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Questions tagged [search-trees]

Questions about search trees, a class of data structures used for storing sorted data for efficient access.

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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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Not all Red-Black trees are balanced?

Intuitively, "balanced trees" should be trees where left and right sub-trees at each node must have "approximately the same" number of nodes. Of course, when we talk about red-black trees*(see definition at the end) being balanced, we actually mean…
Aryabhata
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Why does the splay tree rotation algorithm take into account both the parent and grandparent node?

I don't quite understand why the rotation in the splay tree data structure is taking into account not only the parent of the rating node, but also the grandparent (zig-zag and zig-zig operation). Why would the following not work: As we insert, for…
Bober02
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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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Lock-free, constant update-time concurrent tree data-structures?

I've been reading a bit of the literature lately, and have found some rather interesting data-structures. I have researched various different methods of getting update times down to $\mathcal{O}(1)$ worst-case update time [1-7]. Recently I begun…
A T
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Creating a Self Ordering Binary Tree

I have an assignment where I need to make use a binary search tree and alter it to self order itself such that items that are accessed the most (have a higher priority) are at the top of the tree, the root being the most accessed node. The professor…
OghmaOsiris
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Colour a binary tree to be a red-black tree

A common interview question is to give an algorithm to determine if a given binary tree is height balanced (AVL tree definition). I was wondering if we can do something similar with Red-Black trees. Given an arbitrary uncoloured binary tree (with…
Aryabhata
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Memoization without array

In Cormen et al.'s Introduction to algorithms, section 15.3 Elements of dynamic programming explains memoization as follow: A memoized recursive algorithm maintains an entry in a table for the solution to each subproblem. Each table entry initially…
Pece
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Number of possible search paths when searching in BST

I have the following question, but don't have answer for this. I would appreciate if my method is correct : Q. When searching for the key value 60 in a binary search tree, nodes containing the key values 10, 20, 40, 50, 70, 80, 90 are traversed, not…
avi
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Proof that a randomly built binary search tree has logarithmic height

How do you prove that the expected height of a randomly built binary search tree with $n$ nodes is $O(\log n)$? There is a proof in CLRS Introduction to Algorithms (chapter 12.4), but I don't understand it.
user1675999
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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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Time Complexity proof for Segment Tree implementation of the ranged sum problem

I understand that segment trees can be used to find the sum of sub array of $A$. And that this can done in $\mathcal{O}(\log n)$ time according to the tutorial here. However I'm not able to prove that the querying time is indeed $\mathcal{O}(\log…
Arijit Choudhury
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What data structure would efficiently store integer ranges?

I need to keep a collection on integers in the range 0 to 65535 so that I can quickly do the following: Insert a new integer Insert a range of contiguous integers Remove an integer Remove all integers below an integer Test if an integer is…
WilliamKF
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Hashing using search trees instead of lists

I am struggling with hashing and binary search tree material. And I read that instead of using lists for storing entries with the same hash values, it is also possible to use binary search trees. And I try to understand what the worst-case and…
forrestGump
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