Is All Possible Full Binary Trees easy or hard?

All Possible Full Binary Trees is rated Medium on LeetCode but conceptually challenging if you are new to recursive tree generation. Understanding the odd-node constraint and applying memoization makes the solution manageable.

All Possible Full Binary Trees Python/Java solution

In Python or Java, implement a recursive function that returns all trees with n nodes and store results in a memoization map. For each odd split of nodes between left and right, combine every left subtree with every right subtree under a new root node.

How to solve All Possible Full Binary Trees in O(n)?

Generating all full binary trees cannot be done in strict O(n) time because the output size itself grows exponentially. Any correct solution must build every valid tree structure. The best practical approach uses memoized recursion or dynamic programming with complexity proportional to the number of generated trees.

What is the best approach for All Possible Full Binary Trees?

Recursive generation with memoization is the most common and interview-friendly approach. For each odd split of nodes between left and right subtrees, recursively build all combinations and cache results by node count. This avoids recomputation and efficiently constructs every valid tree.

Is All Possible Full Binary Trees asked at Google/Amazon/Meta?

Tree construction and recursion problems similar to this appear in interviews at companies like Google, Amazon, and Meta. While this exact problem may not always appear, the pattern of generating tree structures using recursion and memoization is a common interview topic.

What data structure is used in All Possible Full Binary Trees?

The problem uses the binary tree data structure combined with recursion and memoization or dynamic programming. A hash map or dictionary typically stores previously computed lists of trees keyed by the number of nodes.

What is the time complexity of All Possible Full Binary Trees?

The complexity depends on the number of full binary trees that can be formed. The algorithm generates every valid tree, which follows a Catalan-like growth pattern. The practical complexity is roughly O(n * F(n)), where F(n) is the number of full binary trees for n nodes.

Description Solution Video 13:18

894. All Possible Full Binary Trees

Medium82.8% acceptance5 companies

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.

A 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

Asked at 5 companies

Salesforce NVIDIA

Google Amazon Microsoft

Topics

13:18

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1# Definition for a binary tree node.
2# class TreeNode:
3#     def __init__(self, val=0, left=None, right=None):
4#         self.val = val
5#         self.left = left
6#         self.right = right
7class Solution:
8    def allPossibleFBT(self, n: int) -> List[Optional[TreeNode]]:
9        

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