Department of Computer and Information Science, School of Science, IUPUI

1. Department of Computer and Information Science,School of Science, IUPUI Fraction Abstract Data Type Dale Roberts, Lecturer Computer Science, IUPUI E-mail: droberts@cs.iupui.edu

2. Abstract Data Type Example • An Abstract Data Type is a data type that is defined by the programmer, not the language. • Like any data type, it is a set of values with operations that act on those values. • Working with ADTs involves three different components: • The public interface, or specification, defines the ADT and how it is used. • The implementation, implements the ADT in code. • The client uses the ADT to perform a task.

3. Defining an ADT • Within C++, you define an ADTs public interface with a header file. • #include “fraction.h”main(){ Fraction x, y; …} • User-defined ADTs are typically capitalized to distinguish them from intrinsic data types.

4. ADT Operations • Several classes of operations are required in order to effectively used ADT. • Constructors – used to create instances of the data type. • Destructors – used to destroy an instance of the data type • Accessors – used to access attributes of the data type. (Such as “get” functions) • Modifiers – used to modify attributes of the data type. (Such as “set” functions) Object-oriented languages provide some of this functionality within the language. In C you must do it yourself.

5. Fraction ADT Specification • The specification for the Fraction ADT requires a discussion of what operations are required. Constructors: Fraction() creates a new variable of type Fraction with the default value of 0/1. Fraction(int n, int d) creates a new variable of type Fraction with the default value of n/d. Note that you need to handle all combinations of positive and negative for n and d in order to determine the sign of the fraction.

6. Fraction ADT (Cont) Destructors: ~Fraction() – frees Fraction variable. Copy: Fraction g = f; – creates a new Fraction g, whose values are copied from f. C++ provides a default copy constructor, or you may write your own: Fraction(const Fraction &) Accessors: i = f.getNumerator(); i = f.getDenominator(); c = f.getSign(); You don’t need to provide you own copy constructor if you don’t use new.

7. Fraction ADT (cont) Modifiers: f.reduceFract() – reduces a fraction to lowest terms. Notice that this is a modifier, and cannot be used in an expression. setNumerator(int); setDenominator(int); setSign(char);

8. Fraction ADT Operations These Operations are designed to be used in an expression. They never modify their arguments. They always return type Fraction. f = Fraction::negateFract(f) // returns -f s = Fraction::addFract(f1,f2) // returns f1 + f2 d = Fraction::subFract(f1,f2) // returns f1 – f2 p = Fraction::mulFract(f1,f2) // returns f1 * f2 q = Fraction::divFract(f1,f2) // returns f1 / f2 i = Fraction::compareFract(f1,f2) // f1 < f2 returns -1, // f1 = f2 returns 0, // f1 > f2 returns 1

9. Fraction ADT I/O Input/Output: Fraction Fraction::getFract(istream, f) – return 1 if OK, 0 if invalid, EOF if end of file. int Fraction::putFract(ostream, f) – writes out fractions with correct sign, does not print denominator if 1

10. Design While we’ve defined an ADT interface, we can’t just start coding quite yet. There are more design decisions to be made before writing code for the implementation. A common error among programmers is to not place enough emphasis on the design step. This is the difference between a “programmer” and an “analyst”.

11. Fraction ADT Design: Data Data-centric analysis begins with the idea that all the operations will be acting on Fractions that have some internal representation. The representation shall be shared among all the operations. Each operation is responsible for maintaining your design rules regarding the representation of Fraction information. typedef enum{ POS, NEG } SignType; class Fraction { private: // data members int numerator; /* numerator and denominator are declared as */ int denominator; /* int to simplify the algorithms, but they */ SignType sign; /* will always be stored >= 0 */ public: // member functions would follow private: // utility functions would follow }; All operations must preserve these rules.

12. Fraction ADT Variables • Now that we’ve decided how to represent the value of a fraction, how are we going to declare variables whose values are fractions? Fraction f1, f2;

13. a c ad + bc  + = b d bd Sum: a c ac  * =  b d bd Product: Fraction ADT Algorithms • You are responsible for designing algorithms that implement all the operations. What process must you follow to implement the operations? then, reduce then, reduce Subtraction involves adding the opposite, and Division involves multiplying by the reciprocal.

14. Fraction ADT Algorithms • Reducing a fraction involves finding the Greatest Common Divisor, and then dividing all the terms by that amount. Euclid’s Algorithm: if x < y, then swap x and y While y is not zero remainder = x mod y x = y y = remainder When you’re done, x is the GCD.

15. Fraction ADT Design Issues • There are three special situations that require special handling. • Negative fraction have sign = NEG. However, arithmetic expects the sign to be in the numerator. We’ll need to move back and forth between “arithmetic” representation of the sign and “standard”. • Fractions may not have zero in the denominator. Dividing by zero is not allowed, even though 0/1 is valid. • Different values of zero will not reduce using reduceFract(). Special coding is required to reduce 0/5 to 0/1.

16. ADT Specification • In C++, the ADT Specification resides in a header file, names like fraction.h. /******** Constructors, Destructors, and Clone **********/ Fraction Fraction(); /* returns 0/1 */ Fraction Fraction( int n, int d ); /* returns n/d */ // void ~Fraction( Fraction f ); Implementation not needed // Fraction(const Fraction &); Implementation not needed

17. Accessors /*********** Accessors **************/ int getNumerator(); int getDenominator(); char getSign();

18. Modifiers /********** Modifiers ***********/ void setNumerator(int); void setDenominator(int); void setSign(char); void reduceFract();

19. Operations /******** Fraction Operations **********/ static Fraction negateFract( const Fraction &f1); static Fraction addFract( const Fraction &f1, const Fraction &f2 ); static Fraction subFract( const Fraction &f1, const Fraction &f2 ); static Fraction mulFract( const Fraction &f1, const Fraction &f2 ); static Fraction divFract( const Fraction &f1, const Fraction &f2 ); static int compareFract( const Fraction &f1, const Fraction &f2 ); /* returns -1 if f1 < f2 0 if f1 == f2 +1 if f1 > f2 */

20. Input/Output /******************* I/O ********************/ static int getFract( istream &infile, Fraction &f); /* returns 1 if a valid fraction is read 0 if an invalid fraction is read EOF if end of file is detected */ static void putFract( ostream &outfile, const Fraction &f );

21. Allowing for multiple #includes #ifndef FRACTION_H #define FRACTION_H #include <iostream> #include "boolean.h" … #endif

22. Sample Client - Declarations #include <iostream> #include "fraction.h" #include "boolean.h" using std::cout; using std::endl; int main() { Fraction f, g, half(1,2), sum, diff, prod, quotient, neg, answer; Boolean done = FALSE; int readResult, cmpResult; ... code would follow }

23. Sample Client – Creating Fractions cout << "Enter your first fraction > "; readResult = Fraction::getFract( cin, f ); if (readResult == 0 ) { cout << "Error entering fraction" << endl; } else if ( f.getNumerator() == 9999 ) { done = TRUE; } else { cout << "Enter another fraction > "; readResult = Fraction::getFract(cin, g); if ( readResult == 0 ) { cout << "Error enterering fraction" << endl; } else { // Perform Calculations

24. Sample Client – Manipulating Fractions // Perform Calculations neg = Fraction::negateFract(f); sum = Fraction::addFract(f,g); diff = Fraction::subFract(f,g); prod = Fraction::mulFract(f,g); quotient = Fraction::divFract(f,g); cmpResult = Fraction::compareFract( f, g ); /* (f + g) - ( f * -(1/2) ) */ answer = Fraction::subFract( Fraction::addFract( f,g ), Fraction::mulFract( f,Fraction::negateFract(half)));

25. Sample Client – Displaying Output /* Display output */ cout << endl; cout << "F1 = "; Fraction::putFract(cout, f); cout << endl; cout << "F2 = "; Fraction::putFract(cout, g); cout << endl; cout << "Neg = "; Fraction::putFract(cout,neg); cout << endl; cout << "Sum = "; Fraction::putFract(cout,sum); cout << " Diff = "; Fraction::putFract(cout,diff); cout << " Prod = "; Fraction::putFract(cout,prod); cout << " Quot = "; Fraction::putFract(cout,quotient); cout << endl; if ( cmpResult == 0 ) cout << "equal" << endl; else if (cmpResult < 0 ) cout << "less" << endl; else cout << "Greater" << endl; cout << "Try one nested: " << endl; out << "(f + g) - ( f * -(1/2) ) = "; Fraction::putFract(cout,answer); cout << endl; cout << "==========================================" << endl;

26. Sample Client – Clean Up • Unlike C, there is no requirement for cleanup when dealing with the Fractions. • When Fractions go out of scope, they are automatically destroyed. There is no need to create and call a freeFract() function. • Creating a Fraction does not require explicit use of a pointer or malloc(). You create a Fraction on the stack simply by declaring a Fraction variable. Using “new” to allocate a fraction on the heap is not required. int function(int x, y) { int z; z = x+y; return z; } // return is pass-by-value (copy) Fraction function(Fraction x, y) { Fraction z; z = fraction::addfract(x,y); return z; } // return is pass-by-value (copy)

27. Sample Execution To enter a fraction enter two integers separated by one space. To indicate end of data enter 9999 for the numerator of the first fraction. Use any denominator. Enter your first fraction > 5 6 Enter another fraction > 3 4 F1 = 5/6 F2 = 3/4 Neg = -5/6 Sum = 19/12 Diff = 1/12 Prod = 5/8 Quot = 10/9 Greater Try one nested: (f + g) - ( f * -(1/2) ) = 2

28. Acknowledgements • The specification for this Fraction ADT comes from Fecteau & Kirchherr. • The implementation is my own.