Lecture 88:- Formulas for 3D Arrays

Here are the formulas for calculating the linear index of an element in a 3D array based on the storage order:

1. Row-Major Formula:

   • Linear index = (index0 * size1 * size2) + (index1 * size2) + index2

   In this formula:

   • index0 is the index of the element along the first dimension (rows).
   • index1 is the index of the element along the second dimension (columns).
   • index2 is the index of the element along the third dimension.
   • size1 is the size (number of elements) along the first dimension (rows).
   • size2 is the size along the second dimension (columns).

2. Column-Major Formula:

   • Linear index = (index2 * size1 * size0) + (index1 * size0) + index0

   In this formula:

   • index2 is the index of the element along the third dimension.
   • index1 is the index of the element along the second dimension (columns).
   • index0 is the index of the element along the first dimension (rows).
   • size0 is the size (number of elements) along the first dimension (rows).
   • size1 is the size along the second dimension (columns).

These formulas assume 0-based indexing, where the indices start from 0.

By using the appropriate formula based on the storage order, you can calculate the linear index of an element in a 3D array. This allows for efficient memory access and indexing when working with multidimensional arrays.