90 lines
2.3 KiB
Python
90 lines
2.3 KiB
Python
#!/usr/bin/env python3
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# The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:
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#
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# 1! + 4! + 5! = 1 + 24 + 120 = 145
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#
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# Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are
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# only three such loops that exist:
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#
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# 169 → 363601 → 1454 → 169
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# 871 → 45361 → 871
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# 872 → 45362 → 872
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#
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# It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,
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#
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# 69 → 363600 → 1454 → 169 → 363601 (→ 1454)
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# 78 → 45360 → 871 → 45361 (→ 871)
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# 540 → 145 (→ 145)
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#
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# Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number
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# below one million is sixty terms.
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#
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# How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?
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from math import factorial
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from projecteuler import timing
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N = 1000000
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chains = [0] * N
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def len_chain(n):
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chain = [0] * 60
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count = 0
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finished = 0
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value = n
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chain[count] = value
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while not finished:
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tmp = 0
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count = count + 1
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# Generate the next number of the chain by taking
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# the digits of the current value, calculating the
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# factorials and adding them.
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while value != 0:
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tmp = tmp + factorial(value % 10)
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value = value // 10
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# If the chain length for the new value has already been
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# calculated before, use the saved value (only chains for
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# values smaller than N are saved).
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if tmp < N and chains[tmp] != 0:
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return count + chains[tmp]
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value = tmp
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# If the current value is already present in the chain,
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# the chain is finished.
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for i in range(count):
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if chain[i] == value:
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finished = 1
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chain[count] = value
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chains[n] = count
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return count
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@timing
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def p074():
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count = 0
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# Simple brute force approach, for every number calculate
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# the length of the chain.
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for i in range(3, N):
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if len_chain(i) == 60:
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count = count + 1
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print('Project Euler, Problem 74')
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print(f'Answer: {count}')
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if __name__ == '__main__':
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p074()
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