# Climbing Stairs


class Solution:
    def climbStairs(self, n: int) -> int:
        """
        # Fibonacci sequence
        # too slow: O(n)
        if n <= 2:
            return n

        first, second = 1, 2
        for _ in range(3, n + 1):
            first, second = second, first + second

        return second
        """

        # DP recurion
        # fastest
        from functools import cache

        @cache
        def f(n):
            if n <= 2:
                return n
            return f(n - 1) + f(n - 2)

        return f(n)

        """
        # Matrix Power Solution
        # O(log n) but slower???
        if n <= 2:
            return n

        import numpy as np

        M = np.array([[1, 1], [1, 0]])
        A = np.array([[1, 1]]) @ np.linalg.matrix_power(M, n - 2) @ np.array([[1], [1]])
        return A[0, 0]
        """


if __name__ == "__main__":
    print(Solution().climbStairs(91))