[leetcode tree]96. 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

给出一个n，求1-n个数可以组成多少种二叉查找树

思路：对每一个root为k的树有多少种来说，那就就需要知道左子树的根k-1可以组成多少种树，同时右子树根为n-1-k时候有多少种树，结果就是左边和右边的种类数相乘

动态规划

1 class Solution(object):
2     def numTrees(self, n):
3         flag = [0]*(n+1)
4         flag[0],flag[1] = 1,1
5         for i in range(2,n+1):
6             for j in range(i):
7                 flag[i] += flag[j]*flag[i-1-j]
8         return flag[n]
9