Search results
Results from the WOW.Com Content Network
This updating is an important part of the disjoint-set forest's amortized performance guarantee. There are several algorithms for Find that achieve the asymptotically optimal time complexity. One family of algorithms, known as path compression, makes every node between the query node and the root point to the root. Path compression can be ...
The pseudocode below determines the lowest common ancestor of each pair in P, given the root r of a tree in which the children of node n are in the set n.children. For this offline algorithm, the set P must be specified in advance. It uses the MakeSet, Find, and Union functions of a disjoint-set data structure.
Next, use a disjoint-set data structure, with a set of vertices for each component, to keep track of which vertices are in which components. Creating this structure, with a separate set for each vertex, takes V operations and O(V) time. The final iteration through all edges performs two find operations and possibly one union operation per edge.
The implementation listed as Implementation of Disjoint-set Forests in C++, by Bo Tian seems not to update the path (it dont do path compression) which is the hole point. — Preceding unsigned comment added by 85.164.124.173 ( talk ) 17:57, 20 July 2011 (UTC) [ reply ]
Two disjoint sets. In set theory in mathematics and formal logic, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. [1] For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two ...
An efficient implementation using a disjoint-set data structure can perform each union and find operation on two sets in nearly constant amortized time (specifically, (()) time; () < for any plausible value of ), so the running time of this algorithm is essentially proportional to the number of walls available to the maze.
The proof of Lemma 2 only considers "Makeset" and "Union", but not "Find"; and indeed path compression will cause a violation of the claim. This raises (again) the following question: — Preceding unsigned comment added by Martin Ziegler (talk • contribs) 09:33, 4 April 2018 (UTC) []
In mathematics, the disjoint union (or discriminated union) of the sets A and B is the set formed from the elements of A and B labelled (indexed) with the name of the set from which they come. So, an element belonging to both A and B appears twice in the disjoint union, with two different labels.