How do you filter the results of the nchoosek(v,k) command?

I used the nchoosek(v,k) command to find out all the 7 number combinations possible using 12 distinct numbers (where v=[5 7 13 14 17 18 21 24 27 35 37 39] and k=7). The result was a 7 X 792 matrix. Is there a way to filter the results in a way where it omits all the combinations which contain consecutive numbers?

Thank you.

[Jan]

What are "consecutive numbers"? Do you mean the values [13, 14] and [17, 18] or the positions in the vector like [5,7] and [7,13]?

A small example would be useful.

[Moataz]

Firstly, thank you for your help. By consecutive numbers I mean, 13,14. I probably could have used a better example. For clarity's sake let v = [5 6 7 8 15 19 24 25 26 31 38 45] where the consecutive numbers are 5,6,7,8 and 24,25,26. I would like to to be able to find all the 7 number combinations using those 12 numbers where there are no consecutive numbers.

[Birdman]

Have you seen my and Jan's answer?

Answer 1

[Birdman]

Something like this?

A=nchoosek(v,k);
A(any([diff(A.')==1].',2),:)=[]

[Jan]

+1. Slightly simplified:

A(any(diff(A, 1, 2) == 1, 2), :) = []

Not shorter, but the time for two transpositions is saved and the unneeded square bracket.

[Birdman]

Hmm, diff function with three input arguments, something I learnt today. Thanks!

[Stephen23]

@Birdman: it is recommended to read the documentation for every operation and function that you use. You would do this for your own work, of course, so why not as well when offering advice on this forum?

[Birdman]

I did not know that it took three input arguments, at least I missed that part. You can not expect someone to read every function's documentation with the highest attention. Now, I will be more careful about it.

[Jan]

@Birdman: You are doing a great job here! It is obvious that you have learned a lot of Matlab tricks in the last months - and share them. Of course you do not know the one or other detail - exactly as me. But fortunately all members of the forum can support each other. You have learnt something while answering in the forum? Fine. A win-win-win situation for the OP, for you and the forum.

Stephen is right: It is recommended to read all docs. And all release notes to know the differences between the Matlab versions. And the docs of the toolboxes you do not have to avoid shadowing built-in functions. And the open and closed bug reports (obviously Walter does this). And Yair's undocumented Matlab, e.g. to know gems like sprintfc. Some users post questions about the PsychToolbox or Octave without mentioning it, so it is useful to have some basic knowledge about these tools also.

On the other hand, it has a value to see both versions side by side:

A(any([diff(A.')==1].',   2), :) = []
A(any(diff(A, 1, 2) == 1, 2), :) = []

Maybe some readers can profit from understanding the differences. And then it is useful for the forum.

Finally, reading something about negotiation techniques is useful also. ;-)

[Birdman]

@Jan: Thank you Jan. It is really nice to be appreciated by a MVP like you and it really pushes me to learn more and more about MATLAB and Simulink. I know that Stephen supports me by saying the things he says but from the time I started contributing to this forum, I find his attitude useful but a little discouraging as well. I read documentation before I answer a question to make sure I guide the OP in the right direction.

For instance, this answer of mine is a lot improved comparing to my first time answers and you suggest your thought in an encouraging way but Stephen focuses on my statement about diff function instead saying positive things( I say this because I know he upvotes answers he likes).

Anyway, I am always open to Stephen's and your suggestions to improve codes and knowledge. Thank you once more Jan. :)

[Jan]

@Birdman: Do not overestimate the Most Vain Person tag. As the reputation points and badges it works as a sweetie for the reward center of my brain and is capable of causing internet addiction. Comparable to the "Likes" or "Followers" in other communities, it is a psychological method to bind the attention of the contributors. When I saw the MVP tag beside my name the first time, my first thought was, that it is time to leave the forum. Well, I'm still here - obviously it works.

I would appreciate your contributions in exactly the same way in a forum without tags, badges or reputation points.

[Birdman]

Actually not overestimating, but being appreciated by someone who is an expert makes me feel good, that is all.

[Jan]

You are an expert in Simulink and with symbolic calculations - two fields I do not have any experiences in.

:-) It is time to stop the flatter. We do not want others to get jealous.

[Birdman]

Yes you are right :)

Answer 2

[Jan]

Creating all combinations and removing the unwanted ones can be very expensive. The number of combinations grows rapidly with the size of the input. Therefore a constructive method might be more efficient, when your RAM explodes.

v     = [5 7 13 14 17 18 21 24 27 35 37 39]
k     = 7;

% Use the first value if the dist
index = ([false, diff(v) == 1]);
v1    = v(index);
w     = v(~index);

% All combinations of the shortened vector:
comb = nchoosek(w, k);

% Create the full set by inflating:
for i1 = v1
  match = any(comb == i1 - 1, 2);
  combx = comb(match, :);
  combx(combx == i1 - 1) = i1;
  comb  = cat(1, comb, combx);
end

This replies the same vectors as Birdman's solution, but in a different order. Maybe you want to apply sortrows afterwards.

If nchoosek(v,k) is too huge for your RAM and many rows are removed, this might be working.