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

//卡特兰数

class Solution {
public:
int numTrees(int n) {
if (n == 0)
{
return 0;
}

int buf[n+1];
buf[0] = 1;
buf[1] = 1;

for (int i = 2; i <= n; i++)
{
int result = 0;
for (int j = 0; j < i; j++)
{
result += buf[j] * buf[i-1-j];
}

buf[i] = result;
}

return buf
;
}
};