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

Author: JawadSher

24 - Dynamic Programming Problems/12 - Combination Sum IV/02 - Top-Down | DP | Approach.cpp

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+class Solution {
+public:
+    // Recursive function to calculate the number of combinations with memoization
+    int solve(vector<int>& nums, int target, vector<int>& dp) {
+        // Base case: If the target becomes negative, no valid combination is possible
+        if(target < 0) return 0;
+
+        // Base case: If the target becomes zero, one valid combination is found
+        if(target == 0) return 1;
+
+        // If the result for the current target has already been calculated, return it
+        if(dp[target] != -1) return dp[target];
+
+        // Initialize a variable to store the number of valid combinations for the current target
+        int ans = 0;
+
+        // Iterate through each number in the array
+        for(int i = 0; i < nums.size(); i++) {
+            // Recursively calculate combinations for the reduced target
+            ans += solve(nums, target - nums[i], dp);
+        }
+
+        // Store the calculated result in the memoization table
+        dp[target] = ans;
+
+        // Return the result for the current target
+        return dp[target];
+    }
+
+    // Main function to calculate the number of combinations for a given target
+    int combinationSum4(vector<int>& nums, int target) {
+        // Initialize a memoization table with -1 (uncomputed state)
+        vector<int> dp(target + 1, -1);
+
+        // Call the recursive function to solve the problem with memoization
+        return solve(nums, target, dp);
+    }
+};