LeetCode494

EX494

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: 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.

Solution:

   这仍旧是一道对背包问题的变形，首先nums中的数分成两组，numP与numN,很容易得到：   sumP + sumN = sum   sumP - sumN = target   =====> sumP = (sum + target)/2   ===================>整道题转换为了：求nums中取数，和为(sum + target)/2的不同组合方式的个数

class Solution {public:    int findTargetSumWays(vector<int>& nums, int S) {        int len = nums.size(), sum = 0;        for (int i = 0; i < len; i++) {            sum += nums[i];        }        //target+sum为奇数时，显然可能的组合方式为0        if (S > sum || S < -sum || (S+sum)%2) {            return 0;        }        return canPartition(nums, (S+sum)/2);    }    //ex416的变形    int canPartition(vector<int>& nums, int target) {        int len = nums.size();        vector<int> dp(target+1, 0);        dp[0] = 1;        for (int i = 0; i < len; i++) {            for (int j = target; j >= nums[i]; j--) {                if (dp[j-nums[i]]) {                    //求个数，所以累加                    dp[j] += dp[j-nums[i]];                }            }        }        return dp[target];    }};