Lecture 86:- Column Major Formula for 2D Arrays

In the context of 2D arrays, the Column Major formula is used to calculate the linear index of an element based on its row and column indices. The formula is typically used when a 2D array is stored in memory as a 1D array in column-major order.

Column Major formula for a 2D array in column-major order:

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index = (column * numRows) + row

In this formula:

• index is the linear index of the element in the 1D representation of the 2D array.
• column is the column index of the element (starting from 0).
• row is the row index of the element (starting from 0).
• numRows is the number of rows in the 2D array.

The formula calculates the linear index by multiplying the column index by the number of rows and adding the row index. This represents the offset from the beginning of the 1D array where the desired element is stored.

For example, consider a 2D array arr with 3 rows and 4 columns:

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arr = [  [1, 2, 3, 4],  [5, 6, 7, 8],  [9, 10, 11, 12] ]

To access the element at row 1, column 2 using the Column Major formula:

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index = (2 * 3) + 1       = 7

So, arr[1][2] is equivalent to arr[7] when the 2D array is stored in memory as a 1D array using column-major order.

The Column Major formula is useful for efficient memory access and element indexing in column-major representation of 2D arrays. It helps map the 2D coordinates to the corresponding linear index in the 1D array.