Merge pull request #80 from atarax665/extended_euclidean_algorithm

[Discrete Mathematics] Extended Euclidean Algorithm

discrete_mathematics/exteded_euclidean_algorithm.rb

@@ -0,0 +1,31 @@
+# https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
+
+def extended_euclidean_gcd(a, b)
+
+  x0, x1 = a, b
+  s, t = 1, 0
+  until x1.zero?
+    q, x2 = x0.divmod(x1)
+    x0, x1 = x1, x2
+    s, t = t, s - q * t
+  end
+  gcd = x0
+  return gcd
+end
+
+puts "GCD(3, 5) = " + extended_euclidean_gcd(3, 5).to_s
+# GCD(3, 5) = 1
+puts "GCD(3, 6) = " + extended_euclidean_gcd(3, 6).to_s
+# GCD(3, 6) = 3
+puts "GCD(6, 3) = " + extended_euclidean_gcd(6, 3).to_s
+# GCD(6, 3) = 3
+
+=begin
+
+Dynamic driver code:
+
+a = gets.to_i
+b = gets.to_i
+puts "GCD (#{a}, #{b} ) = #{extended_euclidean_gcd(a, b)}"
+
+=end