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102 lines
2.0 KiB
Python
102 lines
2.0 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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def fibonacci(n: int) -> int:
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"""
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Computes the Fibonacci number for input n by iterating through n numbers
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and creating an array of ints using the Fibonacci formula.
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Returns the nth element of the array.
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>>> fibonacci(2)
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1
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>>> fibonacci(3)
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2
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>>> fibonacci(5)
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5
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>>> fibonacci(10)
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55
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>>> fibonacci(12)
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144
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"""
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if n == 1 or not isinstance(n, int):
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return 0
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elif n == 2:
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return 1
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else:
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sequence = [0, 1]
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for i in range(2, n + 1):
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sequence.append(sequence[i - 1] + sequence[i - 2])
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return sequence[n]
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def fibonacci_digits_index(n: int) -> int:
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"""
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Computes incrementing Fibonacci numbers starting from 3 until the length
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of the resulting Fibonacci result is the input value n. Returns the term
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of the Fibonacci sequence where this occurs.
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>>> fibonacci_digits_index(1000)
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4782
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>>> fibonacci_digits_index(100)
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476
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>>> fibonacci_digits_index(50)
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237
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>>> fibonacci_digits_index(3)
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12
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"""
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digits = 0
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index = 2
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while digits < n:
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index += 1
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digits = len(str(fibonacci(index)))
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return index
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def solution(n: int = 1000) -> int:
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"""
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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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return fibonacci_digits_index(n)
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if __name__ == "__main__":
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print(solution(int(str(input()).strip())))
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