Calculating array address

Question

Consider array A[1..100,1..100],in which elements are stored in Z representation. An example of 5x5 such array is shown below: 

Base address of array = 1000,size of each element is 1 Byte,and stored in row major, then address of A[100][50] ?

Comments

it should be 1247

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you too getting 1247?

Answer 1

As per the question, RMO is used

therefore the matrix will look like

A[1][1]  A[1][2] ....................................  A[1][100]

                                                             A[2][99]

                                                       A[3][98]

                                             .

                                    .     

                              .

          A[98][3]

      A[99][2]

A[100][1]   A[100][2] ...............................A[100][100]

We want to go to element A[100][50]

means we need Row=100 and column=50

row1 has all 100 elements

row2 to 98 have 1 element only

row 100 has all 100 elements

therefore RMO = base + cross row1 + cross elements of row 2 to 98 + cross 49 elements in row 100 to reach 50th element

                          =  1000 + 100 + 98 + 49

                         =  1247Bytes?

Comments

in general, let count the no.of elements stored before your required element stored in the memory.

no.of elements * size of element

Add Base address

but you have to take care with which no. starts the index

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Yeah
don't think from prospective of formula
for example shape is T
then, the elements will be
 A[1][1]  A[1][2].............................A[1][100]
                                A[2][50]
                                  .
                                 .
 
                                A[100][50]

here you know if u want to reach A[1][1] you need not cross any element, therefore, RMO = base =1000
for A[1][2] = 1000+1
for A[2][5] this kinda arrangement won't exist.
for A[100][50]  = 1000 + cross row 1(100 elements) + 1element in all 98rows

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It should start from A[2][50] and the calculation should be 1000 + 100 + 99 (99 because 1st row is already crossed andfrom 2nd row only 1 element. In 100th element we will get 50th column) please correct me if I'm wrong.