Data Structure - Address Calculation of Multi Dimensional Array Question of Pune University (MCA)

---------------------------------- " Data Structure "-------------------------------------

Array

  Address Calculation of Multi Dimensional Array

§ Addressing formula for the element A[i₁] [i₂] [i₃]….. [i_n] in an N-Dimensional array declared as   A[u₁] [u₂] [u₃]….. [u_n] is 

(1)   Row Major Form

A[i₁] [i₂] [i₃]….. [i_n] = B + W * [ ( i₁ * u₂* u₃*….. *u_n ) + ( i₂ * u₃*….. *u_n ) +…. + ( i_n-1 *u_n  ) + ( i_n ) ]           Where    B  = Base Address of an array A[u₁] [u₂] [u₃]….. [u_n]

W  = Element Size

(2)   Column Major Form

A[i₁] [i₂] [i₃]….. [i_n] = B + W * [ ( u₁ * i₂* i₃*….. *i_n ) + ( u₂ * i₃*….. *i_n ) +…. + ( u_n *i₂  ) + ( i₁ ) ]

                                      Where    B  = Base Address of an array A[u₁] [u₂] [u₃]….. [u_n]

W  = Element Size

Example : A integer array is defined as X[100][40][40].Find the address of cell X[80][30][20].

Here Form of storage is not specified therefore always consider Row Major form and Base address is not given so assume suitable data.

Solution :  Given ,

                              X is an array of integers so element size (W)  = 2

                              Let  Base Address (B) = 1000

                                                                    To find address of  cell  X[80][30][20]

                 Therefore

                                i₁ = 80 , i₂ = 30 , i₃ = 20

                                                                u₁ = 100 , u₂ = 40 , u₃ = 40          

                  As We Know 

                                                        Formula Of Address Calculation in Row Major Form is -

       A[i₁] [i₂] [i₃]….. [i_n] = B + W * [ ( i₁ * u₂* u₃*….. *u_n ) + ( i₂ * u₃*….. *u_n ) +…. + ( i_n-1 *u_n  ) + ( i_n ) ]

                                              Where    B  = Base Address of an array A[u₁] [u₂] [u₃]….. [u_n]                                                     W = Element Size So

Address of  cell  X[80][30][20] =  1000 + 2 * [ (80*40*40) + (30*40) + (20) ]

                                                                                   =  1000 + 2 * [ 128000 + 1200 + 20 ]

                                                                                   =  1000 + 2 * [ 129220 ]

                                                                                   =  1000 + 258440

                                                                                   =  259440

Therefore Address of  cell  X[80][30][20] is 259440 .