add extended euclidean algorithm

aniakubik · abranhe · commit 493ffc8e9d1b · 2020-10-03T02:06:08.000-04:00
diff --git a/math/extendedEuclidean.py b/math/extendedEuclidean.py
@@ -0,0 +1,20 @@
+"""
+    for numbers a, b returns x, y such as x * a + y * b = gcd(a,b)
+"""
+
+def extendedEuclidean(a,b):
+    a_old, b_old = a,b
+    a, b = max(a, b), min(a, b)
+    x, y, old_x, old_y = 0, 1, 1, 0
+    while b != 0:
+        quotient = a // b
+        residue = a % b
+        a, b = b, residue
+        x, old_x = old_x, (old_x - quotient * x)
+        y, old_y = old_y, (old_y - quotient * y)
+    if a_old > b_old:
+        return x, y
+    return y, x
+
+
+ 	
