In this assignment you will supply the implementation of a C++ type for Rational numbers and use it to build a calculator for rationals. You should do this assignment alone. We will supply you with the calculator code, including a header file that specifies type Rational. Your only job is to provide the implementation of Rational.
The main purpose of this assignment is to give you a taste of C++ by implementing a new C++ type. In the process you will also work out the mechanics of compiling and running a C++ program, which are basically the same as running one written in C.
The calculator program (supplied) is a simple line-oriented calculator for
expressions involving rational numbers. Rationals can be entered as either
a positive integer n, meaning n/1, or as a pair of
positive integers separated by a slash: n/d. Numbers can
be combined in expressions in the usual way with the operators +, -, *, and
% (for divide); spaces may separate parts of expressions; and subexpressions
can be surrounded by parentheses. All expressions must be entered on a single
line,
and the calculator
evaluates
the expression on each input line and prints
the result. The end of input is indicated by typing the usual end-of-file character
(ctrl-D on attu). The calculator makes no effort to detect or report errors
such as illegal input or rationals with a denominator of 0. If it
is unable to make sense out of something, it usually returns the result
0/0 and goes on to the next input line.
Note, however, that your job in this assignment is only to implement type
Rational. The calculator program is intended as a way of testing and demonstrating
that your Rational type works properly, but you are not responsible for any
of its quirks or fixing any odd behavior that you discover.
The calculator is implemented as a set of C++ functions. Calculations are
done with a user-defined type Rational that defines the representation
of rational
numbers, constructors for them, and basic arithmetic operations.
This type is specified in a file rational.h; there is a corresponding
implementation file rational.cpp that is empty. Your job is to
provide an implementation of
Rational in file rational.cpp.
You should download file rational.tar (right-click
the link), which contains the starter code. File rational.h in
the starter code contains descriptions of the operations
of the type; these are not repeated here to save space. In addition to the
source code for the calculator, the archive contains a simple Makefile to
build it.
Your implementation of Rationals should return values in lowest (i.e., factored)
terms. In other words, the greatest common divisor of the numerator and denominator
of a Rational should be 1, as far as can be detected by program using type
Rational. This does not constrain how Rationals are actually represented, just
how they can be observed to behave.
One note about how Rational is used in the calculator code.
A Rational is
a very simple object with a numerator and denominator, some constructors, and
some
operations. The calculator creates instances of Rationals as
ordinary variables and parameters. They are not allocated on the heap with
new, or deleted manually later (although they could be if it was
needed).
You should turn in only the file rational.cpp containing your
implementation of type Rational. Use the regular dropbox.