update 70

leetcode/70.py

@@ -0,0 +1,46 @@
+# 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))