An *array* is a fundamental data structure category, and a building block for more complex data structures. In this second tutorial in the data structures and algorithms series, you will learn how arrays are understood and used in Java programming. I'll start with the concept of an array and how arrays are represented in the Java language. I'll then introduce you to one-dimensional arrays and the three ways that you can use them in your Java programs. Finally, we'll explore five algorithms used to search and sort one-dimensional arrays: Linear Search, Binary Search, Bubble Sort, Selection Sort, and Insertion Sort.

Note that this tutorial builds on Data structures and algorithms, Part 1, which introduced the theoretical side of data structures and the algorithms associated with them. That tutorial includes an in-depth discussion of algorithms and how to use space and time complexity factors to evaluate and select the most efficient algorithm for your Java program. We'll get much more hands-on in this tutorial, because I assume you've already read Part 1.

## What is an array?

An *array* is a sequence of elements where each element is associated with at least one index. An *element* is a group of memory locations that store a single data item. An *index* is a nonnegative integer, which in this case is used to uniquely identify an element. This relationship is similar to how a box number uniquely identifies a house on a given street.

The number of indexes associated with any element is the array's *dimension*. In this article, we'll be talking about one-dimensional arrays. The next article in this series introduces multi-dimensional arrays.

Java supports arrays. Each element occupies the same number of bytes, and the exact number depends on the type of the element's data item. Furthermore, all elements share the same type.

## One-dimensional arrays

The simplest kind of array has one dimension. A *one-dimensional array* associates each element with one index. One-dimensional arrays are used to store lists of data items. There are three techniques for creating one-dimensional arrays in Java:

- Use only an initializer
- Use only keyword
`new`

- Use keyword
`new`

with an initializer

### Creating a one-dimensional array with only an initializer

Here's the syntax to create a one-dimensional array using just an initializer:

```
'{' [
```*expr* (',' *expr*)*] '}'

This syntax states that a one-dimensional array is an optional, comma-separated list of expressions appearing between open and close brace characters. Furthermore, all expressions must evaluate to compatible types. For example, in a two-element one-dimensional array of `double`

s, both elements *might* be of type `double`

, or one element might be a `double`

while the other element is a `float`

or an integer type (such as `int`

).

Example:

```
{ 'J', 'a', 'v', 'a' }
```

### Creating a one-dimensional array with the keyword new

The keyword `new`

allocates memory for an array and returns its reference. Here's the syntax for this approach:

```
'new'
```*type* '[' *int_expr* ']'

This syntax states that a one-dimensional array is a region of (positive) `int_expr`

elements that share the same `type`

. Furthermore, all elements are zeroed, and are interpreted as `0`

, `0L`

, `0.0F`

, `0.0`

, `false`

, `null`

, or `'\u0000'`

.

Example:

```
new char[4]
```

### Creating a one-dimensional array with the 'new' keyword and an initializer

Here's the syntax to create a one-dimensional array using the keyword `new`

with an initializer. As you see, it blends the syntax from the previous two approaches:

```
'new'
```*type* '[' ']' '{' [*expr* (',' *expr*)*] '}'

In this case, because the number of elements can be determined from the comma-separated list of expressions, it isn't necessary (or allowed) to provide an `int_expr`

between the square brackets.

Example:

```
new char[] { 'J', 'a', 'v', 'a' }
```

Something to note is that the syntax for creating an array with only an initializer is no different in effect from the syntax using an initializer and a keyword. The initializer-only syntax is an example of *syntactic sugar*, which means syntax that makes the language sweeter, or easier, to use.

## Array variables

By itself, a newly-created one-dimensional array is useless. Its reference must be assigned to an *array variable* of a compatible type, either directly or via a method call. The following two lines of syntax show how you would declare this variable:

```
```*type* *var_name* '[' ']'
*type* '[' ']' *var_name*

Each syntax declares an array variable that stores a reference to a one-dimensional array. Although you can use either syntax, placing the square brackets after `type`

is preferred.

Examples:

```
char[] name1 = { 'J', 'a', 'v', 'a' };
char[] name2 = new char[4];
char[] name3 = new char[] { 'J', 'a', 'v', 'a' };
output(new char[] { 2, 3 }); // output({ 2, 3 }); results in a compiler error
static void output(char[] name)
{
// ...
}
```

In the examples, `name1`

, `name2`

, `name3`

, and `name`

are array variables. The single pair of square brackets states that each stores references to one-dimensional arrays.

Keyword `char`

indicates that each element must store a value of `char`

type. However, you can specify a non-`char`

value if Java can convert it to a `char`

. For example, `char[] chars = { 'A', 10 };`

is legal because `10`

is a small enough positive `int`

(meaning that it fits into the `char`

range of 0 through 65535) to be converted to a `char`

. In contrast, `char[] chars = { 'A', 80000 };`

would be illegal.

An array variable is associated with a `.length`

property that returns the length of the associated one-dimensional array as a positive `int`

; for example, `name1.length`

returns 4.

Given an array variable, you can access any element in a one-dimensional array by specifying an expression that agrees with the following syntax:

```
```*array_var* '[' *index* ']'

Here, `index`

is a positive `int`

that ranges from 0 (Java arrays are zero-based) to one less than the value returned from the `.length`

property.

Examples:

```
char ch = names[0]; // Get value.
names[1] = 'A'; // Set value.
```

If you specify a negative index or an index that is greater than or equal to the value returned by the array variable's `.length`

property, Java creates and throws a `java.lang.ArrayIndexOutOfBoundsException`

object.

## Algorithms for searching and sorting

It is a very common task to search one-dimensional arrays for specific data items, and there are a variety of algorithms for doing it. One of the most popular search algorithms is called Linear Search. Another option is Binary Search, which is usually more performant but also more demanding: in order to use Binary Search, the array's data items must first be *sorted*, or ordered. Although not very performant, *Bubble Sort*, *Selection Sort*, and *Insertion Sort* are all simple algorithms for sorting a one-dimensional array. Each works well enough for shorter arrays.

The next sections introduce each of these algorithms for searching and sorting one-dimensional arrays.

### The Linear Search algorithm

*Linear Search* searches a one-dimensional array of *n* data items for a specific one. It functions by comparing data items from the lowest index to the highest until it finds the specified data item, or until there are no more data items to compare.

The following pseudocode expresses Linear Search used for a one-dimensional array of integers:

```
DECLARE INTEGER i, srch = ...
DECLARE INTEGER x[] = [ ... ]
FOR i = 0 TO LENGTH(x) - 1
IF x[i] EQ srch THEN
PRINT "Found ", srch
END
END IF
NEXT i
PRINT "Not found", srch
END
```

Consider a one-dimensional unordered array of five integers [ 1, 4, 3, 2, 6 ], where integer 1 is located at index 0 and integer 6 is located at index 4. The pseudocode performs the following tasks to find integer 3 in this array:

- Compare the integer at index 0 (1) with 3.
- Because there's no match, compare the integer at index 1 (4) with 3.
- Because there's still no match, compare the integer at index 2 (3) with 3.
- Because there's a match, print
*Found 3*and exit.

Linear Search has a time complexity of O(*n*), which is pronounced "Big Oh of *n*." For *n* data items, this algorithm requires a maximum of *n* comparisons. On average, it performs *n*/2 comparisons. Linear Search offers linear performance.

### Explore Linear Search

To let you experiment with Linear Search, I've created the `LinearSearch`

Java application in Listing 1.

#### Listing 1. A Java example with the Linear Search algorithm (`LinearSearch.java`

)

```
{
public static void main(String[] args)
{
// Validate command line arguments count.
if (args.length != 2)
{
System.err.println("usage: java LinearSearch integers integer");
return;
}
// Read integers from first command-line argument. Return if integers
// could not be read.
int[] ints = readIntegers(args[0]);
if (ints == null)
return;
// Read search integer; NumberFormatException is thrown if the integer
// isn't valid.
int srchint = Integer.parseInt(args[1]);
// Perform the search and output the result.
System.out.println(srchint + (search(ints, srchint) ? " found"
: " not found"));
}
private static int[] readIntegers(String s)
{
String[] tokens = s.split(",");
int[] integers = new int[tokens.length];
for (int i = 0; i < tokens.length; i++)
integers[i] = Integer.parseInt(tokens[i]);
return integers;
}
private static boolean search(int[] x, int srchint)
{
for (int i = 0; i < x.length; i++)
if (srchint == x[i])
return true;
return false;
}
}
```

The `LinearSearch`

application reads a comma-separated list of integers from its first command-line argument. It searches the array for the integer identified by the second command-line argument, and outputs a found/not found message.

To experiment with this application, start by compiling Listing 1:

```
javac LinearSearch.java
```

Next, run the resulting application as follows:

```
java LinearSearch "4,5,8" 5
```

You should observe the following output:

```
5 found
```

Run the resulting application a second time, as follows:

```
java LinearSearch "4,5,8" 15
```

You should observe the following output:

```
15 not found
```

### The Binary Search algorithm

The Binary Search algorithm searches an ordered one-dimensional array of *n* data items for a specific data item. This algorithm consists of the following steps:

- Set low and high index variables to the indexes of the array's first and last data items, respectively.
- Terminate if the low index is greater than the high index. The searched-for data item is not in the array.
- Calculate the middle index by summing the low and high indexes and dividing the sum by 2.
- Compare the searched-for data item with the middle-indexed data item. Terminate if they are the same. The searched-for data item has been found.
- If the searched-for data item is greater than the middle-indexed data item, set the low index to the middle index plus one and transfer execution to Step 2. Binary Search repeats the search in the upper half of the array.
- The searched-for data item must be smaller than the middle-indexed data item, so set the high index to the middle index minus one and transfer execution to Step 2. Binary Search repeats the search in the lower half of the array.

Here is pseudocode representing the Binary Search algorithm for a one-dimensional array of integers:

```
DECLARE INTEGER x[] = [ ... ]
DECLARE INTEGER loIndex = 0
DECLARE INTEGER hiIndex = LENGTH(x) - 1
DECLARE INTEGER midIndex, srch = ...
WHILE loIndex LE hiIndex
midIndex = (loIndex + hiIndex) / 2
IF srch GT x[midIndex] THEN
loIndex = midIndex + 1
ELSE
IF srch LT x[midIndex] THEN
hiIndex = midIndex - 1
ELSE
EXIT WHILE
END IF
END WHILE
IF loIndex GT hiIndex THEN
PRINT srch, " not found"
ELSE
PRINT srch, " found"
END IF
END
```

Binary Search isn't hard to understand. For example, consider a one-dimensional ordered array of six integers [ 3, 4, 5, 6, 7, 8 ], where integer 3 is located at index 0 and integer 8 is located at index 5. The pseudocode does the following to find integer 6 in this array: