# LeetCode 894. All Possible Full Binary Trees

## Description

https://leetcode.com/problems/all-possible-full-binary-trees/

Given an integer `n`, return a list of all possible full binary trees with `n` nodes. Each node of each tree in the answer must have `Node.val == 0`.

Each element of the answer is the root node of one possible tree. You may return the final list of trees in any order.

full binary tree is a binary tree where each node has exactly `0` or `2` children.

Example 1:

```Input: n = 7
Output: [[0,0,0,null,null,0,0,null,null,0,0],[0,0,0,null,null,0,0,0,0],[0,0,0,0,0,0,0],[0,0,0,0,0,null,null,null,null,0,0],[0,0,0,0,0,null,null,0,0]]
```

Example 2:

```Input: n = 3
Output: [[0,0,0]]
```

Constraints:

• `1 <= n <= 20`

## Explanation

For n ≥ 3, we can formulate the recursion: allPossibleFBT(N) = [All trees with left child from allPossibleFBT(x) and right child from allPossibleFBT(n − 1− x), for all x].

## Python Solution

``````# 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:
memo = {0: [], 1: [TreeNode(0)]}

def allPossibleFBT(self, n: int) -> List[Optional[TreeNode]]:
if n not in Solution.memo:
results = []

for x in range(n):
y = n - 1 - x

for left in self.allPossibleFBT(x):
for right in self.allPossibleFBT(y):
node = TreeNode(0)
node.left = left
node.right = right
results.append(node)

Solution.memo[n] = results

return Solution.memo[n]

``````
• Time Complexity: O(2^N).
• Space Complexity: O(2^N).