Lecture 3 Set s

1. Lecture 3 Sets • Introduction to Collections • A set ADT (abstract data type): requirements, contract. • Implementations of sets: using member arrays, linked lists. • Sets in the Java class library. • Example

2. Introduction to Collections • Simply an object that groups multiple elements into a single unit. • Collections are used to store, retrieve, manipulate, and communicate aggregate data. • Typically, they represent data items that form a natural group, e.g. • a poker hand (a collection of cards), • a mail folder (a collection of letters), • a telephone directory (a mapping of names to phone numbers).

3. What Is a Collections Framework? • A unified architecture for representing and manipulating collections • Consists of • Interfaces • Implementations • Algorithms • polymorphic: that is, the same method can be used on many different implementations of the appropriate collection interface.

4. Benefits of the Java Collections Framework • Reduces programming effort • Increases program speed and quality • Allows interoperability among unrelated APIs • Reduces effort to learn and to use new APIs • Reduces effort to design new APIs • Fosters software reuse

5. Interfaces • The core collection interfaces encapsulate different types of collections, • These interfaces allow collections to be manipulated independently of the details of their representation. • Core collection interfaces are the foundation of the Java Collections Framework.

6. Observations • All the core collection interfaces are generic. • For example, this is the declaration of the Collection interface. public interface Collection<E>... • The <E> syntax tells you that the interface is generic. • When you declare a Collection instance you can and should specify the type of object contained in the collection. • Specifying the type allows the compiler to verify (at compile-time) that the type of object you put into the collection is correct, thus reducing errors at runtime

7. Set • A collection that cannot contain duplicate elements. • This interface models the mathematical set abstraction • used to represent Sets, • the cards comprising a poker hand • the courses making up a student's schedule • the processes running on a machine

8. Set applications • Spelling checker: • A spelling checker’s dictionary is a set of words. • The spelling checker highlights any words in the document that are not in the dictionary. • The spelling checker might allow the user to add words to the dictionary. • Relational database system: • A relation is essentially a set of tuples. • Each tuple is distinct. • The tuples are in no particular order.

9. Set ADT: requirements • Requirements: • It must be possible to make a set empty. • It must be possible to test whether a set is empty. • It must be possible to obtain the cardinality of a set. • It must be possible to perform a membership test. • It must be possible to add or remove a member of a set. • It must be possible to test whether two sets are equal. • It must be possible to test whether one set subsumes another. • It must be possible to compute the union, intersection, or difference of two sets. • It must be possible to traverse a set (to go to every element).

10. Set class Diagram We cannot complete this! Why?

11. Set ADT: contract/specification(1) The Set interface // Each Set object is a set whose members are objects. //////////// Accessors //////////// publicboolean isEmpty (); // Return true if and only if this set is empty. publicint size (); // Return the cardinality of this set. publicboolean contains (Object obj); // Return true if and only if obj is a member of this set.

12. Set ADT: contract (2) • Possible contract (continued): publicboolean equals (Set that); // Return true if and only if this set is equal to that. publicboolean containsAll (Set that); // Return true if and only if this set subsumes that.

13. Set ADT: contract (3) • Possible contract (continued): //////////// Transformers //////////// publicvoid clear (); // Make this set empty. publicvoid add (Object obj); // Add obj as a member of this set. publicvoid remove (Object obj); // Remove obj from this set. publicvoid addAll (Set that); // Make this set the union of itself and that.

14. Set ADT: contract (4) • Possible contract (continued): publicvoid removeAll (Set that); // Make this set the difference of itself and that. publicvoid retainAll (Set that); // Make this set the intersection of itself and that. //////////// Iterator //////////// public Iterator iterator(); // Return an iterator that will visit all members of this set, in no // particular order.

15. Summary of set implementations • The array representation is suitable only for small or static sets. • A static set is one in which members are never (or at least infrequently) added or removed. • The SLL(singly link list, covered in a few weeks time) representation is suitable only for small sets. • For general applications, we need a more efficient set representation: search tree or hash table (not considered in this module).

16. Sets in the Java class library • The java.util.Set interface is similar to the Set interface above. • The java.util.TreeSet class implements the java.util.Set interface, representing each set by a search tree (covered later in the module). • The java.util.HashSet class implements the java.util.Set interface, representing each set by a hash table.

17. Example: (1) import java.util.TreeSet; class Colours { public static void main (String [] args) { TreeSet<String> rainbow=new TreeSet<String>(); TreeSet<String> primary=new TreeSet<String>(); TreeSet<String> flag=new TreeSet<String> (); // set up the colours of the rainbow rainbow.add("red"); rainbow.add("orange"); rainbow.add("yellow");rainbow.add("green"); rainbow.add("blue");rainbow.add("indigo"); rainbow.add("violet");

18. Example: (2) primary.add("red"); primary.add(“yellow"); primary.add("blue"); flag.add("red"); flag.add("white"); flag.add("blue"); // printout the cardinality of the sets System.out.println( "the cardinality of set rainbow is “ +rainbow.size()); System.out.println( "the cardinality of set primary is “ +primary.size()); System.out.println( "the cardinality of set flag is “ +flag.size());

19. Example: (3) System.out.println(); System.out.println("rainbow colours in “+ “the national flag"); rainbow.retainAll(flag); System.out.println(rainbow.toString()); System.out.println();   } } This prints out the set, how would you print out the individual colours? Go to the sun java site to find out