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
;
}