Problem 51. Find the two most distant points

Created by Cody Team

Solve Later

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.

Solve

Solution Stats

3225 Solutions
1318 Solvers

Last Solution submitted on Mar 31, 2020

Last 200 Solutions

Problem Comments

5 Comments

5 Comments

Show 2 older comments

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

Solution Comments

Solution 1813949

2 Comments

2 Comments

Qiaoli Xie on 13 May 2019

Since yesterday, I submit the solution ,and it always shows "
While evaluating the solution, the server encountered an error caused by temporary unavailability of MATLAB Service. Wait a few minutes for the MATLAB Service to return, and then rescore."
I don't know how to deal with it?

Isha Desai on 13 May 2019

You should be able to submit solutions now. Sorry for the inconveniene.

Solution 1790572

2 Comments

2 Comments

Paul Smits on 16 Apr 2019

no function squareform either... pffff

goc3 on 22 Apr 2019

Cody utilizes vanilla MATLAB (no toolboxes).

Solution 1790541

1 Comment

1 Comment

Paul Smits on 16 Apr 2019

Why is there "undefined function 'dist' for input arguments of type 'double'."? Works on my machine (and online matlab too)

Solution 1577123

1 Comment

1 Comment

Luyu Wang on 6 Jul 2018

I solved the problem by an tedious approach.

Solution 1050564

1 Comment

1 Comment

yao gang on 11 Nov 2016

remove ' diff ',but adds size -_-

Solution 903112

1 Comment

1 Comment

Jerivington on 6 Jun 2016

:)))))

Solution 393335

1 Comment

1 Comment

priyanka shrivastava on 7 Feb 2014

I am using matlab2010 but dist function is not available in it. Can you tell me how and where can I use this?

Solution 387795

2 Comments

2 Comments

Jon on 17 Jan 2014

Without dist, but with str2num

Carl Witthoft on 23 Nov 2015

I think it works w/ just x*[1;i] . No need to convert from a string.

Solution 267361

1 Comment

1 Comment

Mineralter on 26 Jun 2013

i'm not sure this can always get the right answer,
so i need more debugging.

Solution 151481

2 Comments

2 Comments

Claudia on 16 Nov 2012

what is 'i'? This is strange but works.

Ned Gulley on 16 Nov 2012

@Claudia, "i" is the imaginary number sqrt(-1). Unless you overwrite it, it's always available to you in MATLAB without needing to declare it.

Solution 129842

1 Comment

1 Comment

Jamie Rodgers on 22 Aug 2012

Excuse me?
This solution works fine, but requires the stats toolbox to function!

Solution 116870

4 Comments

4 Comments

Show 1 older comment

Tony on 18 Feb 2013

I dont get whay sort(unique(ix)) will give you the location of the two points. it is wrong for these points (0.9631 0.5468),(0.5211 0.2316),(0.4889,0.6241),(0.6791 0.3955),(0.3670 0.9890),
sort(unique(ix)) will return [1 2 5].

li jian on 23 Mar 2013

I think this solution is not right

Khaled Hamed on 24 Mar 2013

I agree.

Mineralter on 26 Jun 2013

there may be something out of word,
if i put:
p =[1 0; 0 1;0 0; 1/sqrt(2) 1/sqrt(2) ]
your command would not right,
but 'unique' is very admirable.

Solution 113745

1 Comment

1 Comment

Heather on 29 May 2013

This is the smallest solution not to use "dist," which is not in core Matlab. Nicely done!

Solution 81500

1 Comment

1 Comment

Carl Witthoft on 23 Nov 2015

I don't know why Cody allows answers which depend on toolboxes. The whole point should be to write one's own "distance" function.

Solution 38083

1 Comment

1 Comment

Clive Hayward on 12 Feb 2012

Hard to believe you let 'dist' in but not 'pdist'.

Solution 38081

1 Comment

1 Comment

Clive Hayward on 12 Feb 2012

pdist is not allowed!

Solution 29161

1 Comment

1 Comment

Jean-Yves Tinevez on 10 Feb 2012

I find this a little bit unfair: dist is a neural network toolbox function. It is not available in MATLAB core, and the problem does not specify this toolbox is needed.

Solution 6849

1 Comment

1 Comment

Tim on 26 Jan 2012

Shame on me...

Problem Recent Solvers1318

Problem Tags

distance