Chebyshevdistansen

Chebyshev distance, also known as the chessboard distance, is a metric used in mathematics to measure the distance between two points in a grid-based system, such as a chessboard. It is named after the Russian mathematician Pafnuty Chebyshev. This distance metric is particularly useful in scenarios where movement is restricted to horizontal and vertical directions, like the movement of a rook in chess or the Manhattan distance's cousin in a two-dimensional grid.

The Chebyshev distance between two points, (x1, y1) and (x2, y2), is defined as the maximum of the absolute differences of their coordinates. Mathematically, it is expressed as the maximum of |x1 - x2| and |y1 - y2|. This means that the distance is determined by the greatest difference along either the x-axis or the y-axis.

One of the key properties of Chebyshev distance is that it does not satisfy the triangle inequality, which is a fundamental property of many other distance metrics. However, it does satisfy the other properties of a metric, such as non-negativity, identity of indiscernibles, and symmetry.

Chebyshev distance is widely used in various fields, including computer science, particularly in image processing and pattern recognition. It is also used in optimization problems and in the study of graphs and networks. The concept is straightforward yet powerful, providing a simple way to measure distance in scenarios where movement is constrained to specific directions.