Two Dimensional Array in Data Structure
Two Dimension Array Address Calculation
# Two dimensional arrays are called matrices in mathematical and tables in business application.
# Two D- arrays are also called matrix arrays. # We are having standard way of drawing a two-dimensional m X n array P. where m is row and n is column.
|• The number of rows or columns is called the range of the dimension. In the array a. the Range of the first dimension is 3 and the range of the second dimension is 4.Thus array has three rows and four columns.|
|• To implement a two-dimensional array, it is necessary to develop a method of ordering its ele-ments in a linear fashion and of transforming a two-dimensional reference to the linear representation.|
There are two methods of representing a two dimension array in memory.
1st row-major representation 2nd column- major representation
|Address of an element “P[ I ][ J ]” is calculated in two forms |
1st Row Major 2nd Column Major
Formula for calculate address in Row Major Order
M:N Address of P [ I ][ J ] = [((( I – LBr )*N) + ( J – LBc ))* W + Base]
Formula for calculate address in Column Major Order
M:N Address of P [ I ][ J ] = [((( J – LBc )*M)+ ( I – LBr ))* W + Base]
Find the numbers of row and Column. Number of rows (M) will be calculated as = (UBr – LBr) + 1 Number of columns (N) will be calculated as =(UBc – LBc) + 1
B = Base address.
I = Row subscript of element whose address is to be found.
J = Column subscript of element whose address is to be found.
W = Storage Size of one element stored in the array (in byte).
LBr = Lower limit of row/start row index of matrix,
if not given assume 0 (zero).
LBc = Lower bound of column/start column in of
matrix, if not given assume 0 (zero).
M = Number of row of the given matrix.
N = Number of column of the given matrix.