n×mruudukko

An n×m grid, often referred to as an n×m ruudukko in some contexts, is a two-dimensional arrangement of elements in n rows and m columns. This structure is fundamental in various fields, including mathematics, computer science, and game theory. The total number of cells in an n×m grid is the product of n and m, i.e., n * m.

In mathematics, n×m grids are used to represent matrices, which are collections of numbers arranged in rows and columns. These matrices have applications in solving systems of linear equations, transformations in geometry, and numerous other areas. In graph theory, an n×m grid can be viewed as a graph where each cell is a node, and adjacent cells (horizontally or vertically) are connected by edges.

Computer science frequently utilizes n×m grids for data representation and algorithms. Examples include image processing, where an image is often treated as a grid of pixels, and chessboard or board game simulations, where the game state is maintained on an n×m grid. Algorithms like breadth-first search or depth-first search can be applied to grid structures to find paths or analyze connectivity.

The concept of an n×m grid is also prevalent in recreational mathematics and puzzles, such as Sudoku (typically a 9×9 grid) and various tiling problems. The size and shape of the grid, as well as the rules governing the elements within it, define the specific problem or application.