mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-25 04:30:15 +00:00
70 lines
1.2 KiB
Python
70 lines
1.2 KiB
Python
"""
|
||
The Fibonacci sequence is defined by the recurrence relation:
|
||
|
||
Fn = Fn−1 + Fn−2, 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?
|
||
"""
|
||
|
||
|
||
def fibonacci(n):
|
||
if n == 1 or type(n) is not 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]
|
||
|
||
|
||
def fibonacci_digits_index(n):
|
||
digits = 0
|
||
index = 2
|
||
|
||
while digits < n:
|
||
index += 1
|
||
digits = len(str(fibonacci(index)))
|
||
|
||
return index
|
||
|
||
|
||
def solution(n):
|
||
"""Returns the index of the first term in the Fibonacci sequence to contain
|
||
n digits.
|
||
|
||
>>> solution(1000)
|
||
4782
|
||
>>> solution(100)
|
||
476
|
||
>>> solution(50)
|
||
237
|
||
>>> solution(3)
|
||
12
|
||
"""
|
||
return fibonacci_digits_index(n)
|
||
|
||
|
||
if __name__ == "__main__":
|
||
print(solution(int(str(input()).strip())))
|