To gain experience using graphs and topological sorting.
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:
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:
number-of-courses 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. Below are three sample input files:
One algorithm for topological sorting is given below:
When you are done, submit your program by emailing your code to email@example.com.
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