m×nruudukko

m×nruudukko, commonly referred to as a rectangular grid, is a rectangular arrangement of m rows and n columns of units (cells). The size is denoted by m by n (often written m×n). Each cell has coordinates (i, j) with 1 ≤ i ≤ m and 1 ≤ j ≤ n, where i indexes rows and j columns. The grid contains m·n cells. If one models the grid by its vertices rather than cells, the underlying lattice can be described by (m+1)×(n+1) grid points.

As a graph, the m×n grid can be viewed as the Cartesian product P_m × P_n of two path graphs, whose vertices are the cells and whose edges connect horizontally or vertically adjacent cells (a 4-neighborhood). This makes the grid a common structure for algorithms that operate on grid graphs, such as shortest-path or flow problems.

Neighborhoods and variants: in many contexts, diagonally adjacent cells are considered neighbors (8-neighborhood). Grids may be extended by wrapping around at boundaries to form toroidal grids, where opposite edges are connected.

Applications: m×nruudukko is widely used in image processing (pixels arranged in a grid), numerical methods for solving partial differential equations (finite difference methods on rectangular domains), game boards and puzzles, and grid-based pathfinding algorithms like breadth-first search and A*. It provides a simple, regular discretization of rectangular spaces and serves as a canonical model for a wide range of computational problems.