21 lines
659 B
Python
21 lines
659 B
Python
def euclidean_algo(a: int, b: int) -> int:
|
|
while b: a, b = b, a % b
|
|
return a
|
|
|
|
'''
|
|
Calculates coefficients x and y of Bezout's identity: ax + by = gcd(a,b)
|
|
NOTE: Based on the Extended Euclidean Algorithm's Wikipedia page
|
|
'''
|
|
def extended_euclid_algo(a: int, b: int) -> tuple[int, int]:
|
|
(old_r, r) = (a, b)
|
|
(old_s, s) = (1, 0)
|
|
(old_t, t) = (0, 1)
|
|
while r != 0:
|
|
q = old_r // r
|
|
(old_r, r) = (r, old_r - q*r)
|
|
(old_s, s) = (s, old_s - q*s)
|
|
(old_t, t) = (t, old_t - q*t)
|
|
# Bezout cofficients: (old_s, old_t)
|
|
# Greatest Common Divisor: old_r
|
|
# Quotients by the gcd: (t, s)
|
|
return (t, s)
|