LeetCode-in-All

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

impl Solution {
    pub fn find_target_sum_ways(nums: Vec<i32>, s: i32) -> i32 {
        let mut sum: i32 = nums.iter().sum();
        let s = s.abs();
        
        // Invalid cases
        if s > sum || (sum + s) % 2 != 0 {
            return 0;
        }

        let target = (sum + s) / 2;
        let n = nums.len();

        // dp[i] represents the number of ways to form sum i
        let mut dp = vec![vec![0; n + 1]; (target + 1) as usize];
        dp[0][0] = 1;

        // Handle empty knapsack condition
        for i in 0..n {
            if nums[i] == 0 {
                dp[0][i + 1] = dp[0][i] * 2;
            } else {
                dp[0][i + 1] = dp[0][i];
            }
        }

        // Fill the dp table
        for i in 1..=target {
            for j in 0..n {
                dp[i as usize][j + 1] += dp[i as usize][j];
                if nums[j] <= i {
                    dp[i as usize][j + 1] += dp[(i - nums[j]) as usize][j];
                }
            }
        }

        dp[target as usize][n]
    }
}

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