第十五周

494. Target Sum

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• Total Accepted: 19373
• Total Submissions: 44279
• Difficulty: Medium
• Contributors:[email protected]

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:

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.

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思路：

利用递归的方法，用sum记录数组nums中的前a个数相加或相减的值，对于数组nums中的每一个数都通过递归来遍历相加、相减的两种情况，当a = nums.size（）时，判断sum是否等于S，若等于S就在记录个数的变量num上加1。

代码：

class Solution {
public:
    int num = 0;
    int findTargetSumWays(vector& nums, int S) {
        int size = nums.size();
        count(nums, 0, 0, size, S);
        return num;
    }
    
    void count(vector& nums, int sum, int a, int size, int S){
        if(a == size){
            if(sum == S) num ++;
        }
        else{
            count(nums, sum + nums[a], a + 1, size, S);
            count(nums, sum - nums[a], a + 1, size, S);
        }
    }
};