【LeetCode题目记录-6】1~n作为key可以有多少种二叉搜索树（BST）的形式

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

【分析-原创】这是卡特兰数（可以证明），自底向上进行动态规划。

public int numTrees(int n) {
        if (n == 0 || n == 1)
            return 1;
        int[] catalan = new int[n + 1];
        catalan[0] = catalan[1] = 1;
        for (int i = 2; i <= n; i++) {
            for (int j = 0; j < i; j++) {
                catalan[i] += catalan[j] * catalan[i - 1 - j];
            }
        }
        return catalan[n];
    }