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Questions tagged [trees]

Questions about a special kind of graphs, namely connected and cycle-free ones.

See also and .

890 questions
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BIT: What is the intuition behind a binary indexed tree and how was it thought about?

A binary indexed tree has very less or relatively no literature as compared to other data structures. The only place where it is taught is the topcoder tutorial. Although the tutorial is complete in all the explanations, I cannot understand the…
Nikunj Banka
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Longest path in an undirected tree with only one traversal

There is this standard algorithm for finding longest path in undirected trees using two depth-first searches: Start DFS from a random vertex $v$ and find the farthest vertex from it; say it is $v'$. Now start a DFS from $v'$ to find the vertex…
e_noether
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What is the difference between radix trees and Patricia tries?

I am learning about radix trees (aka compressed tries) and Patricia tries, but I am finding conflicting information on whether or not they are actually the same. A radix tree can be obtained from a normal (uncompressed) trie by merging nodes with…
w128
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Algorithm to find diameter of a tree using BFS/DFS. Why does it work?

This link provides an algorithm for finding the diameter of an undirected tree using BFS/DFS. Summarizing: Run BFS on any node s in the graph, remembering the node u discovered last. Run BFS from u remembering the node v discovered last. d(u,v) is…
curryage
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Is there a regular tree language in which the average height of a tree of size $n$ is neither $\Theta(n)$ nor $\Theta(\sqrt{n})$?

We define a regular tree language as in the book TATA: It is the set of trees accepted by a non-deterministic finite tree automaton (Chapter 1) or, equivalently, the set of trees generated by a regular tree grammar (Chapter 2). Both formalisms hold…
john_leo
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Is finding a weight-balanced tree NP-hard?

In the following, we consider binary trees where only the leaves have weights. Let $T$ be a binary tree and $W(T)$ be the sum of the weights of its leaves. Let $T.l$ and $T.r$ be the left child and right child respectively. We define the imbalance…
rex123
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Efficient compression of unlabeled trees

Consider unlabeled, rooted binary trees. We can compress such trees: whenever there are pointers to subtrees $T$ and $T'$ with $T = T'$ (interpreting $=$ as structural equality), we store (w.l.o.g.) $T$ and replace all pointers to $T'$ with pointers…
Raphael
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Why does the formula 2n + 1 find the child 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 indicies of the children of element at index n can be found with $leftchild = 2n + 1$ $rightchild = 2n + 2$ I can…
Keatinge
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Why hasn't functional programming researched dynamic trees?

Dynamic trees play an important role in solving problems such as network flows, dynamic graphs, combinatorial problems ("Dynamic Trees in Practice" by Tarjan and Werneck) and recently merging dictionaries ("A Simple Mergeable Dictionary" by Adam…
JC Saenz
18
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5 answers

What is the earliest use of "trees" in computer science?

I have a little history question, namely, as the title says, I am looking for early uses of trees (as a data structure, search tree, whatever) in computer science.
john_leo
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Can a tree be traversed without recursion, stack, or queue, and just a handful of pointers?

Half a decade ago I was sitting in a data structures class where the professor offered extra credit if anyone could traverse a tree without using recursion, a stack, queue, etc. (or any other similar data structures) and just a few pointers. I came…
NL - SE listen to your users
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On "The Average Height of Planted Plane Trees" by Knuth, de Bruijn and Rice (1972)

I am trying to derive the classic paper in the title only by elementary means (no generating functions, no complex analysis, no Fourier analysis) although with much less precision. In short, I "only" want to prove that the average height $h_n$ of a…
Christian Rinderknecht
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Is there a difference between perfect, full and complete tree?

Is there a difference between perfect, full and complete tree? Or are these the same words to describe the same situation?
Olórin
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Correctness-Proof of a greedy-algorithm for minimum vertex cover of a tree

There is a greedy algorithm for finding minimum vertex cover of a tree which uses DFS traversal. For each leaf of the tree, select its parent (i.e. its parent is in minimum vertex cover). For each internal node: if any of its children is not…
e_noether
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Huffman tree and maximum depth

Knowing the frequencies of each symbol, is it possible to determine the maximum height of the tree without applying the Huffman algorithm? Is there a formula that gives this tree height?
user7060
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