LeetCode-Target Sum

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Description：
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 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

.

Note:

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

题意：给定一个一维整数数组num和一个目标和target，其中一维整数中的每个元素可为正或者负，计算有多少种可能的情况令数组所有元素和为target；

解法：我们需要考虑每一个元素可能的两种情况：正数或者负数；因此，可以利用回溯算法来实现，递归的终止条件是遍历完数组的所有元素，之后，我们需要判断最后的和是否为给定的目标元素；

Java

class Solution {
    public int findTargetSumWays(int[] nums, int S) {
        return countTargetSum(nums, S, 0);
    }
    
    private int countTargetSum(int[] nums, int S, int pos) {
        if (pos == nums.length) {
            if (S == 0) return 1;
            return 0;
        }
        int res = 0;
        res += countTargetSum(nums, S - nums[pos], pos + 1);
        res += countTargetSum(nums, S + nums[pos], pos + 1);
        return res;
    }
}