Questions tagged [avl-trees]

Question 1

Assume I have a binary search tree, and I managed to prove that its height is upper bounded by $1.44 \log(n)$. Now, can I say with confidence that it is, for sure, an AVL tree? or is this condition ...

Question 2

I have a question: given that an AVL tree holds numbers 1, 2, 3, ..., 1000, what are the smallest and largest possible values of the root? I have a feeling it is 500 and 501, but I don't know how to ...

Question 3

I need to find a way to split an AVL tree based on the amount of nodes in the tree, lets assume you get a number $k$ and if the number of nodes in the tree is multiplication of $k$ you need to find ...

Question 4

I found an algorithm for determining if a binary tree is height-balanced. It Gets the height of left and right subtrees using dfs traversal. Return true if the difference between heights is not more ...

Question 5

If you were to define an altered AVL tree where the balance factor (the difference between the height of the left and right subtree) of a node must be less than or equal to the depth of the node (in ...

Question 6

Problem: we have a sequence of numeric values, e.g. [102, 25, 77, 17, 2, 13]. We need to implement 3 operations, each can be at most logarithmic time complexity. <...

Question 7

How many ways can we insert elements { 1, 2, 3, .... 7 } to make an AVL tree so that it does not have any rotation? I broke it down into 2 cases: Case 1: height of tree = 2, (a complete binary tree) ...

Question 8

Looking at the tree on the left it seems that the triangles represent leaves of the avl tree. To arrive at the balancing of -2 besides the node y the right subtree must have 2 nodes while the left ...

Question 9

I'm required to describe an implementation of a data structure that holds key,value pairs, which can be signed integers. We need to be able to init() in O(1), insert(x) in O(logn), delete(x) in O(logn)...

Question 10

AVL trees are height balanced binary search trees. As a consequence of this balance, the height of an AVL tree is logaritmic in its number of nodes. Then, searching and updating AVL-trees can be ...

Question 11

On the Wikipedia page for AVL trees, the time/space complexity for common operations is stated both for average case (in Big Theta) and worst case (in Big O) scenarios. I understand both Big O and Big ...

Question 12

According to Wikipedia: An augmented tree can be built from a simple ordered tree, for example a binary search tree or self-balancing binary search tree, ordered by the 'low' values of the intervals. ...

Question 13

I found an AVL tree implementation on the internet and experimented: For a tree with node count of 2^20, the minimal and maximal tree heights are 16 and 24. While these heights are lg(n)-ish, I am ...

Question 14

What size is the largest AVL tree for which an insertion could trigger a double rotation?

Question 15

One advantage claimed for scapegoat trees over other balanced trees like AVL or red-black(RB trees - just mentioning AVL henceforth) is not needing to store additional balance information. But can't ...

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Questions tagged [avl-trees]

Binary search tree with height of max 1.44 * log(n) is AVL tree or it's not an iff

Possible values of root of AVL tree

Sub-Grouping AVL tree based on nodes amount in O(log(n))

Time Complexity: Determining if a binary tree is balanced

AVL tree with balance factor equal to depth

Ordered sequence with logarithmic insert and remove

Number of ways to insert elements into an AVL tree such that there are no rotations

What does h indicate in this diagram of avl trees?

Find a key in a BBST for which sum of values of keys smaller then it - is maximal

logarithmic height AVL trees

Big O vs. Big Theta for AVL tree operations

Interval Tree by Augmenting an AVL Tree

Height of AVL Tree

AVL Tree rotations

Are AVL&RB Trees without additional storage for balance information in each node feasible?

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