1. Chapter 6 Methods

2. Objectives
To declare methods, invoke methods, and pass arguments to a method.
To use method overloading and know ambiguous overloading.
To determine the scope of local variables.
To learn the concept of method abstraction.
To know how to use the methods in the Math class.
To design and implement methods using stepwise refinement .

3. Introducing Methods
A method is a collection of statements that are grouped together to perform an operation.
Example: when you call the System.out.println method, the system actually executes several statements in order to display a message on the console.

4. Introducing Methods In general, a method has the following syntax:
Modifier returnValueType methodName(list of parameters) {
// Method body; }
Example: a method to find which of two integers is bigger:

5. Introducing Methods, cont.
Method signature is the combination of the method name and the parameter list.
The variables defined in the method header are known as formal parameters.
When a method is invoked, you pass a value to the parameter. This value is referred to as actual parameter or argument.
The modifier which is optional, tells the compiler how to call the method. The static modifier is used for all the methods in this chapter.

6. Introducing Methods, cont.
A method may return a value. The returnValueType is the data type of the value the method returns. If the method does not return a value, the returnValueType is the keyword void. For example, the returnValueType in the main method is void, as well as in System.exit, System.out.println, and JOptionPane.showMessageDialog. The method that returns a value is called a nonvoid method, and the method that does not return a value is called a void method.

7. Calling Methods Testing the max method
This program demonstrates calling a method max to return the largest of the int values:
public class TestMax {
/** Main method */
public static void main (String[] args) {
int i = 5;
int j = 2;
int k = max(i, j);
System.out.println("The maximum between " + i +
" and " + j + " is " + k);
} // end main method
/** Return the max between two numbers */
public static int max(int num1, int num2) {
int result;
if (num1 > num2)
result = num1;
else
result = num2;
return result;
} //end method max
} // end class TestMax

8. animation
Calling Methods, cont.
When the return statement in the max method is executed, the max
method returns the control to its caller (in this case the caller is the
main method).

9. Trace Method Invocation
animation
Trace Method Invocation
i is now 5

10. Trace Method Invocation
animation
Trace Method Invocation
j is now 2

11. Trace Method Invocation
animation
Trace Method Invocation
invoke max(i, j)

12. Trace Method Invocation
animation
Trace Method Invocation
invoke max(i, j)
Pass the value of i to num1
Pass the value of j to num2

13. Trace Method Invocation
animation
Trace Method Invocation
declare variable result

14. Trace Method Invocation
animation
Trace Method Invocation
(num1 > num2) is true since num1 is 5 and num2 is 2

15. Trace Method Invocation
animation
Trace Method Invocation
result is now 5

16. Trace Method Invocation
animation
Trace Method Invocation
return result, which is 5

17. Trace Method Invocation
animation
Trace Method Invocation
return max(i, j) and assign the return value to k

18. Trace Method Invocation
animation
Trace Method Invocation
Execute the print statement

19. CAUTION
A return statement is required for a nonvoid method. The following method is logically correct, but it has a compilation error, because the Java compiler thinks it possible that this method does not return any value.
public static int sign(int n) {
if (n > 0) return 1;
else if (n == 0) return 0;
else if (n < 0) return –1; }
To fix this problem, delete if (n<0) in the code, so that the compiler will see a return statement to be reached regardless of how the if statement is evaluated as follows:
else return –1;

20. Reuse Methods from Other Classes
NOTE: One of the benefits of methods is for reuse. The max method can be invoked from any class besides TestMax. If you create a new class Test, you can invoke the max method using ClassName.methodName (e.g., TestMax.max).
public class Test {
/** Main method */
public static void main (String[] args) {
int i = 5;
int j = 2;
System.out.println("The maximum between " + i +
" and " + j + " is " + TestMax.max(i, j)); }

21. Call Stacks
Each time a method is invoked, the system stores parameters and variables in an area of
memory, known as a stack, which stores elements in last-in first-out fashion. When a
method calls another method the caller’s stack space is kept intact, and new space is
created to handle the new method call. When a method finishes its work, and returns to
Its caller, its associated space is released.
Understanding call stack helps you to understand how methods are invoked:

22. i is declared and initialized
animation
Trace Call Stack
i is declared and initialized

23. j is declared and initialized
animation
Trace Call Stack
j is declared and initialized

24. animation
Trace Call Stack
Declare k

25. animation
Trace Call Stack
Invoke max(i, j)

26. pass the values of i and j to num1 and num2
animation
Trace Call Stack
pass the values of i and j to num1 and num2

27. pass the values of i and j to num1 and num2
animation
Trace Call Stack
pass the values of i and j to num1 and num2

28. animation
Trace Call Stack
(num1 > num2) is true

29. animation
Trace Call Stack
Assign num1 to result

30. Return result and assign it to k
animation
Trace Call Stack
Return result and assign it to k

31. Execute print statement
animation
Trace Call Stack
Execute print statement

32. Call Stack in JBuilder Debugger
JBuilder Optional
Call Stack in JBuilder Debugger
You can see the chain of method invocations in the stack view of the JBuilder debugger.
Stack view
Invoke max
Invoke main

33. void Method Example Program Output: public class TestVoidMethod {
public static void main(String[] args) {
printGrade(78.5); }
public static void printGrade(double score) {
if (score < 0 || score > 100) {
System.out.println("Invalid score");
//return statement to terminate the function
//when the score is invalid
return;
if (score >= 90.0) {
System.out.println('A');
else if (score >= 80.0) {
System.out.println('B');
else if (score >= 70.0) {
System.out.println('C');
else if (score >= 60.0) {
System.out.println('D');
else {
System.out.println('F');
Program Output:

34. void Method Example using GUI
import javax.swing.JOptionPane;
public class TestVoidMethodGui {
public static void main(String[] args) {
String s = JOptionPane.showInputDialog("Enter score: ");
double d = Double.parseDouble(s);
printGrade(d); }
public static void printGrade(double score) {
if (score < 0 || score > 100) {
String output = "Student score is invalid";
JOptionPane.showMessageDialog(null, output);
return;
if (score >= 90.0) {
String output = "Student score is " +score +" and student grade is A";
else if (score >= 80.0) {
String output = "Student score is " +score +" and student grade is B";
else if (score >= 70.0) {
String output = "Student score is " +score +" and student grade is C";
else if (score >= 60.0) {
String output = "Student score is " +score +" and student grade is D";
else {
String output = "Student score is " +score +" and student grade is F";
Program Output:

35. Passing Parameters Suppose you invoke the method using
public static void nPrintln(String message, int n) {
for (int i = 0; i < n; i++)
System.out.println(message); }
Suppose you invoke the method using
nPrintln(“Welcome to Java”, 5);
What is the output?
nPrintln(“Computer Science”, 15);

36. Passing Parameters Suppose you invoke the method using
nPrintln(“Welcome to Java”, 5);
What is the output?
public class Invoke {
public static void main (String args[]) {
nPrintln("Welcome to Java", 5);
} //end main
public static void nPrintln(String message, int n) {
for (int i = 0; i < n; i++)
System.out.println(message);
} // end nPrintln
} // end Invoke

37. Passing Parameters Suppose you invoke the method using
nPrintln(“Computer Science”, 15);
What is the output?
public class Invoke {
public static void main (String args[]) {
nPrintln("Computer Science", 15);
} //end main
public static void nPrintln(String message, int n) {
for (int i = 0; i < n; i++)
System.out.println(message);
} // end nPrintln
} // end Invoke

38. Pass by Value Program Output:
Testing Pass by value. This program demonstrates passing values to the methods:
public class TestPassByValue {
/** Main method */
public static void main(String[] args) {
// Declare and initialize variables
int num1 = 1;
int num2 = 2;
System.out.println("Before invoking the swap method, num1 is " +
num1 + " and num2 is " + num2);
// Invoke the swap method to attempt to swap two variables
swap(num1, num2);
System.out.println("After invoking the swap method, num1 is " +
} //end main
/** Swap two variables */
public static void swap(int n1, int n2) {
System.out.println("Inside the swap method");
System.out.println("Before swapping n1 is " + n1
+ " n2 is " + n2);
// Swap n1 with n2
int temp = n1;
n1 = n2;
n2 = temp;
System.out.println("After swapping n1 is " + n1
} //end swap
} //end TestPassByValue
Program Output:

39. Pass by Value, cont.

40. Exercise
Write a method named footToMeter() that converts feet to meters. The method receives a double variable with actual parameter 68.1 and formal parameter named foot and a return value in meter. (meter = x foot)
Write a method named divisibleBy3() that return true or false. The method receives an integer named number and evaluate whether number is divisible by 3 or not.

41. Solution Program Output:
Write a method named footToMeter() that converts feet to meters. The method receives a double variable with actual parameter 68.1 and formal parameter named foot and a return value in meter. (meter = x foot)
public class ConvertFootToMeter {
public static void main (String args[]) {
System.out.println(footToMeter(68.1));
} //end main
public static double footToMeter(double foot) {
double meter;
meter = 0.305*foot;
return meter;
} // end footConvert
} // end ConvertFootToMeter
Program Output:

42. Solution Program Output:
Write a method named divisibleBy3() that return true or false. The method receives an integer named number and evaluate whether number
is divisible by 3 or not.
import java.util.Scanner;
public class DivisibleThree {
public static void main (String args[]) {
/* Create scanner object */
Scanner scanner = new Scanner(System.in);
/* Read a number */
System.out.print("Enter an integer number: ");
int num = scanner.nextInt();
System.out.println();
/* Print the result */
System.out.println(num + " can be divided by 3? " +divisibleBy3(num));
} //end main method
/* divisibleBy3 method */
public static boolean divisibleBy3(int number) {
if (number%3==0)
return true;
else
return false;
} // end divisibleBy3 method
} // end DivisibleThree class
Program Output:

43. Overloading Methods
The max method that was used earlier works only with the int data type. But what if you need to find which of two floating-point numbers has the maximum value? The solution is to create another method with the same name but different parameters as follows:
public static double max(double num1, double num2) {
if (num1 > num2)
return num1;
else
return num2; }
If you call max with int parameters, the max method that expects int parameters will be invoked; if you call max with double parameters, the max method that expects double parameters will be invoked. This is referred to as method overloading; that is two methods have the same name but different parameter lists within one class. The Java compiler determines which method is used based on the method signature.

44. Overloading Methods
This program creates three methods. The first finds the maximum integer, the second finds the maximum double, and the third finds the maximum among three double values. All three methods are named max.
public class TestMethodOverloading {
/** Main method */
public static void main(String[] args) {
// Invoke the max method with int parameters
System.out.println("The maximum between 3 and 4 is "
+ max(3, 4));
// Invoke the max method with the double parameters
System.out.println("The maximum between 3.0 and 5.4 is "
+ max(3.0, 5.4));
// Invoke the max method with three double parameters
System.out.println("The maximum between 3.0, 5.4, and is "
+ max(3.0, 5.4, 10.14));
} // end main
/** Return the max between two int values */
public static int max(int num1, int num2) {
if (num1 > num2)
return num1;
else
return num2;
} // end max with 2 int parameters
/** Find the max between two double values */
public static double max(double num1, double num2) {
} // end max with 2 double parameters
/** Return the max among three double values */
public static double max(double num1, double num2, double num3) {
return max(max(num1, num2), num3);
} // end max with 3 double parameters
} // end class TestMethodOverloading

45. Overloading Methods
If caller method is max(2,2.5), which method will be invoked?
The max method for finding the maximum of two double values will
be invoked. The argument 2 is automatically converted into a double
value and passed to this method.
BUT, Why max(double,double) is not invoked for the call max(3,4)?
Both max(double,double) and max(int,int) are possible matches for
max(3,4). The Java compiler finds the most specific method for a
method invocation. Since max(int,int) is more specific than
max(double,double), max(int,int) is used to invoke max(3,4).

46. Ambiguous Invocation
Sometimes there may be two or more possible matches for an invocation of a method, but the compiler cannot determine the most specific match. This is referred to as ambiguous invocation. Ambiguous invocation is a compilation error.

47. Ambiguous Invocation public class AmbiguousOverloading {
public static void main(String[] args) {
System.out.println(max(1, 2)); }
public static double max(int num1, double num2) {
if (num1 > num2)
return num1;
else
return num2;
public static double max(double num1, int num2) {
Both max(int,double) and max(double,int) are possible candidates to match max(1,2). Since neither of them
is more specific than the other, the invocation is ambiguous, resulting in a compilation error.

48. Case Study: Computing Taxes with Methods
“Computing Taxes,” uses if statements to check the filing status and computes the tax based on the filing status. Simplify the problem using methods. Each filing status has six brackets.
The code for computing taxes is nearly same for each filing status except that each filing status has different bracket ranges. For example, the single filer status has six brackets [0, 6000], (6000, 27950], (27950, 67700], (67700, ], (141250, ], (307050, ), and the married file jointly status has six brackets [0, 12000], (12000, 46700], (46700, ], (112850, ], (171950, ], (307050, ).

49. ComputeTaxWithMethod
Case Study cont.
The first bracket of each filing status is taxed at 10%, the second 15%, the third 27%, the fourth 30%, the fifth 35%, and the sixth 38.6%. So you can write a method with the brackets as arguments to compute the tax for the filing status. The signature of the method is:
For example, you can invoke computeTax(400000, 6000, 27950, 67700, , ) to compute the tax for single filers with $400,000 of taxable income:
ComputeTaxWithMethod

50. Case Study cont. import javax.swing.JOptionPane;
public class ComputeTaxWithMethod {
public static void main(String[] args) {
// Prompt the user to enter filing status
String statusString = JOptionPane.showInputDialog(
"Enter the filing status:");
int status = Integer.parseInt(statusString);
// Prompt the user to enter taxable income
String incomeString = JOptionPane.showInputDialog(
"Enter the taxable income:");
double income = Double.parseDouble(incomeString);
// Display the result
JOptionPane.showMessageDialog(null, "Tax is " +
(int)(computeTax(status, income) * 100) / 100.0); }
public static double computeTax(double income,
int r1, int r2, int r3, int r4, int r5) {
double tax = 0;
if (income <= r1)
tax = income * 0.10;
else if (income <= r2)
tax = r1 * (income - r1) * 0.15;
else if (income <= r3)
tax = r1 * (r2 - r1) * (income - r2) * 0.27;
else if (income <= r4)
tax = r1 * (r2 - r1) *
(r3 - r2) * (income - r3) * 0.30;
else if (income <= r5)
tax = r1 * (r2 - r1) * (r3 - r2) *
(r4 - r3) * (income - r4) * 0.35;
else
(r4 - r3) * (r5 - r4) * (income - r5) * 0.386;
return tax; }
public static double computeTax(int status, double income) {
switch (status) {
case 0: return
computeTax(income, 6000, 27950, 67700, , );
case 1: return
computeTax(income, 12000, 46700, , , );
case 2: return
computeTax(income, 6000, 23350, 56425, 85975, );
case 3: return
computeTax(income, 10000, 37450, 96700, , );
default: return 0;

51. Scope of Local Variables
A local variable: a variable defined inside a method.
Scope: the part of the program where the variable can be referenced.
The scope of a local variable starts from its declaration and continues to the end of the block that contains the variable. A local variable must be declared before it can be used.

52. Scope of Local Variables, cont.
A variable declared in the initial action part of a for loop header has its scope in the entire loop. But a variable declared inside a for loop body has its scope limited in the loop body from its declaration and to the end of the block that contains the variable as shown below:

53. Scope of Local Variables, cont.
You can declare a local variable with the same name multiple times in different non-nesting blocks in a method, but you cannot declare a local variable twice in nested blocks.

54. Scope of Local Variables, cont.

55. Scope of Local Variables, cont.
// Fine with no errors
public static void correctMethod() {
int x = 1;
int y = 1;
// i is declared
for (int i = 1; i < 10; i++) {
x += i; }
// i is declared again
y += i;

56. Scope of Local Variables, cont.
// With errors
public static void incorrectMethod() {
int x = 1;
int y = 1;
for (int i = 1; i < 10; i++) {
int x = 0;
x += i; }

57. Scope of Local Variables, cont.
CAUTION! DO NOT declare a variable inside a block and then attempt
to use it outside the block, as follows:
// With errors
for (int i = 0; i < 10; i++) { }
System.out.println(i)
The last statement will cause a syntax error because variable i is not
defined outside of the for loop

58. The Math Class The Math class contains the methods needed to
perform basic mathematical functions.
Class constants: PI E
Class methods:
Trigonometric Methods
Exponent Methods
Rounding Methods
min, max, abs, and random Methods

59. Trigonometric Methods
sin(double a)
cos(double a)
tan(double a)
acos(double a)
asin(double a)
atan(double a)
Examples:
Math.sin(0) returns 0.0
Math.sin(Math.PI / 6) returns 0.5
Math.sin(Math.PI / 2) returns 1.0
Math.cos(0) returns 1.0
Math.cos(Math.PI / 6) returns 0.866
Math.cos(Math.PI / 2) returns 0
Radians
toRadians(90)

60. Exponent Methods Examples: exp(double a)
Math.exp(1) returns 2.71
Math.log(2.71) returns 1.0
Math.pow(2, 3) returns 8.0
Math.pow(3, 2) returns 9.0
Math.pow(3.5, 2.5) returns
Math.sqrt(4) returns 2.0
Math.sqrt(10.5) returns 3.24
exp(double a)
Returns e raised to the power of a.
log(double a)
Returns the natural logarithm of a.
log10(double a)
Returns the 10-based logarithm of a.
pow(double a, double b)
Returns a raised to the power of b.
sqrt(double a)
Returns the square root of a.

61. Rounding Methods double ceil(double x)
x rounded up to its nearest integer. This integer is returned as a double value.
double floor(double x)
x is rounded down to its nearest integer. This integer is returned as a double value.
double rint(double x)
x is rounded to its nearest integer. If x is equally close to two integers, the even one is returned as a double.
int round(float x)
Return (int)Math.floor(x+0.5).
long round(double x)
Return (long)Math.floor(x+0.5).

62. Rounding Methods Examples
Math.ceil(2.1) returns 3.0
Math.ceil(2.0) returns 2.0
Math.ceil(-2.0) returns –2.0
Math.ceil(-2.1) returns -2.0
Math.floor(2.1) returns 2.0
Math.floor(2.0) returns 2.0
Math.floor(-2.0) returns –2.0
Math.floor(-2.1) returns -3.0
Math.rint(2.1) returns 2.0
Math.rint(2.0) returns 2.0
Math.rint(-2.0) returns –2.0
Math.rint(-2.1) returns -2.0
Math.rint(2.5) returns 2.0
Math.rint(-2.5) returns -2.0
Math.round(2.6f) returns 3
Math.round(2.0) returns 2
Math.round(-2.0f) returns -2
Math.round(-2.6) returns -3

63. min, max, and abs max(a, b)and min(a, b) abs(a) random() Examples:
Returns the maximum or minimum of two parameters.
abs(a)
Returns the absolute value of the parameter.
random()
Returns a random double value in the range [0.0, 1.0).
Examples:
Math.max(2, 3) returns 3
Math.max(2.5, 3) returns 3.0
Math.min(2.5, 3.6) returns 2.5
Math.abs(-2) returns 2
Math.abs(-2.1) returns 2.1
0.0 <= Math.random() < 1.0

64. The random Method
Generates a random double value greater than or equal to 0.0 and less than 1.0 (0 <= Math.random() < 1.0).
Examples:
In general,

65. View java.lang.Math Documentation
JBuilder Optional
View java.lang.Math Documentation
You can view the complete documentation for the Math class online from

66. View java.lang.Math from JBuilder
JBuilder Optional
View java.lang.Math from JBuilder
You can view the complete documentation for the Math class in JBuilder by choosing Search, Find Classes to display the Find Classes dialog box. Type java.lang.Math in the Class name field to display the documentation of the Math class in the content pane.

67. Case Study: Generating Random Characters
Computer programs process numerical data and characters. You have seen many examples that involve numerical data. It is also important to understand characters and how to process them.
Each character has a unique Unicode between 0 and FFFF in hexadecimal (65535 in decimal). To generate a random character is to generate a random integer between 0 and using the following expression: (note that since 0 <= Math.random() < 1.0, you have to add 1 to )
(int)(Math.random() * ( ))

68. Case Study: Generating Random Characters, cont.
Now let us consider how to generate a random lowercase letter. The Unicode for lowercase letters are consecutive integers starting from the Unicode for 'a', then for 'b', 'c', ..., and 'z'. The Unicode for 'a' is
(int)'a'
So, a random integer between (int)'a' and (int)'z' is
(int)((int)'a' + Math.random() * ((int)'z' - (int)'a' + 1)

69. Case Study: Generating Random Characters, cont.
Now let us consider how to generate a random lowercase letter. The Unicode for lowercase letters are consecutive integers starting from the Unicode for 'a', then for 'b', 'c', ..., and 'z'. The Unicode for 'a' is
(int)'a'
So, a random integer between (int)'a' and (int)'z' is
(int)((int)'a' + Math.random() * ((int)'z' - (int)'a' + 1)

70. Case Study: Generating Random Characters, cont.
All numeric operators can be applied to the char operands. The char operand is cast into a number if the other operand is a number or a character. So, the preceding expression can be simplified as follows:
'a' + Math.random() * ('z' - 'a' + 1)
So a random lowercase letter is
(char)('a' + Math.random() * ('z' - 'a' + 1))

71. Case Study: Generating Random Characters, cont.
To generalize the foregoing discussion, a random character between any two characters ch1 and ch2 with ch1 < ch2 can be generated as follows:
(char)(ch1 + Math.random() * (ch2 – ch1 + 1))

72. The RandomCharacter Class
// RandomCharacter.java: Generate random characters
public class RandomCharacter {
/** Generate a random character between ch1 and ch2 */
public static char getRandomCharacter(char ch1, char ch2) {
return (char)(ch1 + Math.random() * (ch2 - ch1 + 1)); }
/** Generate a random lowercase letter */
public static char getRandomLowerCaseLetter() {
return getRandomCharacter('a', 'z');
/** Generate a random uppercase letter */
public static char getRandomUpperCaseLetter() {
return getRandomCharacter('A', 'Z');
/** Generate a random digit character */
public static char getRandomDigitCharacter() {
return getRandomCharacter('0', '9');
/** Generate a random character */
public static char getRandomCharacter() {
return getRandomCharacter('\u0000', '\uFFFF');

73. Test Program for the RandomCharacter Class
public class TestRandomCharacter {
/** Main method */
public static void main(String args[]) {
final int NUMBER_OF_CHARS = 175;
final int CHARS_PER_LINE = 25;
// Print random characters between '!' and '~', 25 chars per line
for (int i = 0; i < NUMBER_OF_CHARS; i++) {
char ch = RandomCharacter.getRandomLowerCaseLetter();
if ((i + 1) % CHARS_PER_LINE == 0)
System.out.println(ch);
else
System.out.print(ch); }

74. Test Program for The RandomCharacter Class: Output

75. Method Abstraction
You can think of the method body as a black box that contains the detailed implementation for the method.

76. Benefits of Methods Write a method once and reuse it anywhere.
Information hiding. Hide the implementation from the user.
Reduce complexity.

77. Stepwise Refinement (Optional)
The concept of method abstraction can be applied to the process of developing programs. When writing a large program, you can use the “divide and conquer” strategy, also known as stepwise refinement, to decompose it into subproblems. The subproblems can be further decomposed into smaller, more manageable problems.

78. PrintCalender Case Study
Let us use the PrintCalendar example to demonstrate the stepwise refinement approach.

79. Design Diagram

80. Implementation: Top-Down
Top-down approach is to implement one method in the structure chart at a time from the top to the bottom. Stubs can be used for the methods waiting to be implemented. A stub is a simple but incomplete version of a method. The use of stubs enables you to test invoking the method from a caller. Implement the main method first and then use a stub for the printMonth method. For example, let printMonth display the year and the month in the stub. Refer to page chapter 5, page 176.

81. Implementation: Bottom-Up
Bottom-up approach is to implement one method in the structure chart at a time from the bottom to the top. For each method implemented, write a test program to test it. Both top-down and bottom-up methods are fine. Both approaches implement the methods incrementally and help to isolate programming errors and makes debugging easy. Sometimes, they can be used together.
Refer to PrintCalendar class on page