CS 46A - Lecture 9

Pre-class reading

• Sections 4.1 - 4.3

Number Types

• int: integers, no fractional part:

  1, -4, 0

• double: floating-point numbers (double precision):

  0.5, -3.11111, 4.3E24, 1E-14

• A numeric computation overflows if the result falls outside the range for the number type:

  int n = 1000000;
  System.out.println(n * n); // prints -727379968

• Java: 8 primitive types, including four integer types and two floating point types

Primitive Types

Number Types: Floating-point Types

• Rounding errors occur when an exact conversion between numbers is not possible:

  double f = 4.35;
  System.out.println(100 * f); // prints 434.99999999999994

• Java: Illegal to assign a floating-point expression to an integer variable:

  double balance = 13.75;
  int dollars = balance; // Error

Lecture 9 Clicker Question 1

Suppose you want to write a program that works with population data from various countries. Roughly half of the world population lives in India and China, each of which has about 1.2 x 10⁹ inhabitants.

Which of the below is the best argument for selecting an appropriate Java data type? 

1. Use int because a country never has a fractional number of people
2. Use int because it is more accurate than double
3. Use double because an int cannot hold a number as large as  1.2 x 10⁹
4. Use double because an int cannot hold the entire world population

Constants: final

• A final variable is a constant
• Once its value has been set, it cannot be changed
• Named constants make programs easier to read and maintain
• Convention: use all-uppercase names for constants:

  final double QUARTER_VALUE = 0.25;
  final double DIME_VALUE = 0.1;
  final double NICKEL_VALUE = 0.05;
  final double PENNY_VALUE = 0.01;
  payment = dollars + quarters * QUARTER_VALUE + dimes * DIME_VALUE
     + nickels * NICKEL_VALUE + pennies * PENNY_VALUE;

Constants: static final

• If constant values are needed in several methods, declare them together with the instance variables of a class and tag them as static and final
• Give static final constants public access to enable other classes to use them:

  public class Math
  {
     . . .
     public static final double E = 2.7182818284590452354;
     public static final double PI = 3.14159265358979323846;
  }
  
  double circumference = Math.PI * diameter;

Syntax 4.1 Constant Declaration

ch04/cashregister/CashRegister.java

/**
   A cash register totals up sales and computes change due.
*/
public class CashRegister
{
   public static final double QUARTER_VALUE = 0.25;
   public static final double DIME_VALUE = 0.1;
   public static final double NICKEL_VALUE = 0.05;
   public static final double PENNY_VALUE = 0.01;

   private double purchase;
   private double payment;

   /**
      Constructs a cash register with no money in it.
   */
   public CashRegister()
   {
      purchase = 0;
      payment = 0;
   }

   /**
      Records the purchase price of an item.
      @param amount the price of the purchased item
   */
   public void recordPurchase(double amount)
   {
      purchase = purchase + amount;
   }
   
   /**
      Enters the payment received from the customer.
      @param dollars the number of dollars in the payment
      @param quarters the number of quarters in the payment
      @param dimes the number of dimes in the payment
      @param nickels the number of nickels in the payment
      @param pennies the number of pennies in the payment
   */
   public void enterPayment(int dollars, int quarters, 
         int dimes, int nickels, int pennies)
   {
      payment = dollars + quarters * QUARTER_VALUE + dimes * DIME_VALUE
            + nickels * NICKEL_VALUE + pennies * PENNY_VALUE;
   }
   
   /**
      Computes the change due and resets the machine for the next customer.
      @return the change due to the customer
   */
   public double giveChange()
   {
      double change = payment - purchase;
      purchase = 0;
      payment = 0;
      return change;
   }
}

ch04/cashregister/CashRegisterTester.java

/**
   This class tests the CashRegister class.
*/
public class CashRegisterTester
{
   public static void main(String[] args)
   {
      CashRegister register = new CashRegister();

      register.recordPurchase(0.75);
      register.recordPurchase(1.50);
      register.enterPayment(2, 0, 5, 0, 0);
      System.out.print("Change: ");
      System.out.println(register.giveChange());
      System.out.println("Expected: 0.25");

      register.recordPurchase(2.25);
      register.recordPurchase(19.25);
      register.enterPayment(23, 2, 0, 0, 0);
      System.out.print("Change: ");
      System.out.println(register.giveChange());
      System.out.println("Expected: 2.0");
   }
}

Program Run:

• Change: 0.25
  Expected: 0.25
  Change: 2.0
  Expected: 2.0

Lecture 9 Clicker Question 2

What is wrong with the following statement sequence?

double radius = 20;
double circumference = 3.14 * radius;

1. 3.14 is not an accurate representation of π; use 3.14159 instead
2. You should use a named constant, not a literal number 3.14
3. The circumference is actually πr²
4. All of the above

Arithmetic Operators

• Four basic operators:
  • addition: +
  • subtraction: -
  • multiplication: *
  • division: /
• Parentheses control the order of subexpression computation:

  (a + b) / 2

• Multiplication and division bind more strongly than addition and subtraction:

  a + b / 2

Increment and Decrement

• items++ is the same as items = items + 1
• items-- subtracts 1 from items
• 

Integer Division

• / is the division operator
• If both arguments are integers, the result is an integer. The remainder is discarded
• 7.0 / 4 yields 1.75
  7 / 4 yields 1
• Get the remainder with % (pronounced "modulo")
  7 % 4 is 3

Integer Division

Example:

final int PENNIES_PER_NICKEL = 5;
final int PENNIES_PER_DIME = 10;
final int PENNIES_PER_QUARTER = 25;
final int PENNIES_PER_DOLLAR = 100;

// Compute total value in pennies
int total = dollars * PENNIES_PER_DOLLAR + quarters * PENNIES_PER_QUARTER
   + nickels * PENNIES_PER_NICKEL + dimes * PENNIES_PER_DIME + pennies;

// Use integer division to convert to dollars, cents
int dollars = total / PENNIES_PER_DOLLAR;
int cents = total % PENNIES_PER_DOLLAR;

Powers and Roots

• Math class contains methods sqrt and pow to compute square roots and powers
• To compute xⁿ, you write Math.pow(x, n)
• However, to compute x² it is significantly more efficient simply to compute x * x
• To take the square root of a number, use the Math.sqrt; for example, Math.sqrt(x)
• In Java,
  
  can be represented as
  (-b + Math.sqrt(b * b - 4 * a * c)) / (2 * a)

Analyzing an Expression

Mathematical Methods

Cast and Round

• Cast converts a value to a different type:

  double balance = total + tax;
  int dollars = (int) balance;

  Cast discards fractional part.

• Math.round converts a floating-point number to nearest integer:

  long rounded = Math.round(balance); // if balance is 13.75, then
                                      // rounded is set to 14

Syntax 4.2 Cast

Arithmetic Expressions

Lecture 9 Clicker Question 3

What is the value of n after the following sequence of statements?

int n = 10;
n++;
n = n % 10;
n--;
n--;

1. n is 1
2. n is 0
3. n is -1
4. n is -2

Lecture 9 Clicker Question 4

The variable price contains the price of a product in dollars and cents, such as 19.75. You want to get the dollars. What do you do?

1. int dollars = (int) Math.round(price);
2. int dollars = (int) price;
3. int dollars = price / 100;
4. int price = ((int) price * 100) / 100;