# In this lab you will develop a class that models a random walk and write two client ...solved

In this lab you will develop a class that models a random walk and write two client programs that use the class. A random walk is basically a sequence of steps in some enclosed space where the direction of each step is random. The walk terminates either when a maximum number of steps has been taken or a step goes outside of the boundary of the space. Random walks are used to model physical phenomena such as the motion of molecules and economic phenomena such as stock prices.

We will assume that the random walk takes place on a square grid with the point (0,0) at the center. The boundary of the square will be a single integer that represents the maximum x and y coordinate for the current position on the square (so for a boundary value of 10, both the x and y coordinates can vary from -10 to 10, inclusive). Each step will be one unit up, one unit down, one unit to the left, or one unit to the right. (No diagonal movement.)

The RandomWalk class will have the following instance data (all type int):

·         the x coordinate of the current position

·         the y coordinate of the current position

·         the maximum number of steps in the walk

·         the number of steps taken so far in the walk

·         the boundary of the square (a positive integer -- the x and y coordinates of the position can vary between plus and minus this value)

Create a new file RandomWalk.java. You'll define the RandomWalk class incrementally testing each part as you go.

1.       First declare the instance data (as described above) and add the following two constructors and toString method.

·         RandomWalk (int max, int edge) - Initializes the RandomWalk object. The maximum number of steps and the boundary are given by the parameters. The x and y coordinates and the number of steps taken should be set to 0.

·         RandomWalk (int max, int edge, int startX, int startY) -- Initializes the maximum number of steps, the boundary, and the starting position to those given by the parameters.

·         String toString() - returns a String containing the number of steps taken so far and the current position -- The string should look something like: Steps: 12; Position: (-3,5)

2.       Compile what you have so far then open the file TestWalk.java. This file will be used to test your RandomWalk methods. So far it prompts the user to enter a boundary, a maximum number of steps, and the x and y coordinates of a position. Add the following:

·         Declare and instantiate two RandomWalk objects -- one with boundary 5, maximum steps 10, and centered at the origin (use the two parameter constructor) and the other with the values entered by the user.

·         Print out each object. Note that you won't get any information about the boundary or maximum number of steps (think about what your toString method does), but that's ok.

Compile and run the program to make sure everything is correct so far.

1.       Next add the following method to the RandomWalk class: void takeStep(). This method simulates taking a single step either up, down, left, or right. To "take a step" generate a random number with 4 values (say 0, 1, 2, 3) then use if-else statements to change the position (one random value will represent going right, one left, and so on). Your method should also increment the number of steps taken.

2.       Add a for loop to TestWalk.java to have each of your RandomWalk objects take 5 steps. Print out each object after each step so you can see what is going on. Compile and run the program to make sure it is correct so far.

3.       Now add to RandomWalk.java the following two methods. Each should be a single return statement that returns the value of a boolean expression.

·         boolean moreSteps() - returns true if the number of steps taken is less than the maximum number; returns false otherwise

·         boolean inBounds() - returns true if the current position is on the square (include the boundary as part of the square); returns false otherwise.

4.       Add to the RandomWalk class a method named walk that has no parameters and returns nothing. Its job is to simulate a complete random walk. That is, it should generate a sequence of steps as long the maximum number of steps has not been taken and it is still in bounds (inside the square). This should be a very simple loop (while or do... while) --- you will need to call the methods takeStep, moreSteps, and inBounds.

5.       Add to TestWalk.java a statement to instantiate a RandomWalk object with a boundary of 10 and 200 as the maximum number of steps. (You may want to comment out most of the code currently in TestWalk -- especially the user input and the loop that takes five steps -- as the walk method will be easier to test on its own. The /* ... */ style of comment is useful for this. But don't delete that other code, as you'll need it later in the lab.) Then add a statement to have the object walk. Print the object after the walk. Compile and run the program. Run it more than once -- you should be able to tell by the value printed whether the object went out of bounds or whether it stopped because it reached the maximum number of steps.

6.       Now write a client program in a file named DrunkenWalk.java. The program should simulate a drunk staggering randomly on some sort of platform (imagine a square dock in the middle of a lake). The goal of the program is to have the program simulate the walk many times (because of randomness each walk is different) and count the number of times the drunk falls off the platform (goes out of bounds). Your program should read in the boundary, the maximum number of steps, and the number of drunks to simulate. It should then have a loop (a for loop would be a good idea) that on each iteration instantiates a new RandomWalk object to represent a drunk, has the object walk, then determines whether or not the drunk fell off the platform (and updates a counter if it did). After the loop print out the number of times the drunk fell off. Compile and run your program. To see the "randomness" you should run it several times. Try input of 10 for the boundary and 200 for the number of steps first (sometimes the drunk falls off, sometimes not); try 10 for the boundary and 500 for the steps (you should see different behavior); try 50 for the boundary and 200 for the steps (again different behavior).

7.       Now write a second client program in a file named Collisions.java. This program should simulate two particles moving in space. Its goal is to determine the number of times the two particles collide (occupy exactly the same position after the same number of steps -- the steps could be thought of as simulating time). We'll assume the particles are in a very large space so use a large number for the boundary (such as 2,000,000). Use 100,000 for the maximum number of steps. (Don't enter the commas.) Start one particle at (-3, 0) and the other at (3, 0). (You can hardcode these values into the program; no need to enter them.) Your program should contain a loop that has each particle take a step as long as the particles have not exceeded the maximum number of steps. The program then determines how often the particles have collided. Note that in order for your program to know whether or not the two different RandomWalk objects are in the same place it needs to be able to find out the position. Hence, you need to add the following two methods to the RandomWalk class.

·         int getX() - returns the x coordinate of the current position

·         int getY() - returns the y coordinate of the current position

Compile and run your program to make sure it works. As before run it several times.

1.       In your Collisions.java program the condition to determine if the points are at the same position is a bit cumbersome. This is something that would be best put in a separate method. Add a static method to Collisions.java (after the main method) with signature

public static boolean samePosition (RandomWalk p1, RandomWalk p2)

The method should return true if p1 and p2 are at the same position and return false otherwise. Modify your main method so it calls samePosition rather than directly testing to see if the objects are at the same position. Test the program.

1.       In using random walks to simulate behavior it is often of interest to know how far away from the origin the object gets as it moves.

·         Add an instance variable maxDistance (type double) to the RandomWalk class. This should be set to 0 in each constructor.

·         Now the takeStep method needs to update this maximum when a step is taken. We'll add a couple of support methods to the class to do this. First, add a private method named max that takes one double parameters (say num1) and updates maxDistance to be the largest of num1 and the current maxDistance.

·         Add another support method findDistance that calculates the distance from the origin to the current position. Use the Pythagorean theorem to find the distance.

·         Add code to takeStep to update maxDistance. This can be done in a single statement using the max and findDistance methods.

·         Finally add an accessor method to return that distance so a client program can access it:

public double getMaxDistance()

·         Test the maximum by adding statements in TestWalk.java to get and print the maximum distance for each of the objects after the loop that had them take and print out 5 steps (this way you can see if the maximum is correct – each step is printed).