Rowmajor

Row-major order is a method for storing multi-dimensional arrays in linear memory where the elements of a row are stored contiguously. In a two-dimensional array with dimensions rows by cols, the element A[i][j] is stored at memory location base + ((i * cols) + j) * size_of_element. This means the rightmost index varies most rapidly as you traverse memory, while the leftmost index changes more slowly.

This layout favors row-wise iteration. Accessing A[i][0], A[i][1], ..., A[i][cols-1] reads consecutive addresses, improving cache locality. In contrast, iterating column by column (A[0][j], A[1][j], etc.) tends to cause more cache misses because those elements are separated by a whole row’s worth of data.

Languages and libraries commonly associated with row-major storage include C and C++, which store true two-dimensional arrays in row-major order. NumPy for Python uses row-major by default (order='C'), though it can operate with column-major order (order='F') when requested. Other ecosystems, such as Fortran, MATLAB, and R, use column-major order, illustrating how the choice affects indexing, memory access patterns, and interoperability.

Awareness of row-major layout is important when interfacing with libraries, performing manual memory management, or flattening multi-dimensional data into one dimension. Consistent use of the same order avoids index-shifting errors and can improve performance by aligning access patterns with memory layout.