Questions tagged [balanced-search-trees]

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Every AVL tree may be red black tree

I proved by induction that every AVL tree may be colored such that it will be red black tree. The problem is that I can't see an error in my proof. Look at my proof. Induction for height. Let's ...
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2answers
1k views

AVL tree such that each insert causes rotation (single or double)

Could you give me an example of an AVL tree for which inserting an element at an arbitrary (i.e. every) position causes a rotation (double or single)? I have tried to come up with an example, but I ...
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3answers
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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 ($\bf$),...
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1answer
7k views

How the deletion takes place in B+ Tree

My professor was giving a lecture on B+ Trees deletion, and I got very confused. According to him for deleting any key from a B+ Tree: ...
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2answers
2k views

non-binary self balancing tree

I'm looking for a tree data structure that allows to keep the tree balanced in high (minimum high as possible). I mean, suppose a tree where: each node has a parameter k that is the maximum number ...
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1answer
579 views

Example of height-balanced tree that is not weight-balanced

Following this question : Two definitions of balanced binary trees I am having a hard time making sense of the proofs provided and I'm looking for an example of a simple binary tree that is height-...
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1answer
2k views

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 ...
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2answers
3k views

Balance factor changes after local rotations in AVL tree

I try to understand balance factors change after local rotations in AVL trees. Given the rotate_left operation: ...
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1answer
1k views

Red-Black Tree deletion algorithm (CLRS, 3rd edition) : Deleting the root

I have been following the third edition of Introduction to Algorithms (by Cormen, Rivest, et al.), and have been studying the deletion algorithm for red-black trees. However, I am confounded at the ...
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1answer
135 views

State of the art time complexity for getting (tree) descendants by type/attribute

Let's say I have a tree comprised of nodes where each node is of some type (T), where there is a known/fixed number of types (i.e. similar to attributes in an xml document), and where a node can only ...
3
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1answer
510 views

Root Color of a Black Red Tree

It is required that, in a black red tree, the color for the root is always black. However, wikipedia argues that this rule can be omitted as a red root can always be changed to black but not vice ...
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1answer
133 views

Why not use large $k$ in a $k$-ary tree?

Obviously binary trees are great because of $O(\log_2 n)$ search, inserts, and deletes in best case. To "maximize" occurrence of best case, we can use self-balancing trees like red-black trees, AVLs, ...
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3answers
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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 ...
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2answers
3k views

Can a Red Black tree be constructed of only black nodes using RB insert only?

I am trying to construct a red black tree out of only black nodes. I know it is possible getting it after some deletions but I am trying to construct one only via insertion orders. Is it possible? I ...
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3answers
4k views

Memory usage of a BST or hash table?

I would like to use a data structure allowing fast access, either a balanced binary search tree (BST) for $O(\log n)$ access time or an open hash table for constant access time. 1) What is the exact ...
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1answer
999 views

Bounds on the number of rotations in the insertion operation of a Red Black Tree

I am having some trouble understanding why people say that contrary to what happens with AVL trees, there is a bound on the number of rotations occurring in an insertion with a Red Black Tree. From ...
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0answers
17 views

Saving a pointer to the n/4 node in AVL tree [duplicate]

I have an AVL Tree which every node has a filed with a key which is an integer. I need to save a pointer to the Minimum , Maximum and the $\left \lfloor \frac{n}{4} \right \rfloor $ nodes. the first ...
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1answer
1k views

Traversals from the root in AVL trees and Red Black Trees

We all know that for insertion() operation in AVL tree following can happen: We traverse down the tree from root to appropriate node and there insert the key and then for maintaining height balance ...
5
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1answer
543 views

Why aren't tries generally used?

To store say integers (positive), we prefer to use red black BSTs. I have never seen a explicit use of a trie anywhere to store numbers. I believe we can convert numbers to string and store them in ...
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2answers
550 views

Finding median weights in all paths of an AVL tree with weighted nodes

I need some help with proving the complexity of the following problem (I'm new here, so please excuse my "newbie-ness") Given: an AVL tree with keys: $1,2,..,n$, such that each node $i$ in the tree ...
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0answers
182 views

Augment B+ Tree to support given search query

Given a B+ tree with M=3. We assume that the tree is static and it is not necessary to update the B+ tree. Also we know that all key-value pairs are stored in the leaves of the B+ tree. Internal nodes ...
6
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4answers
411 views

Order-preserving update of a sublist of a list of mutable objects in sublinear time

Description Say I have a source list like: ["a","b","c","d"] and want to run a capitalization filter so if I change, "b" to <...
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2answers
5k views

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 ...
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4answers
16k views

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 ...
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2answers
8k views

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 ...
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1answer
1k views

Given a Red-Black Tree of n keys, is there a way to quickly determine if a red-node exists?

My best attempt at a specific case of the problem where $n =$ 256: For a specific case that a RB tree has 256 nodes, we can use the RB tree theorem to deduce that the height of the tree $h \leq 2*lg(...
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2answers
390 views

Balancing a Binary Search Tree

I was reading about binary search trees on it's Wikipedia article. I was a little confused by this image. Why is it that the right branch to the head node does not have a sub-tree? I understand why it ...
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4answers
5k views

Don't understand one step for AVL tree height log n proof

I came across a proof that the an AVL tree has O(log n) height and there's one step which I do not understand. Let $N_h$ represent minimum number of nodes that can form an AVL tree of height h. Since ...
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1answer
5k views

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, ...

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