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Unique Binary Search Trees II

Problem Statement​

Given an integer n, return all the structurally unique BST's (binary search trees), which has exactly n nodes of unique values from 1 to n. Return the answer in any order.

Leetcode Link

Example 1:​

ex1

Input: n = 3
Output: [[1,null,2,null,3],[1,null,3,2],[2,1,3],[3,1,null,null,2],[3,2,null,1]]

Example 2:​

Input: n = 1
Output: [[1]]

Constraints:​

  • 1 <= n <= 8

Code​

Python Code
class Solution:
    def generateTrees(self, n: int) -> List[Optional[TreeNode]]:
        @lru_cache(None)
        def dfs(left, right):
            if left > right: return [None]
            if left == right: return [TreeNode(left)]
            ans = []
            for root in range(left, right+1):
                leftNodes = dfs(left, root - 1)
                rightNodes = dfs(root+1, right)
                for leftNode in leftNodes:
                    for rightNode in rightNodes:
                        rootNode = TreeNode(root, leftNode, rightNode)
                        ans.append(rootNode)
            return ans

        return dfs(1, n)