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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

function findTargetSumWays(nums: number[], s: number): number {
    let sum: number = 0
    s = Math.abs(s)
    for (const num of nums) {
        sum += num
    }
    // Invalid s, just return 0
    if (s > sum || (sum + s) % 2 !== 0) {
        return 0
    }
    const dp: number[][] = new Array((sum + s) / 2 + 1).fill(null).map(() => new Array(nums.length + 1).fill(0))
    dp[0][0] = 1
    // Empty knapsack must be processed specially
    for (let i = 0; i < nums.length; i++) {
        if (nums[i] === 0) {
            dp[0][i + 1] = dp[0][i] * 2
        } else {
            dp[0][i + 1] = dp[0][i]
        }
    }
    for (let i = 1; i < dp.length; i++) {
        for (let j = 0; j < nums.length; j++) {
            dp[i][j + 1] += dp[i][j]
            if (nums[j] <= i) {
                dp[i][j + 1] += dp[i - nums[j]][j]
            }
        }
    }
    return dp[(sum + s) / 2][nums.length]
}

export { findTargetSumWays }

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