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

Author: JawadSher

24 - Dynamic Programming Problems/24 - Partition Equal Subset Sum/03 - Bottom-Up | DP | Approach.cpp

@@ -0,0 +1,49 @@
+class Solution {
+public:
+    // Function to check if a subset sum equal to 'target' exists using dynamic programming
+    int solve(vector<int>& nums, int n, int target) {
+        // dp[i][j] will store whether it's possible to form sum 'j' using the first 'i' elements
+        vector<vector<int>> dp(n+1, vector<int>(target+1, 0));
+
+        // Base case: sum of 0 can always be formed (empty subset)
+        for(int i = 0; i <= n; i++) dp[i][0] = 1;
+
+        // Fill the dp table in bottom-up manner
+        // Iterate over all indices of nums in reverse (from n-1 to 0)
+        for(int index = n-1; index >= 0; index--) {
+            // Iterate over all possible target sums from 1 to the desired target sum
+            for(int t = 1; t <= target; t++) {
+                int include = 0;
+                // If the current number can be included (i.e., target - nums[index] >= 0)
+                if(t - nums[index] >= 0) include = dp[index+1][t - nums[index]];
+                
+                // Exclude the current element (i.e., use the result from the next index with the same target)
+                int exclude = dp[index+1][t];
+
+                // The result for dp[index][t] is the logical OR of including or excluding the element
+                dp[index][t] = include or exclude;
+            }
+        }
+
+        // The final result is stored at dp[0][target], which tells if the target sum can be achieved
+        return dp[0][target];
+    }
+
+    // Main function to check if we can partition the array into two subsets with equal sum
+    bool canPartition(vector<int>& nums) {
+        int n = nums.size();
+        int total = 0;
+
+        // Calculate the total sum of the elements in the array
+        for(auto & num : nums) total += num;
+
+        // If the total sum is odd, it can't be partitioned into two equal subsets
+        if(total & 1) return 0;
+
+        // Set the target as half of the total sum
+        int target = total / 2;
+
+        // Call the solve function to check if a subset with sum equal to 'target' exists
+        return solve(nums, n, target);
+    }
+};