Description

• Marks: 0

Prerequisite:
• Familiar with the CS2030S lab guidelines
• Able to access the Sunre student account (stu.comp.nus.edu.sg) via ssh
• Completed basic vim lessons
Estimating Pi using Monte Carlo Method
The Monte Carlo method for estimating the value of pi is as follows. We have a square of width 2r, and within it, a circle with a radius of r.
We randomly generate k points within the square. We count how many points fall within the circle. Suppose n points out of k fall within the circle.
Since the area of the square is 4r^2 and the area of the circle is pi r^2, the ratio between them is pi/4. The ratio n/k should therefore be pi/4, and pi can be estimated as 4n/k.
Background: Random Number Generator
To estimate pi using the method above, we need to use a random number generation. A random number generator is an entity that spews up one random number after another. We, however, cannot generate a truly random number algorithmically. We can only generate a pseudo-random number. A pseudo-random number generator can be initialized with a seed. A pseudo-random number generator, when initialized with the same seed, always produces the same sequence of (seemingly random) numbers.
Java provides a class java.util.Random that encapsulates a pseudo-random number generator. We can create a random number generator with a seed:
1 Random rng = new Random(1);
We can then call rng.nextDouble() repeatedly to generate random numbers between 0 and 1.
Using a xed seed is important for testing since the execution of the program will be deterministic, even when random numbers are involved.
Files Provided
Inside the directory Lab0 , you will see the following les:
• Skeleton Java les: Point.java , RandomPoint.java , Circle.java , Lab0.java
• Inputs and outputs for Lab0 : inputs∕Lab0.k.in and outputs∕Lab0.k.out for different values of k.
• Bash script: test.sh for testing Lab0 if it estimates pi correctly, by comparing the output when running Lab0 on inputs∕Lab0.k.in to the expected output in
outputs∕Lab0.k.out
• Unit tests for Java classes: Test1.java to Test3.java . These les test individual classes to check if they have the expected behavior.
Your Task
A skeleton code has been given. Your task is to complete the implementation of the classes Point , RandomPoint , Circle , and Lab0 , according to the OO principles that were taught:
abstraction, encapsulation, information hiding, inheritance, tell-don’t-ask.
The Point class
Fill in the class Point with the constructor and the necessary elds. Add a toString method so that a string representation as shown in the examples below is returned. For instance,

should return the string:

You will need to come back to this class and add other methods later. For now, check that your constructor and toString methods are correct.
Some simple tests are provided in the le Test1.java . Note that these test cases are not exhaustive and you are encouraged to test your Point class on your own. Proceed to the next class if you are convinced your Point class is correct.
1 cs2030s@stu1:~Labs∕Lab0$ javac Test1.java
2 cs2030s@stu1:~Labs∕Lab0$ java Test1
3 Point: new at (0, 0).. ok
4 Point: new at (-3.14, 1.59).. ok
As an aside, note that we do not need to explicitly compile Point.java . Since Test1.java refers to the Point class, javac is smart enough to compile Point.java if Point.class is not found, or recompile Point.java if it is newer than Point.class .
The Circle class
Most of the Circle class has been written for you. You need to complete the method contains . The method checks if a given point is contained in the calling Circle object. To
complete this method according to the tell-don’t-ask principle, you will need to add a method in the Point class.
Some simple tests are provided in the le Test2.java . These test cases are not exhaustive and you are encouraged to test your Circle class extensively.
1 cs2030s@stu1:~Labs∕Lab0$ javac Test2.java
2 cs2030s@stu1:~Labs∕Lab0$ java Test2
3 Circle: new at (0, 0) with radius 4).. ok
4 Circle centered at (0, 0) with radius 4 contains (0, 0).. ok
5 Circle centered at (0, 0) with radius 4 does not contain (4, 3).. ok
6 Circle centered at (0, 0) with radius 4 does not contain (3, 4).. ok
7 Circle centered at (2, -3) with radius 0.5 contains (1.8, -3.1).. ok
8 Circle centered at (2, -3) with radius 0.5 does not contain (1.8, -4).. ok
The RandomPoint class
RandomPoint is a subclass of Point that represents a randomly generated point. The random number generator that generates a random point has a default seed of 1. There is a public method setSeed() that we can use to update the seed. Here is how it can be used:
To generate a new point,
1 Point p = new RandomPoint(minX, maxX, minY, maxY);
minX , minY , maxX , maxY represent the minimum and maximum possible x and y values
respectively, for each randomly generated point.
To set the random seed,

Tip: What are the elds and methods that should be associated with the class RandomPoint instead of an instance of RandomPoint ?
Some simple tests are provided in the le Test3.java . These test cases are not exhaustive and you are encouraged to test your RandomPoint class extensively.
1 cs2030s@stu1:~Labs∕Lab0$ javac Test3.java
2 cs2030s@stu1:~Labs∕Lab0$ java Test3
3 RandomPoint: is a subtype of Point.. ok
4 RandomPoint: generate a new point with default seed.. ok
5 RandomPoint: generate a new point with seed 10.. ok
6 RandomPoint: generate a new point with the same seed.. ok
7 RandomPoint: reset seed to 10 and generate a new point.. ok
Lab0
Lab0 is the main program to solve the problem above. The main method is provided. It includes the method to read in the number of points and the seed from the standard input and to print the estimated pi value.
The method estimatePi is incomplete. Determine how you should declare estimatePi , then complete the body by generating random points and count how many fall under the given circle.
Use a circle centered at (0.5,0.5) with radius 0.5 for this purpose. Use long and double within estimatePi for computation to ensure that you have the right precision.
Tip: In Java, using ∕ on two integers result in an integer division. Make sure one of the operand of ∕ is a oating point number if you intend to use ∕ for oating point division.
To run Lab0 and enter the input manually, run
1 java Lab0
The program will pause, waiting for inputs from keyboards. Enter two numbers. The rst is the number of points. The second is the seed.
You can enter the two numbers into a text le, say, TEST , and then run
1 java Lab0 < TEST
Sample inputs and outputs have been provided and can be found under the inputs and outputs directory.
To test your implementation of Lab0 , automatically against the test data given in inputs

Submission