## CS 101 (Spring 1999) Quiz 11: Stable Matchings and Software Design

Quiz Posted
(Wednesdays)
Given in class
(Wednesdays)
14 Apr 21 Apr

• On the date a quiz is given, a die will be thrown by a student in the class.
• Books and notes are put away.
• A question very similar to the chosen published question will be written on the board.
• You have 5 minutes to answer the question.
The questions are intended to be straightforward. If you keep up with the material in the class, almost no preparation may be necessary. The Collaboration Policy allows you to study in groups for the quizzes, but you are on your own when you take the quiz.

You will fare better on the quiz if you try working the problems before looking at the solutions. If you don't understand the question or its answer, please get help.

The problems below are based on stable matching, as discussed in class. We have N slots and N students. The slots propose to the students and the students accept or reject the arrangement.

1. Suppose slot i's first choice is student i. But student i ranks slot i last. What is the result of stable matching given this data?
2. Suppose every slot prefers student N as its first choice. Student N ranks the slots N, N-1, N-2.., 1. How many times is the arrangement involving Student N broken?
3. Same as previous question, but student N ranks the slots 1, 2, 3, ..., N. How many times is the arrangement involving Student N broken?
4. For 4 slots and 4 students, show a table of student/slot and slot/student preferences such that one student's arrangement is broken three times.

[ solution ]