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Questions tagged [balanced-search-trees]

140 questions
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4 answers

Why are Red-Black trees so popular?

It seems that everywhere I look, data structures are being implemented using red-black trees (std::set in C++, SortedDictionary in C#, etc.) Having just covered (a,b), red-black & AVL trees in my algorithms class, here's what I got out (also from…
Jakub Arnold
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Imagine a red-black tree. Is there always a sequence of insertions and deletions that creates it?

Let's assume the following definition of a red-black tree: It is a binary search tree. Each node is colored either red or black. The root is black. Two nodes connected by an edge cannot be red at the same time. Here should be a good definition of a…
alisianoi
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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, given the definition of $\mu$-balanced trees as in the…
Aryabhata
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Why is b-tree search O(log n)?

B-tree is a data structure, which looks like this: If I want to look for some specific value in this structure, I need to go through several elements in root to find the right child-node. The I need to go through several elements in the child-node…
Eenoku
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Don't understand one step for AVL tree height log n proof

I came across a proof that an AVL tree has $O(\log n)$ height and there's one step which I do not understand. Let $N_h$ represent the minimum number of nodes that can form an AVL tree of height $h$. Since we're looking for the minimum number of…
user2635911
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Split in AVL tree with complexity $O(\log n)$

Can the split operation be implemented for AVL trees with complexity $O(\log n)$? I'm interested in links to articles or any specific information about this subject. The split operation divides the AVL tree into two derived AVL trees, based on key.…
Denis Galeev
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A median of an AVL. How to take advantage of the AVL?

Here is the source of my question. Given a self-balancing tree (AVL), code a method that returns the median. (Median: the numerical value separating the higher half of a data sample from the lower half. Example: if the series is 2, 7, 4, 9, 1,…
Maksim Dmitriev
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How many rotations after AVL insertion and deletion

Is it true that inserting an element to an AVL tree requires $O(1)$ rotations? How many rotations, does deletion from AVL require? I've searched for these two questions with no luck so far.
chendoy
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Are degree and order the same thing when referring to a B-Tree?

I know the term order of a B-tree. Recently I heard a new term: B tree with minimum degree of 2. We know that the degree is related to a node but what is the degree of a tree? Does degree impose any kind of a restriction on the height of a B-tree?
Debabratta Jena
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Why most purely functional red-black trees are left-leaning?

Is there any particular reason for picking a left-leaning red-black tree over a regular red-black tree when trying to do a purely functional implementation? I've not researched very deeply into this subject matter but I see that Okasaki's…
Ruan
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Voronoi diagram. Status structure in Fortune's Algorithm

I'm trying to implement the Fortune's Algorithm, however I can't quite figure out how the status structure should be implemented. The following is extrapolated from my Computational Geometry book. The beach line is represented by a balanced binary…
user8469759
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Red-Black tree height from CLRS

The lemma 13.1 of CLRS proves that the height of a red black tree with $n$ nodes is $$h(n) \leq 2\log_2(n+1)$$ There's a subtle step I don't understand. The property 4 reported at the beginning of the chapter states: If a node is red, then both its…
user8469759
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Why is this not a valid Red-Black tree?

I'm having some difficulty understanding the rules for valid red-black tree. If my understanding is correct there are 4 rules that a tree has to follow to be a red-black tree. Every node has a color either red or black. Root of tree is always…
Confused_CS_Student
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Compute height of AVL tree as efficiently as possible

Given an AVL tree, I want to compute its height as efficiently as possible. $\newcommand{\bf}{\text{bf}}\newcommand{\height}{\text{height}}$ Each node of an AVL tree stores its balance factor ($\bf$), defined as $$\bf(v)=\height(v.\text{left}) -…
user40545
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Average depth of a Binary Search Tree and AVL Tree

My professor recently mentioned that the average depth of the nodes in a binary search tree will be $O(log(n))$ where $n$ is the amount of nodes in the tree. I ended up drawing out a bunch of binary search trees and I don't think I am understanding…
Nickknack
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