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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Would someone be able to explain why the Time Complexity here is O(b^d) instead of O(d(b^d))?

So I'm doing an AI course that is talking about time complexities of different tree search algorithms. On this slide it talks about the time complexity of the algorithm, and I'm confused as to why we ...
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Rigorous distinction between search and optimization

I'm working my way through parts of Russell and Norvig's AIMA book for a class, and there's something I've never quite managed to wrap my head around. Chapters 3 and 4 contrast 'search' methods with '...
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Efficient Implementation of join and split operations on semisplaying tree

Splaying trees are a heavily researched of theoretical computer science as they are conjectured to be optimal binary trees. They were first presented by Sleator & Tarjan in Self-Adjusting Binary ...
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Is there a hash-map implementation optimized to favor key lookups based on frequency (if key is referenced the most then it is searched first)?

I have started to play around with HTTP3 which relies on QUIC for transport. I have noticed that I very often have a finite number of Web Transport sessions stream data continuously along side burst-y ...
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2 votes
1 answer
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(Algorithm required) How to determine if a point is in one of many rectangles

What I want to achive ist the following: I have a 2D plane and on this plane I will have a potentially large amount of rectangles (these are specified with 2 coordinates spanning it) Whats the most ...
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2 votes
1 answer
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How did the following derivation of the final weight of a weight-balanced search tree node after rotation to make it balanced occur?

I was reading section 3.2 of Advanced Data Structures by Peter Brass (which is about weight-balanced search trees) for self-study. I got stuck on a proof about rebalancing properties. $\alpha$ and $\...
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what are good data structure algorithm for fast 3D coordinates search?

I want to form data structure for nearby neighbor search for 3D coordinates. What is the best way to do so?
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117 views

Height of AVL Tree

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 ...
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2D segment tree query time complexity

These sources cp-algorithms and geeksforgeeks state that query complexity (for example, submatrix sum) of 2-D segment tree is O(logN * logM), because it first descends the tree in the first ...
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Can Thompson sampling performs better than ucb1 in a Monte Carlo tree search

I made a Monte Carlo tree search (MCTS) algorithm for the travelling salesman problem inspired by this paper which uses UCB1. When I was digging to see where does the UCB1 formula comes from, I read ...
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Finding matches between an input string and a fixed set of strings

I need to compare an input string to multiple strings which I'll refer to as fixed strings, and you can assume the latter won't change. Comparison disregards letters with special characters, only ...
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Question about AVL properties

Assume that the oil company saves for each person that works in the company a record with its name, its salary, its age and its date of birth. You can assume that no two fields are identical for any ...
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More efficient way to parse array into binary search tree

Let's assume I have array which I need to parse into binary tree ...
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Rank operation in search tree, number of nodes between 2 values

What kind of search tree should I use in which I will have operation Rank[x, y] which will return number of existing nodes/values between x and y in time O(depth of tree) so the operations find, ...
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-1 votes
1 answer
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A very simple question about Admissible Heurisitcs

Given admissible heuristics f(s), g(s), h(s). It is true that max(f(s), g(s), h(s)) is still admissible.. but is it still admissible if its max(f(s), g(s) + h(s)). I believe it is not admissible but I ...
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Data structure for interval subset queries

I have a set $S$ of intervals. I'd like to store them in a data structure, so that I can handle the following query efficiently: given a query interval $q$, count the number of intervals $s \in S$ ...
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Search algorithm for multidimensional space with custom topology

First, let's start with the description of the problem in dimension 1: Let $T_0$ be a space with $n$ nodes organized in a tree structure, with $m$ of those nodes defined as target nodes. In this space,...
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Having trouble understanding Red-Black trees

Exam question: Draw the Red Black Tree that results from inserting the following values in the given order: [10, 20, 30, 4, 5, 50] Draw the red connections with a dotted line and the black ones with ...
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Simultaneous binary (n-ary) search

I have a balanced $k$-ary B-tree with $N$ leaves (where N is a power of $k$ for simplicity) and I need to simultaneously locate $\ell$ leaves in it. What is the expected number of nodes I will need to ...
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Trapezoidal Map and Search Tree

i am studying on trapezoidal maps. In the last section, "Analysis" of this paper, it says "The expected query time is indeed O(log n). Again the search structure size can be quadratic ...
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Greedy Best-First Search Performance for Tree and Graph Space

I am currently reviewing the GBFS algorithm and when looking at its completeness I am confused between the difference of it being not optimal in Tree Search for Finite and Infinite Spaces that it is ...
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Should i work with tree representation as an array of nodes and an array of edges

Here is the problem, i have a graphical component that displays a tree. It takes as input an array of nodes and array of edges(eg:an edge has a source and target). I will be performing complex tasks, ...
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1 vote
1 answer
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Does n^(1-1/d) always dominate log^d(n)

Hi I am currently learning about orthogonal range search and found two data structures with two different runtimes and wanted to proof that one always dominates the other. So I found out about k-d-...
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2 votes
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Data Structures for BST where size uniquely determines shape

There are several data structures in which the number of elements uniquely determines the shape. Examples would be binary heaps, arrays, lists, Braun trees, and Merkle mountain ranges. Are there any ...
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2 answers
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If we want to map abbreviations of full-English words (e.g. map "Jan" to "January"), how can we identify abbreviations which map to multiple words?

Short Version: How can we construct a trie which maps abbreviations of names-of-the-month to full-month (we map the abbreviation "mar" to "march")? The set of all abbreviations is ...
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1 answer
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Building Suffix Array from Suffix Tree. Inorder visit when node has more than two children

From the notes: It is not difficult to observe that the suffix array $\texttt{SA}$ of the text $\texttt{T}$ can be obtained from its suffix tree $\texttt{ST}$ by performing an in-order visit: each ...
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Parsing text, then searching it: one entry per position, vs. 1 JSON column per text

I have a Rails application using Postgresql. Texts get added to the application (ranging in size -- as short as a few words, to as long as, say, 5,000 words?). The text gets parsed, both ...
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1 vote
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222 views

Deletion in a Binary search Tree

The teacher explained to us this algorithm for deleting a node in a binary search tree, but I can't understand how it works when the node to be deleted has only one child (I already know how it works ...
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2 votes
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Why does a range query on a segment tree return at most $\lceil \log_2{N} \rceil$ nodes?

If an array $A[1 \ldots N]$ is represented using a segment tree having sets in each interval, why does a range query $[L\ldots R]$ returns at most $\lceil \log_2{N} \rceil$ sets (or disjoint intervals)...
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3 answers
154 views

Finding the number of children of the predecessor node of a given node in a Binary Search Tree(BST)

I have some propositions regarding BSTs , please can someone confirm whether they are true or false: Question : 1.Suppose we have a node $n_1$ with a value $val_1$ i.e $n_1(val_1)$ 2.We wish ...
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3 answers
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Finding the point with minimum x-ordinate, lying between two y-ordinates

Given a set of points $P=p_1,p_2,..p_n$ in $R^2$ in where $p_i=(x_i,y_i)$,finding the point with smallest x-ordinate having y-ordinates between $y_1$ and $y_2$, where $y_1$ and $y_2$ are given as ...
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1 answer
562 views

Average number of inspections

Consider a set of n elements whose key values are $$0, 1, ..., n−1.$$ Let $p(i) (0 ≤ i ≤ n−1) $ be the probability that the element with key i is searched. Assume the following distribution of $p(i)’s$...
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1 answer
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Constructing a data structure supporting prioritized key lookup

so this is more or less a shot in the dark as I am feeling stuck. Maybe some of you have an idea which helps. Here is the problem description (pseudo formal): I want to have a structure $T = \{ \hat{...
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2 votes
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Should a prefix tree (trie) node store only a single character or a string?

I've just implemented a Trie and I thought it would be a good idea to store strings in the Trie nodes in contrast to storing single characters. Storing strings is for sure more space-efficient and ...
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3 answers
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How to convert a Complete Binary Tree to a Priority Search Tree in O(n)?

I would like to know if there is a linear-time algorithm ($\mathcal{O(n)}$ time) to convert a Complete Binary Tree with data left-to-right increasing stored in external nodes, to a Priority Search ...
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2 votes
0 answers
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What's a minimum-window alpha beta search algorithm?

I was skimming the Deep Blue overview paper and on page 242 it says: "The search control does not really implement the regular αβ search algorithm. Rather it implements a minimum-window αβ search ...
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1 vote
1 answer
388 views

Efficiently finding the min-cost path of an AVL tree

It seems that in a full AVL tree, the left edge is always the minimum-cost path. For example, take the following full AVL tree: The min-cost path would be 8-6-5. ...
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Is the internal structure of a red-black-tree dependent on the insertion order?

Is the internal structure of a red-black tree (which nodes are red or black, the disposition of the branches, the location of each value...) dependent on the order in which the elements were inserted? ...
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3 votes
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107 views

Node depth in randomly built binary search tree

It can be proved that randomly built binary search trees of size $n$ are of depth $O(\log n)$ and it is clear that level $k$ has at most $2^{k}$ nodes (root's level is 0). I have an algorithm that ...
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What's the number of leaves in AVL tree

How can I prove that the number of leaves in a balanced BST is $\Omega (N)$ where $N$ is the number of nodes in the tree? I tried somehow to prove that an AVL/Fibonacci tree should have $\Omega (N)$ ...
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How to delete a node from BST tree with 2 chidren?

I googled, read several tutorials and watched several BST node deletion algorithm explanations before posting this question. For some reason, I cannot find a complete explanation of BST node deletion ...
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Scapegoat Trees: Why are they only loosely a-height-balanced?

From Wikipedia: Even a degenerate tree (linked list) satisfies this condition if α=1, whereas an α=0.5 would only match almost complete binary trees. A binary search tree that is α-weight-...
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2 votes
1 answer
280 views

Finding the shortest time to go from one stop to another stop in a train system with many train lines with connection stations

So I was thinking after discussing with my friend the other day, how would I use something like breadth-first or depth-first search to find the fastest time to go from one station to another station ...
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2 answers
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Range Query with conditions

Suppose I have an $N$ length integer array of pairs of the type $[value, key]$. Now, I need to query for range sum. Query is of the type : $l, N, x$ meaning I have to sum up all the $value$ in the ...
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3 votes
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Given a set of intervals $(I_n)_n$ contained in $[0, L]$, compute the longest interval in $[0, L]$ which has empty intersection with all $(I_n)_n$

Let be $(I_n)_n$ a set of $p$ intervals each contained in $[0, L]$ for $L \geq 1$. I define $(J_n = [a_n, b_n])_n$ the set of intervals which have empty intersection with $I_n$ for all $n \in [[1, p]]...
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How Segment trees are used to answer interval stabbing query?

Can anybody explain to me how segment trees are used to answer interval stabbing queries? I have searched and searched and only come with the beginning of the line. From my understanding I need to ...
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108 views

AVL Tree confusion

I have some confusion with regards to AVL trees and the heights of various subtrees. When initially reading the overview of the algorithms purpose(to keep the tree balanced) I thought it put limits ...
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1 vote
1 answer
267 views

What is the minimal degree $d$ required for a B tree with $44*10^6 $ keys so that it's height is less than or equal to $5$

What is the minimal degree $d$ required so a B - tree with $44*10^6$ keys will have a height $h$, such that $h\leq 5$ My attempt was to build the tallest tree possible with minimum degree $d$ and $n =...
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1 vote
1 answer
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Searching a hierarchy for progressive node criteria

In our organization we have various business units that organize their data in different ways. The folder structure can vary, but they abide by business unit practices when making backups etc. I am ...
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Breadth-first traversal: difference between generation and expansion

The question here is to find a path from A(rad) to B(ucharest). I'll be using the initials of the cities in the picture instead of their full names. Some ground-rules: we're traversing in ...
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