Python/project_euler/problem_025/sol1.py

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"""
The Fibonacci sequence is defined by the recurrence relation:
Fn = Fn1 + Fn2, where F1 = 1 and F2 = 1.
Hence the first 12 terms will be:
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144
The 12th term, F12, is the first term to contain three digits.
What is the index of the first term in the Fibonacci sequence to contain 1000
digits?
"""
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def fibonacci(n: int) -> int:
"""
Computes the Fibonacci number for input n by iterating through n numbers
and creating an array of ints using the Fibonacci formula.
Returns the nth element of the array.
>>> fibonacci(2)
1
>>> fibonacci(3)
2
>>> fibonacci(5)
5
>>> fibonacci(10)
55
>>> fibonacci(12)
144
"""
if n == 1 or not isinstance(n, int):
return 0
elif n == 2:
return 1
else:
sequence = [0, 1]
for i in range(2, n + 1):
sequence.append(sequence[i - 1] + sequence[i - 2])
return sequence[n]
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def fibonacci_digits_index(n: int) -> int:
"""
Computes incrementing Fibonacci numbers starting from 3 until the length
of the resulting Fibonacci result is the input value n. Returns the term
of the Fibonacci sequence where this occurs.
>>> fibonacci_digits_index(1000)
4782
>>> fibonacci_digits_index(100)
476
>>> fibonacci_digits_index(50)
237
>>> fibonacci_digits_index(3)
12
"""
digits = 0
index = 2
while digits < n:
index += 1
digits = len(str(fibonacci(index)))
return index
def solution(n: int = 1000) -> int:
"""
Returns the index of the first term in the Fibonacci sequence to contain
n digits.
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>>> solution(1000)
4782
>>> solution(100)
476
>>> solution(50)
237
>>> solution(3)
12
"""
return fibonacci_digits_index(n)
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if __name__ == "__main__":
print(solution(int(str(input()).strip())))