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Assignment 7 - Scheduler

Due: April 28

Objective

To gain experience using graphs and topological sorting.


Task

Directed Acyclic Graphs (DAGs) are an important type of graph with many applications. Recall that a directed graph is one where the edges have a direction. Recall that an acyclic graph is one with no cycles. A cycle is a sequence of edges in a graph where following it will lead you back to the original node. If a graph is directed and acyclic, it is a DAG.

One common usage of DAGs is to represent dependencies between different things. For example, courses in a school generally can have pre-requisites. In the computer science department, taking CPSC 340 depends on having taken CPSC 240. We can represent these pre-requisites with a DAG where an edge from course A to course B means that A is a pre-requisite of B. Below is a DAG representing the dependencies between several required courses for the computer science major:

Note that if there were a cycle in this graph (such as if there were an edge going from 340 back to 110), then the graph would no longer be a DAG. It would also mean it would be impossible to complete the courses because there would be an endless loop of pre-requisites.

Given any DAG, it is possible to produce a topological ordering which is a list of the nodes in the DAG such that every node appears before the ones that it has edges pointing to. A topological ordering for the graph above is:

  1. CPSC 125
  2. CPSC 110
  3. CPSC 225
  4. CPSC 220
  5. CPSC 240
  6. CPSC 350
  7. CPSC 305
  8. CPSC 326
  9. CPSC 340
  10. CPSC 430
  11. CPSC 405

Note that there are multiple topological orderings possible for this DAG.

The process of producing a topological ordering from a DAG is called topological sorting.

Your task for this assignment is to write a program that will take a list of courses and their pre-requisites as input, and print out a topological ordering that one can take the courses in without violating any pre-requisites. If the set of courses can not be taken in any order, you should print out that there is no way to take those courses.

Your program will be given the name of an input file on the command line. The file consists of a list of courses with their pre-requisites in the following format:


course1 number-of-prereqs prereq1 prereq2 ...
course2 number-of-prereqs prereq1 prereq2 ...
...

Each course will be specified with four letters followed by 3 digits. Some courses will of course have no pre-requisites. There will be no more than 100 courses total. Here is an input file representing the CS courses given above. Here is an input file with a cycle. There is no topological ordering possible for this input.

One algorithm for topological sorting is given below:

  1. Set the ordering to empty.
  2. Find the set of nodes with no edges coming into them. Call this the active set.
  3. While there are nodes in the active set:
    1. Move a node N from the active set to the ordering.
    2. For each edge coming out of N and into M:
      1. Remove the edge from the graph.
      2. If M now has no edges coming into it, add it to the active set.
  4. If the graph has any edges left, then there is no topological ordering!
  5. Otherwise, the topological ordering is in the "ordering" list.

Details


General Requirements


Submitting

Submit your program by emailing your source files to ifinlay@umw.edu.

Copyright © 2018 Ian Finlayson | Licensed under a Creative Commons Attribution 4.0 International License.