Two Dimensional Array

Two Dimensional Array,memory representation,address calculation

1. MULTI DIMENSIONAL
ARRAY
DincyR Arikkat
Assistant Professor
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2. 2
Two-Dimensional Arrays
Thearrayswehavediscussedsofarare
knownasone-dimensionalarraysbecause
thedataareorganizedlinearlyinonlyone
direction.
Manyapplicationsrequirethatdatabe
storedinmorethanonedimension.
Onecommonexampleisatable,whichis
anarraythatconsistsofrowsandcolumns.
Atwo-dimensionalarrayconsistsofa
certainnumberofrowsandcolumns.

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
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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.
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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
ElementAddress

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.
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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
ElementAddress

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
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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
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12. 12
Multidimensional Arrays
•Multidimensionalarrayscanhavethree,
four,ormoredimensions.
•TheClanguageconsidersthethree-
dimensionalarraytobeanarrayoftwo-
dimensionalarrays.

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

14. Thank You
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