climing stairs solution

Author: yerim01

climbing-stairs/yerim01.py

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+# Goal: Given n steps, return the number of distinct ways you can climb to the top.
+# Constraints:
+# - You can climb either 1 or 2 steps at each time.
+# - 1 <= n <= 45
+# Approach:
+# f(n) = number of ways to reach step n.
+# The last move must be from step n-1 or step n-2.
+# Therefore, f(n) = f(n-1) + f(n-2).
+# Base case - f(1) = 1, f(2) = 2.
+# Use two variables prev1&prev2 to track the number of of f(n-1)&f(n-2).
+# Iterate a loop, staring from 3.
+# Store prev1 into temp.
+# Update prev1&prev2.
+# Return prev1.
+
+# Time complexity: O(n)
+# - We iterate once
+# Space complexity: O(1)
+# - Only using variables
+
+class Solution:
+    def climbStairs(self, n: int) -> int:
+        if n <= 2:
+            return n
+        
+        prev1 = 2
+        prev2 = 1
+
+        for i in range(3, n+1):
+            temp = prev1
+            prev1 = prev2 + prev1
+            prev2 = temp
+        
+        return prev1