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

Author: JawadSher

24 - Dynamic Programming Problems/05 - Coin Change/03 - Bottom-Up | DP | Approach.cpp

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+class Solution {
+public:
+    // Function to solve the coin change problem using bottom-up dynamic programming
+    int solve(vector<int>& coins, int x) {
+        // Create a dp array where dp[i] represents the minimum number of coins needed to make up amount i
+        vector<int> dp(x + 1, INT_MAX);
+
+        // Base case: 0 coins are needed to make up amount 0
+        dp[0] = 0;
+
+        // Iterate over each amount from 1 to x
+        for(int i = 1; i <= x; i++) {
+            // Check each coin to see if it can contribute to the current amount
+            for(int j = 0; j < coins.size(); j++) {
+                // If the current coin can be used (i - coins[j] >= 0) 
+                // and the subproblem dp[i - coins[j]] has a valid solution (not INT_MAX)
+                if(i - coins[j] >= 0 && dp[i - coins[j]] != INT_MAX) {
+                    // Update dp[i] to the minimum of its current value and the result of using this coin
+                    dp[i] = min(dp[i], 1 + dp[i - coins[j]]);
+                }
+            }
+        }
+
+        // If the amount x cannot be formed with the given coins, return -1
+        if(dp[x] == INT_MAX) return -1;
+
+        // Otherwise, return the minimum number of coins needed to make up amount x
+        return dp[x];
+    }
+
+    // Main function to find the minimum number of coins to make up the given amount
+    int coinChange(vector<int>& coins, int amount) {
+        // Use the bottom-up approach to solve the problem
+        return solve(coins, amount);
+    }
+};