maths: add O(log n) Fibonacci via matrix exponentiation#14557
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maths: add O(log n) Fibonacci via matrix exponentiation#14557AKIB473 wants to merge 2 commits intoTheAlgorithms:masterfrom
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- Implements fibonacci(n) using fast matrix exponentiation - Time complexity: O(log n), Space complexity: O(log n) - Full docstring with Wikipedia reference - Type hints on all parameters and return values - Doctests for edge cases: fib(0), fib(1), fib(10), fib(20), fib(50) - Raises ValueError for negative input
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maths/fibonacci_fast.py
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| def _mat_mul(a: list[list[int]], b: list[list[int]]) -> list[list[int]]: |
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| def fibonacci(n: int) -> int: |
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Describe your change:
Add a new implementation of the Fibonacci sequence using matrix exponentiation, achieving O(log n) time complexity compared to the O(n) iterative approach.
Checklist: