[LeetCode] 494. Target Sum

Problem:

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.

Solution:

class Solution {public:    int findTargetSumWays(vector<int>& nums, int S) {        int sum = accumulate(nums.begin(), nums.end(), 0);        if (sum < S || (sum + S) % 2 != 0) return 0;        return dpFindTargetSumWays(nums, (sum+S)/2);    }        int dpFindTargetSumWays(vector<int>& nums, int n) {        int dp[n + 1] = {0};        dp[0] = 1;                for (auto num : nums) {            for (int i = n; i >= num; i--) {                dp[i] += dp[i-num];            }        }        return dp[n];    }};

本题应用动态编程思想解，这个解参考了discuss中一位大神的解，问题的转化十分巧妙。

具体的分析参考：https://discuss.leetcode.com/topic/76243/java-15-ms-c-3-ms-o-ns-iterative-dp-solution-using-subset-sum-with-explanation?page=1