What is row-major and column-major order in two-dimensional arrays?

Row-major and column-major order are methods of storing two-dimensional arrays in linear storage like memory.

In computer programming, particularly in the context of multi-dimensional arrays, the terms row-major and column-major order refer to the order in which the elements of an array are stored in memory. These terms are especially relevant when dealing with two-dimensional arrays, where the choice between row-major and column-major order can significantly impact the efficiency of your code.

Row-major order is a method where the elements in each row of the array are stored in consecutive memory locations. This means that when you traverse a two-dimensional array in row-major order, you move across each row from left to right, then move down to the next row and repeat the process. This is the default order in many programming languages, including C and Python. For more details on the characteristics of two-dimensional arrays, you can refer to Characteristics of Two-Dimensional Arrays.

On the other hand, column-major order is a method where the elements in each column of the array are stored in consecutive memory locations. In this case, when you traverse the array, you move down each column from top to bottom, then move to the next column on the right and repeat. This is the default order in other languages, such as Fortran and MATLAB. Understanding the Central Processing Unit (CPU) can provide more context on how data storage and retrieval impact performance.

The choice between row-major and column-major order can have a significant impact on the performance of your code. This is because modern computers have a hierarchical memory structure, where accessing data that is stored in consecutive memory locations (as in row-major or column-major order) is faster than accessing data that is scattered around in memory. Therefore, when writing code that involves traversing a two-dimensional array, it's important to take into account the order in which the elements are stored in memory and try to access the elements in a way that aligns with this order. For a deeper understanding of the underlying concepts, you might want to explore the Von Neumann Model and Stored Program Concept and the Array Terminology in computer science.

IB Computer Science Tutor Summary: Row-major and column-major order describe how two-dimensional arrays are stored in memory. In row-major order, elements are stored row by row, while in column-major order, elements are stored column by column. The choice affects code performance since accessing data stored consecutively in memory is faster. Understanding these orders helps in optimising code efficiency.