Unique Binary Search Trees

题目描述：

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

我是先做的Unique Binary Search Trees II，然后用那个方法递归，超时了，应该用动态规划的方法。

递归方法代码如下：（超时！）

public int numTrees(int n) {    return getNum(1, n);}public int getNum(int left,int right){int result=0;if(left>=right)return 1;for(int i=left;i<=right;i++){int leftnum=getNum(left, i-1);int rightnum=getNum(i+1, right);result+=leftnum*rightnum;}return result;}

AD代码如下：

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