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

對1-n組成的ＢＳＴ，如果選定ｉ為根，那１－（ｉ－１）都在根的左子樹裏，（i+1)-n都在根的右子樹裏，轉換為dp問題。

public class Solution {
    public int numTrees(int n) {
        int[] dp = new int[n + 1];
        dp[0] = 1;
        dp[1] = 1;
        for (int i = 2; i <= n; i++) { // i: number of nodes
            for (int j = 0; j < i; j++) { // j: the index of root
                dp[i] += dp[j] * dp[i - 1 - j];
            }
        }
        return dp[n];
    }
}

96. Unique Binary Search Trees