The document provides a detailed overview of arrays, defining them as finite, ordered collections of homogeneous data elements. It discusses the key concepts related to arrays, including types, base addresses, indices, and their representation in one, two, and three dimensions. Additionally, it explains how to calculate the number of elements in various types of arrays using their bounds.

1. Data Structure

2.  Array Definition
 Representation and Analysis
 Single and Multidimensional Array
 Address Calculation

3. ARRAY

4. ARRAY
D
Z
P
34
9
7
7
S
3
22
M

5. ARRAY
[0]
D
Z P S
M
[1] [2] [3] [4] [5] [6] [7] [8]
34
9 7 7
22
[0] [1] [2] [3] [4] [5] [6] [7] [8]
34
9 7 7
22
[0] [1] [2] [3] [4] [5] [6] [7] [8]
Z D S
P
501
503
500
502

6. ARRAY
Definition:
An array is a finite, ordered and collection of homogeneous data elements.
Array as ADT:
An array is an ADT whose objects are sequence of elements of the same type
and the two operations performed on it are store and retrieve.

7. ARRAY: TERMINOLOGY
Type: Type of an array represents the kind of data it is meant for. For instance, and array of
integer, an array of character strings.
Base: The base of an array is the address of the memory location where the first element of
the array is located.
Index: All the elements in an array can be referenced by a subscript like Ai or A[i]. An index is
always an integer value.
Range of indices: Indices of array elements may change from a lower bound (L) to an uppar
bound (U), and these bounds are called the boundaries of an array.
Word: Word denotes the size of an element. In each memory location, a computer can store
an element of word size W, say. The word size varies from machine to machine such as 1 byte
to 8 bytes.

8. ARRAY
W
501
503
500
502
Physical
Memory
Base
[0]
D
Z P S
M
[1] [2] [3] [4] [5] [6] [7] [8]
S K R T
Index
char
C[0:8]
Size=9
34
9 7 7
22
[0] [1] [2] [3] [4] [5]
4
int I[0:5] Size=6
C[l : u]

9. ARRAY REPRESENTATION
1D
2D
3D

10. ARRAY REPRESENTATION
1D
A[l : u]

11. ARRAY REPRESENTATION
2D
A[l1 : u1, l2 : u2]
row1
row2
row3
row4
col1 col5
A[1 : 4, 1 : 5]

12. ARRAY REPRESENTATION
3D
A[l1 : u1, l2 : u2, l3 : u3]
l1 : u1
l3 : u3
l2 : u2

13. ARRAY: NO OF ELEMENTS
1D
In an 1D array, A[l:u], the number of elements is given by
(u-l+1)
A[l : u]

14. ARRAY: NO OF ELEMENTS
2D
A[l1 : u1, l2 : u2]
row1
row2
row3
row4
col1 col5
In a 2D array, A[l:u], the number of elements is given by
(u1-l1+1)(u2-l2+1)

15. ARRAY: NO OF ELEMENTS
A[l1 : u1, l2 : u2, . . . , ln : un]
In a 2D array, A[l:u], the number of elements is given by
∏
𝑖=1
𝑛
( ui − li +1)