Unique Binary Search Trees

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

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解题技巧：

该题求解可行的二叉查找树的数量。二叉查找树可以任意取根，只要满足中序遍历有序的要求，从处理子问题的角度来看，选取一个节点为根，把节点集分为左

右子树，以这个节点为根的可行二叉树数量等于左右子树可行二叉树数量的乘积。总的数量是以所有节点为根的可行结果的累加之和。具体表达式如下：



代码：

#include <iostream>
using namespace std;

int numTrees(int n)
{
if (n <= 0) return 0;
int res[n+1] = {0};
res[0] = 1;
res[1] = 1;
for(int i = 2; i <= n; i ++)
{
for(int j = 0; j < i; j ++)
{
res[i] += res[j] * res[i - j - 1];
}
}
return res
;
}

int main()
{
int n;
while(cin >> n)
cout << numTrees(n)<<endl;
}