mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-23 21:11:08 +00:00
9200a2e543
* from __future__ import annotations
* fixup! from __future__ import annotations
* fixup! from __future__ import annotations
* fixup! Format Python code with psf/black push
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
39 lines
864 B
Python
39 lines
864 B
Python
#!/usr/bin/env python3
|
||
|
||
"""
|
||
This program calculates the nth Fibonacci number in O(log(n)).
|
||
It's possible to calculate F(1_000_000) in less than a second.
|
||
"""
|
||
from __future__ import annotations
|
||
|
||
import sys
|
||
|
||
|
||
def fibonacci(n: int) -> int:
|
||
"""
|
||
return F(n)
|
||
>>> [fibonacci(i) for i in range(13)]
|
||
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]
|
||
"""
|
||
if n < 0:
|
||
raise ValueError("Negative arguments are not supported")
|
||
return _fib(n)[0]
|
||
|
||
|
||
# returns (F(n), F(n-1))
|
||
def _fib(n: int) -> tuple[int, int]:
|
||
if n == 0: # (F(0), F(1))
|
||
return (0, 1)
|
||
|
||
# F(2n) = F(n)[2F(n+1) − F(n)]
|
||
# F(2n+1) = F(n+1)^2+F(n)^2
|
||
a, b = _fib(n // 2)
|
||
c = a * (b * 2 - a)
|
||
d = a * a + b * b
|
||
return (d, c + d) if n % 2 else (c, d)
|
||
|
||
|
||
if __name__ == "__main__":
|
||
n = int(sys.argv[1])
|
||
print(f"fibonacci({n}) is {fibonacci(n)}")
|