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

题目大意：给定数字n，有多少种包含数字1->n的二叉搜索树。

题目难度：Medium

/**
 * Created by gzdaijie on 16/6/5
 * 动态规划,对于n个数, 左边可能有0 -> n-1个数,右边对应有n-1 -> 0个数
 * 公式 f(n) = Σ f(i) * f(n - i - 1), i(0...n-1)
 */
public class Solution {
    public int numTrees(int n) {
        int[] dp = new int[n + 1];
        dp[0] = 1;
        for (int i = 1; i <= n; i++) {
            for (int j = 0; j < i; j++) {
                dp[i] += dp[j] * dp[i - j - 1];
            }
        }
        return dp[n];
    }
}