Two Dimensional Array,memory representation,address calculation

1. MULTI DIMENSIONAL
ARRAY
Dincy R Arikkat
Assistant Professor
1

2. 2
Two-Dimensional Arrays
 The arrays we have discussed so far are
known as one-dimensional arrays because
the data are organized linearly in only one
direction.
 Many applications require that data be
stored in more than one dimension.
 One common example is a table, which is
an array that consists of rows and columns.
 A two-dimensional array consists of a
certain number of rows and columns.

3. 3
FIGURE Two-dimensional Array

4. 4
FIGURE Array Of Arrays

5. 5
FIGURE Memory Layout

6. 6

7. MEMORY REPRESENTATION
OF MATRIX
Row-Major Order
Column-Major Order
7

8. ROW MAJOR
In this method the elements are stored row wise.
i.e. n elements of first row are stored in first n locations, n elements of
second row are stored in next n locations and so on.
8
A[0][0] A[0][1] A[0][2] A[0][3]
A[1][0] A[1][1] A[1][2] A[1][3]
A[2][0] A[2][1] A[2][2] A[2][3]
A[0][0] 200
A[0][1] 201
A[0][2] 202
A[0][3] 203
A[1][0] 204
A[1][1] 205
A[1][2] 206
A[1][3] 207
A[2][0] 208
A[2][1] 209
A[2][2] 210
A[2][3] 211
Element Address

9. COLUMN MAJOR
In this method the elements are stored column wise.
i.e. m elements of first column are stored in first m locations, m elements of second
column are stored in next m locations and so on.
9
A[0][0] A[0][1] A[0][2] A[0][3]
A[1][0] A[1][1] A[1][2] A[1][3]
A[2][0] A[2][1] A[2][2] A[2][3]
A[0][0] 200
A[1][0] 201
A[2][0] 202
A[0][1] 203
A[1][1] 204
A[2][1] 205
A[0][2] 206
A[1][2] 207
A[2][2] 208
A[0][3] 209
A[1][3] 210
A[2][3] 211
Element Address

10. ADDRESS CALCULATION
Row Major System:
Address of A [ I ][ J ] = B.A + [( I – Lr )* N + ( J – Lc ) ]*Size
Column Major System:
Address of A [ I ][ J ] = B.A + [( I – Lr ) + ( J – Lc )*M]*Size
10

11. ADDRESS CALCULATION
B.A = Base address
I = Row subscript of element whose address is to be found
J = Column subscript of element whose address is to be found
Size = Storage Size of one element stored in the array (in byte)
Lr = Lower limit of row/start row index of matrix, if not given assume 0 (zero)
Lc = Lower limit of column/start column index of matrix, if not given assume 0
(zero)
M = Number of row of the given matrix
N = Number of column of the given matrix
Usually number of rows and column of a matrix are given like A[10][15],
A[5][2] but if it is given as A[Lr......Ur][Lc.......Uc]
So in this case number of rows and columns will be calculated as
rows(M)= (Ur-Lr)+1
column(N)=(Uc-Lc)+1
11

12. 12
Multidimensional Arrays
• Multidimensional arrays can have three,
four, or more dimensions.
• The C language considers the three-
dimensional array to be an array of two-
dimensional arrays.

13. 13
FIGURE A Three-dimensional Array (3 x 5 x 4)

14. Thank You
14