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As a result, disjoint-set forests are both asymptotically optimal and practically efficient. Disjoint-set data structures play a key role in Kruskal's algorithm for finding the minimum spanning tree of a graph. The importance of minimum spanning trees means that disjoint-set data structures support a wide variety of algorithms.
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.
When used to implement a set of stacks, the structure is called a spaghetti stack, cactus stack or saguaro stack (after the saguaro, a kind of cactus). [1] Parent pointer trees are also used as disjoint-set data structures. The structure can be regarded as a set of singly linked lists that share part of their structure, in particular, their ...
Once sorted, it is possible to loop through the edges in sorted order in constant time per edge. 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 ...
A graph with three components. In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets.
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.
In that sense it is dual to the union-find data structure, which also maintains a partition into disjoint sets but in which the operations merge pairs of sets. In some applications of partition refinement, such as lexicographic breadth-first search, the data structure maintains as well an ordering on the sets in the partition.
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikimedia Commons; Wikidata item; ... Disjoint-set data structure; Double hashing;