Lecture 85:- Row Major Formula for 2D Arrays 

In the context of 2D arrays, the Row 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 row-major order.

Row Major formula for a 2D array in row-major order:

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index = (row * numColumns) + column

In this formula:

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

The formula calculates the linear index by multiplying the row index by the number of columns and adding the column 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 Row Major formula:

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index = (1 * 4) + 2       = 6

So, arr[1][2] is equivalent to arr[6] when the 2D array is stored in memory as a 1D array using row-major order.

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