2020.9.24

\((xi,yi),(xj,yj)\)

切比雪夫距离\(d1=max\{\left|xi-xj\right|, \left|yi-yj\right|\}\)

容易发现\(d1=\cfrac{\left|\left|xi-xj\right|+\left|yi-yj\right|\right|+\left|\left|xi-xj\right|-\left|yi-yj\right|\right|}{2}\)

\((\cfrac{xi+yi}{2}, \cfrac{xi-yi}{2}),(\cfrac{xj+yj}{2}, \cfrac{xj-yj}{2})\)

哈夫曼距离\(d2=\cfrac{\left|(xi+yi)-(xj+yj)\right|}{2}+\cfrac{\left|(xi-yi)-(xj-yj)\right|}{2}\)

讨论\(xi\)和\(xj\)的大小，以及\(yi\)和\(yj\)的大小，有\(d1=d2\)

把点如此变换可以把切比雪夫距离变成曼哈顿距离