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113 lines
2.5 KiB
Python
113 lines
2.5 KiB
Python
"""
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Combinatoric selections
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Problem 47
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The first two consecutive numbers to have two distinct prime factors are:
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14 = 2 × 7
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15 = 3 × 5
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The first three consecutive numbers to have three distinct prime factors are:
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644 = 2² × 7 × 23
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645 = 3 × 5 × 43
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646 = 2 × 17 × 19.
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Find the first four consecutive integers to have four distinct prime factors each.
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What is the first of these numbers?
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"""
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from functools import lru_cache
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def unique_prime_factors(n: int) -> set:
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"""
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Find unique prime factors of an integer.
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Tests include sorting because only the set really matters,
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not the order in which it is produced.
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>>> sorted(set(unique_prime_factors(14)))
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[2, 7]
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>>> sorted(set(unique_prime_factors(644)))
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[2, 7, 23]
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>>> sorted(set(unique_prime_factors(646)))
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[2, 17, 19]
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"""
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i = 2
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factors = set()
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while i * i <= n:
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if n % i:
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i += 1
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else:
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n //= i
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factors.add(i)
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if n > 1:
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factors.add(n)
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return factors
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@lru_cache
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def upf_len(num: int) -> int:
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"""
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Memoize upf() length results for a given value.
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>>> upf_len(14)
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2
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"""
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return len(unique_prime_factors(num))
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def equality(iterable: list) -> bool:
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"""
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Check equality of ALL elements in an interable.
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>>> equality([1, 2, 3, 4])
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False
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>>> equality([2, 2, 2, 2])
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True
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>>> equality([1, 2, 3, 2, 1])
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False
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"""
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return len(set(iterable)) in (0, 1)
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def run(n: int) -> list:
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"""
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Runs core process to find problem solution.
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>>> run(3)
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[644, 645, 646]
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"""
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# Incrementor variable for our group list comprehension.
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# This serves as the first number in each list of values
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# to test.
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base = 2
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while True:
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# Increment each value of a generated range
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group = [base + i for i in range(n)]
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# Run elements through out unique_prime_factors function
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# Append our target number to the end.
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checker = [upf_len(x) for x in group]
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checker.append(n)
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# If all numbers in the list are equal, return the group variable.
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if equality(checker):
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return group
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# Increment our base variable by 1
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base += 1
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def solution(n: int = 4) -> int:
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"""Return the first value of the first four consecutive integers to have four
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distinct prime factors each.
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>>> solution()
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134043
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"""
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results = run(n)
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return results[0] if len(results) else None
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if __name__ == "__main__":
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print(solution())
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