Chapter 2 Array

Data StructureWinter 2004

Array

• The Array is the most commonly used Data Storage Structure.

• It’s built into most Programming languages.

Creating an Array

• An array is a sequential data abstrction, its name is a reference to an array.

int[ ] intArray; //defines a reference to an array

intArray = new int[100]; //creates the array

Show sample program

• array.java

• lowArray.java

• highArray.java

INSERTION

• Example of insert operation and behavior

– New Item always inserted in the first vacant cell in the array.

• Observations:– Most algorithm knows how many items are

already in the array.– Searching and deleting are however not fast.

DELETING

• Example of delete operation and behavior

– To delete an element first, you must find it.– How long does it take for the worst case?– A deletion requires searching through an

average of N/2 elements and moving the rest of the elements.

INITIALIZATION

• In Java, an array of integers is automatically initialized to 0.

• Unless you specify otherwise,

• You can initialize an array to something beside 0 using this syntax:

int[] intArray ={0,1,2,3,4,5,6,7,8,9};

Accessing Array Elements

• Array elements are accessed using an index number.

temp = intArray[3]; //get 4th element content

intArray[7] = 66;//insert 66 in eighth cell

Linear Search

• What is Linear search?

• Simple-minded way= a sequential search

• N elements array– What is the worst case?– Run time is O (N)

Binary Search

• What is Binary search?– A sorted array is required

• New insert()

• Searching a sorted array by repeatedly dividing the search interval in half.

• Run time is O (log N)

Sample code for ordered array

• ..\ReaderPrograms\ReaderFiles\Chap02\OrderedArray\orderedArray.java

logarithms

Range Comparisons in B-search

10 4 (2 3 = 8)

1000 10

10,000 14

:

:

1,000,000,000 30

Power of Two: 2s -> s + 1 steps

Complexity of algorithm

• Time complexity

• Space complexity

• Time complexity: in big O notation. How much time it takes to process N data elements? Ignore constant details

Complexity of algorithm

for i = 1 to nIf a[i] == x then return a[i]Else i++;

endfor

• What is the complexity?for i = 1 to n

for j = 1 to m If a[i, j] == x then return a[i] else i++;

endforendfor

Complexity of algorithm

• Don’t need constant since N can be very large

– O(N) - worst case for a linear search in an array

– O(N2)– O(log N)

Complexity of algorithm

Example of algorithm Big O

Linear search

Binary Search

Insertion for unordered array

Insertion for ordered array

Deletion for unordered array

Deletion for ordered array

BIG O : O( )

More complex object Array

• What if a complex data structure instead of int as an array element (e.g. person database)

• ..\ReaderPrograms\ReaderFiles\Chap02\ClassData\classDataArray.java

Person()getLastname()displayPerson()

person

FirstnameLastnameage