70 lines
1.7 KiB
Python
70 lines
1.7 KiB
Python
from typing import List, Optional
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from math import sqrt
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from functools import lru_cache
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def to_int(digits: List[int]) -> int:
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return int("".join(map(str, digits)))
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def int_len(n: int) -> int:
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return len(str(n))
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@lru_cache
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def digits_make_sum(digits, remainder: int) -> Optional[List]:
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if len(digits) == 0:
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if remainder == 0:
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return []
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return None
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remainder_digits_count = int_len(remainder)
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if remainder_digits_count > len(digits):
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return None
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if to_int(digits) < remainder:
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return None
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for group_size in range(1, remainder_digits_count + 1):
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digits_list = list(digits)
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rest_value = remainder - to_int(digits_list[:group_size])
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rest_digits = tuple(digits_list[group_size:])
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r = digits_make_sum(rest_digits, rest_value)
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if type(r) is list:
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return [digits_list[:group_size]] + r
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return None
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def digits_sum_to(digits, number: int):
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r = digits_make_sum(digits, number)
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if type(r) is list:
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# print(digits, r, number)
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return True
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return False
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def t(limit: int) -> int:
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r = 0
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for base in range(4, int(sqrt(limit)) + 1):
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n = base * base
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n_digits = tuple(map(int, list(str(n))))
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if digits_sum_to(n_digits, base):
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r += n
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return r
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def euler_719():
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assert(t(10**4) == 41333)
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assert(digits_sum_to((1, 0, 0), 10) == True)
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assert(digits_sum_to((1, 8), 9) == True)
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assert(digits_sum_to((2, 5), 5) == False)
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assert(digits_sum_to((8, 2, 8, 1), 91) == True)
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assert(t(10**6) == 10804656)
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return t(10**12)
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if __name__ == "__main__":
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solution = euler_719()
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print("e719.py: " + str(solution))
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assert(solution == 128088830547982)
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