week4-NO.494. Target Sum

题目

• Total Accepted: 11746
• Total Submissions: 26572
• Difficulty: Medium
• Contributors: kevin.xinzhao@gmail.com

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.

https://leetcode.com/problems/target-sum/#/description

思路

题意是给定一个数组，其中每个数可以赋予正负号的一个，问有多少可能的情况使得赋予符号后的数组和为指定的值。

思路是从构建一颗二叉树，树根的值为0，两条边分别指向正号的a1和负号的a1。其它每个点发出的两条边分别指向正的下一个数和负的下一个数。遍历这棵并记录所有结点的和，到了叶结点，就得到了一种可能的和，将其与给定值做对比，相同则说明得到了一种满足要求的符号分配。

源程序

class Solution {
public:
    int findTargetSumWays(vector<int>& nums, int S) {
        int i = 0,s = 0,n = 0;
        dfs(nums,i + 1,s + nums[i],n,S);
        dfs(nums,i + 1,s - nums[i],n,S);
        return n;
    }
    void dfs(vector<int>& nums,int i,int s,int &n,int S){
        if(i == nums.size()){
            if(s == S)
                n ++;
        }
        else{
            dfs(nums,i + 1,s + nums[i],n,S);
            dfs(nums,i + 1,s - nums[i],n,S);
        }
    }
};