494. Target Sum¶

Difficulty: Medium

494. Target Sum

Medium

You are given an integer array nums and an integer target.

You want to build an expression out of nums by adding one of the symbols '+' and '-' before each integer in nums and then concatenate all the integers.

For example, if nums = [2, 1], you can add a '+' before 2 and a '-' before 1 and concatenate them to build the expression "+2-1".

Return the number of different expressions that you can build, which evaluates to target.

Example 1:

Input: nums = [1,1,1,1,1], target = 3
Output: 5
Explanation: There are 5 ways to assign symbols to make the sum of nums be target 3.
-1 + 1 + 1 + 1 + 1 = 3
+1 - 1 + 1 + 1 + 1 = 3
+1 + 1 - 1 + 1 + 1 = 3
+1 + 1 + 1 - 1 + 1 = 3
+1 + 1 + 1 + 1 - 1 = 3

Example 2:

Input: nums = [1], target = 1
Output: 1

Constraints:

1 <= nums.length <= 20
0 <= nums[i] <= 1000
0 <= sum(nums[i]) <= 1000
-1000 <= target <= 1000

Solution¶

class Solution {
    public int findTargetSumWays(int[] nums, int target) {
        int n = nums.length;
        int sum = 0;
        for (int i = 0; i < n; i++) sum += nums[i];
        if (sum - target < 0) return 0;
        else if ((sum - target) % 2 != 0) return 0;
        else{
            int target1 = (sum - target)  /  2;
            int dp[][] = new int[n + 1][target1 + 1];
            for (int temp[] : dp) Arrays.fill(temp, -1);
            return solve(n - 1, nums, target1, dp);
        }
    }
    private int solve(int ind, int arr[], int target, int dp[][]){
        if(ind == 0){
            if (target == 0 && arr[0] == 0) return 2;
            if (target == 0 || arr[0] == target) return 1;
            return 0;
        }
        if(dp[ind][target] != -1) return dp[ind][target];
        int not_take = solve(ind - 1, arr, target, dp);
        int take = 0;
        if(arr[ind] <= target) take = solve(ind - 1, arr, target - arr[ind], dp);
        return dp[ind][target] = (take + not_take);
    }
}

Complexity Analysis¶

Time Complexity: O(?)
Space Complexity: O(?)

Approach¶

Detailed explanation of the approach will be added here