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# Class Note for EECS 560 with Professor Huan at KU

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COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
4
WORDS
KARMA
25 ?

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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Kansas taught by a professor in Fall. Since its upload, it has received 21 views.

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Date Created: 02/06/15
Key de nitions A binary relation R for a set S is a set of SxS or RE SxS 1 For example SN natural numbers R is a divisor of3 is a divisor of 6 3R6 2 lt for real numbers R 3 is less than 6 3lt6 A relation is o re exive if aRa for all a e S o Symmetric if aRb ltgt bRa o Transitive if aRb and bRc gt aRc Re exive Symmetric Transitive Is a divisor of Yes No Yes lt No No Yes S Yes No Yes Assume all the undergraduate students have only one advisor sharing the same advisor is a binary relation de ned on the set of students Sharing the same advisor Re exive Yes Symmetric Yes Transitive Yes We call a re exive symmetric and transitive relation an equivalence relation If we have an equivalence relation we could partition the set into a group of subsets such that Sl U S2U SnS Si 0 Sj Si ifij for all ij 6 Ln and Q otherwise for example Susan gt Dr Wang Mike gt Dr Smith Tome gt Dr Singh John gt Dr Smith Susan Disjoint set is a data structure for equivalence relation between two operations 1 find returns a unique ID such that ndX ndy if and only if X and y belong to the same class 2 Union merges two classes For the time being lets assume that the elements are called 0123k k D N Design options Hash table or look up table 0 l 2 3 4 5 Find 0 1 Union On Tree representation merge 6 gives merge Gives Find operation returns the root of the tree find 1 0 2 3 4 5 6 ONJkJkt nt Ot n union 03 01 union 13 Nothing

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