[LeetCode] Unique Binary Search Trees

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