Chebyshevdistans

Chebyshev distance, also known as chessboard distance or L∞ distance, is a metric defined for a vector space where the distance between two points is the maximum of their absolute coordinate differences. Imagine a king on a chessboard; the Chebyshev distance is the minimum number of moves the king needs to go from one square to another. Unlike Euclidean distance, which measures the straight-line distance, Chebyshev distance considers movement along any axis independently.

Formally, for two points p = (p1, p2, ..., pn) and q = (q1, q2, ..., qn) in an n-dimensional space, the Chebyshev distance is calculated as D_Chebyshev(p, q) = max(|p1 - q1|, |p2 - q2|, ..., |pn - qn|). This means you find the absolute difference for each dimension and then select the largest of those differences. This metric is particularly useful in contexts where movement is restricted to orthogonal directions, such as in certain types of grid-based simulations or in some computer science applications like image processing. It is also related to the supremum norm of the difference vector.