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).

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