【leetcode刷题】20T49-不同的二叉搜索树

示例:
输入: 3
输出: 5
解释:
给定 n = 3, 一共有 5 种不同结构的二叉搜索树:
   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3

class Solution(object):
    def numTrees(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n < 3:
            return n

        dp = [0] * (n + 1)
        dp[1], dp[2] = 1, 2
        for i in range(3, n + 1):
            # dp[i] = sum(dp[j] * dp[k])
            # j, k 为当前下标前的元素个数，当前下标后的元素个数
            for j in range(i):
                add_one = 1 if j == 0 else dp[j]
                add_two = 1 if j == i - 1 else dp[i - j - 1]
                dp[i] += add_one * add_two
        return dp[-1]