Given n, how many structurally unique BST‘s (binary search trees) that store values 1...n?

For example,
Given n = 3, there are a total of 5 unique BST‘s.

   1         3     3      2      1
    \       /     /      / \           3     2     1      1   3      2
    /     /       \                    2     1         2                 3

class Solution { //卡特兰数
public:
    int numTrees(int n) {
        vector<int> res(n+1,0);
        res[0]=1;
        res[1]=1;
        for(int i=2;i<n+1;i++)
        {
            for(int j=0;j<i;j++)
            {
                res[i]+=res[j]*res[i-j-1];
            }
        }
        return res[n];
    }
};