[leetcode]494. Target Sum

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本文探讨了LeetCode上的一道经典问题——目标和，通过递归深度优先搜索的方法来寻找所有可能的符号组合，使得给定整数数组的元素之和等于目标值S。举例说明了当输入为[1,1,1,1,1]且目标值为3时，存在5种不同的符号分配方式。文章还提供了完整的C++代码实现。

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题目链接：https://leetcode.com/problems/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 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.

class Solution{
public:
    int findTargetSumWays(vector<int>& nums,int S)
    {
        int count=0;
        dfs(nums,count,0,0,S);
        return count;
    }

    void dfs(vector<int>& nums,int &count,int sum,int index,int S)
    {
        if (index==nums.size())
        {
            if(sum==S)
                count+=1;
            return;
        }
        dfs(nums,count,sum+nums[index],index+1,S);
        dfs(nums,count,sum-nums[index],index+1,S);
    }
};