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

 

Analyse: We can select 1~N as the root. Suppose the root is i, then we can put j = 0~i - 1 nodes in its left, and put i - j - 1 nodes in its right. 

Runtime: 0ms.

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