Unique Binary Search Trees

题目名称

Unique Binary Search Trees—LeetCode链接

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

分析

  参考我的上一篇博客Catalan数—求解n个节点能组成的二叉树个数问题

C++代码

class Solution {
public:
int numTrees(int n) {
long prev=0,cur=1;
for(int i=2 ; i <= n; ++i)
{
prev=cur;
cur=((4*i-2)*prev)/(i+1);
}
return cur;
}
};