(LeetCode) 494. Target Sum

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本文探讨了如何通过递归方法解决目标和数问题：给定一个非负整数列表和一个目标值S，找到所有可能的方式为列表中的每个元素分配+或-符号，使得整数之和等于目标S。通过示例说明了算法的有效性和实现过程。

494. 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.

代码

class Solution {
public:
    int findTargetSumWays(vector<int>& nums, int S) {
        int sum = accumulate(nums.begin(), nums.end(), 0);
        return recursive(nums, S, 0, nums.size()-1, sum);
    }

    int recursive(vector<int>& nums, int S, int left, int right, int sum){
        if (sum<abs(S)) return 0;
        if (left==right) return (S==nums[left])+(S==-nums[left]);
        return recursive(nums, S-nums[left], left+1, right, sum-nums[left])+recursive(nums, S+nums[left], left+1, right, sum-nums[left]);

    }
};