(java)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

思路：当i为根节点时，0~i-1都在i的左子树啊，i+1~n都在i的右子树上，而左右子树又都是BST树，根据排列组合的知识，如果左子树有m种可能，右子树有n种可能，则总共有m*n种可能
所以nums
=nums[i]*nums[j] i+j=n-1
代码如下(已通过leetcode)
public class Solution {

public int numTrees(int n) {

int[] res=new int[n+1];

res[0]=1;

res[1]=1;

for(int i=2;i<=n;i++) {

int j=0;

while(j<i) {

res[i]+=res[j]*res[i-1-j];

j++;

}

}

return res
;

}

}