Manhattantávolság

Manhattantávolság, also known as taxicab geometry or Manhattan distance, is a metric used in a grid-like path. It is the distance between two points in a plane with coordinate geometry, calculated as the sum of the absolute differences of their Cartesian coordinates. Imagine a city with a grid of streets, like Manhattan. To travel from one point to another, you cannot move diagonally. You must follow the streets, turning only at intersections. The Manhattantávolság represents the shortest path you could take by only moving along these horizontal and vertical grid lines.

The formula for Manhattantávolság between two points (x1, y1) and (x2, y2) is |x1 - x2| + |y1 - y2|. This differs from the more familiar Euclidean distance, which calculates the straight-line "as the crow flies" distance using the Pythagorean theorem. Manhattantávolság is relevant in scenarios where movement is restricted to orthogonal directions, such as in urban planning, robotics, and certain computer science algorithms like pathfinding in games or analyzing pixel distances on a screen. It is also known as L1 distance or rectilinear distance.