System development with Java

1. System development with Java Instructors: Rina Zviel-Girshin Lecture 11 Rina Zviel-Girshin @ARC

2. Overview • Sequences • Interface • Abstract Rina Zviel-Girshin @ARC

3. Sequences • An infinite sequence is a function whose domain is the set of positive integers. • The function values a1,a2,a3,... are the terms of the sequence.. • If the domain of the function consists of the first n positive integers only, the sequence is called finite sequence. Rina Zviel-Girshin @ARC

4. Arithmetic sequence • A sequence (or a series) is arithmetic if the difference between any two consecutive terms is the same. • A sequence is arithmetic if there is a number d such that an-an-1=d for any n positive integer greater than 1. • The number d is called the common difference of the arithmetic sequence. • The nth term of an arithmetic sequence has the form: an=a1+d(n-1). Rina Zviel-Girshin @ARC

5. Arithmetic sequence example Example: • The sequence whose nth term is 4n+3 is arithmetic. • For this sequence, the common difference between consecutive terms is 4. • 7, 11, 15, 19, . . . 4n+3, . . . Rina Zviel-Girshin @ARC

6. Sum of an arithmetic sequence • The sum of a finite arithmetic sequence is (a1+an)n S(n)= 2 Rina Zviel-Girshin @ARC

7. Geometric sequence • A sequence is geometric if the ratio of any two consecutive terms is the same. • A a sequence is geometric if there is a number r  0, such that bn/bn-1=r for any n positive integer greater than 1. • The number r is called the common ratio of the geometric sequence. • The nth term of a geometric sequence has the form bn=b1*rn-1. Rina Zviel-Girshin @ARC

8. Geometric sequence example Example: • The sequence whose nth term is 2n is geometric. • For this sequence, the common ratio between consecutive terms is 2. • 2, 4, 8, 16, . . ., 2n, . . . Rina Zviel-Girshin @ARC

9. Sum of an geometric sequence • The sum of a finite arithmetic sequence is b1(rn -1) S(n)= • (r-1) Rina Zviel-Girshin @ARC

10. Question • We want to implement arithmetic, geometric and other series. • We want to print a current term and a sum. • Let’s see what both series have in common? • What is different? Rina Zviel-Girshin @ARC

11. Interface • We can define Series interface to hold the following methods: • next() • sum() • We can define Printable interface to hold the following method: • print() Each sequence will implement those interfaces. Rina Zviel-Girshin @ARC

12. Interfaces interface Series { void next(); double sum(); } interface Printable{ void print(); } Rina Zviel-Girshin @ARC

13. Arithmetic class Arithmetic implements Series, Printable{ int index, term, first, delta; public Arithmetic(int first,int delta) { this.delta=delta; this.first=first; term=first; index=1;} public void next() { term=first+delta* index++; } public double sum() { return (first+term)*index/2; } public void print() { System.out.print(“an=" + term + ";sum=" + sum());} } Rina Zviel-Girshin @ARC

14. Geometric // a little bit different implementation class Geometric implements Series, Printable{ int index, term, first, ratio; public Geometric(int first, int ratio) { this.ratio=ratio; this.first=first; term=first; index=1; } public void next() { term=term*ratio; index++; } public double sum() { return first*Math.pow(ratio,index-1)/(ratio-1); } public void print() { System.out.print(“bn=" + term + ";sum=" + sum());} } Rina Zviel-Girshin @ARC

15. Another implementation • Can we implement those classes differently? • Do we have the same data fields? • Do we have the same implementation for any methods? • print() method is the same for both series. System.out.print(“bn=" + term + ";sum=" + sum()); • So we can build an abstract class for this problem. Rina Zviel-Girshin @ARC

16. Abstract class abstract class AbstractSeries implements Series, Printable { int index=1, term=1, first; public void print() { System.out.println("an=" + term + ";sum=" + sum()); } } Rina Zviel-Girshin @ARC

17. Arithmetic implementation class Arithmetic extends AbstractSeries implements Series, Printable{ int delta; public Arithmetic(int first,int delta) { this.delta=delta; this.first=first; term=first; index=1;} public void next() { term=first+delta* index++; } public double sum() { return (first+term)*index/2; } } Rina Zviel-Girshin @ARC

18. Any Questions? Rina Zviel-Girshin @ARC