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Describe the formula of finding the location (address) of particular element in 2D array using example.
Answer:
1.
In case of Column
Major Order:
The formula is:
LOC (A [J, K]) = Base (A) + w [M (K-1) + (J-1)]
Here
LOC (A [J, K]) : is the location of the element in the
Jth row and Kth column.
Base (A) : is
the base address of the array A.
w : is
the number of bytes required to store single element of the array A.
M : is
the total number of rows in the array.
J : is
the row number of the element.
K : is
the column number of the element.
E.g.
A 3 x 4 integer array A is as below:
Subscript Elements Address
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10
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20
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50
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60
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90
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40
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30
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80
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75
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55
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65
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79
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(1,1)
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(2,1)
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(3,1)
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(1,2)
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(2,2)
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(3,2)
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(1,3)
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(2,3)
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(3,3)
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(1,4)
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(2,4)
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(3,4)
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1000
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1002
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1004
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1006
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1008
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1010
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1012
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1014
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1016
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1018
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1020
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1022
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Suppose we have to find the location of A [3, 2]. The
required values are:
Base (A) : 1000
w : 2 (because an integer takes 2 bytes
in memory)
M : 3
J : 3
K : 2
Now put these values in the given formula as below:
LOC (A [3, 2]) = 1000 + 2 [3 (2-1) + (3-1)]
= 1000 + 2 [3 (1) + 2]
= 1000 + 2 [3 + 2]
= 1000 + 2 [5]
= 1000 + 10
= 1010
2.
In case of Row
Major Order:
The formula is:
LOC (A [J, K]) = Base (A) + w [N (J-1) + (K-1)]
Here
LOC (A [J, K]) : is the location of the element in the
Jth row and Kth column.
Base (A) : is
the base address of the array A.
w : is
the number of bytes required to store single element of the array A.
N : is
the total number of columns in the array.
J : is
the row number of the element.
K : is
the column number of the element.
E.g.
A 3 x 4 integer array A is as below:
Subscript Elements Address
|
10
|
|
60
|
|
30
|
|
55
|
|
20
|
|
90
|
|
80
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65
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50
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40
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75
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79
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(1,1)
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(1,2)
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(1,3)
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(1,4)
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(2,1)
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(2,2)
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(2,3)
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(2,4)
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(3,1)
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(3,2)
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(3,3)
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(3,4)
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1000
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1002
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1004
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1006
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1008
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1010
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1012
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1014
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1016
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1018
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1020
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1022
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Suppose we have to find the location of A [3, 2]. The
required values are:
Base (A) : 1000
w : 2 (because an integer takes 2 bytes
in memory)
N : 4
J : 3
K : 2
Now put these values in the given formula as below:
LOC (A [3, 2]) = 1000 + 2 [4 (3-1) + (2-1)]
= 1000 + 2 [4 (2) + 1]
= 1000 + 2 [8 + 1]
= 1000 + 2 [9]
= 1000 + 18
= 1018
http://
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Contributed by:
Rohit kakria
I am software developer
Resourse address on xpode.com
http://www.xpode.com/Print.aspx?Articleid=500
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