Description

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

Return a list of all possible full binary trees with N nodes. Each element of the answer is the root node of one possible tree.

Each node of each tree in the answer must have node.val = 0.

You may return the final list of trees in any order.

Example 1:

Input: 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]]
Explanation:

[leetcode] 894. All Possible Full Binary Trees_二叉树

Note:

  • 1 <= N <= 20

分析

题目的意思是：给定一个值，输出所有满足条件的完全二叉树。这道题的思路根以前做过的输出所有二叉树类似，就是在遍历过程中，先选定根结点的位置，然后向左向右进行递归拓展，求出所有的左二叉树，然后求出所有的右二叉树，最后两两进行组合就能得到最终的二叉树的组合。终止条件是当前的N为0，如果N为1，说明就只需要构造一个结点返回就行了。其他的按照我刚才说的递归+循环就行了。

代码

# 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[TreeNode]:
        if(N%2==0):
            return []
        if(N==1):
            return [TreeNode(0)]
        res=[]
        for L in range(1,N,2):
            R=N-1-L
            
            l_list=self.allPossibleFBT(L)
            r_list=self.allPossibleFBT(R)
            for l_item in l_list:
                for r_item in r_list:
                    root=TreeNode(0)
                    root.left=l_item
                    root.right=r_item
                    res.append(root)
        return res

参考文献

​​[LeetCode] Simple to Understand | Python Recursion​​