Chapter Goals

• To understand integer and floating-point numbers
• To recognize the limitations of the numeric types
• To become aware of causes for overflow and roundoff errors
• To understand the proper use of constants
• To write arithmetic expressions in Java
• To use the String type to manipulate character strings
• To write programs that read input and produce formatted output

Number Types

• Every value in Java is either:
  • a reference to an object
  • one of the eight primitive types
• Java has eight primitive types:
  • four integer types
  • two floating-point types
  • two other

Primitive Types

Type	Description	Size
int	The integer type, with range -2,147,483,648 (Integer.MIN_VALUE) . . . 2,147,483,647 (Integer.MAX_VALUE)	4 bytes
byte	The type describing a single byte, with range -128 . . . 127	1 byte
short	The short integer type, with range -32768 . . . 32767	2 bytes
long	The long integer type, with range -9,223,372,036,854,775,808 . . . 9,223,372,036,854,775,807	8 bytes
double	The double-precision floating-point type, with a range of about ±10308 and about 15 significant decimal digits	8 bytes
float	The single-precision floating-point type, with a range of about ±1038 and about 7 significant decimal digits	4 bytes
char	The character type, representing code units in the Unicode encoding scheme	2 bytes
boolean	The type with the two truth values false and true	1 bit

Number Literals

• A number that appears in your code
• If it has a decimal, it is floating point
• If not, it is an integer

Number Literals

Overflow

• Generally use an int for integers
• Overflow occurs when
  • The result of a computation exceeds the range for the number type
• Example

  int n = 1000000;
  System.out.println(n * n); // Prints –727379968, which is clearly wrong

  • 10¹² is larger that the largest int
  • The result is truncated to fit in an int
  • No warning is given
• Solution: use long instead
• Generally do not have overflow with the double data type

Rounding Errors

• Rounding errors occur when an exact representation of a floating-point number is not possible.
• Floating-point numbers have limited precision. Not every value can be represented precisely, and roundoff errors can occur.
• Example

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

• Use double type in most cases

Constants: final

• Use symbolic names for all values, even those that appear obvious.
• 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
  • Tag them as static and final
  • The static reserved word means that the constant belongs to the class
• Give static final constants public access to enable other classes to use them:
• Declaration of constants in the Math class

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

• Using a constant

  double circumference = Math.PI * diameter;

Syntax 4.1 Constant Declaration

section_1/CashRegister.java

section_1/CashRegisterTester.java

Program Run:

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

Self Check 4.1

Which are the most commonly used number types in Java?

• Answer: int and double

Self Check 4.2

Suppose you want to write a program that works with population data from various countries. Which Java data type should you use?

• Answer: The world’s most populous country, China, has about 1.2 x 10⁹ inhabitants. Therefore, individual population counts could be held in an int. However, the world population is over 6 × 10⁹. If you compute totals or averages of multiple countries, you can exceed the largest int value. Therefore, double is a better choice. You could also use long, but there is no benefit because the exact population of a country is not known at any point in time.

Self Check 4.3

Which of the following initializations are incorrect, and why?

1. int dollars = 100.0;
2. double balance = 100;

• Answer: The first initialization is incorrect. The right hand side is a value of type double, and it is not legal to initialize an int variable with a double value. The second initialization is correct — an int value can always be converted to a double.

Self Check 4.4

What is the difference between the following two statements?

final double CM_PER_INCH = 2.54;

and

public static final double CM_PER_INCH = 2.54;

• Answer: The first declaration is used inside a method, the second inside a class.

Self Check 4.5

What is wrong with the following statement sequence?

double diameter = . . .;
double circumference = 3.14 * diameter;

• Answer: Two things
  1. You should use a named constant, not the magic number 3.14
  2. 3.14 is not an accurate representation of π.

Arithmetic Operators

• Four basic operators:
  • addition: +
  • subtraction: -
  • multiplication: *
  • division: /
• Expression: combination of variables, literals, operators, and/or method calls

  (a + b) / 2

• Parentheses control the order of the computation

  (a + b) / 2

• Multiplication and division have a higher precedence than addition and subtraction

  a + b / 2

• Mixing integers and floating-point values in an arithmetic expression yields a floating-point value

  7 + 4.0 is the floating-point value 11.0

Increment and Decrement

• The ++ operator adds 1 to a variable (increments)
• counter++; // Adds 1 to the variable counter
• The -- operator subtracts 1 from the variable (decrements)
• counter--; // Subtracts 1 from counter
• 
  Figure 1 Incrementing a Variable

Integer Division and Remainder

• Division works as you would expect, as long as at least one of the numbers is a floating-point number.
• Example: all of the following evaluate to 1.75
  7.0 / 4.0
  7 / 4.0
  7.0 / 4
• If both numbers are integers, the result is an integer. The remainder is discarded
  • 7 / 4 evaluates to 1
• Use % operator to get the remainder with (pronounced "modulus", "modulo", or "mod")
  • 7 % 4 is 3

Integer Division and Remainder

• To determine the value in dollars and cents of 1729 pennies
  • Obtain the dollars through an integer division by 100

  int dollars = pennies / 100; // Sets dollars to 17

  • To obtain the remainder, use the % operator

  int cents = pennies % 100; // Sets cents to 29

• Integer division and the % operator yield the dollar and cent values of a piggybank full of pennies.

Integer Division and Remainder

Powers and Roots

• Math class contains methods sqrt and pow to compute square roots and powers
• To take the square root of a number, use Math.sqrt; for example, Math.sqrt(x)
• To compute xⁿ, you write Math.pow(x, n)
  • To compute x² it is significantly more efficient simply to compute x * x
• In Java,
  
  can be represented as
  
  b * Math.pow(1 + r / 100, n)

Analyzing an Expression

Mathematical Methods

Converting Floating-Point Numbers to Integers - Cast

• The compiler disallows the assignment of a double to an int because it is potentially dangerous
  • The fractional part is lost
  • The magnitude may be too large
  • This is an error

  double balance = total + tax;
  int dollars =  balance; // Error: Cannot assign double to int

• Use the cast operator (int) to convert a convert floating-point value to an integer.

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

• Cast discards fractional part
• You use a cast (typeName) to convert a value to a different type.

Converting Floating-Point Numbers to Integers - Rounding

• 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

Self Check 4.6

A bank account earns interest once per year. In Java, how do you compute the interest earned in the first year? Assume variables percent and balance of type double have already been declared.

• Answer: double interest = balance * percent / 100;

Self Check 4.7

In Java, how do you compute the side length of a square whose area is stored in the variable area?

• Answer: double sideLength = Math.sqrt(area);

Self Check 4.8

The volume of a sphere is given by

If the radius is given by a variable radius of type double, write a Java expression for the volume.

• Answer:
  4 * PI * Math.pow(radius, 3) / 3
  or (4.0 / 3) * PI * Math.pow(radius, 3),
  but not (4 / 3) * PI * Math.pow(radius, 3)

Self Check 4.9

What are the values of 1729 / 100 and 1729 % 100?

• Answer: 17 and 29

Self Check 4.10

If n is a positive number, what is (n / 10) % 10?

• Answer: It is the second-to-last digit of n. For example, if n is 1729, then n / 10 is 172, and (n / 10) % 10 is 2.

Calling Static Methods

• Can not call a method on a number type

  double root = 2.sqrt(); // Error

• Use a static method instead.
• A static method does not operate on an object:

  double root = Math.sqrt(2); // Correct

• Static methods are declared inside classes
• Calling a static method:
  

Reading Input

• When a program asks for user input
  • It should first print a message that tells the user which input is expected

  System.out.print("Please enter the number of bottles: "); // Display prompt

• This message is called a prompt
  • Use the print method, not println, to display the prompt
  • Leave a space after the colon
• System.in has minimal set of features
  • Must be combined with other classes to be useful
• Use a class called Scanner to read keyboard input.

Reading Input - Scanner

• To obtain a Scanner object:

  Scanner in = new Scanner(System.in);

• Use the Scanner's nextInt method to read an integer value:

  System.out.print("Please enter the number of bottles: ");
  int bottles = in.nextInt();

• When the nextInt method is called,
  • The program waits until the user types a number and presses the Enter key;
  • After the user supplies the input, the number is placed into the bottles variable;
  • The program continues.
• Use the nextDouble method to read a floating-point number:

  System.out.print("Enter price: ");
  double price = in.nextDouble();

• To use the Scanner class, import it by placing the following at the top of your program file:

  import java.util.Scanner;

Reading Input

A supermarket scanner reads bar codes. The Java Scanner reads numbers and text.

Syntax 4.3 Input Statement

Formatted Output

• Use the printf method to specify how values should be formatted.
• Printf lets you print this
  Price per liter: 1.22
• Instead of this
  Price per liter: 1.215962441314554
• This command displays the price with two digits after the decimal point:

  System.out.printf("%.2f", price);

Formatted Output

• You can also specify a field width:

  System.out.printf("%10.2f", price);

• This prints 10 characters
  • Six spaces followed by the four characters 1.22
    
• This command

   System.out.printf("Price per liter:%10.2f", price);

• Prints

  Price per liter:      1.22

Formatted Output

 

You use the printf method to line up your output in neat columns.

Formatted Output

Formatted Output

• You can print multiple values with a single call to the printf method.
• Example

  System.out.printf("Quantity: %d Total: %10.2f", quantity, total);

• Output explained:
  

section_3/Volume.java

Program Run:

• Please enter the price for a six-pack: 2.95
  Please enter the price for a two-liter bottle: 2.85
  Pack price per liter:      1.38
  Bottle price per liter:    1.43
  

Self Check 4.11

Write statements to prompt for and read the user’s age using a Scanner variable named in.

• Answer:

  System.out.print("How old are you? ");
  int age = in.nextInt();

Self Check 4.12

What is wrong with the following statement sequence?

System.out.print("Please enter the unit price: ");
double unitPrice = in.nextDouble();
int quantity = in.nextInt();

• Answer: There is no prompt that alerts the program user to enter the quantity.

Self Check 4.13

What is problematic about the following statement sequence?

System.out.print("Please enter the unit price: ");
double unitPrice = in.nextInt();

• Answer: The second statement calls nextInt, not nextDouble. If the user were to enter a price such as 1.95, the program would be terminated with an “input mismatch exception”.

Self Check 4.14

What is problematic about the following statement sequence?

System.out.print("Please enter the number of cans");
int cans = in.nextInt();

• Answer: There is no colon and space at the end of the prompt. A dialog would look like this:
  
  Please enter the number of cans6

Self Check 4.15

What is the output of the following statement sequence?

int volume = 10;
System.out.printf("The volume is %5d", volume);

• Answer: The total volume is    10

  There are four spaces between is and 10. One space originates from the format string (the space between s and %), and three spaces are added before 10 to achieve a field width of 5.

Self Check 4.16

Using the printf method, print the values of the integer variables bottles and cans so that the output looks like this:

Bottles:         8
Cans:           24

The numbers to the right should line up. (You may assume that the numbers have at most 8 digits.)

• Answer: Here is a simple solution:

  System.out.printf("Bottles: %8d\n", bottles);
  System.out.printf("Cans:    %8d\n", cans);

  Note the spaces after Cans:. Alternatively, you can use format specifiers for the strings. You can even combine all output into a single statement:

  System.out.printf("%-9s%8d\n%-9s%8d\n",
  "Bottles: ", bottles, "Cans:", cans);

Problem Solving: First Do It By Hand

• Very important step for developing an algorithm
  • Carry out the computations by hand first
• Pick concrete values for a typical situation to use in a hand calculation.
• Problem: A row of black and white tiles needs to be placed along a wall. First and last are black.
• Compute the number of tiles needed and the gap at each end, given the space available and the width of each tile.
  
• Use numbers
  • Total width: 100 inches
  • Tile width: 5 inches
• The first tile must always be black,
  • and then we add some number of white/black pairs:
    

Problem Solving: First Do It By Hand

• The first tile takes up 5 inches, leaving 95 inches to be covered by pairs.
  • Each pair is 10 inches wide.
  • The number of pairs needed is 95 / 10 = 9.5.
  • Discard the fractional part.
• We need 9 tile pairs or 18 tiles, plus the initial black tile => 19 tiles.
  • Tiles span 19 × 5 = 95 inches
  • Gap is 100 – 19 × 5 = 5 inches
• Distribute the gap at both ends
  • gap is (100 – 19 × 5) / 2 = 2.5 inches

Problem Solving: First Do It By Hand

• Devise an algorithm with arbitrary values for the total width and tile width.
• The pseudocode
  
  

  number of pairs = integer part of (total width - tile width) / (2 x tile width)
  number of tiles = 1 + 2 x number of pairs
  gap at each end = (total width - number of tiles x tile width) / 2

Self Check 4.17

Translate the pseudocode for computing the number of tiles and the gap width into Java.

• Answer:

  int pairs = (totalWidth - tileWidth) / (2 * tileWidth);
  int tiles = 1 + 2 * pairs;
  double gap = (totalWidth - tiles * tileWidth) / 2.0;

  
  Be sure that pairs is declared as an int.

Self Check 4.18

Suppose the architect specifies a pattern with black, gray, and white tiles, like this:

Again, the first and last tile should be black. How do you need to modify the algorithm?

• Answer: Now there are groups of four tiles (gray/ white/gray/black) following the initial black tile. Therefore, the algorithm is now

  number of groups = integer part of (total width - tile width) /(4 x tile width)
  number of tiles = 1 + 4 x number of groups

  The formula for the gap is not changed.

Self Check 4.19

A robot needs to tile a floor with alternating black and white tiles. Develop an algorithm that yields the color (0 for black, 1 for white), given the row and column number. Start with specific values for the row and column, and then generalize.

• Answer: The answer depends only on whether the row and column numbers are even or odd, so let’s first take the remainder after dividing by 2. Then we can enumerate all expected answers:

• Rows%2	Columns%2	Color
  0	0	0
  0	1	1
  1	0	1
  1	1	0

  In the first three entries of the table, the color is simply the sum of the remainders. In the fourth entry, the sum would be 2, but we want a zero. We can achieve that by taking another remainder operation:
  

  color = ((row % 2) + (column % 2)) % 2 

Self Check 4.20

For a particular car, repair and maintenance costs in year 1 are estimated at $100; in year 10, at $1,500. Assuming that the repair cost increases by the same amount every year, develop pseudocode to compute the repair cost in year 3 and then generalize to year n.

• Answer: In nine years, the repair costs increased by $1,400. Therefore, the increase per year is $1,400 / 9 ≈ $156. The repair cost in year 3 would be $100 + 2 x $156 = $412. The repair cost in year n is $100 + n x $156. To avoid accumulation of roundoff errors, it is actually a good idea to use the original expression that yielded $156, that is,

  Repair cost in year n = 100 + n x 1400 / 9

Self Check 4.21

The shape of a bottle is approximated by two cylinders of radius r₁ and r₂ and heights h₁ and h₂, joined by a cone section of height h₃.

Using the formulas for the volume of a cylinder, V = π r² h, and a cone section

develop pseudocode to compute the volume of the bottle. Using an actual bottle with known volume as a sample, make a hand calculation of your pseudocode.

• Answer: The pseudocode follows from the equations:
  
  Measuring a typical wine bottle yields
  r₁ = 3.6, r₂ = 1.2, h₁ = 15, h₂ = 7, h₃ = 6 (all in centimeters).
  Therefore,
  bottom volume = 610.73
  top volume = 31.67
  middle volume = 135.72
  total volume = 778.12
  The actual volume is 750 ml, which is close enough to our computation to give confidence that it is correct.

String Type

• A string is a sequence of characters.
• You can declare variables that hold strings

  String name = "Harry";

• A string variable is a variable that can hold a string
• String literals are character sequences enclosed in quotes
• A string literal denotes a particular string

  "Harry"

• String length is the number of characters in the string
  • The length of "Harry" is 5
• The length method yields the number of characters in a string
  int n = name.length();
• A string of length 0 is called the empty string
  • Contains no characters
  • Is written as ""

Concatenation

• Concatenating strings means to put them together to form a longer string
• Use the + operator:
• Example:

  String fName = "Harry";
  String lName = "Morgan";
  String name = fName + lName;

• Result:

  "HarryMorgan"

• To separate the first and last name with a space

  String name = fName + " " + lName;

• Results in

  "Harry Morgan"

Concatenation

• If one of the arguments of the + operator is a string
  • The other is forced to become to a string:
  • Both strings are then concatenated
• Example

  String jobTitle = "Agent";
  int employeeId = 7;
  String bond = jobTitle + employeeId;

• Result

  "Agent7"

Concatenation in Print Statements

• Useful to reduce the number of System.out.print instructions

  System.out.print("The total is ");
  System.out.println(total);

  versus

  System.out.println("The total is " + total);

String Input

• Use the next method of the Scanner class to read a string containing a single word.

  System.out.print("Please enter your name: ");
  String name = in.next();

• Only one word is read.
• Use a second call to in.next to get a second word.

Escape Sequences

• To include a quotation mark in a literal string, precede it with a backslash ( \ )

  "He said \"Hello\""

• Indicates that the quotation mark that follows should be a part of the string and not mark the end of the string
• Called an escape sequence
• To include a backslash in a string, use the escape sequence \\

  "C:\\Temp\\Secret.txt"

• A newline character is denoted with the escape sequence \n
• A newline character is often added to the end of the format string when using System.out.printf:

   System.out.printf("Price: %10.2f\n", price);

Strings and Characters

• A string is a sequences of Unicode characters.
• A character is a value of the type char.
  • Characters have numeric values
• Character literals are delimited by single quotes.
  • 'H' is a character. It is a value of type char
• Don't confuse them with strings
  • "H" is a string containing a single character. It is a value of type String.

Strings and Characters

• String positions are counted starting with 0.
  
• The position number of the last character is always one less than the length of the string.
• The last character of the string "Harry" is at position 4
• The charAt method returns a char value from a string
• The example

  String name = "Harry";
  char start = name.charAt(0);
  char last = name.charAt(4);

  • Sets start to the value 'H' and last to the value 'y'.

Substrings

• Use the substring method to extract a part of a string.
• The method call str.substring(start, pastEnd)
  • returns a string that is made up of the characters in the string str,
    • starting at position start, and
    • containing all characters up to, but not including, the position pastEnd.
• Example:

  String greeting = "Hello, World!";
  String sub = greeting.substring(0, 5); // sub is "Hello"

  
• To extract "World"

  String sub2 = greeting.substring(7, 12);

  
• Substring length is past the end - start
  

Substrings

• If you omit the end position when calling the substring method, then all characters from the starting position to the end of the string are copied.
• Example

  String tail = greeting.substring(7); // Copies all characters from position 7 on

• Result
  • Sets tail to the string "World!".
• To make a string of one character, taken from the start of first
  • first.substring(0, 1)
• 

section_5/Initials.java

Program Run:

• Enter your first name: Rodolfo
  Enter your significant other's first name: Sally
  R&S
  
  

String Operations

Self Check 4.22

What is the length of the string "Java Program"?

• Answer: The length is 12. The space counts as a character.

Self Check 4.23

Consider this string variable

String str = "Java Program";

Give a call to the substring method that returns the substring "gram".

• Answer: str.substring(8, 12) or str.substring(8)

Self Check 4.24

Use string concatenation to turn the string variable str from Self Check 23 into "Java Programming".

• Answer: str = str + "ming";

Self Check 4.25

What does the following statement sequence print?

String str = "Harry";
int n = str.length();
String mystery = str.substring(0, 1) + str.substring(n - 1, n);
System.out.println(mystery);;

• Answer: Hy

Self Check 4.26

Give an input statement to read a name of the form “John Q. Public”.

Answer:

String first = in.next();
String middle = in.next();
String last = in.next();

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