Taxicab geometry

The Manhattan metric (also Manhattan distance, Mannheim, taxi or city block metric ) is a metric in which the distance between two points is defined as the sum of the absolute differences of their individual coordinates:

The underlying geometry was first studied by Hermann Minkowski.

Your name has to overcome this distance definition of the checkerboard -like plant of the building blocks and the orthogonal street grid of Manhattan, forcing a taxi driver, the distance between two addresses by lining up the "vertical " and " horizontal " path sections. The inner city of Mannheim has a similar structure.

A taxi driver who plans his route through such a system, lays back on the way to his goal of getting the same route length, provided he uses only way that will bring him closer to his goal. He never leaves an aligned to the grid rectangle whose opposite corners are at the starting point and the destination point.

The Manhattan metric is the sum of the norm (1- norm) of a vector space metric generated.

For example, in the graph on the Manhattan metric in a two-dimensional space, so that

Results, with and, the black dots are.