2022-01-17 11:25:27 +01:00
|
|
|
#!/usr/bin/env python3
|
|
|
|
|
|
|
|
|
|
"""Algorithme d'Euclide étendu
|
|
|
|
|
|
|
|
|
|
Calcule le PGCD de deux nombres et trouve les coefficients de Bezout.
|
|
|
|
|
"""
|
|
|
|
|
|
|
|
|
|
import sys
|
|
|
|
|
|
2022-01-17 12:45:09 +01:00
|
|
|
def main():
|
|
|
|
|
assert len(sys.argv) == 3
|
|
|
|
|
a = int(sys.argv[1])
|
|
|
|
|
b = int(sys.argv[2])
|
2022-01-17 11:25:27 +01:00
|
|
|
|
|
|
|
|
# Initialisation
|
2022-01-17 12:45:09 +01:00
|
|
|
r = ["r", a, b]
|
|
|
|
|
u = ["u", 1, 0]
|
|
|
|
|
v = ["v", 0, 1]
|
|
|
|
|
q = ["q", "", a // b]
|
2022-01-17 11:25:27 +01:00
|
|
|
|
|
|
|
|
# Séquence
|
2022-01-17 12:45:09 +01:00
|
|
|
while True:
|
|
|
|
|
r.append(r[-2] % r[-1])
|
|
|
|
|
u.append(u[-2] - (q[-1] * u[-1]))
|
|
|
|
|
v.append(v[-2] - (q[-1] * v[-1]))
|
|
|
|
|
if r[-1] == 0:
|
|
|
|
|
q.append("")
|
|
|
|
|
break
|
|
|
|
|
q.append(r[-2] // r[-1])
|
|
|
|
|
|
|
|
|
|
print_table(r, u, v, q)
|
|
|
|
|
|
|
|
|
|
def print_table(r, u, v, q):
|
|
|
|
|
"""Représentation de l'algorithme"""
|
|
|
|
|
for i in range(len(r)):
|
|
|
|
|
print(f"{r[i]:^5} {u[i]:^5} {v[i]:^5} {q[i]:^5}")
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
if __name__ == "__main__":
|
|
|
|
|
main()
|
