# Questions tagged [avl-trees]

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### Self-balancing BST supporting in-order-sequential multi-insertions / multi-deletions in logn+klogk time?

Given a self-balancing binary search tree of size $n$, I want to perform the following operations: InsertInOrderSequentialBatch an ordered sequence of $k$ values (...
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### AVL-tree insertion complexity proof

I tried to figure out the proof of insertion operation in AVL-tree is O(log n), but I do not know how. I also tried to find it somewhere on the Internet, but I could not find any good results. Do you ...
318 views

### is it possible to create an avl tree given any set of numbers?

I am studying balanced trees, especially AVL trees. My question is whether is it possible to create an avl tree given any set of numbers. is it possible to prove the following statement? Let $A$ be ...
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### Every AVL tree can be colored to be a red-black tree

I want to prove any AVL tree can be turnt into a red-black tree by coloring nodes appropriately. Let $h$ be the height of a subtree of an AVL tree. It is given that such a coloring is constrained by ...
324 views

### What exactly is the difference between a Balanced Binary Search Tree and an AVL tree?

I'm learning some Data Structures and I cannot figure out the difference between the Balanced BST and the AVL Tree. From my understanding, an AVL tree is a balanced tree with the height difference <...
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### proof non-empty AVL tree

The vertex of a binary tree is called an single child if it has a father's vertex but does not have a neighbor. The root is not considered an single child. let mark in numOnly a number of vertices ...
88 views

### What is the maximal difference between the depths of 2 leaves in AVL tree?

I'm wondering what's the answer of the following question: What is the maximal difference between the depths of 2 leaves in an AVL tree? Intuitively I think that it shouldn't exceed $log n$ but have ...
177 views

### Worst Case for AVL Tree Balancing after Deletion

After deleting a node in an AVL tree, self-balancing (zig-zag rotation or the left-right balancing) maintains O(logn) time that is not guaranteed in other unbalanced trees (like BST). The Balancing ...
178 views

### Augmenting AVL tree to calculate sum of subtree

Suggest a way to augment an AVL tree to support a $O(\log n)$ implementation of the function calculateSum(key), which receives a key of a node and returns the sum ...
14 views

### What is the insertion algorithm for an AVL tree with balance constraint of 2?

What would be the insertion algorithm for a modified AVL tree where the balance constraint is 2 instead of 1? Would be the same as a regular AVL tree?
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### Managing an hotel using AVL trees - Data Structures

I have a Data Structure question where I need to manage an hotel, each room has a number between $1-n$ and it can be occupied or not. Available Data structures: AVL* Trees, B-Trees, Arrays, Stacks, ...
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### Why multiple rotations might be needed after deletion in an AVL tree if after insertion there can be at most one needed?

I understand that after deletion you have to retrace to update ancestors and after insertion you do the similar however at most one rotation will be performed. The question is why is there the ...
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### is AVL tree is better than heap for sorting purpose?

for sorting n elements what is better to use AVL tree or heap data structure and why? Can someone explain in brief?
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### How to prove that in an AVL tree with height h, the depth of every leaf node is at least $\lceil h/2 \rceil$

I have an AVL tree with height h. I understand how to get h $\thickapprox$ 1.440 log N. However, I can't figure out how to calculate the minimum depth of a leaf node from root. I tried constructing a ...
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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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### Is the following a AVL tree? [closed]

I have a tree as Is it an AVL tree? it seems to balanced for me.
166 views

### 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 ...
975 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 ...
233 views

### 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 ...
341 views

### 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 ...
166 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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### 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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### 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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### 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 ...