Create 02 - Top-Down | DP | Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/14 - Minimum Cost for Tickets/02 - Top-Down | DP | Approach.cpp

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+class Solution {
+public:
+    // Recursive function to calculate the minimum cost using memoization
+    int solve(vector<int>& days, vector<int>& costs, int n, int index, vector<int>& dp) {
+        // Base case: if the index is out of bounds, no cost is required
+        if (index >= n) 
+            return 0;
+
+        // If the result is already computed for the current index, return it (memoization)
+        if (dp[index] != -1) 
+            return dp[index];
+
+        // **Cost for a 1-day pass**:
+        // Move to the next day and add the cost of a 1-day pass
+        int cost1 = solve(days, costs, n, index + 1, dp) + costs[0];
+        
+        // **Cost for a 7-day pass**:
+        // Find the first day not covered by the 7-day pass (days[index] + 7)
+        int i; 
+        for (i = index; i < n && days[i] < days[index] + 7; i++);
+        // Recursively calculate the cost from that day and add the cost of a 7-day pass
+        int cost7 = solve(days, costs, n, i, dp) + costs[1];
+        
+        // **Cost for a 30-day pass**:
+        // Find the first day not covered by the 30-day pass (days[index] + 30)
+        for (i = index; i < n && days[i] < days[index] + 30; i++);
+        // Recursively calculate the cost from that day and add the cost of a 30-day pass
+        int cost30 = solve(days, costs, n, i, dp) + costs[2];
+
+        // Store the minimum cost for the current index in the memoization table
+        dp[index] = min(cost1, min(cost7, cost30));
+
+        // Return the computed minimum cost for the current index
+        return dp[index];
+    }
+
+    // Main function to calculate the minimum cost of traveling
+    int mincostTickets(vector<int>& days, vector<int>& costs) {
+        // Create a memoization table initialized to -1
+        vector<int> dp(days.size() + 1, -1);
+        // Start calculating from the first day
+        return solve(days, costs, days.size(), 0, dp);
+    }
+};