49 lines
1.3 KiB
Python
49 lines
1.3 KiB
Python
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from lib_misc import sum_proper_divisors
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def euler_095():
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NO_CHAIN = set()
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PROPER_DIVISOR_CACHE = {}
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def sum_proper_divisors_cached(n):
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if n in PROPER_DIVISOR_CACHE:
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return PROPER_DIVISOR_CACHE[n]
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r = sum_proper_divisors(n)
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PROPER_DIVISOR_CACHE[n] = r
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return r
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def chain(n):
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chain = []
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next_number = n
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while next_number not in chain:
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if next_number >= 10**6 or next_number == 0 or next_number in NO_CHAIN:
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for c in chain:
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NO_CHAIN.add(c)
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return None
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chain.append(next_number)
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next_number = sum_proper_divisors_cached(next_number)
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chain.append(next_number)
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return chain
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chains = [[]]
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for i in range(1, 10**6 + 1):
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c = chain(i)
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if c and c[0] == c[-1]:
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if len(c) == len(chains[0]):
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# There might be multiple different chains with the same length
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# so keep all of them to get the smalles element.
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chains.append(c)
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elif len(c) > len(chains[0]):
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chains = [c]
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elems = [e for c in chains for e in c]
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return min(elems)
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if __name__ == "__main__":
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solution = euler_095()
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print("e095.py: " + str(solution))
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assert(solution == 14316)
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