In this homework you will write a program to detect cycles in a graph.

• Study the notes on graphs, especially the Graph.hs we wrote in class.
• Use the graphs as array representation.
• Create 3 graphs using this represntation with at least 10 vertices. One should be acyclic. The other two should be cyclic. One should have a cycle with length less than 4, and the other should have a cycle with length greater than 8.
• Write a program hasCycle with the following contract.

  hasCycle:: ArrayGraph Int -> IO(Bool)
  

• Create test harnesses to show that your program works.

What to do

• Cut and paste the program pieces from the file Graph.hs to get started including the definition for the type ArrayGraph and code for creating grpahs as arrays, and programs that manipulate graphs as starting points. .
• Alter the functions that you have cut and pasted so that they implement hasCycle as described above.
• Be sure and rename functions so that names of the altered functions describe what the functions do. I will assign points according to how well you name your functions.
• I suggest you work in stages, cutting and pasting only a few pieces of a time.
• Be sure and create test harnesses that test your code. Test it as you proceed, so that you know each piece works, before you alter new pieces that depend upon previously altered pieces,
• Create a main function that illustrates that your code works.

What to turn in.

• A file by containing the working code of hasCycle.
• Include your name (as the author of the program) on the very first line
• At least 3 graphs as described above.
• Be sure you include tests
• Uploaded the file to blackboard
• Due on final exam day Tuesday, December 8, 2009.

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