LeetCode-in-Net.github.io

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

using System;
using System.Collections.Generic;

public class Solution {
    public int FindTargetSumWays(int[] nums, int s) {
        int sum = 0;
        s = Math.Abs(s);
        foreach (int num in nums) {
            sum += num;
        }
        // Invalid s, just return 0
        if (s > sum || (sum + s) % 2 != 0) {
            return 0;
        }
        int[][] dp = new int[(sum + s) / 2 + 1][];
        for (int i = 0; i < dp.Length; i++) {
            dp[i] = new int[nums.Length + 1];
        }
        dp[0][0] = 1;
        // empty knapsack must be processed specially
        for (int 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 (int i = 1; i < dp.Length; i++) {
            for (int 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];
    }
}

This site is open source. Improve this page.