53 lines
1.4 KiB
Python
53 lines
1.4 KiB
Python
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def is_non_bouncy(n: int):
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digits = list(map(int, list(str(n))))
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decreasing = True
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increasing = True
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for i in range(len(digits) - 1):
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increasing = increasing and digits[i] <= digits[i + 1]
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decreasing = decreasing and digits[i] >= digits[i + 1]
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return increasing or decreasing
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def non_bouncy_below_naiv(digits: int):
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threshold = 10 ** digits
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non_bouncy = sum([1 for i in range(1, threshold) if is_non_bouncy(i)])
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return non_bouncy
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def non_bouncy_below(digits: int):
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# increasing
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s = [1 for _ in range(1, 10)]
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result = sum(s)
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for _ in range(digits - 1):
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s = [sum(s[i:]) for i in range(9)]
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result += sum(s) - 9
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# The -9 is to avoid double counting 11, 22, 33 for increasing and
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# decreasing.
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# decreasing
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decreasing_count = 0
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s = [i + 1 for i in range(1, 10)]
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for _ in range(digits - 1):
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# print(s)
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decreasing_count += sum(s)
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s = [sum(s[:i]) + 1 for i in range(1, 10)]
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result += decreasing_count
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return result
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def euler_113():
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assert non_bouncy_below_naiv(6) == 12951
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assert non_bouncy_below(6) == 12951
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assert non_bouncy_below(10) == 277032
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assert is_non_bouncy(134468)
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assert is_non_bouncy(66420)
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assert (not is_non_bouncy(155349))
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return non_bouncy_below(100)
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if __name__ == "__main__":
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solution = euler_113()
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print("e113.py: " + str(solution))
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assert(solution == 51161058134250)
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