Chapter 6 Arrays

Objectives

· To describe why an array is necessary in programming (§6.1).

· To learn the steps involved in using arrays: declaring array reference variables and creating arrays (§6.2).

· To initialize the values in an array (§6.2).

· To simplify programming using JDK 1.5 enhanced for loop (§6.2).

· To copy contents from one array to another (§6.3).

· To develop and invoke methods with array arguments and ruturn type (§6.4-6.5).

· To sort an array using the selection sort algorithm (§6.6).

· To search elements using the linear or binary search algorithm (§6.7).

· To declare and create multidimensional arrays (§6.8).

· To declare and create multidimensional arrays (§6.9 Optional).

Declaring Array Variables

F datatype[] arrayRefVar;

Example:

double[] myList;

F datatype arrayRefVar[]; // This style is allowed, but not preferred

Example:

double myList[];

Creating Arrays

arrayRefVar = new datatype[arraySize];

Example:

myList = new double[10];

myList[0] references the first element in the array.

myList[9] references the last element in the array.

Declaring and Creating
in One Step

F datatype[] arrayRefVar = new

datatype[arraySize];

double[] myList = new double[10];

F datatype arrayRefVar[] = new
datatype[arraySize];

double myList[] = new double[10];

The Length of an Array

Once an array is created, its size is fixed. It cannot be changed. You can find its size using

arrayRefVar.length

For example,

myList.length returns 10

Default Values

When an array is created, its elements are assigned the default value of

0 for the numeric primitive data types,

'\u0000' for char types, and

false for boolean types.

Indexed Variables

The array elements are accessed through the index. The array indices are 0-based, i.e., it starts from 0 to arrayRefVar.length-1. In the example in Figure 6.1, myList holds ten double values and the indices are from 0 to 9.

Each element in the array is represented using the following syntax, known as an indexed variable:

arrayRefVar[index];

Using Indexed Variables

After an array is created, an indexed variable can be used in the same way as a regular variable. For example, the following code adds the value in myList[0] and myList[1] to myList[2].

myList[2] = myList[0] + myList[1];

Array Initializers

F Declaring, creating, initializing in one step:

double[] myList = {1.9, 2.9, 3.4, 3.5};

This shorthand syntax must be in one statement.

Declaring, creating, initializing Using the Shorthand

Notation

double[] myList = {1.9, 2.9, 3.4, 3.5};

This shorthand notation is equivalent to the following statements:

double[] myList = new double[4];

myList[0] = 1.9;

myList[1] = 2.9;

myList[2] = 3.4;

myList[3] = 3.5;

CAUTION

Using the shorthand notation, you have to declare, create, and initialize the array all in one statement. Splitting it would cause a syntax error. For example, the following is wrong:

double[] myList;

myList = {1.9, 2.9, 3.4, 3.5};

Processing Arrays

See the examples in the text.

· (Initializing arrays)

· (Printing arrays)

· (Summing all elements)

· (Finding the largest element)

· (Finding the smallest index of the largest element)

Enhanced for Loop

JDK 1.5 introduced a new for loop that enables you to traverse the complete array sequentially without using an index variable. For example, the following code displays all elements in the array myList:

for (double value: myList)

System.out.println(value);

In general, the syntax is

for (elementType value: arrayRefVar) {

// Process the value

}

You still have to use an index variable if you wish to traverse the array in a different order or change the elements in the array.

Example: Assigning Grades

F Objective: read student scores (int), get the best score, and then assign grades based on the following scheme:

– Grade is A if score is >= best–10;

– Grade is B if score is >= best–20;

– Grade is C if score is >= best–30;

– Grade is D if score is >= best–40;

– Grade is F otherwise.

Copying Arrays

Often, in a program, you need to duplicate an array or a part of an array. In such cases you could attempt to use the assignment statement (=), as follows:

list2 = list1;

Copying Arrays

Using a loop:

int[] sourceArray = {2, 3, 1, 5, 10};

int[] targetArray = new int[sourceArray.length];

for (int i = 0; i < sourceArrays.length; i++)

targetArray[i] = sourceArray[i];

The arraycopy Utility

arraycopy(sourceArray, src_pos, targetArray, tar_pos, length);

Example:

System.arraycopy(sourceArray, 0, targetArray, 0, sourceArray.length);

Passing Arrays to Methods

public static void printArray(int[] array) {

for (int i = 0; i < array.length; i++) {

System.out.print(array[i] + " ");

}

}

Anonymous Array

The statement

printArray(new int[]{3, 1, 2, 6, 4, 2});

creates an array using the following syntax:

new dataType[]{literal0, literal1, ..., literalk};

There is no explicit reference variable for the array. Such array is called an anonymous array.

Pass By Value

Java uses pass by value to pass parameters to a method. There are important differences between passing a value of variables of primitive data types and passing arrays.

FFor a parameter of a primitive type value, the actual value is passed. Changing the value of the local parameter inside the method does not affect the value of the variable outside the method.

FFor a parameter of an array type, the value of the parameter contains a reference to an array; this reference is passed to the method. Any changes to the array that occur inside the method body will affect the original array that was passed as the argument.

Simple Example

public class Test {

public static void main(String[] args) {

int x = 1; // x represents an int value

int[] y = new int[10]; // y represents an array of int values

m(x, y); // Invoke m with arguments x and y

System.out.println("x is " + x);

System.out.println("y[0] is " + y[0]);

}

public static void m(int number, int[] numbers) {

number = 1001; // Assign a new value to number

numbers[0] = 5555; // Assign a new value to numbers[0]

}

}

Call Stack

When invoking m(x, y), the values of x and y are passed to number and numbers. Since y contains the reference value to the array, numbers now contains the same reference value to the same array.

Heap

The JVM stores the array in an area of memory, called heap, which is used for dynamic memory allocation where blocks of memory are allocated and freed in an arbitrary order.

Example:
Passing Arrays as Arguments

F Objective: Demonstrate differences of passing primitive data type variables and array variables.

Returning an Array from a Method

int[] list1 = new int[]{1, 2, 3, 4, 5, 6};

int[] list2 = reverse(list1);

Example: Counting Occurrence of Each Letter

F Generate 100 lowercase letters randomly and assign to an array of characters.

F Count the occurrence of each letter in the array.

Searching Arrays

Searching is the process of looking for a specific element in an array; for example, discovering whether a certain score is included in a list of scores. Searching is a common task in computer programming. There are many algorithms and data structures devoted to searching. In this section, two commonly used approaches are discussed, linear search and binary search.

Linear Search

The linear search approach compares the key element, key, sequentially with each element in the array list. The method continues to do so until the key matches an element in the list or the list is exhausted without a match being found. If a match is made, the linear search returns the index of the element in the array that matches the key. If no match is found, the search returns -1.

public class LinearSearch {
 /** The method for finding a key in the list */
 public static int linearSearch(int[] list, int key) {
 for (int i = 0; i < list.length; i++)
 if (key == list[i])
 return i;
 return -1;
 }
}

Binary Search

For binary search to work, the elements in the array must already be ordered. Without loss of generality, assume that the array is in ascending order.

e.g., 2 4 7 10 11 45 50 59 60 66 69 70 79

The binary search first compares the key with the element in the middle of the array.

· If the key is less than the middle element, you only need to search the key in the first half of the array.

· If the key is equal to the middle element, the search ends with a match.

· If the key is greater than the middle element, you only need to search the key in the second half of the array.

The binarySearch method returns the index of the search key if it is contained in the list. Otherwise, it returns –insertion point - 1. The insertion point is the point at which the key would be inserted into the list.

/** Use binary search to find the key in the list */

public static int binarySearch(int[] list, int key) {

int low = 0;

int high = list.length - 1;

while (high >= low) {

int mid = (low + high) / 2;

if (key < list[mid])

high = mid - 1;

else if (key == list[mid])

return mid;

else

low = mid + 1;

}

return -1 - low;

}

The Arrays.binarySearch Method

Since binary search is frequently used in programming, Java provides several overloaded binarySearch methods for searching a key in an array of int, double, char, short, long, and float in the java.util.Arrays class. For example, the following code searches the keys in an array of numbers and an array of characters.

int[] list = {2, 4, 7, 10, 11, 45, 50, 59, 60, 66, 69, 70, 79};

System.out.println("Index is " +

java.util.Arrays.binarySearch(list, 11));

char[] chars = {'a', 'c', 'g', 'x', 'y', 'z'};

System.out.println("Index is " +

java.util.Arrays.binarySearch(chars, 't'));

For the binarySearch method to work, the array must be pre-sorted in increasing order.

Sorting Arrays

Sorting, like searching, is also a common task in computer programming. It would be used, for instance, if you wanted to display the grades from Listing 6.2, “Assigning Grades,” in alphabetical order. Many different algorithms have been developed for sorting. This section introduces two simple, intuitive sorting algorithms: selection sort and insertion sort.

Selection Sort

Selection sort finds the largest number in the list and places it last. It then finds the largest number remaining and places it next to last, and so on until the list contains only a single number. Figure 6.17 shows how to sort the list {2, 9, 5, 4, 8, 1, 6} using selection sort.

Selection Sort

public class SelectionSort {
 /** Main method */
 public static void main(String[] args) {
 // Initialize the list
 double[] myList = {5.0, 4.4, 1.9, 2.9, 3.4, 3.5};
 
 // Print the original list
 System.out.println("My list before sort is: ");
 printList(myList);
 
 // Sort the list
 selectionSort(myList);
 
 // Print the sorted list
 System.out.println();
 System.out.println("My list after sort is: ");
 printList(myList);
 }
 
 /** The method for printing numbers */
 static void printList(double[] list) {
 for (int i = 0; i < list.length; i++)
 System.out.print(list[i] + " ");
 System.out.println();
 }
 
 /** The method for sorting the numbers */
 static void selectionSort(double[] list) {
 for (int i = list.length - 1; i >= 1; i--) {
 // Find the maximum in the list[0..i]
 double currentMax = list[0];
 int currentMaxIndex = 0;
 
 for (int j = 1; j <= i; j++) {
 if (currentMax < list[j]) {
 currentMax = list[j];
 currentMaxIndex = j;
 }
 }
 
 // Swap list[i] with list[currentMaxIndex] if necessary;
 if (currentMaxIndex != i) {
 list[currentMaxIndex] = list[i];
 list[i] = currentMax;
 }
 }
 }
}
 
Insertion Sort
 
 
public class InsertionSort {
 /** Main method */
 public static void main(String[] args) {
 // Initialize the list
 double[] myList = {5.0, 4.4, 1.9, 2.9, 3.4, 3.5};
 
 // Print the original list
 System.out.println("My list before sort is: ");
 printList(myList);
 
 // Sort the list
 insertionSort(myList);
 
 // Print the sorted list
 System.out.println();
 System.out.println("My list after sort is: ");
 printList(myList);
 }
 
 /** The method for printing numbers */
 static void printList(double[] list) {
 for (int i = 0; i < list.length; i++) {
 System.out.print(list[i] + " ");
 }
 System.out.println();
 }
 
 /** The method for sorting the numbers */
 public static void insertionSort(double[] list) {
 for (int i = 1; i < list.length; i++) {
 /** insert list[i] into a sorted sublist list[0..i-1] so that
 list[0..i] is sorted. */
 double currentElement = list[i];
 int k;
 for (k = i - 1; k >= 0 && list[k] > currentElement; k--) {
 list[k + 1] = list[k];
 }
 
 // Insert the current element into list[k+1]
 list[k + 1] = currentElement;
 }
 }
}

Two-dimensional Arrays

// Declare array ref var

dataType[][] refVar;

// Create array and assign its reference to variable

refVar = new dataType[10][10];

// Combine declaration and creation in one statement

dataType[][] refVar = new dataType[10][10];

// Alternative syntax

dataType refVar[][] = new dataType[10][10];

Declaring Variables of Two-dimensional Arrays and Creating Two-dimensional Arrays

int[][] matrix = new int[10][10];

or

int matrix[][] = new int[10][10];

matrix[0][0] = 3;

for (int i = 0; i < matrix.length; i++)

for (int j = 0; j < matrix[i].length; j++)

matrix[i][j] = (int)(Math.random() * 1000);

double[][] x;

Two-dimensional Array Illustration

Declaring, Creating, and Initializing Using Shorthand Notations

You can also use an array initializer to declare, create and initialize a two-dimensional array. For example,

Lengths of Two-dimensional Arrays

int[][] x = new int[3][4];

.

int[][] array = {

{1, 2, 3},

{4, 5, 6},

{7, 8, 9},

{10, 11, 12}

};

Ragged Arrays

Each row in a two-dimensional array is itself an array. So, the rows can have different lengths. Such an array is known as a ragged array. For example,

int[][] matrix = {

{1, 2, 3, 4, 5},

{2, 3, 4, 5},

{3, 4, 5},

{4, 5},

{5}

};

Multidimensional Arrays

Occasionally, you will need to represent n-dimensional data structures. In Java, you can create n-dimensional arrays for any integer n.

The way to declare two-dimensional array variables and create two-dimensional arrays can be generalized to declare n-dimensional array variables and create n-dimensional arrays for n >= 3. For example, the following syntax declares a three-dimensional array variable scores, creates an array, and assigns its reference to scores.

double[][][] scores = new double[10][5][2];

Example: Calculating Total Scores

F Objective: write a program that calculates the total score for students in a class. Suppose the scores are stored in a three-dimensional array named scores. The first index in scores refers to a student, the second refers to an exam, and the third refers to the part of the exam. Suppose there are 7 students, 5 exams, and each exam has two parts--the multiple-choice part and the programming part. So, scores[i][j][0] represents the score on the multiple-choice part for the i’s student on the j’s exam. Your program displays the total score for each student.