Questions tagged [search-trees]
Questions about search trees, a class of data structures used for storing sorted data for efficient access.
313
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Combining chunks on an infinite grid into regions
I am working on an floorplan application where I save elements on an infinite grid in a sparse manner. Specifically, I have the following Python class representing a sparse grid (basically a ...
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Expectimax Pruning
I found the following question in my book:
For probabilistic games like backgammon, where there is a resource
limit, the RB-Expectimax algorithm is used.
Assume that it is known that the heuristic ...
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Monte Carlo Tree Search for Robo Rally AI
I want to implement an AI capable of playing the game RoboRally (https://en.wikipedia.org/wiki/RoboRally) using Monte Carlo Tree Search (MCTS). In RoboRally, there are 2-8 characters controlled by (...
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Simplified Memory Bounded A*
I have been studying the SMA* algorithm and I am having trouble understanding the backup operation. Specifically, I don't understand why the f value of a child node should be the maximum of its own f ...
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Visualizing How of KD-tree Data Structure Splits Space
I am trying to understand how KD-tree works when we insert a node and how it splits the xy plane, please. Below $[5, 4]$ splits the xy-plane into left and right parts while $[2,6]$ splits it into top ...
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Performing fuzzy search queries on a large database of strings
I have a large database of strings (~10 million)
I need to perform fuzzy search queries which would find the best match inside that database.
The best match meaning the one that has the highest 'score'...
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Is there a faster alternative to Aho-Corasick when searching for any occurrence rather than all occurrences of each of the substrings?
Aho-Corasick can result in a quadratic number of matches because it finds all occurrences of each searched-for substring. What is a faster algorithm or modification to this one to simply determine if ...
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Finding Optimal Configuration of Formula without trying every Permutation
I have a math problem I need to solve so I can complete an optimisation in a computer program. My initial approach was just to brute force all the possible permutations but it got out of hand quite ...
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BSTs with repeating keys
The problem is to count number of unique binary search trees with keys $a_1,a_2,...,a_n$, given that some of the keys are not unique. For example, $a$ could be 2, 1, 1, 4, 3, 4.
We could try an ...
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Approximating the median of the complement of a set
Given an integer $n$ and a tree set $S$, I would like to find the approximate median $x$ of the integer set $T := \{i \in \mathbb N : i < n \wedge i \notin S\}$. There are no constraints to the ...
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Randomly generated binary search trees case comparison
Although not an assignment, just out of curiosity; I am trying to compare a two cases
A scenario where I pick a tree out of the set of possible binary search trees on the keys $1,2,\ldots,n$, with ...
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Confusion about B-Tree
In a B-Tree, one of the rules is:
Every node (except the root) is at least half full
But then, in a 4-way B-Tree, we have the following case. Suppose we want to insert $10,20,30,40$ to the tree.
After ...
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Representing graph as a search tree
How do I convert a graph to a search tree? Here's the question-
The problem is that I don't know how to represent interconnections in a graph on a tree. In the diagram A is connected to D, and same ...
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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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(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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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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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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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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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 $s \in S$ ...
D.W.♦
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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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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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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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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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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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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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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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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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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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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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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 $T = \{ \hat{...
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Should a prefix tree (trie) node store only a single character or a string?
I've just implemented a Trie and I thought it would be a good idea to store strings in the Trie nodes in contrast to storing single characters.
Storing strings is for sure more space-efficient and ...
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How to convert a Complete Binary Tree to a Priority Search Tree in O(n)?
I would like to know if there is a linear-time algorithm ($\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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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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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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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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