Programming withData Structures and Algorithms
Programming with
As we have discussed in class, sometimes, check-expect
just isn't enough. When you are testing complex functions, or
perhaps even relations (as in the case of this assignment), you will
need to put time and effort into building testing oracles.
In this assignment, you will develop oracles to test purported solutions to the Stable Marriage Problem. A summary of the problem is this:
Assume you have n men and n women. Each man wants to marry one woman, and each woman one man. Each woman ranks the men by assigning each one a unique number between 0 and n-1 (i.e., she provides a total ordering of the men). The men rank the women in the same way. A programmer is asked to design and implement a program that generates n pairings of men with women. The program's generated marriages are stable if there are no two people of the opposite sex who would prefer each other to their current partners.
Though the problem wording may make it sound frivolous, there are many problems of this nature. Consider assigning TAs to classes; matching residents with hospitals; pairing students for homeworks; and much more. Of course, some of these problems represent a slight variation on the theme (maybe the women don't rank every man, or are allowed to give some of them the same rank; maybe you have only partial information for making the assignment; etc.). Ultimately, however, this problem in its many guises has wide application.
Being confident that your software is correct involves more than just writing code you think is right. However, almost no software complex enough to be useful can be proved correct by hand in a reasonable amount of time. Naturally, a computer scientist's solution to this problem is to write automated testing. Your job, in this assignment, is to build an automated testing oracle for a hypothetical solution to the stable marriage problem.
Your oracle's job is to generate and feed test inputs to this solution, and test the correctness of the output. In the past, you did this by comparing the output to a precomputed correct answer. This assumes two things: that there is only one right answer, and that it is easy for you to find it. In the real world, either or both of these can and will be false (How do you know what the right answer to an arbitrary instance of the problem is if the original problem was to write a program to find it?)
You've got your work cut out for you: we give you a correct solution to the stable marriage problem to help you write and test your oracle. You submit your oracle, and we unleash hell's own fury of incorrect solutions at it, each with its own subtle flaw.
By downloading oracle-support.rkt and putting (require "oracle-support.rkt") at the top of your code, you will have access to the following struct and function:
(define-struct: marriage ([woman : Integer$]
[man : Integer$))
matchmaker : ((Listof: (Listof: Integer$)) (Listof: (Listof: Integer$)) -> (Listof: Marriage$))
Each purported solution will be a function like matchmaker
that consumes two arguments, both of which are
(Listof: (Listof: Integer$))s in which every list
(both inner and outer, for both lists) is of the
same size (call it n—but n is naturally not fixed).
The first list provides the womens' preferences, the second one those for the
men (though you should convince yourself it doesn't matter which one
is which). Each inner list corresponds to a specific man or woman and
contains a list of n numbers, index from 0 to
(- n 1), where each number refers to the index of the
opposite-sex person in the other list, and the list is sorted in order
of preference from greatest to least. The functions generate a list
of n marriages, in which the numbers refer to the
indices of the men and women in the input lists.
Your assignment has three tasks:
generate-input that (surprise, surprise!)
generates input. Above, we have described only the shapes of the inputs;
you will have to infer the constraints we've left out. Your function must
generate a list of rankings for a specified number of men or women. Here's
the contract:generate-input : (Integer$ -> (Listof: (Listof: Integer$)))
valid? : ((Listof: (Listof: Integer$)) (Listof: (Listof: Integer$))
(Listof: Marriage$) -> Boolean$)
generate-input and valid?, write a function
named oracle that tests whether an algorithm is a valid
solution to the stable marriage problem.oracle : (((Listof: (Listof: Integer$)) (Listof: (Listof: Integer$)) ->
(Listof: Marriage$)) -> Boolean$)true if an algorithm always produces a stable set
of marriages (it is up to you to determine the magnitude of "always").
To do well on this assignment, you will want to spend time considering all the different ways that output could be either invalid or inconsistent with the original problem statement. Be thorough! That's the name of the game when testing.
A Racket file, oracle.rkt, containing your implementation
of the functions described above.