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Let's define distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ as $$|x_2-x_1| + |y_2-y_1|$$.

There are given some points.
I think how to find maximum distance between two arbitrary points (among given points). My inituition is following:
Let's find point $(x, y)$ such that $x+y$ is maximal and $(a, b)$ such that $a+b$ is minimal. I don't know idea about corectness. It is only intuition. Could you help me, please ?

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Your idea as stated is incorrect. For example consider the points $$ \{(-100,100),(100,-100),(1,1),(-1,1)\} $$

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  • $\begingroup$ You are right, so can you help me solve this problem ? I think also about third dimension. $\endgroup$ Commented Dec 28, 2015 at 18:38
  • $\begingroup$ I think that the only solution that will always work is to try every pair of points. $\endgroup$ Commented Dec 28, 2015 at 18:40
  • $\begingroup$ Ok, maybe I say more. I would like to find algorithm for this problem. $\endgroup$ Commented Dec 28, 2015 at 19:03
  • $\begingroup$ Post a new question. Perhaps you should post the question to a programming site like stackoverflow. $\endgroup$ Commented Dec 28, 2015 at 19:04

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