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# Runtime: 73 ms (Top 74.11%) | Memory: 15.7 MB (Top 42.55%)
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# Definition for a binary tree node.
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# class TreeNode:
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# def __init__(self, val=0, left=None, right=None):
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# self.val = val
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# self.left = left
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# self.right = right
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class Solution:
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    def generateTrees(self, n: int) -> List[Optional[TreeNode]]:
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        # define a sorted list of the numbers, for each num in that list , leftvalues
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        # are left tree and right val are rightree, then for each number create a tree
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        # assign the left and right to that root and append the root to the ans
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        nums = list(range(1, n + 1))
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        def dfs(nums):
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            if not nums:
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                return [None]
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            ans = []
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            for i in range(len(nums)):
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                leftTrees = dfs(nums[:i])
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                rightTrees = dfs(nums[i + 1 :])
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                for l in leftTrees:
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                    for r in rightTrees:
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                        root = TreeNode(nums[i])
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                        root.left = l
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                        root.right = r
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                        ans.append(root)
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            return ans
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        return dfs(nums)