Scheduling Prerequisites
The prerequisites of some MIT subjects are given in the following table:
| Direct Prerequisites | Subject |
|---|---|
| 18.01 | 6.042 |
| 18.01 | 18.02 |
| 18.01 | 18.03 |
| 8.01 | 8.02 |
| 8.01 | 6.01 |
| 6.042 | 6.046 |
| 18.02, 18.03, 8.02, 6.01 | 6.02 |
| 6.01,6.042 | 6.006 |
| 6.01 | 6.034 |
| 6.02 | 6.004 |
In the following sets of subjects, specify whether the set is a chain, anti-chain, or neither:
(Hint, draw a DAG for the subjects first!)
-
6.042, 6.046, 6.01
-
18.01, 6.02, 6.004
A chain need not contain every possible element. -
6.042, 6.02, 6.034
-
What is the length of the longest anti-chain?
-
How many terms do you need to graduate if you take classes following the schedule given by a topological sort of the DAG?
Topological sorting provides a schedule for taking one class per term, so the number of terms is the number of classes.