Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 1 Chapter 5 Methods.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 2 Objectives F To define methods, invoke methods, and pass arguments to a method (§5.2-5.5). F To develop reusable code that is modular, easy-to-read, easy-to- debug, and easy-to-maintain. (§5.6). F To use method overloading and understand ambiguous overloading (§5.7). F To design and implement overloaded methods (§5.8). F To determine the scope of variables (§5.9). F To know how to use the methods in the Math class (§§5.10- 5.11). F To learn the concept of method abstraction (§5.12). F To design and implement methods using stepwise refinement (§5.12).

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 Calling a Methods F In order to use the method, you need to call or invoke the methods; F Two ways to call a methods depend upon if method: –return value int larger = max (3, 4); // calling max (3, 4) ad assigns the result to larger System.out.println(max(3, 4); –not returns a value u the method returns void, a call to method must be a statement. System.out.println(“Welcome to Java!”); 3

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 4 Method A Java method is a collection of statements that are grouped together to perform an operation. When you call the System.out.println method, for example, the system actually executes several statements in order to display a message on the console. Now you will learn how to create your own methods with or without return values, invoke a method with or without parameters, overload methods using the same names, and apply method abstraction in the program design. modifier returnValueType methodName(list of parameters) { // Method body; } A method definition consists of a method header and a method body. The Java Tutorials – Defining MethodsThe Java Tutorials – Defining Methods

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 Listing 5.1 –TestMax 5 // this program contains the main method and max method. // The main method is just like any other method except that it is invoked by JVM. public class TestMax { /** Main method */ public static void main(String[] args) { int i = 5; int j = 2; int k = max(i, j); // is calling method max System.out.println("The maximum between " + i + " and " + j + " is " + k); } /** when the max method is calling, variable i’s value 5 is passing to num1, and variable j’s value 2 is passing to num in the max 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; } }

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 Methods headers 6 Here are all the parts of a method: Modifiers: The modifier, which is optional, tells the compiler how to call the method. This defines the access type of the method. Return Type: A method may return a value. The returnValueType is the data type of the value the method returns. Method Name: This actual name of method, named max, has two int parameters, num1 & num2, the larger of which it returned by the methods.. The method name and the parameter list together constitute the method signature. Parameters: A parameter is like a placeholder. When a method is invoked, you pass a value to the parameter. Method Body: The method body contains a collection of statements that define what the method does.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 Object-Oriented Programming Concepts F Defining Methods Defining Methods F http://docs.oracle.com/javase/tutorial/java/c oncepts/index.html http://docs.oracle.com/javase/tutorial/java/c oncepts/index.html 7

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 8 Problem int sum = 0; for (int i = 1; i <= 10; i++) sum += i; System.out.println("Sum from 1 to 10 is " + sum); sum = 0; for (int i = 20; i <= 30; i++) sum += i; System.out.println("Sum from 20 to 30 is " + sum); sum = 0; for (int i = 35; i <= 45; i++) sum += i; System.out.println("Sum from 35 to 45 is " + sum); Find the sum of integers from 1 to 10, from 20 to 30, and from 35 to 45, respectively.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 9 Problem int sum = 0; for (int i = 1; i <= 10; i++) sum += i; System.out.println("Sum from 1 to 10 is " + sum); sum = 0; for (int i = 20; i <= 30; i++) sum += i; System.out.println("Sum from 20 to 30 is " + sum); sum = 0; for (int i = 35; i <= 45; i++) sum += i; System.out.println("Sum from 35 to 45 is " + sum);

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 10 Solution public class SumRang { public static int sum(int i1, int i2) { int sum = 0; for (int i = i1; i <= i2; i++) sum += i; return sum; } public static void main(String[] args) { System.out.println("Sum from 1 to 10 is " + sum(1, 10)); System.out.println("Sum from 20 to 30 is " + sum(20, 30)); System.out.println("Sum from 35 to 45 is " + sum(35, 45)); } // end of main } //end of class SumRange

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 11 Defining Methods A method is a collection of statements that are grouped together to perform an operation.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 12 Method Signature Method signature is the combination of the method name and the parameter list.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 13 Formal Parameters The variables defined in the method header are known as formal parameters. Simply parameters are place holders.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 14 Actual Parameters When a method is invoked, you pass a value to the parameter. This value is referred to as actual parameter or argument.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 15 Return Value Type 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.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 Calling a Method 16 To use a Method, you have to call or invoke it. There are two ways to call a Methods, whether the method returns a value or not.  If the method return a value, a call to the method is usually treated as value int larger = max (3, 4); Call max (3, 4) and assigns the result to methods to the variable larger. System.out.println(max(3, 4);  If the method returns void, then a call of the method must be statement System.out.println(“Welcome to Java!”);

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 17 Calling Methods Testing the max method. This program demonstrates calling a method max to return the largest of the int values- Listing 5.1 Video LinkListing 5.1 Video Link (This program contain main method and the max method.) public class TestMax { /** Main method is just like any other method except that it is invoked by the JVM*/ public static void main(String[] args) { // main method is always the same int i = 5; int j = 2; int k = max(i, j); //the main method invokes max (i, j), then variable I’s value 5 is passed to num1, & j’s value 2 System.out.println("The maximum between " + i + " and " + j + " is " + k); } /** Return the max between two numbers */ public static int max(int num1, int num2) { // max method int result; if (num1 > num2) result = num1; else result = num2; return result; // the max method is executed when the return statement in the max method is executed, the max method returns //the control to its caller } } TestMax

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 18 Calling Methods, cont. animation When a program calls a method, program control is transferred to the called method. The statement in main may invoke other methods that are defined in the class. In this example, the main method invokes max(i, j), which is define in the same class with the main method.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 22 Trace Method Invocation invoke max(i, j) Pass the value of i to num1 Pass the value of j to num2 animation

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 24 Trace Method Invocation (num1 > num2) is true since num1 is 5 and num2 is 2 animation

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 27 Trace Method Invocation return max(i, j) and assign the return value to k animation

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 29 CAUTION A return statement is required for a value-returning method. The method shown below in (a) is logically correct, but it has a compilation error because the Java compiler thinks it possible that this method does not return any value. To fix this problem, delete if (n < 0) in (a), so that the compiler will see a return statement to be reached regardless of how the if statement is evaluated. //return -1; (does not keep all the variable)

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 30 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 ).

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 31 Call Stacks Each time a method is invoked (called), the system stores parameters and variables in the memory known as a stack, which stores elements in LIFO (Last-in-first-out).

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 42 void Method & Example void is a Java keyword. Used at method declaration and definition to specify that the method does not return any type, the method returns void. It is not a type and there is no void references The example listing 5.2 program is a type of method does not return a value. The method performs some actions. TestVoidMethod Video Link on void method

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 43 Passing Parameters 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(“Computer Science”, 15); What is the output? The power of a method is its ability to work with parameters. You can use println to print any string; You can use max to find the maximum between any two int values. When calling a method, you need to provide arguments, this know as parameter order association. The following method prints a message n times.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 44 Pass by Value This program demonstrates passing values to the methods. Increment public class TestPassByValue { // the program creates a method for swapping two variables. /** 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 " + num1 + " and num2 is " + num2); } /** Swap two variables- The swap method is invoked by passing two arguments. */ public static void swap(int n1, int n2) { System.out.println("\tInside the swap method"); System.out.println("\t\tBefore swapping n1 is " + n1 + " n2 is " + n2); // Swap n1 with n2 int temp = n1; n1 = n2; n2 = temp; System.out.println("\t\tAfter swapping n1 is " + n1 + " n2 is " + n2); } } Listing 5.5

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 45 Pass by Value, cont. Swap method is invoked, num1 is 1 and num2 is 2. After swap method is invoked, num1 is still 1 and num2 is still 2. Their values have not been swapped, but the value of the arguments num1 and num2 are passed to n1 and n2 (use temp location) with their own memory locations independet

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 46 Modularizing Code Methods can be used to reduce redundant coding and enable code reuse. Methods can also be used to modularize code and improve the quality of the program. Listing 5.6 program. GreatestCommonDivisorMethod PrimeNumberMethod Video Note Modularize

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 47 Overloading Methods Overloading the max Method public static double max(double num1, double num2) { if (num1 > num2) return num1; else return num2; } TestMethodOverloading

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 48 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.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 49 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) { if (num1 > num2) return num1; else return num2; }

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 50 Problem: Converting Decimals to Hexadecimals Write a method that converts a decimal integer to a hexadecimal. Decimal2HexConversion

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 51 Scope of Local Variables Scope: the part of the program where the variable can be referenced. A local variable: a variable defined inside a method. 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.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 52 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.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 53 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.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 54 Scope of Local Variables, cont. A local variable must be declared and assigned a value before it can be used.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 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 for (int i = 1; i < 10; i++) { y += i; }

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 56 Scope of Local Variables, cont. // With no errors public static void incorrectMethod() { int x = 1; int y = 1; for (int i = 1; i < 10; i++) { int x = 0; x += i; }

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 57 Method Abstraction You can think of the method body as a black box that contains the detailed implementation for the method.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 58 Benefits of Methods Write a method once and reuse it anywhere. Information hiding. Hide the implementation from the user. Reduce complexity.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 59 The Math Class F Class constants: –PI –E F Class methods: –Trigonometric Methods –Exponent Methods –Rounding Methods –min, max, abs, and random Methods

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 60 Trigonometric Methods F sin(double a) F cos(double a) F tan(double a) F acos(double a) F asin(double a) F atan(double a) Radians toRadians(90) 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

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 61 Exponent Methods  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. Web Link: Class MathClass Math Examples: 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 22.91765 Math.sqrt(4) returns 2.0 Math.sqrt(10.5) returns 3.24

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 62 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).

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 63 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

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 64 min, max, and abs  max(a, b) and min(a, b) 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

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 66 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,

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 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. As introduced in Section 2.9, 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 65535 using the following expression: (note that since 0 <= Math.random() < 1.0, you have to add 1 to 65535.) (int)(Math.random() * (65535 + 1))

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 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)

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 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)

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 70 Case Study: Generating Random Characters, cont. As discussed in Chapter 2., 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))

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 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))

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 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'); } TestRandomCharacter RandomCharacter

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 73 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.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 74 PrintCalender Case Study Let us use the PrintCalendar example to demonstrate the stepwise refinement approach. PrintCalendar

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 81 Implementation: Top-Down A Skeleton for printCalendar 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. Thus, your program may begin like this:

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 82 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.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 1 Chapter 5 Methods.

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Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807 1 Chapter 5 Methods.

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