Last week, two of the discussion questions were:⁺

• 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. 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 a fish moving six times.

• Copy the Histogram Lab folder from my CS 420 folder on Dragon (under Network Neighborhood) to the Temp folder. Open the histogram project and edit main.cpp.

• Construct a coin using the default Coin constructor. Also construct an integer variable, initialized to 0, representing the fish location.

• Research the Coin interface 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, move the fish to the right if the coin comes up heads, and to the left if the coin comes up tails.

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

Add multiple runs.

• In order to keep track of how many times the fish 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 ininitialize each of them to 0. (Question: how many additional integer variables will you need?)

• Embed the code you wrote earlier in a loop, in order to run the simulation 1000 times. Remember that the fish needs to start at location 0 each time. After each run, increment the appropriate location counter rather than printing out the final location of the fish.

• After running the simulation 1000 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.

• Copy the statements from your stand-alone aquarium program (or from ABhouse) that create and initialize a CMU graphics window^* and paste them into your main function. Copy and paste the statements to set the pen and brush color and the call to WaitNClear also.

• For each of your final location counts, draw a rectangle whose width is proportional to the number of times the fish ended up in that final location. Look at your aquarium program (or ABhouse or display.cpp) to review how to draw a rectangle using the CMU graphics package.

  The upper-left corner of the first rectangle (representing -6) should be at pixel location (100, 150). The upper-left corner of each of the other rectangles should be 10 pixels below the lower-left corner of the rectangle above it. The height of each rectangle should be 20. The width should be the number of times the fish ended up in that location. (You may use numeric constants for all of the parameters to DrawRectangle except the width. Or you may use variables and adjust the variable representing the rectangle top for each rectangle.)

• Run your program several times to test it. When it runs correctly, you may remove the cout statements that printed the various final location counters.

• If you like, make each bar in the histogram a different color. Test your program again. You may also wish to look at the demo program in the CMU graphics package to see how to write text to a graphics window, and then modify your own program to add text (such as the final location each bar represents, and the exact total for each location) to add clarity to your histogram.

Print and save your modifications.

• Print your main function. Remove the object code from the project (there is an option under the Project Menu to do this). Copy the Histogram Lab folder from the Temp folder to your floppy disk. You should then remove the folder from the Temp folder on the C: drive.

• Be sure to turn in the printout of your main function.

⁺These questions came from the Advanced Placement Computer Science Marine Biology Simulation Case Study, available from the College Board for face-to-face teaching purposes.

^*The CMU Graphics Library was created by the Carnegie Mellon University School of Computer Science and is used in their introductory programming courses. It is available from Mark Stehlik's Advanced Placement page.