Create: 0123-best-time-to-buy-and-sell-stock-iii.cpp

cpp/0123-best-time-to-buy-and-sell-stock-iii.cpp

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+class Solution {
+public:
+    int maxProfitFromDay(int day, int canBuy, int transactionsRemaining,
+                         vector<int>& prices,
+                         vector<vector<vector<int>>>& dp) {
+        int n = prices.size();
+
+        // Base cases
+        if (day == n || transactionsRemaining == 0) return 0;
+
+        // Return already computed state
+        if (dp[day][canBuy][transactionsRemaining] != -1) {
+            return dp[day][canBuy][transactionsRemaining];
+        }
+
+        int profit = 0;
+        if (canBuy) {
+            // Option 1: Buy the stock today
+            int buyToday = -prices[day] + maxProfitFromDay(day + 1, 0, transactionsRemaining, prices, dp);
+            // Option 2: Skip buying today
+            int skipToday = maxProfitFromDay(day + 1, 1, transactionsRemaining, prices, dp);
+            profit = max(buyToday, skipToday);
+        } else {
+            // Option 1: Sell the stock today
+            int sellToday = prices[day] + maxProfitFromDay(day + 1, 1, transactionsRemaining - 1, prices, dp);
+            // Option 2: Skip selling today
+            int skipToday = maxProfitFromDay(day + 1, 0, transactionsRemaining, prices, dp);
+            profit = max(sellToday, skipToday);
+        }
+
+        return dp[day][canBuy][transactionsRemaining] = profit;
+    }
+
+    int maxProfit(vector<int>& prices) {
+        int n = prices.size();
+        // 3D DP: dp[day][canBuy][transactionsRemaining]
+        vector<vector<vector<int>>> dp(n, vector<vector<int>>(2, vector<int>(3, -1)));
+
+        // Start at day 0, with option to buy, and 2 transactions allowed
+        return maxProfitFromDay(0, 1, 2, prices, dp);
+    }
+};
+