LeetCode Unique Binary Search Trees

题目：

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

思想：n个节点除去跟节点还有n-1个节点，左子树的节点数为0，1，...，相应的右子树的节点数为n-1，n-2，...0；
则f(n) = f(0)f(n-1)+f(1)f(n-2)+...+f(n-2)f(n-1)+f(n-1)f(1)

class Solution {
public:
int numTrees(int n) {
if(n == 0)
return 1;
if(n == 1)
return 1;
if(n >= 2) {
int sum = 0;
for(int i = 0; i < n; i++)
sum += numTrees(i)* numTrees(n-1-i);
return sum;
}
}
};