Create 03 - Bottom-Up | DP | Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/32 - Best Time To Buy and Sell Stock II/03 - Bottom-Up | DP | Approach.cpp

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+class Solution {
+public:
+    // Function to calculate the maximum profit using an iterative dynamic programming approach
+    int solve(vector<int>& prices) {
+
+        int n = prices.size(); // Get the number of days
+
+        // Create a 2D DP table to store the maximum profit for each state
+        // dp[index][buy]:
+        // - `index` represents the current day
+        // - `buy` represents whether buying (1) or selling (0) is allowed on this day
+        vector<vector<int>> dp(n + 1, vector<int>(2, 0));
+
+        // Base cases: No profit can be made after the last day
+        dp[n][0] = 0; // No stock in hand, no profit
+        dp[n][1] = 0; // Stock in hand, no profit
+
+        // Iterate backward from the second last day to the first day
+        for (int index = n - 1; index >= 0; index--) {
+            // Iterate over the two states: buy (1) and sell (0)
+            for (int buy = 0; buy <= 1; buy++) {
+                int profit = 0; // Initialize profit for the current state
+
+                if (buy) {
+                    // If we are allowed to buy:
+                    // - Option 1: Buy the stock today (-prices[index]) and move to the next day with buy=0
+                    // - Option 2: Skip buying today and move to the next day with buy=1
+                    int buyStock = -prices[index] + dp[index + 1][0];
+                    int notBuyStock = 0 + dp[index + 1][1];
+                    profit = max(buyStock, notBuyStock);
+                } else {
+                    // If we are allowed to sell:
+                    // - Option 1: Sell the stock today (+prices[index]) and move to the next day with buy=1
+                    // - Option 2: Skip selling today and move to the next day with buy=0
+                    int sellStock = +prices[index] + dp[index + 1][1];
+                    int notSellStock = 0 + dp[index + 1][0];
+                    profit = max(sellStock, notSellStock);
+                }
+
+                // Store the profit for the current state in the DP table
+                dp[index][buy] = profit;
+            }
+        }
+
+        // The maximum profit starting from day 0 with the ability to buy (buy=1)
+        return dp[0][1];
+    }
+
+    // Main function to calculate the maximum profit
+    int maxProfit(vector<int>& prices) {
+        return solve(prices); // Call the solve function
+    }
+};