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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

object Solution {
    def findTargetSumWays(nums: Array[Int], s: Int): Int = {
        val sum = nums.sum
        val absS = Math.abs(s)

        if (absS > sum || (sum + absS) % 2 != 0) {
            return 0
        }

        val target = (sum + absS) / 2
        val dp = Array.ofDim[Int](target + 1, nums.length + 1)

        dp(0)(0) = 1

        for (i <- nums.indices) {
            if (nums(i) == 0) {
                dp(0)(i + 1) = dp(0)(i) * 2
            } else {
                dp(0)(i + 1) = dp(0)(i)
            }
        }

        for (i <- 1 to target) {
            for (j <- nums.indices) {
                dp(i)(j + 1) = dp(i)(j)
                if (nums(j) <= i) {
                    dp(i)(j + 1) += dp(i - nums(j))(j)
                }
            }
        }

        dp(target)(nums.length)
    }
}

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