59 lines
1.1 KiB
Python
59 lines
1.1 KiB
Python
from math import gcd
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from functools import lru_cache
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@lru_cache
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def r(n):
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assert n > 0
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if n == 1:
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return 1
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else:
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return 10**(n - 1) + r(n - 1)
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def r_closed_form(n):
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assert n > 0
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return (10**n - 1) // 9
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def r_modulo_closed_form(n, m):
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assert n > 0 and m > 0
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return ((pow(10, n, 9 * m) - 1) // 9) % m
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def a(n):
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assert gcd(n, 10) == 1
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k = 1
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while True:
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if r_modulo_closed_form(k, n) == 0:
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return k
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k += 1
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def euler_129():
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# Comparing naiv to efficient implementations to find potential bugs.
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for n in range(5, 1000):
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assert r(n) == r_closed_form(n)
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for m in range(2, 20):
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assert (r_closed_form(n) % m) == r_modulo_closed_form(n, m)
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assert a(7) == 6
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assert a(41) == 5
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assert a(17) == 16
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target = 10**6
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delta = 200
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for n in range(target, target + delta):
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if gcd(n, 10) == 1:
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if (av := a(n)):
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if av > target:
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return n
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return None
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if __name__ == "__main__":
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solution = euler_129()
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print("e129.py: " + str(solution))
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assert(solution == 1000023)
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