Target Sum

问题来源

问题描述

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.
Example1

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.

问题分析

中文大意就是给出一系列数字，仅通过+/-操作来得出目标值，计算一共有多少种方法可以得到该值。我在这里采用的是最笨的枚举法来解决问题，复杂度为 O(n^2)。然而实际上此题可以用动态规划的方法来解题，具体可参考此处

解决代码

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