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74 lines
1.3 KiB
Python
74 lines
1.3 KiB
Python
"""
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The Fibonacci sequence is defined by the recurrence relation:
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Fn = Fn-1 + Fn-2, where F1 = 1 and F2 = 1.
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Hence the first 12 terms will be:
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F1 = 1
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F2 = 1
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F3 = 2
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F4 = 3
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F5 = 5
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F6 = 8
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F7 = 13
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F8 = 21
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F9 = 34
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F10 = 55
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F11 = 89
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F12 = 144
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The 12th term, F12, is the first term to contain three digits.
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What is the index of the first term in the Fibonacci sequence to contain 1000
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digits?
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"""
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from collections.abc import Generator
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def fibonacci_generator() -> Generator[int]:
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"""
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A generator that produces numbers in the Fibonacci sequence
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>>> generator = fibonacci_generator()
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>>> next(generator)
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1
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>>> next(generator)
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2
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>>> next(generator)
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3
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>>> next(generator)
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5
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>>> next(generator)
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8
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"""
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a, b = 0, 1
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while True:
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a, b = b, a + b
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yield b
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def solution(n: int = 1000) -> int:
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"""Returns the index of the first term in the Fibonacci sequence to contain
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n digits.
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>>> solution(1000)
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4782
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>>> solution(100)
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476
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>>> solution(50)
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237
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>>> solution(3)
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12
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"""
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answer = 1
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gen = fibonacci_generator()
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while len(str(next(gen))) < n:
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answer += 1
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return answer + 1
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if __name__ == "__main__":
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print(solution(int(str(input()).strip())))
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