></div><div class="ttdeci">void extendedEuclid(T A, T B, T *GCD, T2 *x, T2 *y)</div><div class="ttdef"><b>Definition:</b> extended_euclid_algorithm.cpp:70</div></div>
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<div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
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</div><!-- fragment --><div class="dynheader">
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@@ -267,24 +267,24 @@ template<typename T1 , typename T2 > </div>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> {</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">if</span> (B > A)</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(A, B); <span class="comment">// Ensure that A >= B</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 class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> T2 s = 0, s0 = 1;</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> T2 t = 1, t0 = 0;</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> T1 r = B, r0 = A;</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">while</span> (r != 0) {</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> T1 quotient = r0 / r;</div>
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||||
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a>(&r, &r0, quotient);</div>
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||||
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a>(&s, &s0, quotient);</div>
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||||
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a>(&t, &t0, quotient);</div>
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||||
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> }</div>
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||||
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> *GCD = r0;</div>
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||||
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> *x = s0;</div>
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||||
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> *y = t0;</div>
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||||
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 41</span> {</div>
|
||||
<div class="line"><span class="lineno"> 42</span> <span class="keywordflow">if</span> (B > A)</div>
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||||
<div class="line"><span class="lineno"> 43</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(A, B); <span class="comment">// Ensure that A >= B</span></div>
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||||
<div class="line"><span class="lineno"> 44</span> </div>
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||||
<div class="line"><span class="lineno"> 45</span> T2 s = 0, s0 = 1;</div>
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||||
<div class="line"><span class="lineno"> 46</span> T2 t = 1, t0 = 0;</div>
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||||
<div class="line"><span class="lineno"> 47</span> T1 r = B, r0 = A;</div>
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||||
<div class="line"><span class="lineno"> 48</span> </div>
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||||
<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">while</span> (r != 0) {</div>
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||||
<div class="line"><span class="lineno"> 50</span> T1 quotient = r0 / r;</div>
|
||||
<div class="line"><span class="lineno"> 51</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a>(&r, &r0, quotient);</div>
|
||||
<div class="line"><span class="lineno"> 52</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a>(&s, &s0, quotient);</div>
|
||||
<div class="line"><span class="lineno"> 53</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a>(&t, &t0, quotient);</div>
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||||
<div class="line"><span class="lineno"> 54</span> }</div>
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||||
<div class="line"><span class="lineno"> 55</span> *GCD = r0;</div>
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||||
<div class="line"><span class="lineno"> 56</span> *x = s0;</div>
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||||
<div class="line"><span class="lineno"> 57</span> *y = t0;</div>
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<div class="line"><span class="lineno"> 58</span>}</div>
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<div class="ttc" id="aextended__euclid__algorithm_8cpp_html_abe92d63a0ff9bda7e304df510d5dd217"><div class="ttname"><a href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a></div><div class="ttdeci">void update_step(T *r, T *r0, const T2 quotient)</div><div class="ttdef"><b>Definition:</b> extended_euclid_algorithm.cpp:24</div></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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@@ -312,16 +312,16 @@ Here is the call graph for this function:</div>
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||||
</div><div class="memdoc">
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||||
<p>Main function. </p>
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||||
<div class="fragment"><div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> {</div>
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||||
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> uint32_t a, b, <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>;</div>
|
||||
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> int32_t x, y;</div>
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||||
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> a >> b;</div>
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||||
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d">extendedEuclid</a>(a, b, &<a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>, &x, &y);</div>
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||||
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> << <span class="stringliteral">" "</span> << x << <span class="stringliteral">" "</span> << y << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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||||
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#a1792ac7c33aaf26b860ab55f5652ab25">extendedEuclid_1</a>(a, b, &<a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>, &x, &y);</div>
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||||
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> << <span class="stringliteral">" "</span> << x << <span class="stringliteral">" "</span> << y << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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||||
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">return</span> 0;</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="fragment"><div class="line"><span class="lineno"> 87</span> {</div>
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||||
<div class="line"><span class="lineno"> 88</span> uint32_t a, b, <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>;</div>
|
||||
<div class="line"><span class="lineno"> 89</span> int32_t x, y;</div>
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<div class="line"><span class="lineno"> 90</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> a >> b;</div>
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||||
<div class="line"><span class="lineno"> 91</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d">extendedEuclid</a>(a, b, &<a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>, &x, &y);</div>
|
||||
<div class="line"><span class="lineno"> 92</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> << <span class="stringliteral">" "</span> << x << <span class="stringliteral">" "</span> << y << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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||||
<div class="line"><span class="lineno"> 93</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#a1792ac7c33aaf26b860ab55f5652ab25">extendedEuclid_1</a>(a, b, &<a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>, &x, &y);</div>
|
||||
<div class="line"><span class="lineno"> 94</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> << <span class="stringliteral">" "</span> << x << <span class="stringliteral">" "</span> << y << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 95</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 96</span>}</div>
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<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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||||
<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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||||
<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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@@ -388,11 +388,11 @@ template<typename T , typename T2 > </div>
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</table>
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</dd>
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</dl>
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||||
<div class="fragment"><div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> {</div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> T temp = *r;</div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> *r = *r0 - (quotient * temp);</div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> *r0 = temp;</div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span>}</div>
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||||
<div class="fragment"><div class="line"><span class="lineno"> 24</span> {</div>
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||||
<div class="line"><span class="lineno"> 25</span> T temp = *r;</div>
|
||||
<div class="line"><span class="lineno"> 26</span> *r = *r0 - (quotient * temp);</div>
|
||||
<div class="line"><span class="lineno"> 27</span> *r0 = temp;</div>
|
||||
<div class="line"><span class="lineno"> 28</span>}</div>
|
||||
</div><!-- fragment -->
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||||
</div>
|
||||
</div>
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||||
@@ -402,7 +402,7 @@ template<typename T , typename T2 > </div>
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