Questions tagged [search-trees]
Questions about search trees, a class of data structures used for storing sorted data for efficient access.
294
questions
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16 views
When do insertions and deletions get enacted in a buffer tree?
Buffer trees are $(a, b)$-trees in which each node in the tree gets an associated buffer for storing operations to be conducted on elements in the tree. While I appreciate the idea of amortizing the I/...
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35 views
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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0answers
28 views
Some nodes in binary search had broken.how we can fix it in-place by swapping nodes?
Given a binary search tree(can have any height) .Some nodes its value
changed and violate bst property how we can recover binary search
tree property in-place by just swapping a node with its ...
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0answers
44 views
Find largest $k$ numbers in Max Heap in $O(n\log k)$
I have a data stream with $n$ numbers and I want to find the largest $k$ of them ($k \ll n$). I want to use a priority queue with max heap of size $k$, so I will have space complexity $O(k)$, which is ...
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0answers
26 views
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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71 views
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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0answers
34 views
Creating Priority Search Tree bottom up from a Complete Binary Search tree in O(n)
I have a Complete Binary Search Tree of points ordered(sorted) on the y-axis (such that the point with the mid y of all the points is the root and its left children have decreasing y from the root and ...
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0answers
18 views
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 ...
1
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1answer
32 views
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, ...
1
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1answer
13 views
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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22 views
Data structure for a queue of weighted elements
Consider a queue of elements with weights $w_0, w_1 \ldots, w_{n-1}$. The queue supports two operations:
Inserting one element at the back of the queue
Reducing the weight of one element in the ...
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0answers
24 views
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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2answers
93 views
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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1answer
36 views
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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0answers
12 views
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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0answers
8 views
Minimal t needed in B tree for the lowest reading time
I've got an assignment, which I was asked to calculate the minimal t needed in a B tree, to have the optimal searching time.
So here it is:
We've been told that in a specific B tree, with unknown t, ...
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2answers
84 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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1answer
33 views
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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1answer
29 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 ...
0
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3answers
53 views
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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1answer
127 views
Average number of inspections
Consider a set of n elements whose key values are $$0, 1, ..., nā1.$$ Let $p(i) (0 ā¤ i ā¤ nā1) $ be the probability that the element with key i is searched. Assume the following distribution of $p(i)ās$...
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1answer
25 views
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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17 views
Why do b*trees partition 2 nodes into 3?
I'm writing a b*tree library in Rust. I'm thinking it might be better to make the purposeful decision to only implement half of the b* optimizations. (And not because it is easier, although it is.)
...
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0answers
124 views
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 ...
2
votes
0answers
28 views
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 Ī±Ī² search algorithm. Rather it implements a minimum-window Ī±Ī² search ...
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1answer
152 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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0answers
131 views
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? ...
3
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0answers
58 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 ...
3
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0answers
312 views
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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1answer
612 views
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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0answers
52 views
Scapegoat Trees: Why are they only loosely a-height-balanced?
From Wikipedia:
Even a degenerate tree (linked list) satisfies this condition if Ī±=1,
whereas an Ī±=0.5 would only match almost complete binary trees.
A binary search tree that is Ī±-weight-...
2
votes
1answer
96 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 ...
0
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2answers
56 views
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 ...
3
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1answer
39 views
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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186 views
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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0answers
73 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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1answer
120 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 =...
1
vote
1answer
28 views
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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0answers
39 views
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 ...
1
vote
1answer
497 views
UCT (Upper Confidence bounds applied to Trees)
For UCT (Upper Confidence bounds applied to Trees), why If given infinite time and memory, UCT theoretically converges to Minimax. ?
Besides, I do not quite understand how UCT deals with the flaw of ...
4
votes
1answer
78 views
Nodes in a binary search tree that span a range
I have a binary search tree of height $h$ with an integer in each leaf. I also have a range $[\ell,u]$. I want to find a set of nodes that span the range $[\ell,u]$, i.e., a set $S$ of nodes such ...
2
votes
1answer
187 views
How to merge a lot of trees into one single graph?
I have a few different trees, which resemble what the AST that compilers often deal with.
For example:
tree 1
( (a, b), (c, d) )
Imagine that each tree split represents the function "add", then ...
11
votes
4answers
5k views
Can the pre-order traversal of two different trees be the same even though they are different?
This question pretty much explains that they can, but does not show any examples of there being two different trees with the same pre-order traversal.
It is also mentioned that the in-order ...
1
vote
1answer
223 views
Space complexity of breadth-first search
I read that breadth-first search has to store (at most) $1+b+b^2+Ā·Ā·Ā·+b^d$
nodes in memory ---more than depth-first search---, where $d$ is the depth of a solution, and $b$ is the branching factor.
...
1
vote
1answer
36 views
R-tree insertion procedure when leaf is full
I am implementing an R-tree with the quadratic splitting method.
However in most articles I have read there a piece of information that is missing or misleading (or the most probably case, I ...
4
votes
2answers
1k views
How to find sum of maximum K elements in range in array
Recently, I came up to the following problem:
Given array $A$ of size $n$ and integer $k$, We should answer $Q$ questions of the type:
for given range $[l, r]$ we should find sum of the $k$ maximum ...
2
votes
0answers
123 views
Red-black tree trinode restructuring after insertion and deletion
When performing an insertion/deletion on a red-black tree, how can be argued or proved that it requires at most one/two trinode restructuring(s) respectively?
My thoughts so far were: after inserting ...
8
votes
3answers
779 views
How to count in linear time worst-case?
This question and this question got me thinking a little bit. For sorting an array of length $n$ with $k$ unique elements in $O(n + k \log k)$, we need to be able to store counts of values in the ...
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0answers
75 views
Probabilistic switching between breath-first and depth-first
I am reading Artificial Intelligence: Making Machines "Think" by Neill Graham. He gives an overview of graph search using either the breadth-first (BF) or depth-first (DF) search algorithms, and ...
1
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1answer
215 views
Two Minimax AIs playing against each other
I am trying to have my Minimax AI chess players play against each other.
I was a bit confused about an implementation detail.
Let's call black my first minimax AI ...
