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63 lines
1.6 KiB
Python
63 lines
1.6 KiB
Python
"""
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Project Euler 62
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https://projecteuler.net/problem=62
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The cube, 41063625 (345^3), can be permuted to produce two other cubes:
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56623104 (384^3) and 66430125 (405^3). In fact, 41063625 is the smallest cube
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which has exactly three permutations of its digits which are also cube.
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Find the smallest cube for which exactly five permutations of its digits are
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cube.
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"""
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from collections import defaultdict
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def solution(max_base: int = 5) -> int:
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"""
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Iterate through every possible cube and sort the cube's digits in
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ascending order. Sorting maintains an ordering of the digits that allows
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you to compare permutations. Store each sorted sequence of digits in a
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dictionary, whose key is the sequence of digits and value is a list of
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numbers that are the base of the cube.
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Once you find 5 numbers that produce the same sequence of digits, return
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the smallest one, which is at index 0 since we insert each base number in
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ascending order.
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>>> solution(2)
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125
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>>> solution(3)
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41063625
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"""
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freqs = defaultdict(list)
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num = 0
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while True:
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digits = get_digits(num)
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freqs[digits].append(num)
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if len(freqs[digits]) == max_base:
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base = freqs[digits][0] ** 3
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return base
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num += 1
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def get_digits(num: int) -> str:
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"""
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Computes the sorted sequence of digits of the cube of num.
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>>> get_digits(3)
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'27'
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>>> get_digits(99)
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'027999'
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>>> get_digits(123)
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'0166788'
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"""
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return "".join(sorted(list(str(num**3))))
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if __name__ == "__main__":
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print(f"{solution() = }")
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