Distance between Manhattan and cherbihov and their mutual transformation; distance between Manhattan and Xuefu

Distance between Manhattan and cherbihov and their mutual transformation; distance between Manhattan and Xuefu

This article only discusses the distance between the two-dimensional space and the chibbihov.

Manhattan distance Definition

Set two points in the plane space. Their coordinates are $ (x1, y1) $, $ (x2, y2) $

$ Dis = | x1-x2 | + | y1-y2 | $

That is, the sum of the two-point horizontal and vertical Coordinate Difference

Boil a chestnut

In the figure, the distance between $ A and B $ is $ AC + BC = 4 + 3 = 7 $.

 

Distance Definition

Set two points in the plane space. Their coordinates are $ (x1, y1) $, $ (x2, y2) $

Then $ dis = max (| x1-x2 |, | y1-y2 |) $

That is, the maximum horizontal and vertical coordinate difference between two points

Boil another Chestnut

$ Dis = max (AC, BC) = AC = 4 $

 

Relationship between the two

The two definitions seem to have no wool relationship, but in fact, these two distances can beMutual Conversion!

In the simplest case, in a two-dimensional coordinate system, set the origin to $ (0, 0) $

If it is represented by the Manhattan distance, a point with a distance of $1 $ from the origin will constitute a square with a side length of $1 $.

 

If it is represented by a cut-over distance, a point with a distance of $1 $ from the source will constitute a square with a side length of $2 $.

 

 

What do you find by carefully comparing the two images?

That's right!

The second image is obtained by doubling the first image and rotating $45 ^ {\ circ} $.

Then, based on what is messy in the vector matrix

The vertex $ (x, y) $ in the first graph corresponds to the vertex $ (\ dfrac {x + y} {2}) in the second graph }, \ dfrac {x-y} {2}) $

In this way, we can convert each other.