Second Summer 2002


Lab Notes Two: Sample problems. The solutions.

Here are examples of solutions, I skip the statement, I write only the sample solutions.

/***************************************************************************

  This is the solution to the first problem in the first problem set: it 
  displays the first five powers of the first five numbers: 1, 2, 3, 4, 5. 
  This is a bit of an overkill, but that's only because the problem is so
  elementary. Still, you should notice then that the third, fourth, and 
  fifth powers are being computed from previously calculated values. 

****************************************************************************/ 

class One { 

    public static void main(String[] args) { 

	int number = 1;
        int square = number * number; 
        int fourthPower = square * square; 

	System.out.print("First five powers of " + number + ": "); 

	System.out.println( number              + " " + 
                            square              + " " +
                            number * square     + " " + 
                            fourthPower         + " " + 
			    number * fourthPower );
	// done with 1. 

	number += 1;
        square = number * number; 
        fourthPower = square * square; 

	System.out.print("First five powers of " + number + ": "); 

	System.out.println( number              + " " + 
                            square              + " " +
                            number * square     + " " + 
                            fourthPower         + " " + 
			    number * fourthPower );
	// done with 2. 

	number += 1;
        square = number * number; 
        fourthPower = square * square; 

	System.out.print("First five powers of " + number + ": "); 

	System.out.println( number              + " " + 
                            square              + " " +
                            number * square     + " " + 
                            fourthPower         + " " + 
			    number * fourthPower );
	// done with 3. 

	number += 1;
        square = number * number; 
        fourthPower = square * square; 

	System.out.print("First five powers of " + number + ": "); 

	System.out.println( number              + " " + 
                            square              + " " +
                            number * square     + " " + 
                            fourthPower         + " " + 
			    number * fourthPower );
	// done with 4

	number += 1;
        square = number * number; 
        fourthPower = square * square; 

	System.out.print("First five powers of " + number + ": "); 

	System.out.println( number              + " " + 
                            square              + " " +
                            number * square     + " " + 
                            fourthPower         + " " + 
			    number * fourthPower );
	// done with 5 

	// -- finished 


    } 
} 

/******************************************************************************

  This is the solution to the second problem in the first problem set. Note 
  that you need ConsoleReader, which is available from the second set of lab 
  notes (Lab Two) off the class notes page or from the book. Once you get the 
  Consolereader class off the web notes place it in a file of its own, with 
  the name ConsoleReader.java in the same directory with Two.java and whose 
  source code is written below, then compile Two.java. 

*******************************************************************************/

class Two {
    public static void main(String[] args) { 

	ConsoleReader console = new ConsoleReader(System.in); 

	System.out.print("Please enter your first integer number, ");  
	System.out.println("then press Enter.");

	int n1 = console.readInt(); 

	System.out.print("Please enter your second integer number, ");  
	System.out.println("then press Enter.");

	int n2 = console.readInt(); 

	int sum = n1 + n2; 
	System.out.println(n1 + " + " + n2 + " = " + sum); 

	int diff = n1 - n2; 
	System.out.println(n1 + " - " + n2 + " = " + diff); 

	int prod = n1 * n2; 
	System.out.println(n1 + " * " + n2 + " = " + prod); 

	double avg = sum / 2.0; 
	System.out.println("avg(" + n1 + ", " + n2 + ") = " + avg);

	int dist = Math.abs(n1 - n2); 
	System.out.println("dist(" + n1 + ", " + n2 + ") = " + dist); 


	long max = Math.round(avg + dist / 2.0); 
        // neat trick; can you explain it? 

	System.out.println("max(" + n1 + ", " + n2 + ") = " + max); 


	long min = Math.round(avg - dist / 2.0); 
        // neat trick; can you explain it? 

	System.out.println("min(" + n1 + ", " + n2 + ") = " + min); 
          

    } 
}

/****************************************************************************

  This is the solution to the third problem on the first problem set. It 
  also needs the ConsoleReader class which can be taken from lab notes 2 
  (see problem 2 above for more details). This is not a hard problem the 
  difficulty (if any) is *only* in the conversion formulas. I decided to 
  use three named constants to avoid magic numbers and I express miles,
  and feet, as integers, while the number of inches is reported as a double. 

******************************************************************************/ 

class Three {
    public static void main(String[] args) {
	// create a console reader for user input, call it console 
	ConsoleReader console = new ConsoleReader(System.in); 

	// let the user know you're ready to receive input 
	System.out.println("Please enter the measurement in meters: "); 

	// get the measurement in meters from the user 
	double measurement = console.readDouble(); 

	// define three constants needed in the conversion 
	final double METERS_PER_MILE = 1609;
	final double METERS_PER_FOOT = 0.3048;  
	final double METERS_PER_INCH = 1/39.37;

	// first compute the number of miles
	int miles = (int) (measurement / METERS_PER_MILE); 

	// take those miles away from the measurement 
	// first make a copy of the original value of the measurement 
	double original = measurement;
        // then take the miles away
	measurement -= miles * METERS_PER_MILE; 

	// then compute the number of feet from the remaining distance 
	int feet = (int) (measurement / METERS_PER_FOOT); 

	// take the feet away from the measurement
	measurement -= feet * METERS_PER_FOOT; 

	// then compute the number of inches in the remaining distance 
	double inches = (measurement / METERS_PER_INCH); 

	// print title of report
	System.out.print("Your original measurement of ");
        System.out.print(original); 
        System.out.print(" meters has been converted.\n");

	// print conversion results 
	System.out.println("  " + miles + " miles,"); 
	System.out.println("  " + feet + " feet, and"); 
	System.out.println("  " + inches + " inches."); 

    } 
} 


/**********************************************************************

  This is the solution to problem four in first problem set. Note 
  that just as in problem 2 you need to have the ConsoleReader class 
  in a file in the same directory before compiling this class 

***********************************************************************/ 

class Four {
    public static void main(String[] args) {

	// get a connection to the keyboard 
	ConsoleReader console = new ConsoleReader(System.in); 

	// let the user know you're ready to receive the value for the radius 
	System.out.println("Please enter value for radius then hit enter."); 

	// get the value 
	double radius = console.readDouble(); 

	// echo value to user 
	System.out.println("Thank you. The radius is " + radius); 

	// apply formulas 
	double areaCircle           =     Math.PI * radius * radius; 
	double circumferenceCircle  = 2 * Math.PI * radius;
	double areaSphere           = 4 * Math.PI * radius * radius; 
	double volumeSphere         = 4 * Math.PI * radius * radius / 3;

        // as you can see I have an error here in the volume formula!

	// report the computed values
	System.out.println("Here are the computed values."); 

	System.out.println("Area of the circle: " + areaCircle); 
	System.out.println("Circumference: "      + circumferenceCircle); 
	System.out.println("Area of a sphere: "   + areaSphere); 
	System.out.println("Volume of sphere: "   + volumeSphere); 

    } 
}


/******************************************************************************

  This is the solution for the fifth problem in the first set. Like in
  problem 2 you need to have ConsoleReader.java in the same directory before
  compiling this class (Five.java). The problem gets the values from the user
  and then applies formulas and reports the computed values. 

*******************************************************************************/ 

class Five {
    public static void main(String[] args) {

	// get a connection to the keyboard 
	ConsoleReader console = new ConsoleReader(System.in); 

	// greet the user, ask for first value
	System.out.println("Please enter the value for the first side."); 
	double side1 = console.readDouble(); 

	// echo value to user
	System.out.println("Thanks. Side one is " + side1); 

	// ask for second value 
	System.out.println("Please enter the value for the second side."); 
	double side2 = console.readDouble(); 

	// echo second value 
	System.out.println("Thanks. Side two is " + side1); // side2!!

	// apply formulas, compute required quantities 
	double area = side1 * side2; 
	double perimeter = (side1 + side2 ) * 2; 
	double diagonal = Math.sqrt(side1 * side1 + side2 * side2); 

	// report all computed value 
	System.out.println("Area is: " + area + 
                           "\nPerimeter is: " + perimeter +
                           "\nDiagonal is: " + diagonal); 

    } 
}


/*****************************************************************************

  This is the solution to problem six in first problem set. ConsoleReader 
  is needed, use it as described in problem 2. This is a typical problem in 
  which you carefully need to cover roundoff errors so use Math.round after 
  you transform the problem in whole units (cents). 

******************************************************************************/ 

class Six {
    public static void main(String[] args) {

	// get a connection to the keyboard 
	ConsoleReader console = new ConsoleReader(System.in); 

	// ask the user for the amount due 
	System.out.println("Type the amount due then press enter."); 
	// read it 
	double due = console.readDouble(); 

	// ask the user for the amount received 
	System.out.println("Type the amount received then press enter."); 
	// read it 
        double received = console.readDouble(); 

	// assume received is bigger than due and compute difference 
	double difference = (received - due); 
	// you need to return this as change so make it a whole number
	// of cents regardless of how many decimals the user has entered  
  	int diff = (int)(Math.round(difference * 100)); 

	// tell the user what change you are processing 
	System.out.println("Give " + diff / 100.00 + " in change as follows: "); 

	// number of quarters; integer division 
	int quarters = diff / 25; 
	// report it 
	System.out.println("   " + quarters + " quarters"); 

	// adjust the remaining change (modulo) 
	diff = diff % 25;

	// compute the number of dimes
	int dimes = diff / 10; 
	// report it 
	System.out.println("   " + dimes + " dimes"); 

	// adjust remaining cents (notice shortcut operator) 
	diff %= 10; // notice anything compared to the previous assignment? 

	// these are the cents 
	int cents = diff; 
	// report them too 
	System.out.println("   " + cents + " cents"); 


    } 
}


/**********************************************************************

  This is the solution to problem seven in the first problem set. 
  Need ConsoleReader in the same directory before you can compile 
  it (see problem 2). Formulas used are straightforward, easy. 

***********************************************************************/ 

class Seven {
    public static void main(String[] args) {

	// get a connection to the keyboard 
	ConsoleReader console = new ConsoleReader(System.in); 

	// greet the user, ask for number of gallons 
	System.out.println("Please enter the number of gallons then press enter.");
	// read number of gallons
	double gallons = console.readDouble(); 

	// ask for fuel efficiency
	System.out.println("Please enter the fuel efficiency " + 
                           "(miles/gallon) then press enter. "); 
	// read user input  
	double efficiency = console.readDouble(); 

	// ask for price per gallon 
	System.out.println("Please enter the price per gallon, then press enter."); 
	// read price from user 
	double price = console.readDouble(); 

	// computer how far the user can go with that much gas 
	double howFar = efficiency * gallons; 

	// compute how much that will cost 
	double totalCost = price * gallons; 

	// divide this by howFar and multiply by 100 to get price per 100 miles 
	double pricePer100Miles = totalCost / howFar * 100; 

	System.out.println("With the gas in the tank you can go " + 
			   howFar + " miles, \nat a cost of "     + 
                           pricePer100Miles + " per 100 miles."); 

    } 
}

/*******************************************************************************

  This is the solution to problem eight in the first set of problems. You 
  need ConsoleReader in the same directory before compiling, as detailed at 
  problem 2. Essentially you read a number as string, and write it back as
  required, with a comma separating the thousands (the last three digits). As
  before, no error checking is done, user is assumed to be program-friendly. 

********************************************************************************/ 

class Eight {
    public static void main(String[] args) {

	// get a connection to the keyboard 
	ConsoleReader console = new ConsoleReader(System.in); 

	// ask the user to enter a number 
	System.out.print("Please enter an integer >= 1000: "); 

	// read the number, assume the user types the right thing 
	String number = console.readLine(); 

	// report the number with the comma separating the thousands 
	System.out.println(// first write digits up to thousands 
			   number.substring(0, number.length() - 3) + 
			   "," + // then write the comma 
			   // and the remaining part (the thousands)
			   number.substring(number.length()-3));
    } 
}

/*************************************************************************

  This is the solution to the nineth problem in the first problem 
  set. You need ConsoleReader in the same directory, as explained in 
  problem 2, before you can compile this program. This program assumes 
  that the user types in a number that contains a comma separating the 
  thousands from the rest of the number. 

**************************************************************************/ 

class Nine {
    public static void main(String[] args) {

	// get a connection to the keyboard 
	ConsoleReader console = new ConsoleReader(System.in); 

	// ask the user for input 
	System.out.print("Please enter an integer between 1,000 and 999,999: ");
	// read user's input 
	String number = console.readLine(); 

	// get the first part (no comma or thousands) 
	String firstPart = number.substring(0, number.length() - 4); 
	// get last three digits 
	String lastThreeDigits = number.substring(number.length() - 3); 

	// print the two without the comma 
	System.out.println(firstPart + lastThreeDigits); 

    } 
}

/*************************************************************************

  This is the solution to the tenth problem in the first problem set. 
  Given the hint it's straightforward. We define two patterns and we
  print them accordingly to obtain the desired output. 

**************************************************************************/ 

class Ten {
    public static void main(String[] args) {

	// first pattern, comb-shaped 
	String comb   = "+--+--+--+\n" + 
                        "|  |  |  |\n"; 

	// second pattern, bottom line 
	String bottom = "+--+--+--+\n"; 

	// print the grid for the user 
	System.out.println(comb + comb + comb + bottom); 

    } 
}

/****************************************************************************

  This is the solution to problem eleven of the first problem set. You
  read from the user a string of digits and then make sure the resulting
  string is at least 5 characters long. Once you have that, just print the
  characters one by one separated by blank spaces. We just print the last
  five, and we know we have at least five characters in the string because
  we have taken care to pad it with a string of five blanks from the start.

*****************************************************************************/ 

class Eleven {
    public static void main(String[] args) {

	// open a connection with the keyboard 
	ConsoleReader console = new ConsoleReader(System.in); 

	// tell the user to enter a number
	System.out.print("Please enter a number between 0 and 99999: "); 
	// read the number the user types 
	String number = console.readLine(); 

	// pad the number with five spaces 
	number = "     " + number; // thus string has at least 5 characters

	int i = number.length() - 1; // index of last char in string 

	// print the last five digits of the number 
	// note the order in which we print the chars and their indices 
	System.out.print(number.substring(i-4, i-3) + " "); 
	System.out.print(number.substring(i-3, i-2) + " "); 
	System.out.print(number.substring(i-2, i-1) + " "); 
	System.out.print(number.substring(i-1, i)   + " "); 
	System.out.print(number.substring(i)        + " \n"); 
    } 
}


/************************************************************************** 

  This is the solution to problem twelve in the first problem set. We 
  first compute the constant for the conversion from degrees to radians
  and then we repeatedly use the value of this constant, stored as x.  

***************************************************************************/ 

class Twelve {
    public static void main(String[] args) {

	double x = Math.PI / 180; // degreesToRadians constant  

	System.out.println
	    (" 0 degrees: " + Math.sin( 0    ) + " " + Math.cos( 0    ));

        System.out.println
	    ("30 degrees: " + Math.sin(30 * x) + " " + Math.cos(30 * x));

        System.out.println
	    ("45 degrees: " + Math.sin(45 * x) + " " + Math.cos(45 * x)); 

        System.out.println
	    ("60 degrees: " + Math.sin(60 * x) + " " + Math.cos(60 * x));

        System.out.println
	    ("90 degrees: " + Math.sin(90 * x) + " " + Math.cos(90 * x));

    } 
}


/**************************************************************************

  This is the solution to problem thirteen in the first problem set. You 
  need ConsoleReader in the same directory, as explained in problem two, 
  before you can compile and run this program. 

***************************************************************************/ 

class Thirteen {
    public static void main(String[] args) {

        // open a keyboard connection 
	ConsoleReader console = new ConsoleReader(System.in); 

        // greet the user and ask for input 
	System.out.println("Hello, my name is Hal!"); 
	System.out.println("What is your name?"); 

        // get user input store it in String variable called name 
	String name = console.readLine(); 

        // echo the data to the user and ask for request 
	System.out.println("Hello, " + name + ". I am glad to meet you."); 
	System.out.println("What would you like me to do?"); 

        // get the request 
	String request = console.readLine(); 

        // end the conversation politely 
	System.out.println("I am sorry, " + name + ". I cannot do that."); 

    } 
}

/*******************************************************************************

  This is the solution to problem fourteen in the first problem set. You 
  need ConsoleReader in the same directory, as explained in problem two, to
  compile and run this program. Note that the hint in the text is almost all
  you need, minus one trick that makes sure that we can never divide by zero
  and also produces an n of 1 when x is zero (avoiding division by zero too). 

********************************************************************************/ 

class Fourteen {
    public static void main(String[] args) {

	// get a connection to the keyboard 
	ConsoleReader console = new ConsoleReader(System.in); 

	// greet user, ask for input 
	System.out.println("Please enter number of gallons then press enter."); 
	// get number of gallons 
	double gallons = console.readDouble(); 

	// ask for fuel efficiency 
	System.out.println("Please enter fuel efficiency in miles per gallon."); 
	// get it from user 
	double efficiency = console.readDouble(); 

	// ask for desired distance 
	System.out.println("Please enter distance in miles you want to cover.");
	// get distance 
        double distance = console.readDouble(); 

	// prepare the answer 
	String answer = " not "; 

	// compute x, the difference between what you can and what you want 
	double x = efficiency * gallons - distance; 

	// avoid division by zero with this, can you see how? 
	double epsilon = 0.00001; 
	// make n 1 if x >= 0 and 0 otherwise 
	long n = Math.round( ( (x + Math.abs(x) ) * x + epsilon) / 
                             (              2 * x * x + epsilon)
                           ); 
	// why can't n be int? what do I need to do if I want it to be an int? 

	// report the correct answer 
	System.out.println("You will" + 
                           answer.substring(0, 5 - 4 * (int)n) + 
                           "make it."); 
	// why do I need to convert n from the long it is to an int here? 

    } 
}
Worthwhile observation made by a student one semester:

The solution you have just seen is OK. The epsilon variable is needed above so we don't divide by 0 (zero). But when x is negative and much smaller than epsilon the result is incorrect. What do we do? (This is problem P2.18 page 99 in the book). The trick is to think of the problem in physical terms: if you're really using a car and if in your calculations you use an epsilon that is small enough, e.g. about 0.1in (or smaller, like 0.001 of the car's length) then

  1. for negative x above this small value the formula says: "You will make it!"
  2. and for all practical purposes that's correct, since you can walk that distance
  3. but we need to be aware of the approximation, we definitely need to!
  4. Other than this "negative micron" case, the formula is perfect.
So that's it. But does anyone have a formula that covers even this case with accuracy?

/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

  This is the solution to problem fifteen in the first problem set.
  You need to have ConsoleReader in a file in the same directory before 
  you can compile and run this. This problem adds 24 hours to the hours
  difference to avoid negative values and takes the remainder with 24 
  to avoid values bigger than 24 (number of hours in a day). It also 
  transforms the hours into minutes to absorb possible negative values
  from the difference between given minutes. 

 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */ 

class Fifteen {
    public static void main(String[] args) {

	// get a connection to the keyboard 
	ConsoleReader console = new ConsoleReader(System.in); 

	// greet the user, ask for time 
	System.out.print("Please enter the first time: "); 
	// get the first time as a string (in military format)
	String first = console.readLine(); 

	// compute the number of hours from first two characters 
	int hours1 = Integer.parseInt(first.substring(0, 2)); 
	// compute minutes from next two characters 
	int minutes1 = Integer.parseInt(first.substring(2, 4)); 

	// ask for second time
	System.out.print("Please enter the second time: "); 
	// get it 
	String second = console.readLine(); 

	// compute hours, same as before 
	int hours2 = Integer.parseInt(second.substring(0, 2)); 
	// compute minutes 
	int minutes2 = Integer.parseInt(second.substring(2, 4)); 

	// compute the difference between hours, add 24 then divide
        // by 24 and take the remainder to express the hour difference 
	int difHours  = (hours2 + 24 - hours1) % 24; 
	// make these hours into minutes 
	int hrsToMins = difHours * 60; 
	// compute straight difference between given minutes, could be < 0
	int difMins   = minutes2 - minutes1; 
	// add this to total count of minutes 
	hrsToMins    += difMins; 

	// report total count of minutes in hours and minutes 
	System.out.println(
          hrsToMins / 60 + " hours " + hrsToMins % 60 + " minutes"
        ); 

    } 
}


/*******************************************************************************

  This is the solution to problem number sixteen in the first problem
  set. The program attempts to use a different way of computing the average 
  of two numbers a and b by computing (1/a + 1/b)*a*b/2 in stages. It is OK
  if the numbers entered are restricted to integers, but to correctly compute
  at all stages in the program we need to circumvent integer division which
  can result in a loss of precision. So we turn everything in float and all
  is well after that. You need ConsoleReader as explained in problem 2. 

********************************************************************************/ 


class Sixteen { 
    public static void main(String[] args) {
	ConsoleReader console = new ConsoleReader(System.in);
	// one change below 
	float total = 0;
	System.out.println("Please enter a positive number:");
	// second change below 
	float x1 = (float)Integer.parseInt(console.readLine());
	System.out.println("total = " + total);
	total = total + 1 / x1;
	System.out.println("total = " + total);
	System.out.println("Please enter a positive number:");
	// third change below 
	float x2 = (float)Integer.parseInt(console.readLine());
	total = total + 1 / x2;
	System.out.println("total = " + total);
	total = total * x1 * x2 / 2;
	System.out.println("total = " + total);
	System.out.println("The average is " + total);
	// that's it, three changes overall
    }
}


/****************************************************************************

  This is the solution to problem seventeen in the first set of problems.

  The text gives a suggestion that is enough to solve the problem, although 
  in this particular case you can't do it directly as suggested. But reading 
  the section on constants in the book you can come up with the following 
  absolutely obvious solution: 

*****************************************************************************/ 


class Seventeen { 
    public static void main(String[] args) {

	// define the letters as strings
	final String LETTER_H = "*   *\n*   *\n*****\n*   *\n*   *\n\n";
	final String LETTER_E = "*****\n*    \n*****\n*    \n*****\n\n";
	final String LETTER_L = "*    \n*    \n*    \n*    \n*****\n\n";
	final String LETTER_O = " *** \n*   *\n*   *\n*   *\n *** \n\n";

	// print them one after another 
	System.out.println(
          LETTER_H + LETTER_E + LETTER_L + LETTER_L + LETTER_O
        );

    }
}


/***********************************************************************************

  Solution to problem eighteen in the first problem set. Use ConsoleReader 
  from lab notes as explained in problem set 2. The trick here (as hinted in the 
  text) is to transform a number for a month in the position in the string where 
  the month name is starting, all names being made of the same length, and then 
  concatenated together in one final string. 

************************************************************************************/ 

class Eighteen { 
    public static void main(String[] args) {

	String monthNames = "January   " +
                            "February  " +
                            "March     " +
                            "April     " +
                            "May       " +
                            "June      " +
                            "July      " +
                            "August    " +
      	                    "September " + // longest
                            "October   " +
                            "November  " +
                            "December  "    ;

	// open a connection with the keyboard 
	ConsoleReader console = new ConsoleReader(System.in); 

	// greet the user, and ask for input 
	System.out.println("Please enter a month number from 1 to 12."); 
	// get month name 
	int month = console.readInt(); 
	// report the name of the month 
	System.out.println(
            monthNames.substring("September ".length() * (month-1), 
                                 "September ".length()*month));

	// formula uses the length of the longest name 
    }
}


/******************************************************************************

  This is solution to problem nineteen in the first set. We start from the 
  MakePassword problem on page 79 in the text. Following the hint the rest 
  becomes straightforward, including how you get the last four digits of the
  product between the random number and the age, to concatenate to initials. 
  Note that you need to import the Random class from the java.util package. 

  Honestly: a better way to get random numbers is Math.random, but we stay
  within the framework of the book for just this problem, from Chapter 2. 

*******************************************************************************/ 

import java.util.Random; // need to import this to work with random numbers 

class Nineteen { 
    public static void main(String[] args) {
	String firstName  = "William"; 
	String middleName = "Jefferson"; 
	String lastName    = "Clinton"; 

	// extract initials 

	String initials = 
            firstName.substring (0, 1) + 
	    middleName.substring(0, 1) + 
	    lastName.substring  (0, 1);

	// append age 

	int age = 54; 

	int r = new Random().nextInt(1000); 

	// multiply age by random number

	String product = (age * r) + ""; 

	// concatenate initials with last four digits of product 

	String password = initials + product.substring(product.length() - 4); 

	System.out.println("Your password is: " + password); 

    }
}

This last problem was from the previous administration.


Last updated: Jun 14, 2002 by Adrian German for A201