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