894. All Possible Full Binary Trees

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# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def allPossibleFBT(self, n: int) -> List[Optional[TreeNode]]:

        if n == 0:
            return []
        if n == 1:
            return [TreeNode()]
        if n == 2:
            return []

        res = []
        for i in range(1, n-1):
            left = self.allPossibleFBT(i)
            right = self.allPossibleFBT(n-i-1)

            if not left or not right:
                continue

            for l in left:
                for r in right:
                    node = TreeNode()
                    node.left = l
                    node.right = r
                    res.append(node)

        return res

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# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    @cache
    def allPossibleFBT(self, n: int) -> List[Optional[TreeNode]]:
        
        if n % 2 == 0: return []
        if n == 1: return [TreeNode(0)]
        res = []
        for i in range(1, n, 2):
            for left in self.allPossibleFBT(i):
                for right in self.allPossibleFBT(n - 1 - i):
                    root = TreeNode(0)
                    root.left = left
                    root.right = right
                    res.append(root)
        return res