Chebyshev distance and Manhattan distance

        Today ，when I solve the problem of Meeting Point, I learned new knowledge about Chebyshev distance ,we can check its definition from wiki http://en.wikipedia.org/wiki/Chebyshev_distance 
     
        Chebyshev distance is a metric defined on a vector space where the distance between two vector is the greatest of their differences along any coordinate dimension. for example, in two dimension, point(x,y) to its 8 adjacent points are 1(see images below, left is represent chebyshev distance, right is Manhattan distance)

chebyshev distance

Manhattan distance

   
       The relationship between Chebyshev distance (also know as Linf) and Manhattan distance(also know as L1) is subtle, in one dimension , they are equivalent; in two dimension, all points whose Chebyshev distance equal to r with point(x,y) become a circles in the form of square, with side of length 2r, very interesting, all points whose Manhattan distance equal  to r with point(x,y) also become a circles in the form of square, with side of length sqrt(2)*r , we can rotate an scale the axis to transform Chebyshev distance to manhattan distance.
       But  what's more, the equivalence is not generalize to high dimension

       so what is the advantage of Manhattan distance?  independent, more precisely, Manhattan distance calculation is independent between dimensions. 
    
      now you can finish the problem meeting point , of course , if you want to pass system test, you must implement tricky.