53 lines
1.3 KiB
Python
53 lines
1.3 KiB
Python
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import re, sys
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def gcd(a, b):
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while b != 0:
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b, a = a % b, b
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return a
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def get_q_list(m, a):
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l = []
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while a:
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r, q = m % a, m // a
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m, a = a, r
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l.append(q)
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return l
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def get_p_n(n, q_list):
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if n == 0:
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return q_list[0]
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if n == 1:
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return q_list[0] * q_list[1] + 1
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return q_list[n] * get_p_n(n - 1, q_list) + get_p_n(n - 2, q_list)
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def get_x0(a, b, m):
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q_list = get_q_list(m, a)
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n = len(q_list) - 1
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p = get_p_n(n-1, q_list)
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x = ((-1)**n*p*b)%m
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return x, f'x={x}mod{m}'
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def solve(task):
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f = re.fullmatch(r'(\d+)x=(\d+)mod(\d+)', task)
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if f == None:
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return "Usage Example: py chain_fraction.py '7x=8mod13'"
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a, b, m = int(f.groups()[0]), int(f.groups()[1]), int(f.groups()[2])
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d = gcd(a, m) # Находим НОД
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if d == 1: # нод = 1 => 1 решение
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return get_x0(a, b, m)[1]
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if d > 1 and b % d != 0:
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return 'No solutions'
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else:
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d = gcd(gcd(a, b), m)
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a1, b1, m1 = a // d, b // d, m // d
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x0 = get_x0(a1, b1, m1)[0]
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s = ""
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for k in range(d):
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s += f'x={(x0+m1*k)%m}mod{m}\n'
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return s[:-1]
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if __name__ == "__main__":
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if len(sys.argv) != 2:
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print("Usage Example: py chain_fraction.py '7x=8mod13'")
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sys.exit(1)
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print(solve(sys.argv[1]))
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