Problem 51. Find the two most distant points

Created by Cody Team

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Given a collection of points, return the indices of the rows that contain the two points most distant from one another. The input vector p has two columns corresponding to the x and y coordinates of each point. Return ix, the (sorted) pair of indices pointing to the remotest rows. There will always be one unique such pair of points.

So if

 p = [0 0]
     [1 0]
     [2 2]
     [0 1]

Then

 ix = [1 3]

That is, the two points p(1,:) and p(3,:) are farthest apart.

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Last Solution submitted on May 09, 2025

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Jean-Marie Sainthillier on 19 Jul 2012

More easy that it seems.

Carl Witthoft on 20 Nov 2015

You need to specify "Euclidean" distance :-)

Jerivington on 6 Jun 2016

Good problem, not too hard but required thinking

Dima Panna on 3 Jun 2019

Please add the next test :
p = [0,0;
2,1;
2,6;
1,6];
ix_correct = [1 3];
assert(isequal(mostDistant(p),ix_correct))

The solutions of the form:
[~,indx]=max(dist(p'));
unique(indx)

will fail, the last line will return an extra index [1,3,4] instead of just [1,3]

heart on 8 Feb 2020

refer to
Convex Hull therom and the Graham's Scan method

Can Tekin on 12 Jun 2020

Peter on 16 Aug 2023

Nice one!

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Problem 51. Find the two most distant points

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Problem 51. Find the two most distant points

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