494. 目标和

题目链接

class Solution {
public:
    int findTargetSumWays(vector<int>& nums, int target) {
        int sum = 0;
        for (int i = 0; i < nums.size(); i++) {
            sum += nums[i];
        }
        // left - (sum - left) = target
        // left = (sum + target) / 2
        if (abs(target) > sum) return 0;
        if ((sum + target) % 2 == 1) return 0;
        // 背包需装的大小
        int bagsize = (sum + target) / 2;
        vector<int> dp(bagsize + 1, 0);
        // j下标代表装的大小，dp[j]代表装下容量j的方法数
        dp[0] = 1;
        for (int i = 0; i < nums.size(); i++) {
            for (int j = bagsize; j >= nums[i]; j--) {
                dp[j] +=  dp[j - nums[i]];
            }
        }
        return dp[bagsize];
    }
};

总结

• 装满背包，递推公式dp[j] += dp[j - nums[i]];