Chapter 5 – Decisions

Chapter Goals

• To implement decisions using if statements
• To compare integers, floating-point numbers, and strings
• To write statements using the Boolean data type
• To develop strategies for testing your programs
• To validate user input

The if Statement

• The if statement allows a program to carry out different actions depending on the nature of the data to be processed.

This elevator panel “skips” the thirteenth floor. The floor is not actually missing—the computer that controls the elevator adjusts the floor numbers above 13.

int actualFloor;
if (floor > 13)
{
   actualFloor = floor - 1;
}
else
{
   actualFloor = floor;
}

The if Statement

• Flowchart with two branch
  
• You can include as many statements in each branch as you like.

The if Statement

• Flowchart with one branches
  
  
• When there is nothing to do in the else branch, omit it entirely

  int actualFloor = floor;
  if (floor > 13)
  {
     actualFloor--;
  } // No else needed

The if Statement

An if statement is like a fork in the road. Depending upon a decision, different parts of the program are executed.

Syntax 5.1 The if Statement

section_1/ElevatorSimulation.java

Program Run:

• Floor: 20
  The elevator will travel to the actual floor 19

Self Check 5.1

In some Asian countries, the number 14 is considered unlucky. Some building owners play it safe and skip both the thirteenth and the fourteenth floor. How would you modify the sample program to handle such a building?

• Answer: Change the if statement to

  if (floor > 14)
  {
     actualFloor = floor - 2;
  }

Self Check 5.2

Consider the following if statement to compute a discounted price:

if (originalPrice > 100)
{
   discountedPrice = originalPrice - 20;
}
else
{
   discountedPrice = originalPrice - 10;
}

What is the discounted price if the original price is 95? 100? 105?

• Answer: 85. 90. 85.

Self Check 5.3

Compare this if statement with the one in Self Check 2:

if (originalPrice < 100)
{
   discountedPrice = originalPrice - 10;
}
else
{
   discountedPrice = originalPrice - 20;
}

Do the two statements always compute the same value? If not, when do the values differ?

• Answer: The only difference is if originalPrice is 100. The statement in Self Check 2 sets discountedPrice to 90; this one sets it to 80.

Self Check 5.4

Consider the following statements to compute a discounted price:

discountedPrice = originalPrice;
if (originalPrice > 100)
{
   discountedPrice = originalPrice - 10;
}

What is the discounted price if the original price is 95? 100? 105?

• Answer: 95. 100. 95.

Self Check 5.5

The variables fuelAmount and fuelCapacity hold the actual amount of fuel and the size of the fuel tank of a vehicle. If less than 10 percent is remaining in the tank, a status light should show a red color; otherwise it shows a green color. Simulate this process by printing out either "red" or "green".

• Answer:

  if (fuelAmount < 0.10 * fuelCapacity)
  {
     System.out.println("red");
  }
  else
  {
     System.out.println("green");
  }

Avoid Duplication in Branches

• If you have duplicate code in each branch, move it out of the if statement.
• Don't do this

  if (floor > 13)
  {
     actualFloor = floor - 1;
     System.out.println("Actual floor: " + actualFloor);
  }
  else
  {
     actualFloor = floor;
     System.out.println("Actual floor: " + actualFloor);
  }

Avoid Duplication in Branches (continued)

• Do this instead

  if (floor > 13)
  {
     actualFloor = floor - 1;
  }
  else
  {
     actualFloor = floor;
  }
  System.out.println("Actual floor: " + actualFloor);

• It will make the code much easier to maintain.
• Changes will only need to be made in one place.

Comparing Values: Relational Operators

In Java, you use a relational operator to check whether one value is greater than another.

Comparing Values: Relational Operators

• Relational operators compare values:
  

  Java	Math Notation	Description
  >	>	Greater than
  >=	≥	Greater than or equal
  <	<	Less than
  <=	≤	Less than or equal
  ==	=	Equal
  !=	≠	Not equal

• The == denotes equality testing:

  floor = 13; // Assign 13 to floor
  
  if (floor == 13) // Test whether floor equals 13

• Relational operators have lower precedence than arithmetic operators:

  floor - 1 < 13

Syntax 5.2 Comparisons

Comparing Floating-Point Numbers

• Consider this code:

  double r = Math.sqrt(2);
  double d = r * r -2;
  if (d == 0)
  {
     System.out.println("sqrt(2)squared minus 2 is 0");
  }
  else
  {
     System.out.println("sqrt(2)squared minus 2 is not 0 but " + d);
  }

• It prints:
   sqrt(2)squared minus 2 is not 0 but 4.440892098500626E-16
• This is due to round-off errors
• When comparing floating-point numbers, don’t test for equality.
  • Check whether they are close enough.

Comparing Floating-Point Numbers

• To avoid roundoff errors, don't use == to compare floating-point numbers.
• To compare floating-point numbers test whether they are close enough: |x - y| ≤ ε

  final double EPSILON = 1E-14;
  if (Math.abs(x - y) <= EPSILON)
  {
     // x is approximately equal to y
  }

• ε is commonly set to 10^-14

Comparing Strings

• To test whether two strings are equal to each other, use equals method:

  if (string1.equals(string2)) . . .

• Don't use == for strings!

  if (string1 == string2) // Not useful

• == tests if two strings are stored in the same memory location
• equals method tests equal contents

Comparing Strings - compareTo method

• compareTo method compares strings in lexicographic order - dictionary order.
• string1.compareTo(string2) < 0 means:
  • string1 comes before string2 in the dictionary
• string1.compareTo(string2) > 0 means:
  • string1 comes after string2 in the dictionary
• string1.compareTo(string2) == 0 means:
  • string1 and string2 are equal
• Lexicographic Ordering
  

Lexicographic Ordering

• Differences in dictionary ordering and ordering in Java
  • All uppercase letters come before the lowercase letters. "Z" comes before "a"
  • The space character comes before all printable characters
  • Numbers come before letters
  • Ordering of punctuation marks varies
• To see which of two terms comes first in the dictionary, consider the first letter in which they differ
  
  

Comparing Objects

• The == operator tests whether two object references are identical,
  • whether they refer to the same object.
• Look at this code

  Rectangle box1 = new Rectangle(5, 10, 20, 30);
  Rectangle box2 = box1;
  Rectangle box3 = new Rectangle(5, 10, 20, 30);

  • box1 == box2 is true
  • box1 == box3 is false
• Use the equals method to test if two rectangles have the same content
  box1.equals(box3)
  • They have the same upper-left corner and the same width and height
• Caveat: equals must be defined for the class

Object Comparison

Testing for null

• null reference refers to no object:

  String middleInitial = null; // Not set
  if ( . . . )
  {
     middleInitial = middleName.substring(0, 1);
  }

• Can be used in tests:
  

  if (middleInitial == null)
  {
     System.out.println(firstName + " " + lastName);
  }
  else
  {
     System.out.println(firstName + " " + middleInitial + ". " + lastName);
  }

• Use ==, not equals, to test for null
• null is not the same as the empty string ""

Relational Operator Examples

Self Check 5.6

Which of the following conditions are true, provided a is 3 and b is 4?
a. a + 1 <= b
b. a + 1 >= b
c. a + 1 != b

• Answer: (a) and (b) are both true, (c) is false.

Self Check 5.7

Give the opposite of the condition floor > 13

• Answer: floor <= 13

Self Check 5.8

What is the error in this statement?

if (scoreA = scoreB)
{
   System.out.println("Tie");
}

• Answer: The values should be compared with ==, not =.

Self Check 5.9

Supply a condition in this if statement to test whether the user entered a Y:

System.out.println("Enter Y to quit.");
String input = in.next();
if (. . .)
{
   System.out.println("Goodbye.");
}

• Answer: input.equals("Y")

Self Check 5.10

Give two ways of testing that a string str is the empty string.

• Answer: str.equals("") or str.length() == 0

Self Check 5.11

What is the value of s.length() if s is

a. the empty string ""?
b. the string " " containing a space?
c. null?

• Answer: (a) 0; (b) 1; (c) an exception occurs.

Self Check 5.12

Which of the following comparisons are syntactically incorrect? Which of them are syntactically correct, but logically questionable?

String a = "1";
String b = "one";
double x = 1;
double y = 3 * (1.0 / 3);

a. a == "1"
b. a == null
c. a.equals("")
d. a == b
e. a == x
f. x == y
g. x - y == null
h. x.equals(y)

• Answer: Syntactically incorrect: e, g, h. Logically questionable: a, d, f.

Multiple Alternatives: Sequences of Comparisons

• Multiple if statements can be combined to evaluate complex decisions.
• You use multiple if statements to implement multiple alternatives.
• Example: damage done by earthquake of a given magnitude on the Richter scale:

• if (richter >= 8.0)
  {
     description = "Most structures fall";
  }
  else if (richter >= 7.0)
  {
     description = "Many buildings destroyed";
  }
     else if (richter >= 6.0)
  {
     description = "Many buildings considerably damaged, some collapse";
  }
     else if (richter >= 4.5)
  {
     description = "Damage to poorly constructed buildings";
  }
  else
  {
     description = "No destruction of buildings";
  }

• As soon as one of the four tests succeeds:
  • The effect is displayed
  • No further tests are attempted.
• If none of the four cases applies
  • The final else clause applies
  • A default message is printed.

Multiple Alternatives

The 1989 Loma Prieta earthquake that damaged the Bay Bridge in San Francisco and destroyed many buildings measured 7.1 on the Richter scale.

Multiple Alternatives - Flowchart

Multiple Alternatives

• The order of the if and else if matters
• Error

  if (richter >= 4.5) // Tests in wrong order
  {
     description = "Damage to poorly constructed buildings";
  }
  else if (richter >= 6.0)
  {
     description = "Many buildings considerably damaged, some collapse";
  }
  else if (richter >= 7.0)
  {
     description = "Many buildings destroyed";
  }
  else if (richter >= 8.0)
  {
     description = "Most structures fall";
  }

• When using multiple if statements, test general conditions after more specific conditions.

Multiple Alternatives

• In this example, must use if/else if/else sequence, not just multiple independent if statements
• Error

  if (richter >= 8.0) // Didn't use else
  {
     description = "Most structures fall";
  }
  if (richter >= 7.0)
  {
     description = "Many buildings destroyed";
  }
  if (richter >= 6.0)
  {
     description = "Many buildings considerably damaged, some collapse";
  }
  if (richter >= 4.5)
  {
     "Damage to poorly constructed buildings";
  }

• The alternatives are no longer exclusive.

Self Check 5.13

In a game program, the scores of players A and B are stored in variables scoreA and scoreB. Assuming that the player with the larger score wins, write an if/ else if/else sequence that prints out "A won", "B won", or "Game tied".

• Answer:

  if (scoreA > scoreB)
  {
     System.out.println("A won");
  }
  else if (scoreA < scoreB)
  {
     System.out.println("B won");
  }
  else
  {
     System.out.println("Game tied");
  }

Self Check 5.14

Write a conditional statement with three branches that sets s to 1 if x is positive, to –1 if x is negative, and to 0 if x is zero.

• Answer:

  if (x > 0) { s = 1; }
  else if (x < 0) { s = -1; }
  else { s = 0; }

Self Check 5.15

How could you achieve the task of Self Check 14 with only two branches?

• Answer: You could first set s to one of the three values:

  s = 0;
  if (x > 0) { s = 1; }
  else if (x < 0) { s = -1; }

Self Check 5.16

Beginners sometimes write statements such as the following:

if (price > 100)
{
   discountedPrice = price - 20;
}
else if (price <= 100)
{
   discountedPrice = price - 10;
}

Explain how this code can be improved.

• Answer: The if (price <= 100) can be omitted (leaving just else), making it clear that the else branch is the sole alternative.

Self Check 5.17

Suppose the user enters -1 into the earthquake program. What is printed?

• Answer: No destruction of buildings.

Self Check 5.18

Suppose we want to have the earthquake program check whether the user entered a negative number. What branch would you add to the if statement, and where?

• Answer: Add a branch before the final else:

  else if (richter < 0)
  {
     System.out.println("Error: Negative input");
  }

Nested Branches

• Nested set of statements:
  • An if statement inside another
    
• Example: Federal Income Tax
  • Tax depends on marital status and income
    
• We say that the income test is nested inside the test for filing status
• Two-level decision process is reflected in two levels of if statements in the program
• Computing income taxes requires multiple levels of decisions.
  

Nested Branches - Flowchart

section_4/TaxReturn.java

section_4/TaxCalculator.java

Program Run:

• Please enter your income: 80000
  Are you married? (Y/N) Y
  Tax: 10400.0

Self Check 5.19

What is the amount of tax that a single taxpayer pays on an income of $32,000?

• Answer: 3200.

Self Check 5.20

Would that amount change if the first nested if statement changed from

if (income <= RATE1_SINGLE_LIMIT) 

to

if (income < RATE1_SINGLE_LIMIT)

• Answer: No. Then the computation is 0.10 × 32000 + 0.25 × (32000 – 32000).

Self Check 5.21

Suppose Harry and Sally each make $40,000 per year. Would they save taxes if they married?

• Answer: No. Their individual tax is $5,200 each, and if they married, they would pay $10,400. Actually, taxpayers in higher tax brackets (which our program does not model) may pay higher taxes when they marry, a phenomenon known as the marriage penalty.

Self Check 5.22

How would you modify the TaxCalculator.java program in order to check that
the user entered a correct value for the marital status (i.e., Y or N)?

• Answer: Change else in line 22 to

  else if (maritalStatus.equals("N"))

  and add another branch after line 25:

  else
  {
     System.out.println(
     "Error: Please answer Y or N.");
  }

Self Check 5.23

Some people object to higher tax rates for higher incomes, claiming that you might end up with less money after taxes when you get a raise for working hard. What is the flaw in this argument?

• Answer: The higher tax rate is only applied on the income in the higher bracket. Suppose you are single and make $31,900. Should you try to get a $200 raise? Absolutely: you get to keep 90 percent of the first $100 and 75 percent of the next $100.

Problem Solving: Flowcharts

• A flowchart shows the structure of decisions and tasks that are required to solve a problem.
• Flowcharts are made up of elements for tasks, input/output, and decisions.


Figure 6 Flowchart Elements

• Link tasks and input/output boxes in the sequence in which they should be executed.

Problem Solving: Flowcharts

• Whenever you need to make a decision, draw a diamond with two outcomes
  
  
  Figure 7 Flowchart with Two Outcomes


Figure 8 Flowchart with Multiple Choices

Problem Solving: Flowcharts

• Each branch of a decision can contain tasks and further decisions.
• Never point an arrow inside another branch.
• BAD - spaghetti code
  

Problem Solving: Flowcharts

• GOOD - better design
  
  In the future the cost for international shipments may be different from that to Alaska and Hawaii.
• Spaghetti code has so many pathways that it becomes impossible to understand.

Self Check 5.24

Draw a flowchart for a program that reads a value temp and prints “Frozen” if it is less than zero.

• Answer:
  

Self Check 5.25

What is wrong with this flowchart?

• Answer: The “True” arrow from the first decision points into the “True” branch of the second decision, creating spaghetti code.

Self Check 5.26

How do you fix the flowchart of Self Check 25?

• Answer: Here is one solution. In Section 5.7, you will see how you can combine the conditions for a more elegant solution.
  

Self Check 5.27

Draw a flowchart for a program that reads a value x. If it is less than zero, print “Error”. Otherwise, print its square root.

• Answer:
  

Self Check 5.28

Draw a flowchart for a program that reads a value temp. If it is less than zero, print “Ice”. If it is greater than 100, print “Steam”. Otherwise, print “Liquid”.

• Answer:
  

Problem Solving: Selecting Test Cases

• Black-box testing: a testing method that does not take the structure of the implementation into account.
• White-box testing uses information about the structure of a program.
  • Perform unit tests of each method
• Code coverage is a measure of how many parts of a program have been tested.
  • Look at every if/else branch to see that each of them is reached by some test case
• Boundary test cases are test cases that are at the boundary of acceptable inputs.
• It is a good idea to design test cases before implementing a program.

Problem Solving: Selecting Test Cases

• A plan for the TaxReturn class
  • There are two possibilities for the marital status and two tax brackets for each status, yielding four test cases
  • Test a handful of boundary conditions, such as an income that is at the boundary between two brackets, and a zero income.
  • Test an invalid input, such as a negative income
• Test cases and expected outcomes
  

Self Check 5.29

Using Figure 1 on page 181 as a guide, follow the process described in this section to design a set of test cases for the ElevatorSimulation.java program in Section 5.1. 30. What is a boundary test case for the algorithm in How To 5.1 on page 193? What is

• Answer:
  

Self Check 5.30

What is a boundary test case for the algorithm in How To 5.1 on page 193? What is the expected output?

• Answer: A boundary test case is a price of $128. A 16 percent discount should apply because the problem statement states that the larger discount applies if the price is at least $128. Thus, the expected output is $107.52.

Self Check 5.31

Using Figure 4 on page 197 as a guide, follow the process described in Section 5.6 to design a set of test cases for the Earthquake.java program in Section 5.3.

• Answer:
  

Self Check 5.32

Suppose you are designing a part of a program for a medical robot that has a sensor returning an x- and y-location (measured in cm). You need to check whether the sensor location is inside the circle, outside the circle, or on the boundary (specifically, having a distance of less than 1 mm from the boundary). Assume the circle has center (0, 0) and a radius of 2 cm. Give a set of test cases.

• Answer:
  

Boolean Variables and Operators

• To store the evaluation of a logical condition that can be true or false, you use a Boolean variable.
• The boolean data type has exactly two values, denoted false and true.
  

  boolean failed = true;

• Later in your program, use the value to make a decision

  if (failed) // Only executed if failed has been set to true
  {
     . . .
  }

• A Boolean variable is also called a flag because it can be either up (true) or down (false).
  

Boolean Variables and Operators

• You often need to combine Boolean values when making complex decisions
• An operator that combines Boolean conditions is called a Boolean operator.
• The && operator is called and
  • Yields true only when both conditions are true.
• The || operator is called or
  • Yields the result true if at least one of the conditions is true.
  

Boolean Variables and Operators

• To test if water is liquid at a given temperature

  if (temp > 0 && temp < 100) { System.out.println("Liquid"); }

• Flowchart
  

Boolean Variables and Operators

• To test whether water is not liquid at a given temperature

  if (temp <= 0 || temp >= 100) { System.out.println("Not liquid"); }

• Flowchart
  

Boolean Variables and Operators

Boolean Variables and Operators

• To invert a condition use the not Boolean operator
• The ! operator takes a single condition
  • Evaluates to true if that condition is false and
  • Evaluates to false if the condition is true
• To test if the Boolean variable frozen is false:

  if (!frozen) { System.out.println("Not frozen"); }

Self Check 5.33

Suppose x and y are two integers. How do you test whether both of them are zero?

• Answer: x == 0 && y == 0

Self Check 5.34

How do you test whether at least one of them is zero?

• Answer: x == 0 || y == 0

Self Check 5.35

How do you test whether exactly one of them is zero?

• Answer: (x == 0 && y != 0) || (y == 0 && x != 0)

Self Check 5.36

What is the value of !!frozen?

• Answer: The same as the value of frozen.

Self Check 5.37

What is the advantage of using the type boolean rather than strings "false"/"true" or integers 0/1?

• Answer: You are guaranteed that there are no other values. With strings or integers, you would need to check that no values such as "maybe" or –1 enter your calculations.

Application: Input Validation

• You need to make sure that the user-supplied values are valid before you use them.
• Elevator example: elevator panel has buttons labeled 1 through 20 (but not 13)
• The number 13 is invalid

  if (floor == 13)
  {
     System.out.println("Error: There is no thirteenth floor.");
  }

• Numbers out of the range 1 through 20 are invalid

  if (floor <= 0 || floor > 20)
  {
     System.out.println("Error: The floor must be between 1 and 20.");
  }

• To avoid input that is not an integer

  if (in.hasNextInt())
  {
     int floor = in.nextInt();
     Process the input value.
  }
  else
  {
     System.out.println("Error: Not an integer.");
  }

Section_8/ElevatorSimulation2.java

Program Run:

• Floor: 13
  Error: There is no thirteenth floor.
  

Self Check 5.38

In the ElevatorSimulation2 program, what is the output when the input is
a. 100?
b. –1?
c. 20?
d. thirteen?

• Answer:
  (a) Error: The floor must be between 1 and 20.
  (b) Error: The floor must be between 1 and 20.
  (c) 19
  (d) Error: Not an integer.

Self Check 5.39

Your task is to rewrite lines 19–26 of the ElevatorSimulation2 program so that there is a single if statement with a complex condition. What is the condition?

if (. . .)
{
   System.out.println("Error: Invalid floor number");
}

• Answer: floor == 13 || floor <= 0 || floor > 20

Self Check 5.40

In the Sherlock Holmes story “The Adventure of the Sussex Vampire”, the inimitable detective uttered these words: “Matilda Briggs was not the name of a young woman, Watson, … It was a ship which is associated with the giant rat of Sumatra, a story for which the world is not yet prepared.” Over a hundred years later, researchers found giant rats in Western New Guinea, another part of Indonesia. Suppose you are charged with writing a program that processes rat weights. It contains the statements

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

What input checks should you supply?

• Answer: Check for in.hasNextDouble(), to make sure a researcher didn't supply an input such as oh my. Check for weight <= 0, because any rat must surely have a positive weight. We don’t know how giant a rat could be, but the New Guinea rats weighed no more than 2 kg. A regular house rat (rattus rattus) weighs up to 0.2 kg, so we’ll say that any weight > 10 kg was surely an input error, perhaps confusing grams and kilograms. Thus, the checks are

  if (in.hasNextDouble())
  {
     double weight = in.nextDouble();
     if (weight < 0)
     {
        System.out.println("Error: Weight cannot be negative.");
     }
     else if (weight > 10)
     {
        System.out.println("Error: Weight > 10 kg.");
     }
     else
     {
        Process valid weight.
     }
  }
  else
  }
     System.out.print("Error: Not a number");
  }

Self Check 5.41

Run the following test program and supply inputs 2 and three at the prompts. What happens? Why?

import java.util.Scanner
public class Test
{
   public static void main(String[] args)
   {
      Scanner in = new Scanner(System.in);
      System.out.print("Enter an integer: ");
      int m = in.nextInt();
      System.out.print("Enter another integer: ");
      int n = in.nextInt();
      System.out.println(m + " " + n);
   }
}

• Answer: The second input fails, and the program terminates without printing anything.