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<title>Algorithms_in_C++: math/extended_euclid_algorithm.cpp File Reference</title>
<title>TheAlgorithms/C++: math/extended_euclid_algorithm.cpp File Reference</title>
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<div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
<div id="projectname">TheAlgorithms/C++<span id="projectnumber">&#160;1.0.0</span>
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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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@@ -120,7 +137,9 @@ Include dependency graph for extended_euclid_algorithm.cpp:</div>
<div class="dyncontent">
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<p><a href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:abe92d63a0ff9bda7e304df510d5dd217" id="r_abe92d63a0ff9bda7e304df510d5dd217"><td class="memTemplParams" colspan="2">template&lt;typename T , typename T2 &gt; </td></tr>
@@ -142,6 +161,8 @@ Functions</h2></td></tr>
\[\text{gcd}(a, b) = a \times x + b \times y \]
</p>
<p> This is also used in finding Modular multiplicative inverse of a number. (A * B)M == 1 Here B is the MMI of A for given M, so extendedEuclid (A, M) gives B. </p>
<p class="definition">Definition in file <a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html">extended_euclid_algorithm.cpp</a>.</p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="acba15ca55b3e7dcb91f3c65d72ba052d" name="acba15ca55b3e7dcb91f3c65d72ba052d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#acba15ca55b3e7dcb91f3c65d72ba052d">&#9670;&#160;</a></span>extendedEuclid()</h2>
@@ -189,9 +210,11 @@ template&lt;typename T , typename T2 &gt; </div>
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<p class="definition">Definition at line <a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html#l00071">71</a> of file <a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html">extended_euclid_algorithm.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 71</span> {</div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordflow">if</span> (B &gt; A)</div>
<div class="line"><span class="lineno"> 73</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 &gt;= B</span></div>
<div class="line"><span class="lineno"> 73</span> std::swap(A, B); <span class="comment">// Ensure that A &gt;= B</span></div>
<div class="line"><span class="lineno"> 74</span> </div>
<div class="line"><span class="lineno"> 75</span> <span class="keywordflow">if</span> (B == 0) {</div>
<div class="line"><span class="lineno"> 76</span> *GCD = A;</div>
@@ -204,14 +227,8 @@ template&lt;typename T , typename T2 &gt; </div>
<div class="line"><span class="lineno"> 83</span> *y = temp - (A / B) * (*y);</div>
<div class="line"><span class="lineno"> 84</span> }</div>
<div class="line"><span class="lineno"> 85</span>}</div>
<div class="ttc" id="aextended__euclid__algorithm_8cpp_html_acba15ca55b3e7dcb91f3c65d72ba052d"><div class="ttname"><a href="#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:71</div></div>
<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 class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d5d/extended__euclid__algorithm_8cpp_acba15ca55b3e7dcb91f3c65d72ba052d_cgraph.svg" width="248" height="60"><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="aextended__euclid__algorithm_8cpp_html_acba15ca55b3e7dcb91f3c65d72ba052d"><div class="ttname"><a href="#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> <a href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html#l00071">extended_euclid_algorithm.cpp:71</a></div></div>
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@@ -260,9 +277,11 @@ template&lt;typename T1 , typename T2 &gt; </div>
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<p class="definition">Definition at line <a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html#l00042">42</a> of file <a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html">extended_euclid_algorithm.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 42</span> {</div>
<div class="line"><span class="lineno"> 43</span> <span class="keywordflow">if</span> (B &gt; A)</div>
<div class="line"><span class="lineno"> 44</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 &gt;= B</span></div>
<div class="line"><span class="lineno"> 44</span> std::swap(A, B); <span class="comment">// Ensure that A &gt;= B</span></div>
<div class="line"><span class="lineno"> 45</span> </div>
<div class="line"><span class="lineno"> 46</span> T2 s = 0, s0 = 1;</div>
<div class="line"><span class="lineno"> 47</span> T2 t = 1, t0 = 0;</div>
@@ -278,13 +297,8 @@ template&lt;typename T1 , typename T2 &gt; </div>
<div class="line"><span class="lineno"> 57</span> *x = s0;</div>
<div class="line"><span class="lineno"> 58</span> *y = t0;</div>
<div class="line"><span class="lineno"> 59</span>}</div>
<div class="ttc" id="aextended__euclid__algorithm_8cpp_html_abe92d63a0ff9bda7e304df510d5dd217"><div class="ttname"><a href="#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:25</div></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d5d/extended__euclid__algorithm_8cpp_a1792ac7c33aaf26b860ab55f5652ab25_cgraph.svg" width="276" height="86"><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="aextended__euclid__algorithm_8cpp_html_abe92d63a0ff9bda7e304df510d5dd217"><div class="ttname"><a href="#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> <a href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html#l00025">extended_euclid_algorithm.cpp:25</a></div></div>
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<p>Main function. </p>
<p class="definition">Definition at line <a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html#l00088">88</a> of file <a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html">extended_euclid_algorithm.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 88</span> {</div>
<div class="line"><span class="lineno"> 89</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"> 90</span> int32_t x, y;</div>
<div class="line"><span class="lineno"> 91</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; a &gt;&gt; b;</div>
<div class="line"><span class="lineno"> 91</span> std::cin &gt;&gt; a &gt;&gt; b;</div>
<div class="line"><span class="lineno"> 92</span> <a class="code hl_function" href="#acba15ca55b3e7dcb91f3c65d72ba052d">extendedEuclid</a>(a, b, &amp;<a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>, &amp;x, &amp;y);</div>
<div class="line"><span class="lineno"> 93</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; y &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 93</span> std::cout &lt;&lt; <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; y &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 94</span> <a class="code hl_function" href="#a1792ac7c33aaf26b860ab55f5652ab25">extendedEuclid_1</a>(a, b, &amp;<a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>, &amp;x, &amp;y);</div>
<div class="line"><span class="lineno"> 95</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; y &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 95</span> std::cout &lt;&lt; <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; y &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 96</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 97</span>}</div>
<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>
<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>
<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>
<div class="ttc" id="aextended__euclid__algorithm_8cpp_html_a1792ac7c33aaf26b860ab55f5652ab25"><div class="ttname"><a href="#a1792ac7c33aaf26b860ab55f5652ab25">extendedEuclid_1</a></div><div class="ttdeci">void extendedEuclid_1(T1 A, T1 B, T1 *GCD, T2 *x, T2 *y)</div><div class="ttdef"><b>Definition</b> extended_euclid_algorithm.cpp:42</div></div>
<div class="ttc" id="agcd__iterative__euclidean_8cpp_html_ae48807fa2b7000afae599e67f327545e"><div class="ttname"><a href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a></div><div class="ttdeci">int gcd(int num1, int num2)</div><div class="ttdef"><b>Definition</b> gcd_iterative_euclidean.cpp:15</div></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d5d/extended__euclid__algorithm_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="374" height="208"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
</div>
<div class="ttc" id="aextended__euclid__algorithm_8cpp_html_a1792ac7c33aaf26b860ab55f5652ab25"><div class="ttname"><a href="#a1792ac7c33aaf26b860ab55f5652ab25">extendedEuclid_1</a></div><div class="ttdeci">void extendedEuclid_1(T1 A, T1 B, T1 *GCD, T2 *x, T2 *y)</div><div class="ttdef"><b>Definition</b> <a href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html#l00042">extended_euclid_algorithm.cpp:42</a></div></div>
<div class="ttc" id="agcd__iterative__euclidean_8cpp_html_ae48807fa2b7000afae599e67f327545e"><div class="ttname"><a href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a></div><div class="ttdeci">int gcd(int num1, int num2)</div><div class="ttdef"><b>Definition</b> <a href="../../d4/da0/gcd__iterative__euclidean_8cpp_source.html#l00015">gcd_iterative_euclidean.cpp:15</a></div></div>
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<p class="definition">Definition at line <a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html#l00025">25</a> of file <a class="el" href="../../d9/d5d/extended__euclid__algorithm_8cpp_source.html">extended_euclid_algorithm.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 25</span> {</div>
<div class="line"><span class="lineno"> 26</span> T temp = *r;</div>
<div class="line"><span class="lineno"> 27</span> *r = *r0 - (quotient * temp);</div>