Which statement about an AVL tree is correct?

Question

BlackTom AI · Accepted Answer

To begin evaluating the statements about an AVL tree, recall that an AVL tree is a self-balancing binary search tree (BST) that maintains a strict balance condition.
Option 1: 'It is a BST where the heights of the left and right subtrees of any node differ by at most 1.' This matches the formal definition of an AVL tree: for every node, the height difference (balance factor) between its left and right subtrees is at most 1, ensuring logarithmic height and efficient operations.
Option 2: 'It is any balanced tree.' This is too vague. Not every balanced tree is an AVL tree, because AVL imposes a specific balance constraint at every node, whereas other balanced trees (like red-black trees) use different balancing criteria.
Option 3: 'It is a BST where every node has at most one child.' This describes a degenerate or skewed tree, not an AVL tree. AVL trees require node degrees that allow two children in many nodes to satisfy the balance conditions, not a limit to at most one child.
Option 4: 'It is a complete binary tree with heap property.' This combines two concepts (completeness and heap property) that are not part of the AVL definition. AVL trees focus on node balance, not completeness or heap ordering, so this is inaccurate for describing AVL trees.

Which statement about an AVL tree is correct?

查看解析

登录即可查看完整答案

类似问题

AVL_V_6 Binary Search Tree shown below is an AVL Tree.

AVL_BLRT_6 Refer to the AVL Tree shown in image below. Given that the node with the value 60 has just been inserted, after identifying which node becomes unbalanced first, describe the necessary rotation(s) to restore the tree's balance.

AVL_IDOff_16 Refer to the AVL Tree shown in image below. Considering that the node with the value 40 has been just inserted, After inserting the node with the value 40 , which node first becomes unbalanced?

AVL_BF_7 Refer to the AVL Tree shown in image below. Balance factor for Node 6 is ____.

AVL_BLRT_11 Refer to the AVL Tree shown in image below. Given that the node with the value 21 has just been inserted, after identifying which node becomes unbalanced first, describe the necessary rotation(s) to restore the tree's balance.

AVL_IDOff_6 Refer to the AVL Tree shown in image below. Considering that the node with the value 60 has been just inserted, After inserting the node with the value 60, which node first becomes unbalanced?

AVL_V_5 The following is a valid AVL Tree.

AVL_BF_4 Refer to the AVL Tree shown in image below. Balance factor of 25 is ___.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单