Up-Trees
(Review) A Set of Elements
(Review) Equivalence Relation
(Review) Another Equivalence Relation
The FIND Operation
FIND -- an Example
The UNION Operation
Time Complexity
Up-Tree Example
FIND using Up-Trees
UNION using Up-Trees
Time Complexity using Basic Up-Trees
Improving on the Basic Implementation
Enhanced UNION
Enhanced UNION (Cont)
Enhanced FIND
Path Compression
Worst-Case Analysis of Running Time for UNION-FIND using Path-Compressed Up-Trees
Ackermann’s Function
Inverse Ackermann’s Function
Theorem
Applying the UNION-FIND ADT to Constructing Minimum Spanning Trees for Graphs
Example Graph + Minimum Spanning Tree
Kruskal’s Algorithm
Email: tanimoto@cs.washington.edu
Home Page: http://www.cs.washington.edu/people/faculty/tanimoto.html
Download presentation source