Study Plan For Algorithms - Part48

1. 不同的二叉搜索树 II
给定一个整数 n ，请生成并返回所有由 n 个节点组成且节点值从 1 到 n 互不相同的不同 二叉搜索树 。

class Solution:
    def generateTrees(self, n: int) -> List[Optional[TreeNode]]:
        if n == 0:
            return []
        return self.generateTreesHelper(1, n)

    def generateTreesHelper(self, start, end):
        if start > end:
            return [None]
        all_trees = []
        for i in range(start, end + 1):
            left_trees = self.generateTreesHelper(start, i - 1)
            right_trees = self.generateTreesHelper(i + 1, end)
            for l in left_trees:
                for r in right_trees:
                    current_tree = TreeNode(i)
                    current_tree.left = l
                    current_tree.right = r
                    all_trees.append(current_tree)
        return all_trees        

2. 不同的二叉搜索树
给定一个整数 n ，求恰由 n 个节点组成且节点值从 1 到 n 互不相同的 二叉搜索树 有多少种？

class Solution:
    def numTrees(self, n: int) -> int:
        dp = [0] * (n + 1)
        dp[0] = 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]