mirror of
https://github.com/TheAlgorithms/Python.git
synced 2025-03-30 18:36:43 +00:00
64 lines
1.5 KiB
Python
64 lines
1.5 KiB
Python
"""
|
||
Project Euler Problem 25: https://projecteuler.net/problem=25
|
||
1000-digit Fibonacci Number
|
||
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 solution(first_digit_occurrence: int = 1000) -> int:
|
||
"""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
|
||
"""
|
||
|
||
if first_digit_occurrence < 1:
|
||
raise ValueError("Parameter search_limit must be greater than or equal to one.")
|
||
|
||
last_number, new_number = 0, 1
|
||
|
||
last_two_numbers, sequenced_numbers = [last_number, new_number], [1]
|
||
|
||
while len(str(last_two_numbers[last_number])) <= first_digit_occurrence:
|
||
output = last_two_numbers[last_number] + last_two_numbers[new_number]
|
||
|
||
if len(str(output)) == first_digit_occurrence:
|
||
break
|
||
|
||
last_two_numbers[last_number], last_two_numbers[new_number] = (
|
||
last_two_numbers[new_number],
|
||
output,
|
||
)
|
||
|
||
sequenced_numbers.append(output)
|
||
|
||
return len(sequenced_numbers) + 1
|
||
|
||
|
||
if __name__ == "__main__":
|
||
print(f"{solution() = }")
|