extended euclidean python

def extended_euclidean(a, b):
    if b == 0:
        return a, 1, 0
    else:
        d, x, y = extended_euclidean(b, a % b)
        return d, y, x - (a // b) * y

This Python code defines a function extended_euclidean that calculates the greatest common divisor (gcd) of two numbers a and b using the extended Euclidean algorithm. The algorithm computes the gcd along with the coefficients x and y such that ax + by = gcd(a, b).

• Parameters: a and b are integers for which the gcd is to be calculated.
• Base Case: If b is zero, the function returns a as the gcd along with coefficients x = 1 and y = 0.
• Recursive Case: Otherwise, it calls itself recursively with arguments (b, a % b) to compute the gcd d, along with coefficients x and y. The updated x is y, and the updated y is (x - (a // b) * y). The algorithm continues until b becomes zero.

This function returns the gcd of a and b, along with coefficients x and y such that ax + by = gcd(a, b).