**CSE 374 16wi - Homework 6** **Due: Thursday, March 10, at 23.00** --- # Synopsis In this assignment you will supply the implementation of a C++ type for Rational numbers. You should do this assignment alone. We will supply you with a small calculator program that evaluates arithmetic expressions using your code. You can use this to experiment with and test your implementation. But your only job is to provide an implementation of type `Rational`. # Type `Rational` `Rational` is specified in file `rational.h`; there is a corresponding implementation file `rational.cpp` in the starter code that is empty. Your job is to supply an implementation of `Rational` in file `rational.cpp`. You should download the archive [rational.tar](http://courses.cs.washington.edu/courses/cse374/16wi/hws/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; to save space these are not repeated here. The archive also contains the source code for a small calculator program that uses `Rationals` and 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 a program using type `Rational`. Furthermore, as far as an observer can tell, the denominator of a `Rational` should always be non-negative; the numerator may be positive or negative as appropriate. This does not constrain how `Rationals` are actually represented, just how they can be observed to behave. You should implement type `Rational` as defined in `rational.h`. You may not modify the contents of this header file or add or delete anything from it. You are free, of course, to include additional helper functions and data in your `rational.cpp` implementation file if these are useful. You do not need to check for or deal with rationals that have a denominator of 0 or similar issues. If a client of type `Rational` creates a `Rational` with a denominator of 0, or if a calculation produces such a result, simply create that result and return it. # The Calculator 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 % (the % is used to indicate division of two rationals since / is used to enter a single rational value). Spaces may separate parts of expressions, and subexpressions can be surrounded by parentheses. One limitation is that the calculator only implements binary operators; in particular it doesn't support unary minus. To compute $-r$, you can evaluate $0-r$. 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` in Linux shell windows). The calculator makes no effort to detect or report errors such as illegal input, additional characters on the input line following a complete expression, or rationals with a denominator of 0. If it is unable to make sense out of something, it usually generates the result $0/0$ and goes on to process the next input line. Remember 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 for fixing any odd behavior that you may discover. # What to Turn In You should turn in only the file `rational.cpp` containing your implementation of type `Rational`. Be sure to include your name at the top of the file. Use the [regular dropbox](https://catalyst.uw.edu/collectit/dropbox/summary/aaronb22/37118).