1. Arrays
Week 2

2. Data Structures Data structure Types of data structures
A particular way of storing and organising data in a computer so that it can be used efficiently
Types of data structures
Based on memory allocation
Static (or fixed sized) data structures (Arrays)
Dynamic data structures (Linked lists)
Based on representation
Linear (Arrays/linked lists)
Non-linear (Trees/graphs)

3. Array: motivation You want to store 5 numbers in a computer
Define 5 variables, e.g. num1, num2, ..., num5
What, if you want to store 1000 numbers?
Defining 1000 variables is a pity!
Requires much programming effort
Any better solution?
Yes, some structured data type
Array is one of the most common structured data types
Saves a lot of programming effort (cf variable names)

4. What is an Array? A collection of data elements in which
all elements are of the same data type, hence homogeneous data
An array of students’ marks
An array of students’ names
An array of objects (OOP perspective!)
elements (or their references) are stored at contiguous/ consecutive memory locations
Array is a static data structure
An array cannot grow or shrink during program execution – its size is fixed

5. Basic concepts Array name (data) Index/subscript (0...9)
The slots are numbered sequentially starting at zero (Java, C++)
If there are N slots in an array, the index will be 0 through N-1
Array length = N = 10
Array size = N x Size of an element = 40
Direct access to an element

6. Homogeneity
Index: 1 2 3 4 5 6 7 8 9
All elements in the array must have the same data type 5 10 18 30 45 50 60 65 70 80
Value:
Value: 1 2 4 3
5.5
10.2
18.5
45.6
60.5
Index: 1 2 4 3
Index:
Value:
‘A’
10.2 55
‘X’
60.5
Not an array

7. Contiguous Memory
Array elements are stored at contiguous memory locations
No empty segment in between values (3 & 5 are empty – not allowed)
Index: 1 2 3 4 5 6 7 8 9
Value: 5 10 18 30 45 50 60 65 70 80 1 2 3 4 5 6 7 8 9
Index:
Value: 5 10 18 45 60 65 70 80

8. Declaring and Creating Arrays
Arrays are objects that occupy memory
Created dynamically with keyword new
int c[] = new int[ 12 ];
Equivalent to int c[]; // declare array variable c = new int[ 12 ]; // create array
We can create arrays of objects too
String b[] = new String[ 100 ];

9. Using Arrays Array_name[index] For example, in Java
System.out.println(data[4]) will display 0
data[3] = 99 will replace -3 with 99

10. Using Arrays Array_name[index] For example, in Java
System.out.println(data[4]) will display 0
data[3] = 99 will replace -3 with 99

11. Using Arrays Using an array initializer Use initializer list
Items enclosed in braces ({})
Items in list separated by commas
int n[] = { 10, 20, 30, 40, 50 };
Creates a five-element array
Index values of 0, 1, 2, 3, 4
Do not need keyword new

12. Using Arrays (Cont.)
To declare an array follow the type with (empty) []s
int[] grade; //or
int grade[]; //both declare an int array
In Java arrays are objects so must be created with the new keyword
To create an array of ten integers:
int[] grade = new int[10];
Note that the array size has to be specified, although it can be specified with a variable at run-time

13. Examples Using Arrays (Cont.)
Calculating the value to store in each array element
creates a 10-element array and assigns to each element one of the even integers from 2 to 20 (2, 4, 6, …, 20).

14. Examples Using Arrays (Cont.)

15. Examples Using Arrays (Cont.)
Output:

16. Examples Using Arrays (Cont.)
Summing the elements of an array
Array elements can represent a series of values
We can sum these values

17. 22-Feb-19
Computer Science Department

18. Some more concepts data[ -1 ] always illegal
data[ 10 ] illegal   (10 > upper bound)
data[ 1.5 ] always illegal
data[ 0 ] always OK
data[ 9 ] OK
Q. What will be the output of?
data[5]  + 10
data[3] = data[3] + 10

19. Array’s Dimensionality
One dimensional (just a linear list)
e.g.,
Only one subscript is required to access an individual element
Two dimensional (matrix/table)
e.g., 2 x 4 matrix (2 rows, 4 columns) 5 10 18 30 45 50 60 65 70 80
Col 0
Col 1
Col 2
Col 3
Row 0 20 25 60 40
Row 1 30 15 70 90

20. Multidimensional arrays
Tables with rows and columns
Two-dimensional array
Declaring two-dimensional array b[2][2]
int b[][] = { { 1, 2 }, { 3, 4 } };
1 and 2 initialize b[0][0] and b[0][1]
3 and 4 initialize b[1][0] and b[1][1]
int b[][] = { { 1, 2 }, { 3, 4, 5 } };
row 0 contains elements 1 and 2
row 1 contains elements 3, 4 and 5

21. Multidimensional arrays (Cont.)
Creating multidimensional arrays
Can be allocated dynamically
3-by-4 array
int b[][]; b = new int[ 3 ][ 4 ];
Rows can have different number of columns
int b[][]; b = new int[ 2 ][ ]; // allocate rows b[ 0 ] = new int[ 5 ]; // allocate row b[ 1 ] = new int[ 3 ]; // allocate row 1

22. Multidimensional arrays (Cont.)
Column 0
Column 1
Column 2
Column 3
Row 0
a[ 0 ][ 0 ]
a[ 0 ][ 1 ]
a[ 0 ][ 2 ]
a[ 0 ][ 3 ]
Row 1
a[ 1 ][ 0 ]
a[ 1 ][ 1 ]
a[ 1 ][ 2 ]
a[ 1 ][ 3 ]
Row 2
a[ 2 ][ 0 ]
a[ 2 ][ 1 ]
a[ 2 ][ 2 ]
a[ 2 ][ 3 ]
Column index
Row index
Array name

23. Multidimensional arrays (Cont.)

24. Multidimensional arrays (Cont.)

25. Searching Arrays: Linear Search and Binary Search
Finding elements in large amounts of data
Determine whether array contains value matching key value
Linear searching
Binary searching

26. Searching Arrays: Linear Search and Binary Search (Cont.)
Compare each array element with search key
If search key found, return element index
If search key not found, return –1 (invalid index)
Works best for small or unsorted arrays
Inefficient for larger arrays

27. Linear Search

28. Linear Search(Cont.) Output: Key 34 found at index: 6

29. Binary Search Binary search Efficient for large, sorted arrays
Eliminates half of the elements in search through each pass
Compare middle array element to search key
If element equals key
Return array index
If element is less than key
Repeat search on first half of array
If element is greater then key
Repeat search on second half of array
Continue search until
element equals search key (success)
Search contains one element not equal to key (failure)

30. Binary Search (Cont.)

31. Binary Search (Cont.) Output: Key 14's position: 6

32. Binary Search Example