From a3e9ee2ece3e4471b6a613ae975e8dfcbb959793 Mon Sep 17 00:00:00 2001
From: Abhinav Anand <manasgmishra@gmail.com>
Date: Fri, 22 Jan 2021 13:38:45 +0530
Subject: [PATCH] extended_euclidean_algorithm.rb

---
 .../exteded_euclidean_algorithm.rb            | 31 +++++++++++++++++++
 1 file changed, 31 insertions(+)
 create mode 100644 discrete_mathematics/exteded_euclidean_algorithm.rb

diff --git a/discrete_mathematics/exteded_euclidean_algorithm.rb b/discrete_mathematics/exteded_euclidean_algorithm.rb
new file mode 100644
index 0000000..8b7c17d
--- /dev/null
+++ b/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, 6) = 3
+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