Create Min Cost Climbing Stairs - Leetcode 746.py

Author: gahogg

Min Cost Climbing Stairs - Leetcode 746.py

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+class Solution:
+    def minCostClimbingStairs(self, cost: List[int]) -> int:
+        # Recursive Solution
+        n = len(cost)
+
+        def min_cost(i):
+            if i < 2:
+                return 0
+
+            return min(cost[i-2] + min_cost(i-2),
+                       cost[i-1] + min_cost(i-1))
+
+        return min_cost(n)
+        # Time: O(2^n)
+        # Space: O(n)
+
+
+class Solution:
+    def minCostClimbingStairs(self, cost: List[int]) -> int:
+        # Top Down DP (Memoization)
+        n = len(cost)
+        memo = {0:0, 1:0}
+        def min_cost(i):
+            if i in memo:
+                return memo[i]
+            else:
+                memo[i] = min(cost[i-2] + min_cost(i-2),
+                              cost[i-1] + min_cost(i-1))
+                return memo[i]
+
+        return min_cost(n)
+        # Time: O(n)
+        # Space: O(n)
+
+
+class Solution:
+    def minCostClimbingStairs(self, cost: List[int]) -> int:
+        # Bottom Up DP (Tabulation)
+        n = len(cost)
+        dp = [0] * (n+1)
+        
+        for i in range(2, n+1):
+            dp[i] = min(dp[i-2] + cost[i-2], dp[i-1] + cost[i-1])
+        
+        return dp[-1]
+
+        # Time: O(n)
+        # Space: O(n)
+
+
+class Solution:
+    def minCostClimbingStairs(self, cost: List[int]) -> int:
+        # Bottom Up DP (Constant Space)
+        n = len(cost)
+        prev, curr = 0, 0
+
+        for i in range(2, n+1):
+            prev, curr = curr, min(cost[i-2] + prev, cost[i-1] + curr)
+        
+        return curr
+
+        # Time: O(n)
+        # Space: O(1)
+