96. 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

 解题思路：

当选定一个节点之后，他的左子树的种类数目*右子树的种类数目

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