Create 04 - Space Optimized | DP | Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/02 - Min Cost Climbing Stairs/04 - Space Optimized | DP | Approach.cpp

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+class Solution {
+public:
+    // Function to calculate the minimum cost to climb the stairs using optimized tabulation
+    int solve(vector<int>& cost, int n) {
+        // Step 1: Initialize two variables to store the minimum cost for the previous two steps
+        int i_1 = cost[1];  // Represents the cost to reach the first step (index 1)
+        int i_2 = cost[0];  // Represents the cost to reach the second step (index 0)
+
+        // Step 2: Iterate through the cost array starting from the third step (index 2)
+        for (int i = 2; i < n; i++) {
+            // The minimum cost to reach the current step is the cost at this step plus the minimum
+            // of the costs from the two previous steps (i-1 and i-2)
+            int curr = cost[i] + min(i_1, i_2);
+            
+            // Update the variables for the next iteration
+            i_2 = i_1;  // Move the previous step to i_2
+            i_1 = curr;  // Set the current minimum cost as i_1
+        }
+
+        // Step 3: The minimum cost to reach the top is the minimum of the last two steps
+        return min(i_1, i_2);
+    }
+
+    // Main function to calculate the minimum cost to climb to the top of the stairs
+    int minCostClimbingStairs(vector<int>& cost) {
+        // Call the `solve` function with the cost array and its size
+        return solve(cost, cost.size());
+    }
+};