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) {
        // Note: The Solution object is instantiated only once and is reused by each test case.
        vector<vector<int> > vec;
        vector<int> one;
        for(int i=0;i<=n;i++){
            one.resize(n-i+1,0);
            vec.push_back(one);
        }
        for(int j=0;j<n;j++){
            vec[j][0]=1;
            vec[j][1]=1;
        }
　　　　　vec[n][0]=1;
        for(int j=2;j<=n;j++){
            for(int i=0;i<=n-j;i++){
                for(int k=0;k<j;k++){
                    vec[i][j]+=vec[i][k]*vec[i+k+1][j-k-1];
                }
            }
        }
        return vec[0][n];
    }
};