A three dimensional array in C++ is declared as int A [a] [b] [c]. Consider that array elements are stored in row major order and indexing begin from 0. Here the address of an item at the location A [r] [s] [t] computed in terms of word length w of an integer is 

The correct answer is & A [0] [0] [0] + w (b*c*r* + c*s + t)

EXPLANATION:

In C++, for a 3-dimensional array declared as int A[a][b][c], the memory is allocated in a sequence such that it increases with 'c' first, then 'b', and finally 'a'. This is because the elements are stored in row-major order.

• So, when we are trying to find the address of an element A[r][s][t]:
  • 't' will contribute to its value directly, because we are moving in the 'c' dimension,
  • 's' will have to consider all 'c' steps we have to take for every shift in the 'b' direction, hence 's' contributes 'c*s' shifts,
  • 'r' will have to consider all 'bc' steps we have to take for every shift in the 'a' direction, hence 'r' contributes 'bc*r' shifts.

Therefore, the correct formula would be: & A[0][0][0] + w * (b*c*r + c*s + t)

So, the correct answer would be option 2: & A [0] [0] [0] + w (bcr + c*s + t)