problem:https://leetcode.com/problems/partition-equal-subset-sum/

        经典背包问题。找到是否存在恰好装满sum / 2的物体，可以优化为1D的。

class Solution {
public:
    bool canPartition(vector<int>& nums) {
        int n = nums.size();
        int sum = accumulate(nums.begin(), nums.end(), 0);
        if (sum % 2)return false;
        sum /= 2;
        vector<vector<bool>> dp(n, vector<bool>(sum + 1, false));
        for (int i = 0; i < n; i++)
            dp[i][0] = true;

        if(nums[0] <= sum) dp[0][nums[0]] = true;
        for (int i = 1; i < n; i++) {
            for (int k = nums[i]; k <= sum; k++) 
            {
                dp[i][k] = dp[i - 1][k];
                int num = k - nums[i];
                dp[i][k] = dp[i][k] | dp[i - 1][num];
            }
            if (dp[i][sum]) return true;
        }
        
        return false;
    }
};