mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-23 21:11:08 +00:00
4700297b3e
* Enable ruff RUF002 rule * Fix --------- Co-authored-by: Christian Clauss <cclauss@me.com>
102 lines
2.0 KiB
Python
102 lines
2.0 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: 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]
|
|
|
|
|
|
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.
|
|
|
|
>>> 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())))
|