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

Author: JawadSher

24 - Dynamic Programming Problems/14 - Minimum Cost for Tickets/03 - Bottom-Up | DP | Approach.cpp

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+class Solution {
+public:
+    // Function to calculate the minimum cost using dynamic programming
+    long long solve(vector<int>& days, vector<int>& costs, int n) {
+        // Create a DP table to store the minimum cost for each starting day
+        // Initialize all values to a very large number (LLONG_MAX)
+        vector<long long> dp(n + 1, LLONG_MAX);
+        
+        // Base case: if there are no more days to cover, the cost is 0
+        dp[n] = 0;
+
+        // Traverse the days array from the last travel day to the first
+        for (int k = n - 1; k >= 0; k--) {
+            // **Cost for a 1-day pass**:
+            // Add the cost of a 1-day pass and move to the next day
+            long long cost1 = dp[k + 1] + costs[0];
+            
+            // **Cost for a 7-day pass**:
+            // Find the first day not covered by the 7-day pass (days[k] + 7)
+            int i;
+            for (i = k; i < n && days[i] < days[k] + 7; i++);
+            // Add the cost of a 7-day pass and use the precomputed result from dp[i]
+            long long cost7 = dp[i] + costs[1];
+            
+            // **Cost for a 30-day pass**:
+            // Find the first day not covered by the 30-day pass (days[k] + 30)
+            for (i = k; i < n && days[i] < days[k] + 30; i++);
+            // Add the cost of a 30-day pass and use the precomputed result from dp[i]
+            long long cost30 = dp[i] + costs[2];
+
+            // Store the minimum cost for day k in the DP table
+            dp[k] = min(cost1, min(cost7, cost30));
+        }
+
+        // Return the minimum cost starting from the first day
+        return dp[0];
+    }
+
+    // Main function to calculate the minimum cost of traveling
+    int mincostTickets(vector<int>& days, vector<int>& costs) {
+        // Call the solve function with the days, costs, and number of days
+        return solve(days, costs, days.size());
+    }
+};