Add extended euclidean algorithm

Author: Snaffys

HW1-EuclideanAlgorithm/src/euclid.py

@@ -0,0 +1,37 @@
+# a = b * q + r 
+def gcd(a, b):
+    if b == 0:
+        return (a, 1, 0)
+
+    a = abs(a)
+    b = abs(b)
+    if(b > a):
+        a, b = b, a   
+
+    old_a_coef = 1
+    old_b_coef = 0
+    current_a_coef = 0
+    current_b_coef =1
+    
+    while (a % b) > 0:
+        q = a // b
+        new_a_coef = old_a_coef - current_a_coef * q
+        new_b_coef = old_b_coef - current_b_coef * q
+        old_a_coef = current_a_coef
+        old_b_coef = current_b_coef
+        current_a_coef = new_a_coef
+        current_b_coef = new_b_coef
+
+        r = a % b
+        a = b
+        b = r
+    return (b, current_a_coef, current_b_coef)
+
+def main():
+    a = int(input("Enter first number: "))
+    b = int(input("Enter second number: "))
+    result, a_mult, b_mult = (gcd(a, b))
+    print("GCD is:", result, "\nlinear combination:", result, "=", a, "*", a_mult,"+", b, "*", b_mult)
+
+if __name__ == "__main__":
+    main()