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39 lines
999 B
Python
39 lines
999 B
Python
"""
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Problem 34: https://projecteuler.net/problem=34
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145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.
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Find the sum of all numbers which are equal to the sum of the factorial of their digits.
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Note: As 1! = 1 and 2! = 2 are not sums they are not included.
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"""
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from math import factorial
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DIGIT_FACTORIAL = {str(d): factorial(d) for d in range(10)}
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def sum_of_digit_factorial(n: int) -> int:
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"""
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Returns the sum of the factorial of digits in n
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>>> sum_of_digit_factorial(15)
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121
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>>> sum_of_digit_factorial(0)
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1
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"""
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return sum(DIGIT_FACTORIAL[d] for d in str(n))
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def solution() -> int:
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"""
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Returns the sum of all numbers whose
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sum of the factorials of all digits
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add up to the number itself.
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>>> solution()
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40730
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"""
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limit = 7 * factorial(9) + 1
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return sum(i for i in range(3, limit) if sum_of_digit_factorial(i) == i)
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if __name__ == "__main__":
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print(f"{solution() = }")
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