Leetcode 86. Unique Binary Search Trees

本题利用BST的特性来用DP求解。由于BST的性质，所以root左子树的node全部<root。而右子树的node全部>root。

左子树 = [1, j-1], root = j, 右子树 = [j+1, n]

dp[n] = sum(dp[j - 1] * dp[n - j - 1])

 1 def numTrees(self, n):
 2         """
 3         :type n: int
 4         :rtype: int
 5         """
 6         dp = [0]*(n+1)
 7         dp[0] = 1
 8         dp[1] = 1
 9
10         for i in range(2, n+1):
11             for j in range(i):
12                 dp[i] += dp[j]*dp[i-j-1]
13
14         return dp[n]