[Leetcode]@python 96. Unique Binary Search Trees

题目链接

https://leetcode.com/problems/unique-binary-search-trees/

题目原文

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.

题目大意

求二叉树的棵数

解题思路

使用动态规划：n=0时，为空树，那么dp[0]=1; n=1时，显然也是1，dp[1]=1；n=2时，dp[2]=2; 对于n>2时，dp[n]=dp[0]dp[n-1]+dp[1]dp[n-2]+......+dp[n-1]*dp[0]

代码

class Solution(object):
    def numTrees(self, n):
        """
        :type n: int
        :rtype: int
        """
        dp = [1, 1, 2]
        if n <= 2:
            return dp[n]
        else:
            dp += [0 for i in range(n - 2)]
            for i in range(3, n + 1):
                for j in range(1, i + 1):
                    dp[i] += dp[j - 1] * dp[i - j]
            return dp[n]