ITEC 120 2007fall ibarland, jdymacek

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hw14
Jail time
arrays

Due 2007.Dec.1007¹ (Fri), 17:00. No late work accepted.

In the kingdom of Wunhundredtwentia, the jail system is extensive, with 200 cells all in a row. Each cell's door has a key, which when turned toggles the door's lock. That is, if the door was unlocked, then turning the key locks it; if locked, then turning unlocks it.

The Royal Jailer has a curious habit: Every evening, he turns the key in every single door -- numbers 1 through 200. Then, he goes back and turns the key in every other door -- numbers 2, 4, 6, ..., 200. Then, he goes back and turns the key in every third door -- numbers 3, 6, 9, ..., 198. Then, he turns the key in every fourth door -- numbers 4, 8, 12, ..., 200. And so on, until he finishes by turning the key in every 200th door (which is just one door: cell #200). After that, he falls asleep, and anybody in an unlocked cell can escape during the night. (At the start of the evening, all cells are initially locked.)

You and a baker's dozen of your friends have been framed, and falsely convicted of Meandering with Intent to Jay-walk, and are scheduled to be executed at dawn. Fortunately, each of you can name which cell to be locked away in.

Which cells do you choose?

Hints:

• What Java data type reasonably corresponds to a door's open/closed status? What Java data type reasonably corresponds to a row of 200 numbered doors?
• The magic number 200 or 201 should not occur more than once in your code! Use some name like NUM_CELLS, and refer to that name.
• For early testing, use a more manageable value for NUM_CELLS, like 10, while writing and testing the program.
• It's perfectly fine to use 201 vector locations (numbered zero through 200), and never happen to use the location numbered zero²
• As ever, use auxiliary functions to accomplish well-defined subtasks. (In particular, one very helpful subtask might correspond to the jailer making a single pass.)
• Make sure you can call your function a second time, and still get a correct answer!
• Printing the status of 200 doors is a bit unwieldy. A great helper function would be one which just prints out the indices of the open doors.

Extra credit, 2-5pts:
Once your program tells you the answer, augment the answer with an explanation. Not just what the pattern is, but why that pattern occurs. (This is a nice illustration of the difference between knowing an answer, and understanding the answer.) No points if the explanation isn't written clearly (you may want to run it by a roommate).

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©2007, Ian Barland, Radford University Last modified 2007.Dec.14 (Fri)

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