Lintcode 1208. Target Sum

You are given a list of non-negative integers, a1, a2, ..., an, and a target, S. Now you have 2 symbols + and -. For each integer, you should choose one from + and - as its new symbol.

Find out how many ways to assign symbols to make sum of integers equal to target S.

Example

Example 1:

Input: nums is [1, 1, 1, 1, 1], S is 3. 
Output: 5
Explanation: 

-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

There are 5 ways to assign symbols to make the sum of nums be target 3.

Example 2:

Input: nums is [], S is 3. 
Output: 0
Explanation: 
There are 0 way to assign symbols to make the sum of nums be target 3.

Notice

1. The length of the given array is positive and will not exceed 20.
2. The sum of elements in the given array will not exceed 1000.
3. Your output answer is guaranteed to be fitted in a 32-bit integer.

Solution:
Backpacking DP problem.

Code (Java):

public class Solution {
    /**
     * @param nums: the given array
     * @param s: the given target
     * @return: the number of ways to assign symbols to make sum of integers equal to target S
     */
    public int findTargetSumWays(int[] nums, int s) {
        // Write your code here
        
        if (nums == null || nums.length == 0) {
            return 0;
        }
        
        int sum = 0;
        for (int num : nums) {
            sum += num;
        }
        
        if (s > Math.abs(sum)) {
            return 0;
        }
        
        int[][] dp = new int[nums.length + 1][2 * sum + 1];
        dp[0][sum] = 1; // index = num + sum;
        
        for (int i = 1; i <= nums.length; i++) {
            for (int j = 0; j < 2 * sum + 1; j++) {
                if (j - nums[i - 1] >= 0) {
                    dp[i][j] = dp[i - 1][j - nums[i - 1]];
                }
                
                if (j + nums[i - 1] < 2 * sum + 1) {
                    dp[i][j] += dp[i - 1][j + nums[i - 1]];
                }
            }
        }
        
        return dp[nums.length][s + sum];
    }
}