96. Unique Binary Search Trees

Given an integer n, return the number of structurally unique BST’s (binary search trees) which has exactly n nodes of unique values from 1 to n.

动态规划。找动态规划方程，我们知道当加入第 i 个节点时，他的位置只能为：(左上) -> i -> （左下）。那么这道题目就很简单了，左上和右下的数目都是已知的。

class Solution:
    def numTrees(self, n: int) -> int:
        dp = [0 for _ in range(n + 1)]
        dp[0] = 1
        dp[1] = 1
        if n > 1:
            dp[2] = 2
        for i in range(3, n + 1):
            for j in range(i):
                dp[i] += dp[i - 1 - j] * dp[j]
        
        return dp[n]