35
votes
Accepted
What is the difference between radix trees and Patricia tries?
I found this post very helpful.
To see the difference between Patricia tries and radix trees, it is important to understand:
The notion of radix, since Patricia tries are radix trees with radix ...
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32
votes
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Is there a difference between perfect, full and complete tree?
Yes, there is a difference between the three terms and the difference can be explained as:
Full Binary Tree: A Binary Tree is full if every node has 0 or 2 children. Following are examples of a full ...
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28
votes
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Can the pre-order traversal of two different trees be the same even though they are different?
Tree Examples (image):
...
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18
votes
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What are the applications of Rose trees?
You seem to have an overly "data structures and algorithms" mindset. Not every tree is some kind of search tree. Data structures are often designed to correspond to or capture aspects of a domain ...
17
votes
BIT: What is the intuition behind a binary indexed tree and how was it thought about?
I think that the original paper by Fenwick is much clearer.
The answer above by @templatetypedef requires some "very cool observations" about the indexing of a perfect binary tree, which are ...
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14
votes
Accepted
Do Kruskal's and Prim's algorithms yield the same minimum spanning tree?
Found this which states that if all the conditions I mentioned above are met, a graph necessarily has a unique MST. Therefore, in terms of my question, Kruskal's and Prim's algorithms necessarily ...
13
votes
Algorithm to find diameter of a tree using BFS/DFS. Why does it work?
The intuition behind is very easy to understand. Suppose I have to find longest path that exists between any two nodes in the given tree.
After drawing some diagrams we can observe that the longest ...
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13
votes
What is the earliest use of "trees" in computer science?
Wikipedia says that the first use of tree in mathematics was by Cayley in 1857.
Since the use in computer science is taken directly from mathematics, it seems more fundamental to ask when they ...
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12
votes
Accepted
Count total number of k length paths in a tree
This can be solved in $\mathcal{O}(n \log n)$ by using the smaller-to-larger merging technique. Root the tree at an arbitrary vertex. We will calculate for every subtree an array where the $d$th ...
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11
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What is the earliest use of "trees" in computer science?
According to Donald Knuth's TAOCP, Vol. 1, pg. 459 the following papers might be considered as one of the first appearances of trees in CS.
H. G. Kahrimanian, Analytical Differentiation by a Digital ...
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11
votes
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What is the difference between a R-tree and a BVH?
Note that we want to be able to retrieve, for any query range, the points that are inside, or sometimes the points that are closest to that query range. That's why a bounding-volume hierarchy is ...
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10
votes
Accepted
Binary rooted tree isomorphism
There is a classical linear time algorithm for rooted tree isomorphism due to Aho, Hopcroft and Ullman. The algorithm actually uses a simple isomorphism invariant. See for example lecture notes of ...
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10
votes
Accepted
What algorithm should I use to find a minimal tree that include certain nodes within a graph?
This is the famous Steiner tree problem in graphs, which is known as NP-hard.
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9
votes
Accepted
Why is the running time for BFS $O(b^{d+1})$?
This represents a difference between the kinds of problems the CS algorithms community usually uses BFS to solve, vs the kinds of problems the CS artificial intelligence community usually uses BFS to ...
D.W.♦
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9
votes
Why does the formula 2n + 1 find the child node in a binary heap?
I would like to propose my revisited version of Hiroki's answer.
Currently it's been sitting in peer-review (https://cs.stackexchange.com/review/suggested-edits/66932) for a while, so it's not being ...
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Time Complexity to find height of a BST
Your algorithm runs in linear time on all inputs. The algorithm visits each node of the tree exactly once, and does $O(1)$ work per node. Therefore it runs in time $\Theta(n)$, where $n$ is the number ...
- 275k
9
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Can the pre-order traversal of two different trees be the same even though they are different?
Counting argument
The number of unlabeled binary trees of $n$ nodes is the $n^\text{th}$ Catalan number $C_n=(2n)!/(n!(n+1)!).$ For example there are 5 binary trees of 3 nodes,
...
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8
votes
Accepted
What is the chance that this code terminates?
This is an example of a branching process. The behavior of a branching process depends on the expected number of children, which in your case is $1.25 > 1$. When this number is at most 1, the ...
- 275k
8
votes
Accepted
Time complexity of Depth First Search
The book is counting the number of times each line is executed throughout the entire execution of a call of DFS, rather than the number of times it is executed in each call of the subroutine DFS-VISIT....
- 275k
8
votes
Why is the running time for BFS $O(b^{d+1})$?
The bounds $O(|V|+|E|)$ and $O(b^d)$ are talking about different things. The former is appropriate when you know what $V$ and $E$ are in advance, and they're both finite. The latter is ...
- 81.4k
8
votes
Can the pre-order traversal of two different trees be the same even though they are different?
Lets assume you consider trees of $n$ nodes. Now take any binary tree with $n$ nodes and name the nodes according to their pre-order numbering. Then clearly the pre-order sequence of the tree will be $...
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7
votes
Algorithm to find diameter of a tree using BFS/DFS. Why does it work?
Update 3 and corrected answer
There's an error in the linked solution set (see update 2 below), but it can be easily corrected with @Yuval Filmus's suggestion in the question's comment, which further ...
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7
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What is the earliest use of "trees" in computer science?
Isaiah: ""And there shall come forth a rod out of the stem of Jesse, and a Branch shall grow out of his roots"
The tree as a data model for genealogical information is very ancient indeed.
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votes
Have I invented a new data structure?
I've never seen this data structure before. However, it doesn't seem like a good choice for storing a set of words, for most purposes. I see three significant disadvantages:
Performance. Looking up ...
D.W.♦
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7
votes
Accepted
Building segment tree without adding extra elements to its size
A segment tree is not required to be full (which is what I believe you mean), however it will always be complete. That is, every level, except possibly the last, is filled.
Take a look at the ...
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How to select a binary tree node uniformly at random
The algorithm works just fine.
Note that each node's size field tells you the total number of nodes in the subtree rooted at that node. Throughout this answer, I'm ...
- 81.4k
7
votes
Why does the formula 2n + 1 find the child node in a binary heap?
Let us consider first the case in which node indices are 1-based (start at 1). The nodes in a heap are arranged so that node $1x_1x_2\ldots x_\ell$ (given in binary) is reached by starting at the root ...
- 275k
7
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What is the point of traversing a binary tree in preoder, inorder or postorder?
Different traversals of a binary tree exist to suffice different data dependencies between the nodes.
Let's have a comparison between different traversals of a tree. Note that aside from in-fix ...
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7
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Can the same node appear twice in a tree?
A tree is defined to be a set of nodes, with a parent-child relationship that satisfies certain properties. Thus, it doesn't make sense to ask whether a node can "appear" twice.
In your code snippet,...
D.W.♦
- 156k
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