Last Update: Nov. 9, 2025

Assignment 5 (PS5): Methods with Return, Input, Formatting, Conditionals

This assignment focuses on methods with parameters and returns. It will use methods in the StdDraw class, the Math class, and the printf method.

Due: 11:55 PM, Sunday, Nov. 16, 2025.

• Grading rubric
• Elements of programming style

Part 0: Text Input/Output (Scanner and Printf) and Conditionals.

Part 1. Cashier [input/output, arithmetic operators; data range and precision; Math class]

The program reads in unit price, quantity, sales tax, and paid amount. It then determines the amount of change, if any, that would be received; and prints the numbers of 50 dollars, 20 dollars, 10 dollars, 5 dollars, 1 dollars, quarters, dimes, nickels, and pennies that should be returned. Maximize the dollars/coins with the highest value. Follow the format below:

        Welcome to Cashier!
        
        Enter the unit price: 1.28
        Enter the quantity: 1
        Enter the sales tax rate: 6.0
        The total owed amount is $1.36 ($1.28 plus 6.00% tax)
        Enter the paid amount: 5.00
        Your change of $3.64 is given as:
        0 50 dollars
        0 20 dollars
        0 10 dollars
        0 5 dollars
        3 1 dollars
        2 quarters
        1 dime
        0 nickels
        4 pennies
        

Implementation Details

• The output depends on the amount paid and amount owed. You will need the if statement to test whose one is larger: paid or owed. The example is for the case of paid is higher than owed. If paid is less than owed, the program should print a message saying:

          You still owe $xx.xx.
          

  If paid is equal to owed, the output should be:

          Thank you for paying the exact amount!
          

• Please define a method

          static String getChanges(double owed, double paid)
          

  This method will compute the output String after getting all user inputs (that is, the output starting from the line Your change of ...). A suggestion is that you test this method directly in main without the need to repeatedly giving input by keyboard.
• We suggest that you test your program with many cases. One test case is owed = 98.76, paid = 103.56.
• A common problem is how to handle the mixed double and integer operations. You may consider using an integer after you have the change. Some integer operators such as % can be quite handy.
• You should use System.out.printf and String.format to control the output format, in particular, of the currency and tax rate. String.format has the same control as System.out.prinf(), where String.format returns and System.out.printf prints.
• Don't forget to place the following declaration at the top of your program, to be able to read user input:

          import java.util.Scanner; // so that I can use Scanner 
          

Please put the solution into a file named Cashier.java. You should also use Cashier as the name of the class.

Discussions

The strategy of maximizing the dollars/coins with the highest value is also referred to as a greedy strategy. The greedy strategy produces a solution that uses the minimum number of dollars/coins in dispensing change for the American currency system. However, there are currency systems that use different denominations for which this property is not valid. One example is the old British coin system consisting of a halfpenny, a penny, threepence, sixpence, a shilling (12 pence), a florin (24 pence), a half-crown (30 pence), a crown (60 pence), a pound (240 pence), and a guinea (252 pence).

1. Can you give an amount of change so that the greedy strategy does not produce the minimum number of coins in the old British system?

Part 2: Monte Carlo Simulation (Conditional, Accumulative Loop)

Monte Carlo methods are widely used in many fields, in particular physical and mathematical fields when it is impossible to obtain a closed-form expression or infeasible to apply a deterministic algorithm. According to this link: "The modern version of the Monte Carlo method was invented in the late 1940s by Stanislaw Ulam, while he was working on nuclear weapon projects at the Los Alamos National Laboratory. It was named, by Nicholas Metropolis, after the Monte Carlo Casino, where Ulam's uncle often gambled."

In this part, we will implement the classical Monte Carlo example: computing the value of Pi. The setup of the problem is as follows. There is a 1 by 1 square. There is a circle with radius 0.5 in the square. A picture of the setup is shown below.

The basic idea of Monte Carlo in this setting is simple. As your program "drops" points randomly into the square, some of the points will drop into the circle, and some will not. Suppose the program drops N points and H are in the circle. Then H divided by N (called hit ratio) should be proportional to the ratio of the area of the circle and that of the square. Please derive pi from this expression.

We provide a skeleton to get you started. The details of requirements on your program consist of the following:

• Your program will define a method named getN to ask the user for the number N. If the user input is less than 5, the method will just print an error message and exit (System.exit(1)); otherwise, the method returns the user input number. The signature of the method is:

          public static int getN();
          

• Your program will use Math.random() to generate random numbers.
• Your program will define a method named isInCircle() to check if a point at (x, y) is in the circle. The signature of the method is:

          public static boolean isInCircle(double x, double y);
          

• Your program will estimate the value of pi as points are dropped. Your program should define and use a method named estimatePi, which returns the current estimate of Pi:

          public static double estimatePi(int pointsInCircle, int pointsDroppedSoFar);
          

• Your program will output the estimate of pi so that you can observe how the accuracy of the estimation changes as more points are dropped. As the accuracy changes faster initially, we use the following schedule to determine when to output an estimation of pi:
  • your program will output its estimation every 5 iterations before 50 points are dropped;
  • then your program will output its estimation every 50 iterations before 1000 points are dropped;
  • then your program will output its estimation every 1000 iterations. For each estimation, please print the iteration number (e.g., 5, 10, 15, 50, 100, ...), followed by a tab (\t), and followed by your current estimation of p.

  An example output is MonteCarloPi_sample_out.txt.

• You need to save the output of a run when the number of points is 5000, and then generate a plot of the progress where the x-axis should be the iteration number, and the y-axis should be your current estimation of pi. Please name your plot MonteCarloPi.png (or another common image format) containing the chart generated. You can use any graphing software (e.g., MS Excel) to produce the plot. Just make sure to export it into the .png format.
• The output control condition should be tested using a single Boolean expression, instead of multiple cases:

              if () {
                   output estimate of pi
              }
          

  We enforce this condition so that you can practice more complex Boolean expressions.

Please name your class MonteCarloPi and save the class in a file named MonteCarloPi.java.

Part 3: Submit Your Assignment

Please submit electronically for assignment #5 and make sure you submit (1) Cashier.java, Cashier.doc (or Cashier.txt), and (2) MonteCarloPi.java.java. Please be sure that you choose the .java file, NOT the .class file when uploading. The .class file is the compiled version of your code which we cannot examine and grade. So, please make sure you submit *.java files. Also, remember that you always need to include the header.

    //*******************************************************************
    //
    //   File: FileName.java          Assignment No.: 5
    //
    //   Author: <your name>      Email: <your email>
    //
    //   Class: ClassName
    // 
    //   Time spent on this problem: 
    //   --------------------
    //      Please give a description about your design. 
    //
    //*******************************************************************

The submission repository for ps5 is https://gitee.com/simmonsong/ct-xmuf25-ps5.

Please follow the instructions in Assignments Submission to submit your assignments.

Git introduction is a help document for git utilization..

Enjoy!