Question

Multidimensional arrays can be stored in row major order, as in C++, or in column major order, as in Fortran. Develop the access functions for both of these arrangements for three-dimensional arrays. Please explain step my step.

Answer 1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

1st column major:

assume you have an array dimensioned [m,n,o] where m=3, n=5,o=2. and you want to find elemt [i,j,k] where i=2,j=2,k=1

the 30 elements are stored as followes array is store asfollows

   0   3   6  9  12               15   18   21   24  27

   1   4   7 10 13                16  19   22   25   28

   2   5   8 11 14                17   20  23   26   29

to find element [2,2,1]   assuming C++ arraynumbering where everything starts with 0 (Fortran starts at 1so theformula would be slightly different) since k=1 you are looking foran element in 2nd plane row 2 col 2 or element # 23

k * (m*n)+(i*m)+j                       element [2,2,1] is in the 2nd plane ∴there is kcomplete m*n elements before it

1 *(3*5)+(2*3)+2                        sinceit's in column 2 there are icomplete columns of m elements beforeit and it

15 + 6+2                                     is the j element in that column thatyou are interested in

23

row major :

assume you have an array dimensioned [m,n,o] where m=3, n=5,o=2. and you want to find elemt [i,j,k] where i=2,j=2,k=1

the 30 elements are stored as followes array is store asfollows

0    1   2    3   4                          15   16   17   18  19

5   6   7   8   9                          20   21   22   23  24  

10 11 12 13 14                         25   26   27 28   29

to find element [2,2,1]   assuming C++ arraynumbering where everything starts with 0 (Fortran starts at 1so theformula would be slightly different) since k=1 you are looking foran element in 2nd plane row 2 col 2 or element # 27

k * (m*n)+(j*n)+i                       element [2,2,1] is in the 2nd plane ∴there is kcomplete m*n elements before it

1 *(3*5)+(2*5)+2                        sinceit's in column 2 there are jcomplete rows of n elementsbefore it and it

15 +10+2                                     is the i element in that rowthat you are interested in

   27

Kindly revert for any queries

Thanks.