This document discusses the set abstract data type (ADT). It defines a set as a collection of elements drawn from a single universe with no duplicates and no ordering. The document outlines common set operations and provides examples of using sets to represent collections like articles or students. It then describes two common implementations of sets - using a bit vector for a finite set of elements, or linked lists for more flexible sets. Code snippets are provided for common set operations like insertion, deletion, union and intersection under both implementations.

1. SET ADT
Jun Y. Ercia

2. The Set ADT
Learning Outcomes
At the end of this lesson, students should be able to
• discuss set processing
• define a set abstract data type
• compare set implementations
• demonstrate how a set can be used to solve problems
• write codes for various set implementations

3. The Set ADT
 a collection of elements.
Properties
1. Elements are drawn from a single universe
2. Each element is either a member of the set or not.
3. Elements may be a set in itself or a primitive
4. No duplicate elements
5. No particular ordering of elements
Examples
o Set of first 5 natural numbers: {1,2,3,4,5}
o {x | x is a positive integer and x < 100}
o {x | x is a driver with > 10 years of driving experience and 0 accidents in the last 3 years}

4. Operations on a Set

5. Examples
1. Sets: Articles in Yahoo Science (A), Technology (B), and Sports (C)
o Find all articles on Wright brothers.
o Find all articles dealing with sports medicine
2. Sets: Students in CS10 (A), CS20 (B), and CS40 (C)
o Find all students enrolled in these courses
o Find students registered for CS10 only
o Find students registered for both CS10 and CS20

6. Uses of Sets in Computing
• Many applications deal with sets
1. Compilers have symbol tables (set of keywords, classes, etc.)
2. Dictionary is a set of words.
3. Routers have sets of forwarding rules.
4. Web servers have set of clients, etc

7. Implementation of Set ADT
1. Bit-Vector implementation of set
▪ The set is represented by a bit-vector (i.e., an array containing 0’s and 1’s or, equivalently,
true or false) in which the ith bit (cell) is true if i is a member of the set.
▪ Suitable for applications in which the set to be represented is a subset of a small finite
universal set.
0 1 2 3 4 5 6 7 8 9 10

8. Code for inserting new element into a set

9. Code for deleting an element from a set

10. Code for determining whether the set is empty

11. Code for determining whether the element is a
member of a set

12. Code for making the set empty

13. Code for union of two sets

14. Code for intersection of two sets

15. Code for difference of two sets

16. Implementation of Queue ADT
▪ Linked List implementation of Set [SLL]
▪ The entire set is represented by a linked list of nodes.
▪ Suitable for applications in which the set to be
represented does not necessarily have to be a subset of
some finite universal set.

17. Code for inserting new element into a set

18. Code for deleting an element from a set

19. Code for determining whether the set is empty

20. Code for determining whether the element is a
member of a set

21. Code for making the set empty

22. Code for union of two sets

23. Code for intersection of two sets

24. Code for difference of two sets

25. Set Implementation Issue
• Are the elements of the set belongs to a universal set or a subset of some universal set?