extended_euclidean_gcd.py: Add Extended Euclidean

This adds Extended Euclidean Algorithm with Python implementation of
the same. This implementation uses the iterative method of the
algorithm, takes two values and gives out the gcd along with the
polynomial equation to get inverse directly if the gcd is 1. The code
uses generic notations and naming standard used in documentation along
with that found in Wikipedia.

Closes #3

Author: thekaleidoscope

euclidean_gcd/Python/extended_euclidean_gcd.py

@@ -0,0 +1,29 @@
+# Element style: gcd(a,b)-> a*x + b*y = r = gcd(a,b)
+
+# Inverse of elements if gcd(a,b)==1:
+# * a^-1 mod (b) = x mod(b)
+# * b^-1 mod (a) = y mod(a)
+
+# Naming is according to Bézout's identity, matching to that on Wikipedia
+
+
+def extended_euclidean_gcd(a, b):
+    x, y, u, v = 0, 1, 1, 0
+    while a != 0:
+        q, r = b//a, b % a
+        m, n = x-u*q, y-v*q
+        b, a, x, y, u, v = a, r, u, v, m, n
+
+    gcd = b
+    return gcd, x, y
+
+
+def main():
+    a, b = 26, 15
+    gcd, x, y = extended_euclidean_gcd(a, b)
+    print("GCD of {} and {} is {}".format(a, b, gcd))
+    print("The Equation : {}*{} + {}*{} = {}".format(a, x, b, y, gcd))
+
+
+if __name__ == '__main__':
+    main()