What Is The Manhattan Distance?

The Manhattan Distance is used to calculate the distance between two coordinates in a grid-like path.

Imagine you are on holidays in New York City, you are visiting the Empire State Building and decide to walk to The Morgan Library & Museum by the route below. From the map it is easy to see why Manhattan Distance is also known as city block distance or taxicab geometry.

Unlike the green line from the picture we cannot walk directly to the destination since we are constrained to the city's coordinate axes, therefore we would follow something more similar to the red line.