Row-major and column-major order are two methods for storing two-dimensional arrays in linear memory, such as computer RAM.

In the realm of computer programming, particularly when working with multi-dimensional arrays, the terms row-major and column-major order refer to the specific arrangement in which the elements of an array are stored in memory. This distinction is crucial for two-dimensional arrays, as the choice between these storage orders can significantly influence the performance of your code.

In row-major order, the elements of each row in the array are stored in consecutive memory locations. This means that when traversing a two-dimensional array in this order, you move left to right across each row before proceeding down to the next row and repeating the process. This storage format is the default in many programming languages, including C and Python. For additional insights into the properties of two-dimensional arrays, further reading is encouraged.

Conversely, column-major order stores the elements of each column in consecutive memory locations. When traversing an array in column-major order, you move top to bottom down each column, then shift to the next column on the right and continue this pattern. This format is the default in languages such as Fortran and MATLAB. Gaining an understanding of this order can provide valuable context regarding how data storage and retrieval affect performance.

The decision between row-major and column-major order can greatly impact the efficiency of your code. Modern computers have a hierarchical memory structure, which means that accessing data stored in consecutive memory locations (as is the case with row-major or column-major order) is typically faster than accessing data that is scattered throughout memory. Consequently, when writing code that involves traversing a two-dimensional array, it is essential to consider the order in which the elements are stored in memory and to access them in a manner that aligns with this order. For a more comprehensive understanding of the underlying concepts, exploring related topics in computer science is recommended.

Summary for IB Computer Science:
Row-major and column-major order describe the memory storage methods for two-dimensional arrays. In row-major order, elements are stored sequentially row by row, while in column-major order, elements are stored column by column. The choice between these orders can affect code performance, as accessing data stored consecutively in memory is generally faster. Understanding these storage methods is essential for optimizing code efficiency.