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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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 ...
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2answers
651 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 ...
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22 views
Is the following “get tree next key” algorithm correct? [closed]
I want to create a non-recursive algorithm for finding in a binary search tree the smallest entry larger than a given key. The tree cannot contain duplicates. There are parent pointers for every node.
...
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0answers
43 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 ...
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3answers
550 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
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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 ...
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1answer
44 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 ...
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21 views
How does a binary tree waste memory when stored as nodes and references?
I'm researching binary trees and came across this section describing storage methods.
It states that:
In a language with records and references, binary trees are typically constructed by having a ...
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0answers
93 views
How many maximum height AVL trees given height?
I am having some trouble finding a recursive formula for finding the number of maximum height AVL trees of height h. Height 0 has 1, height 1 has 2, height 2 has 4, height 3 has 8, etc. is that ...
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0answers
13 views
Best asymptotic randomized multidimensional index?
What data structure has the best asymptotic running time for nearest-neighbor search on multidimensional data? I am interested in both preprocessing time and query time, but let's restrict attention ...
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2answers
83 views
How do I know which direction I should rotate a node in an AVL Tree?
I'm studying AVL Trees in my programming class and we got this exercise dealing with right, left, left-right and right-left rotations as a way to check if we understand the theoretical concept of AVL ...
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1answer
36 views
Search on Conformant Problem: solution for subset of a belief state
I am having trouble understanding the following statement.
I have understood why in a sensorless/conformant problem, if there exists a solution (a sequence of actions) for a belief state $b$, then it ...
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36 views
Calculating maximum number of splits that can occur during insertion of $n$ keys in B Tree of order $m$
I can calculate this by trying out manually inserting $n$ keys in $m$ order B Tree as follows:
Assume median to be selected for split be left biased. That is $m/2$. For example, if $m=4$, then a ...
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2answers
64 views
Efficient way to find matching date ranges?
We have a set of problems involving date ranges - a pair of dates representing a start date and an end date. In some places, we have say 1000 of these and need to find the ones that overlap a separate ...
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0answers
35 views
Efficient data structure for multidimensional searching on intervals and keys
I am searching for a data structure that can capture a database, which is consisted of one column of intervals (like [0, 2], [4, 6]) and one/two columns of keys (...
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1answer
45 views
Data Structures - Segment Trees
I was learning about segment trees and came across this:
We have an array arr[0 . . . n-1]. We should be able to
1 Find the sum of elements from index l to r where 0 <= l <= r <= n-1
...
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0answers
20 views
B/B+ trees without leftmost pointers
In both B-trees and B+trees, a node (a.k.a page) contains K keys and K+1 pointers:
node = [ ptr_1, key_1, ... , ptr_K , key_K , ptr_(K+1) ]
Now suppose that I ...
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1answer
1k views
How many rotations after AVL insertion and deletion
Is it true that inserting an element to an AVL tree requires $O(1)$ rotations?
How many rotations, does deletion from AVL require?
I've searched for these two questions with no luck so far.
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1answer
50 views
Searching and inserting in $O(n)$ when $n$ is the size of the key
Edit: The solution to my problem is called a trie ; according to Section 8.1 of Peter Brass book "Advanced Data Structures", for a given alphabet $A$ and a word $w$ of length $n$ on this alphabet, a ...
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1answer
282 views
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2answers
994 views
Time Complexity to find height of a BST
Below is a question I was asked in an Interview
What is the best case time complexity to find the height of a Binary Search Tree?
I answered it explaining using the below algorithm
$\mathrm{...
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0answers
27 views
Example of binary trees with maximum rotation distance
In the 1988 paper Rotation Distance, Triangulations, and Hyperbolic Geometry, Sleator, Tarjan and Thurston show that for any pair of $n$-node binary trees, the maximum rotation distance between them ...
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0answers
141 views
Analysis expected depth of a binary search tree given random values?
I have a guess about the problem above. Suppose I have a binary search tree $T$ initially empty. Suppose I drawn $x_1,\ldots,x_k$ (from some real interval $[a,b]$) keys and I want to insert the keys ...
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52 views
How many roots are there in an undirected root
Given an undirected tree with 7 nodes how many roots would this tree have. My intuition tells me that because the tree is undirected it would either be 7 or 0. How would I solve this?
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0answers
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Search tree with associative union and worst case insert/delete better than O(n)? [duplicate]
Is there a search tree where union is associative, so $a \cup (b \cup c) = (a \cup b) \cup c$ gives a tree with the same structure?
A complete binary tree would be such a tree, but for example a red-...
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121 views
Find optimal path in BFS and DFS
In UCS it is clear that we find the cheapest cost path. In BFS and DFS we can get the order of output nodes. But How can we find the optimal path in BFS ans DFS in following cases?
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57 views
Generation vs expansion BFS
I can not understand the difference between generation and expansion of nodes. How the time and space complexity of BFS are different in each two scenarios?
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0answers
15 views
Segment-tree construction: do we recurse into both children?
This question is about segment-tree as described in this Wikipedia article.
When constructing the tree (inserting the new input-interval), if the input-interval doesn't contain the node-interval we ...
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1answer
614 views
Optimal data structure for sorted list
Most of the resources on the web I have encountered say that "sorted arrays and other sorted data structures are implemented with binary search trees (BSTs)".
Even though B-trees are a generalization ...
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1answer
102 views
Can ropes (AVL trees) be interned?
Can AVL trees be interned for fast equality comparison? Is there work on interning data-structures or can you show that this cannot be done in better than $O(n)$ time?
I recently implemented a rope ...
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2answers
279 views
Infix search in millions of strings
Let's say we have millions of strings (each of them < 100 characters):
alpha
allo
blah
hello world
orlando
...
I know how a binary search tree or a trie can ...
0
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1answer
161 views
All possible Red Black Trees with this set {1,2,3,4,5}
I have to write all possible Red Black Trees which can represent these 5 numbers {1,2,3,4,5}.
Now we have 120 ways to write 1,2,3,4,5
...
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1answer
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how does rotation works in AVL trees and what is a good way to understand it?
If we consider this tree with T1 and T2 as subtrees, and we want to rotate on x (rotating the edge between T1 and x), what is the result? how does it work then? Does the x stay in its place and T1 ...
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1answer
456 views
How to calculate number of nodes opened by BFS?
In the below diagram, each node takes up a space of 2KB. I need to find the total memory consumed to reach the goal : I
I know that the equation for BFS is
b1 + b2 + ...... + (bd+1 - b)
Where b is ...
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1answer
35 views
data structure admitting top items with prefix
A trie can answer a query for all items with a certain prefix in $O(m + \log n)$ time, where $m$ is the number of matches and $n$ is the number of items. A trie also supports $O(\log n)$ insertion and ...
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171 views
Time complexity of inorder run on B+ tree (without leavesa link)
I quite sure that it should be $O(n)$, but I didn't found any information about it and I'm not sure how to prove it. Maybe in 2-3 tree the max number of node (include the leaves) is $2n$ and in each ...
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Time complexity proof of finding the $i$ object in binary search tree is $O(h+i)$ by inorder
I'm looking for time complexity proof of finding the $i$ object in binary search tree is $O(h+i)$ by inorder run. when $h$ is the height of the tree.
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27 views
Unusual function - operations on lists / sets - possible optimization
I have a problem.
Below I present a function in Python.
...
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245 views
Deletion of record from B+ tree
I was going through the B+ tree deletion operation from the book Database System Concepts, 6th Edition by Henry F. Korth. One particular thing caught my attention.
A B+ tree is given. We have to ...
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1answer
135 views
Avarage height of Red-Black tree [closed]
I wrote a program to discover how height of the tree is relative to the number of elements in the tree (nodes).
On first test I filled array with 10-50-100-200...-1000 elements of random numbers from ...
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1answer
1k views
How many node does the final B-tree have?
I'm currently studying the B-Trees chapter of Introduction to Algorithms. One of the question from the chapter is:
Suppose that we insert the keys $\{1,2,...,n\}$ into an empty B-tree with minimum ...
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0answers
117 views
Iterate over two different non-binary tree graph [closed]
I'm working to solve a problem based on two non-binary tree graphs, that they need to be iterated together in order to find a valid combination.
I did a basic implementation that works, but it have a ...
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1answer
108 views
Understanding B tree key deletion step from CLRS algorithm
CLRS explains B tree key deletion as follows:
If the key $k$ is in node $x$ and $x$ is a leaf, delete the key $k$ from $x$.
If the key $k$ is in node $x$ and $x$ is an internal node, do the ...
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1answer
116 views
How to validate a connect X game (Tick-Tak-Toe,Gomoku,…)?
Currently I am working on a Gomoku AI (or generally Connect-X games).
Implementing the search tree was no problem, but then I got to the point where I had to implement the value function and was ...
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1answer
262 views
return a key of a node with maximum value within a range of keys in B+ tree
I've been asked a question about B+ Tree.
The question is: Suppose we have object of the following type:
...
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1answer
76 views
How to delete element from B*-tree?
Every article on web (and books I have checked) gives detailed explanation on insertion operation in B*-trees but most of them don't even mention deletion (or if they do they just state that it's ...
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Comparison of Depth First Search Trees
Does anyone know of an algorithm who is able to return how similar a DFS Tree is from another DFS Tree? (Or any kind of tree in general)
I'm not looking for a true or false. Instead, I would like it ...
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30 views
AVL Tree Inner Nodes
If k is the height of an AVL Tree, the minimal number of inner nodes is:
N(k) = N(k-1) + N(k-2) +1.
Why is this formula true?
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1answer
264 views
What do we benefit from using ternary search trees rather than binary search trees?
Ternary search trees are very common in the text editing area. They could be used to implement Auto complete feature, spell checking, Partial-Match searching, Near-Neighbor Searching & many many ...
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0answers
337 views
Tight upper bound on height of a red-black tree
"Introduction to Algorithms" by Cormen et al., 3rd edition, Lemma 13.1 states that
A red-black tree with $n$ internal nodes has height at most $2\log(n+1)$,
i.e. $h \le 2\log(n+1)$.
Can equality ...
