Leetcode 86. 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

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])

 def numTrees(self, n):
         """
         :type n: int
         :rtype: int
         """
         dp = [0]*(n+1)
         dp[0] = 1
         dp[1] = 1

         for i in range(2, n+1):
             for j in range(1,i+1):
                 dp[i] += dp[j-1]*dp[i-j]

         return dp[n]