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Fixes: #2630 Add doctests and support for negative numbers (#2626)

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* add type hints to math/extended euclid

* math/extended euclid - add doctest

* math/extended euclid: remove manual doctest

* change algorithm for negative numbers

* improve naming of variables

* Update extended_euclidean_algorithm.py

Co-authored-by: Dhruv <dhruvmanila@gmail.com>
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Joyce 2020-10-07 17:53:14 +08:00 committed by GitHub
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1 changed files with 50 additions and 37 deletions
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maths/extended_euclidean_algorithm.py
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@ -3,59 +3,72 @@ Extended Euclidean Algorithm.
Finds 2 numbers a and b such that it satisfies
the equation am + bn = gcd(m, n) (a.k.a Bezout's Identity)
https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
"""
# @Author: S. Sharma <silentcat>
# @Date: 2019-02-25T12:08:53-06:00
# @Email: silentcat@protonmail.com
# @Last modified by: PatOnTheBack
# @Last modified time: 2019-07-05
# @Last modified by: pikulet
# @Last modified time: 2020-10-02
import sys
from typing import Tuple
def extended_euclidean_algorithm(m, n):
def extended_euclidean_algorithm(a: int, b: int) -> Tuple[int, int]:
"""
Extended Euclidean Algorithm.
Finds 2 numbers a and b such that it satisfies
the equation am + bn = gcd(m, n) (a.k.a Bezout's Identity)
>>> extended_euclidean_algorithm(1, 24)
(1, 0)
>>> extended_euclidean_algorithm(8, 14)
(2, -1)
>>> extended_euclidean_algorithm(240, 46)
(-9, 47)
>>> extended_euclidean_algorithm(1, -4)
(1, 0)
>>> extended_euclidean_algorithm(-2, -4)
(-1, 0)
>>> extended_euclidean_algorithm(0, -4)
(0, -1)
>>> extended_euclidean_algorithm(2, 0)
(1, 0)
"""
a = 0
a_prime = 1
b = 1
b_prime = 0
q = 0
r = 0
if m > n:
c = m
d = n
else:
c = n
d = m
# base cases
if abs(a) == 1:
return a, 0
elif abs(b) == 1:
return 0, b
while True:
q = int(c / d)
r = c % d
if r == 0:
break
c = d
d = r
old_remainder, remainder = a, b
old_coeff_a, coeff_a = 1, 0
old_coeff_b, coeff_b = 0, 1
t = a_prime
a_prime = a
a = t - q * a
while remainder != 0:
quotient = old_remainder // remainder
old_remainder, remainder = remainder, old_remainder - quotient * remainder
old_coeff_a, coeff_a = coeff_a, old_coeff_a - quotient * coeff_a
old_coeff_b, coeff_b = coeff_b, old_coeff_b - quotient * coeff_b
t = b_prime
b_prime = b
b = t - q * b
# sign correction for negative numbers
if a < 0:
old_coeff_a = -old_coeff_a
if b < 0:
old_coeff_b = -old_coeff_b
pair = None
if m > n:
pair = (a, b)
else:
pair = (b, a)
return pair
return old_coeff_a, old_coeff_b
def main():
@ -63,9 +76,9 @@ def main():
if len(sys.argv) < 3:
print("2 integer arguments required")
exit(1)
m = int(sys.argv[1])
n = int(sys.argv[2])
print(extended_euclidean_algorithm(m, n))
a = int(sys.argv[1])
b = int(sys.argv[2])
print(extended_euclidean_algorithm(a, b))
if __name__ == "__main__":