leetCode---Target Sum

一. 题目：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: 5Explanation: -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 = 3There 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.

二. 思路分析

         这道题给了我们一个数组，和一个目标值，让我们给数组中每个数字加上正号或负号，然后求和要和目标值相等，求有多少中不同的情况。对于这种求多种情况的问题，最想到的方法使用递归来做，尝试每次添加“+”或者“-”，当count为nums数组的大小的时候，判断sum与S是否相等，如果相等就result++。我们从第一个数字，调用递归函数，在递归函数中，分别对目标值进行加上当前数字调用递归，和减去当前数字调用递归，这样会涵盖所有情况。参见代码如下：

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