Questions tagged [avl-trees]

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AVL tree balance property states for the two subtrees of a node, their height can differ at most one. Why can't it be zero?

I was thinking that if they were equal, say they are required to be zero this would be enforce the balance property more effectively. Can anyone explain why 1 is a satisfactory rather than just them ...
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1answer
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Is the following a AVL tree? [closed]

I have a tree as Is it an AVL tree? it seems to balanced for me.
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Finding rank of newly inserted node in AVL tree augmented with rank of node

My prof was talking about how to augment a tree to efficiently find the key with a given rank. On the way to getting the right answer (store the size of the subtree rooted at each node), he proposed ...
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1answer
50 views

AVL Tree - Print ascending using in-order

Trying to understand how to write proof of correctness. Searched over the internet on how to write proof of correctness but can't find a good solution for it. The following sorting algorithm is ...
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0answers
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Optimizing AVL Tree operations for sequential data

I'm working on an implementation of a data structure that needs a tree-like data structure for accelerating look-ups. The interesting part about this data structure is that the only operations on the ...
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0answers
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How to create an AVL tree, given it's pre-order traversal?

Given the pre-order traversal, we can easily obtain the necessary Binary Search Tree(BST- not necessarily balanced). However, the problem arises when we have to decide the balancing manually(this was ...
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1answer
37 views

Is it possible to balance a already constructed un-balanced AVL tree, with no prior information of last insert?

Im learning about tree data structures, and had a question that i couldnt find answer to so I came here. Usually when we balance a tree, we insert keys and keep checking balance factor, as soon as it ...
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1answer
254 views

AVL tree worst case height proof

The worst case height of AVL tree is $1.44 \log n$. How do we prove that? I read somewhere about Fibonacci quicks but did not understand it.
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1answer
31 views

avl trees rotations question

As you can see in this tree its unbalanced at the root with a balanced factor of $-2$. You can also perform a Right left rotation or a Right Right rotation. Which do you have to pick in this case?
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How many maximum height AVL trees given height?

I am having some trouble finding a recursive formula for finding the number of maximum height AVL trees of height h. Height 0 has 1, height 1 has 2, height 2 has 4, height 3 has 8, etc. is that ...
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2answers
111 views

How do I know which direction I should rotate a node in an AVL Tree?

I'm studying AVL Trees in my programming class and we got this exercise dealing with right, left, left-right and right-left rotations as a way to check if we understand the theoretical concept of AVL ...
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1answer
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AVL Rotations Abbreviations

I read that there are 4 types of rotations: Left rotation Right rotation Left-Right rotation Right-Left rotation What are the corresponding abbreviations: RL,LR,RR,LL? Is there a reference how to ...
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1answer
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AVL trees are not weight-balanced?

In a previous question there was a definition of weight balanced trees and a question regarding red-black trees. This question is to ask the same question, but for AVL trees. The question is, ...