Questions tagged [trees]
Questions about a special kind of graphs, namely connected and cycle-free ones.
707
questions
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Proving that a preorder traversal of a rooted tree can be performed in linear time
Definition:
Let $T(V, E)$ be a rooted tree with root $r$.
If $T$ has no other vertices, then the root by itself constitutes the preorder traversal of $T$.
If $\lvert V \rvert > 1$, let $T_1, T_2, \...
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0answers
15 views
Better version of heavy-light decomposition: always draw path to largest subtree
Can someone tell me if this works? It seems to be easier to implement and also creates slightly less paths (though still O(log N) ).
The problem: given any tree of size N, find a way to split it into ...
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22 views
What are R trees? How it works?
I have just read about some data structure which are used rarely, one of them is R trees.
I searched a little about it and found that it is used for spatial search. The Wikipedia page says that it can ...
1
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0answers
16 views
Equally optimal nodes during minimax with alpha-beta pruning
Alpha-beta pruning is an optimization for minimax that reduces the number of nodes visited without changing the final result. However, both minimax and alpha-beta only return the optimal node value (...
0
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1answer
37 views
AVL-tree insertion complexity proof
I tried to figure out the proof of insertion operation in AVL-tree is O(log n), but I do not know how.
I also tried to find it somewhere on the Internet, but I could not find any good results. Do you ...
1
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1answer
37 views
Relation between mathematical functions and trees?
I try to express datastructures in a form of mathematical functions. For example an array or a dictionary is just a function to me.
Is there a good way to model a tree in terms of functions?
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2answers
31 views
Efficiently enumerating all “good” strings given the ability to say whether a partial specification can be good
Suppose that I want to enumerate all English language words of length 5.
If I've got nothing more than a check of whether an arbitrary string is an English word, I have to do 5^26 calculations.
...
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1answer
32 views
MCTS how to prevent Selecting a TERMINAL state in TRAVERSAL Phase?
Hello I am currently working on an implementation of MCTS and I ran into the problem that my tree traversal policy selects nodes with terminal game states. Furthermore how do I prevent selecting a ...
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18 views
How to find diffrenet ways to implement merge and delete_min operation in binomial heap?
I have searched on the internet to find different ways to learn binomial heap operations. What I have found is not quite helpful for me.For example, for delete min operation the algorithm says:
...
0
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1answer
40 views
2-3 tree: Sum of leaves in a given range
I am implementing a 2-3 tree, where every leaf has a unique key and a value, and I need to write an algorithm which finds the sum of values of the leaves which ...
1
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1answer
48 views
What is the Number of epochs with no improvement after which training will be stopped.?
I am trying to make a Convolutional neural network. Training the images of different brands of Logos. Have 100 images per class and there are 40 classes. I have trained the model now want to check ...
0
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1answer
36 views
How does CNN deal with rotation invariant pictures?
I am trying to make a CNN model . Training the image . Want to know that When we apply kernel on image and take out the features of images. That features are rotation invariant or we have to apply ...
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2answers
64 views
How to make efficient path minimum queries in a tree?
Given a tree in which each node has a given value, I want to process "Path Minimum Queries": given two nodes, what is the minimal value of any node on the shortest path between them?
My ...
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1answer
26 views
minimum number of edges that should be added to an undirected graph to make it a tree
Basically, it's this rosalind problem.
You're given a number of nodes and an adjacency list.
My initial guess was that the answer was the number of connected components minus 1, since by joining every ...
0
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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 ...
0
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1answer
45 views
Two definitions of Safe Edge
I ran into an interview two days ago and came across one strange definition of safe edge.
We are given an undirected weighted Graph $G = (V,E)$ with all distinct edge weights. Assume that the graph is ...
6
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1answer
174 views
Finding n farthest leaves in a tree
Given a tree $T$, I want to find a subset $N$ of $n$ leaves that are farthest apart. I.e., I want to find $N$ that maximizes function:
$$f(N)=\sum\limits_{x_1,x_2 \in N, x_1 \neq x_2}{dist(x_1,x_2)}$$
...
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1answer
47 views
Finding largest disjoint subtrees spanning nodes
I have a taxonomy (tree) of product categories. To each leaf product category, I have assigned a shop department where the products of a given category can be found.
Now for each department, I would ...
1
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1answer
56 views
facts on tree and MST
We are given an Undirected, Weighted and Connected Graph $G$, (non-negative weights, all distinct) with one property that shortest path between any two vertexes on this graph is on MST.
The following ...
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1answer
20 views
How to (Efficiently) Sort a List of Items with Parent/Child Relationship
I have a list of items that have a parent/child/grandchild/etc. type of relationship. Each item has a list of descendants, and an _.isDescendentOf(other) member ...
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2answers
40 views
How to index a tree to allow efficient search for paths?
By "indexing" I mean assigning addresses or labels or whatever to nodes to make them easier to locate, similar (in its effect, not necessarily in the implementation) to how a database can be ...
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1answer
28 views
Height of a 2-3-4 tree
Consider the following 2-3-4 tree.
Does this have a height of 3 or 2 ?
If I count from the external nodes ie. the ones with the square boxes then height should be 3.
Not sure if they are to be ...
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1answer
37 views
How to prove that insert complexity in binary search tree is minimum O(log n)?
Is it connected to BST search O(log n) or height log n?
How to prove that insert will give give you correct BST in minimum O(log n) time?
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0answers
30 views
efficient DELETE in proto-Van Emde Boas Tree?
TLDR: CLRS is claiming that a certain "pseudo" or "proto" tree structure does not have fast deletion, but I seem to have an algorithm that is efficient, and I would like to know ...
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0answers
27 views
Given two 2-3 trees I would like to merge them in $O(n_1+n_2)$
Given two 2-3 trees I would like to merge them in $O(n_1+n_2)$
I've solved before that if I get an ordered list then I can turn it into 2-3 tree in $O(n)$.
My questions is how can I turn two trees ...
2
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1answer
97 views
Number of nodes at given depth in binary tree
Show that there is no comparison sort whose running time is linear for at least half of the $n!$ inputs of length $n$. What about a fraction of $1/n$ of the inputs of length $n$? What about a fraction ...
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0answers
36 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
43 views
For every node of a tree, find the nearest ancestor node such that val[node] is coprime to val[ancestor]
Problem Statement : Given a tree with N nodes rooted at node 1. Each node is associated with a value. Determine the closest ancestor that contains the value coprime to the current node value. (Note ...
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1answer
34 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, ...
2
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1answer
158 views
Bellman Ford facts and specific question
The Bellman-Ford algorithm checks all edges in each step, and if for each edge the following:
$d(v)>d(u)+w(u,v)$
holds, then $d(v)$ will be updated. $w(u,v)$ is the weight of edge $(u, v)$ and $d(u)...
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1answer
50 views
MST and some facts via an example
$M$ is an MST of the Weighted Graph - $GR$.
Let $A$ be a vertex of $GR$ then $M-${$A$} is also MST of $GR-${$A$}.
Let $A$ be a leaf of $M$ then $M-${$A$} is also MST of $GR-${$A$}.
If $e$ is a edge ...
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27 views
data structure Q with priotry queue which allow us to find the median in $O(1)$ and the data structure need to support the following operations
I've got this question from an exercise and i'm not sure if it is possible to do so
Think of new data structure Q with priotry queue which allow us to find the median in $O(1)$ and the data structure ...
0
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1answer
141 views
Analysis of updating vertex and one example?
I see the following image on google:
And I want to find Amortized Cost for Updating of each vertex on Dijkstra algorithm. I have an answer $O(E/V)$. I'm get stuck it means at this answer we should ...
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0answers
13 views
Fast but simple fully persistent trie
I need fast (not worse than about log of the sum of maximum number of nodes and the maximum number of subnodes per node) and fully persistent trie.
I need an easy (quick to code) implementation.
The ...
0
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0answers
22 views
Trying to convert algorithm from recursive to iterative
I have this algorithm to sum binary tree branches from leftmost branch to rightmost one, so the solution is an array of sums:
...
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0answers
45 views
Prove that $T(n)=\omega(n)$?
Edit: can someone provide clear answer with all details
Given:
$T(n)=T(n/10)+T(an)+n$ while $a$ is a const and $T(n)=1:(n<10)$
I was asked to find the minimum value for $a$ for which $T(n)=\omega(n)...
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0answers
26 views
Finding differences and similarities between tree graphs
Are there any known techniques for "diffing" trees, such as phylogenetic trees?
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1answer
45 views
How do you find the height of the recurrence tree $T(n,k)=T(\frac{n}{2},k)+T(n,\frac{k}{4})+nk$
I try to find tree height such that first i define:
$H(n,k)=H(\frac{n}{2},k)+H(n,\frac{k}{4})+1$
then find height of left branch of tree=logn & right branch of tree=logk,but now why height of tree ...
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0answers
9 views
tool to insert nodes in a tree with queries
I have a tree where each node has a type. Multiple nodes can have the same type.
I want to insert new nodes in this tree at some specific positions specified by queries,
such as :
...
4
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1answer
48 views
BVH construction without sorting
Common algorithms for creating bounding-volume-hierarchies (BVH) rely on grouping primitives together that are not necessarily adjacent in memory. This is either done by rearranging the primitives ...
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28 views
sum selected nodes of a set in $\log n$ time
Given a sum operation of a dynamic set $S$ of length $n$ which includes integer pairs $(x, y)$. The sum operation is defined as taking two inputs $a$ and $b$ such that $a \leq b$. The sum operation ...
4
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2answers
77 views
Can Edge Belong to a cycle if it is part of multiple BFS products
Given a simple connected undirected graph. with V vertices and E edges.
Let e be some edge from E.
If I perform |V| different BFS runs - meaning started each time from a different vertex - and in ...
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0answers
29 views
LOUDS Succinct Tree Representation
I am trying to make my Trie tree structure as compact as possible. While searching about this I came across to "Level order Unary Degree Sequence " i.e. LOUDS representations using bit ...
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2answers
28 views
Is the heap in “Data Structures Algorithms in Java” by Goodrich, Tamassia, and Goldwasser missing sentinel leaves?
In the book, Data Structures Algorithms in Java Sixth Edition by Goodrich, Tamassia, and Goldwasser on page 339, there is an
"Example of a heap storing 13 entries with integer keys. The last ...
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1answer
67 views
What does it mean that B-tree leaves carry no information?
According to Wikipedia B-tree page, Knuth's definition fifth property is "All leaves appear in the same level and carry no information.".
What does it mean that they carry no information?
...
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14 views
How do you prove that this tree path calculation function works, from first principles mathematically?
I recently got an amazing answer to an SO question about how to calculate the path in a tree to an item, where you give it the corresponding array index, and the ...
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0answers
62 views
Are some algorithms inherently recursive?
Are some algorithms inherently recursive?
As in, rewriting it in tail-recursive/iterative form with a stack is still needed, and there is no way to do it otherwise.
I am asking because I struggled to ...
3
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1answer
117 views
How to detect “tree-able” set-families?
A set-family (a set of sets of elements) is called tree-able if the elements can be arranged on a directed tree such that each element appears in exactly one node, and each set in the family ...
1
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1answer
384 views
Why does the formula floor((i-1)/2) find the parent node in a binary heap?
I learned that when you have a binary heap represented as a vector / list / array with indicies [0, 1, 2, 3, 4, 5, 6, 7, 8, ...] the index of the parent of element at index i can be found with
parent ...
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1answer
31 views
