# nayuki/Project-Euler-solutions

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b7f686d Jan 23, 2017
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 # # Solution to Project Euler problem 25 # Copyright (c) Project Nayuki. All rights reserved. # # https://www.nayuki.io/page/project-euler-solutions # https://github.com/nayuki/Project-Euler-solutions # import itertools # Because the target number is relatively small, we simply compute each Fibonacci number starting # from the beginning until we encounter one with exactly 1000 digits. The Fibonacci sequence grows # exponentially with a base of about 1.618, so the numbers in base 10 will lengthen by one digit # after every log10(1.618) ~= 4.78 steps on average. This means the answer is at index around 4780. def compute(): DIGITS = 1000 prev = 1 cur = 0 for i in itertools.count(): # At this point, prev = fibonacci(i - 1) and cur = fibonacci(i) if len(str(cur)) > DIGITS: raise RuntimeError("Not found") elif len(str(cur)) == DIGITS: return str(i) # Advance the Fibonacci sequence by one step prev, cur = cur, prev + cur if __name__ == "__main__": print(compute())