Create Extended_Euclidean_Algorithm.rb (#2949)

Extended_Euclidean_Algorithm/Extended_Euclidean_Algorithm.rb

@@ -0,0 +1,36 @@
+=begin
+Extended Euclidean Algorithm 
+==============================
+GCD of two numbers is the largest number that divides both of them.
+A simple way to find GCD is to factorize both numbers and multiply common factors.
+  
+GCD(a,b) = ax + by
+If we can find the value of  x and y then we can easily find the 
+value of GCD(a,b) by replacing (x,y) with their respective values.
+=end
+
+def extended_gcd(a, b, x, y) #Function for extended Euclidean Algorithm  
+
+  #Base Case 
+  return b if a == 0
+
+  x1, y1 = 1, 1 #To store results of recursive call 
+  gcd = extended_gcd(b % a, a, x1, y1)
+  #Update x and y using results of recursive call  
+  x = y1 - (b / a) * x1
+  y = x1
+  return gcd
+end
+
+x , y = 1, 1
+a = gets.to_i
+b = gets.to_i
+puts "GCD of numbers #{a} and #{b} is #{extended_gcd(a, b, x, y)}"
+
+=begin
+INPUT:
+27
+81
+OUTPUT:
+GCD of numbers 27 and 81 is 27
+=end