Lab: Histograms

Consider the following exercises.⁺

• One can simulate the movement of a fish in an aquarium by repeatedly flipping a coin. When "heads" is flipped, the fish moves one foot to the right; when "tails" is flipped, it moves one foot to the left. (We are assuming a long, narrow aquarium.) Assume that the fish's initial location is labeled 0 and that locations to the right are positive while locations to the left are negative. For example, the fish in its initial location has left and right neighbors at locations -1 and +1, respectively. What are the possible positions of the fish, relative to its starting position, at the end of a simulation with six coin flips? Explain. (Don't worry about the tank being too short.)

• Conduct several such simulations, each with six coin flips as described in the exercise above, and keep track of where the fish ends up after each simulation. Is the fish more likely to end up in one position than another? Explain why or why not.

     -6   xxxxx
     -4   xxxxxxxxx
     -2   xxxxxxxxxxxxxx
      0   xxxxxxxxxxxxxxxxx
      2   xxxxxxxxxxxxxx
      4   xxxxxxxxx
      6   xxxxx

Simulate an object moving six times.

• Download the files for the Histogram program to your working space. Create a project containing all the files in the Code folder and edit the file HistogramLab.java.

• Research the class documentation for the Coin class to learn how to construct a coin using the default Coin constructor. Then construct an integer variable to represent the object's location. Initialize it to 0.

• Research the Coin class documentation to learn how to toss a coin and how to determine whether the tossed coin is showing heads or tails. Modify your program to toss the coin six times. Each time you toss the coin, update the location variable to reflect a move to the right if the coin comes up heads, or a move to the left if the coin comes up tails.

• After moving the object six times, print its final location. Run your program several times to test it.

Add multiple runs.

• In order to keep track of how many times the object ends up in each location over the course of many runs of the simulation, create an integer variable to represent each of the possible final locations, e.g., minusSixCount, zeroCount, etc. Be sure to initialize each of them to 0. (Question: how many integer variables will you need to represent all of the possible final locations?)

• Embed the code you wrote earlier in a loop, in order to run the simulation 1000 times. Remember that the object needs to start at location 0 each time. Rather than printing out 1000 final location values, just increment the appropriate location counter after each run. (Note that there's a constant called NUM_ITERATIONS that you should use instead of "hard-coding" the number 1000 throughout your code.)

• After running the simulation NUM_ITERATIONS times, print the number of times the fish ended up in each of the possible final locations. Run your program several times to test it. Do your results seem to make sense? You may wish to double-check that the various counts add up to 1000.

Draw a histogram.

• Remove the comments around the block of code that constructs a histogram object.  Research the Histogram class documentation to learn how to call the two-parameter plot method, then call it for each of the possible final locations.

• Run your program several times to test it. You may also want to experiment with running it different numbers of times; for example, run the program several times with NUM_ITERATIONS set to 10, then several times with NUM_ITERATIONS set to 20 and 100. How does the behavior change as the number of iterations changes? Why? What do the labels to the left of the bars in the histogram represent?

• When you're sure that your program runs correctly, you may remove the System.out.println statements that printed the various final location counters. Also remove the statement at the beginning of the main method that said what the program would do once it was written.

• Update the class documentation for HistogramLab.java to accurately describe the purpose and behavior of the class from a user's perspective.  Focus on what the program does, rather than how it does it. Include your name and the date as well as the names of anyone from whom you received help. Providing proper documentation is an important step towards writing well-structured and reusable programs.

⁺These questions came from the Advanced Placement Computer Science Marine Biology Simulation Case Study, available from the College Board.