Python Program for Extended Euclidean algorithms

Python Program for Extended Euclidean algorithms

Last Updated : 21 Jun, 2022

Python3

# Python program to demonstrate working of extended 
# Euclidean Algorithm 
    
# function for extended Euclidean Algorithm 
def gcdExtended(a, b): 
    # Base Case 
    if a == 0 : 
        return b,0,1
            
    gcd,x1,y1 = gcdExtended(b%a, a) 
    
    # Update x and y using results of recursive 
    # call 
    x = y1 - (b//a) * x1 
    y = x1 
    
    return gcd,x,y 
    

# Driver code 
a, b = 35,15
g, x, y = gcdExtended(a, b) 
print("gcd(", a , "," , b, ") = ", g)

Output:

gcd(35, 15) = 5

Time Complexity: O(log(max(A, B)))

Auxiliary Space: O(log(max(A, B))), keeping recursion stack in mind.

Please refer complete article on Basic and Extended Euclidean algorithms for more details!

Python Program for Extended Euclidean algorithms

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