how to generate all possible combination from a sequence

how to generate all possible combination from a n-dimensional vector without repetition of numbers.. i wanted combination of vec = 1:11;

eg:

vec = [1 2 3]
result = [
1 2 3;
1 3 2;
2 3 1;
2 1 3;
3 2 1;
3 1 2];

[Stephen23]

Your question is erroneous: these are not the combinations of vec, but are actually the permutations.

The difference is very simple:

• if the order does not matter: combinations.
• if the order is important: permutations.

You should make a complaint to your high school that they did not teach these basic mathematical terms correctly. Ask for your money back!

Answer 1

[Stephen23]

>> perms(1:3)
ans =
     3     2     1
     3     1     2
     2     3     1
     2     1     3
     1     2     3
     1     3     2

[Elysi Cochin]

when i do perms(1:11), its showing

out of memory....

is there any way to solve it....

[Matt J]

Computing the result as uint8

   A=perms(uint8(1:11))

should reduce memory requirements to 0.4 GB for A. If you don't have that much, start clearing variables...

[John D'Errico]

People don't realize just how easy it is to create a huge array.

There are factorial(11) permutations of a vector of length 11.

factorial(11)
ans =
    39916800

But that forma an array with that many rows, but 11 columns.

factorial(11)*11
ans =
   439084800

Stored in double precision, how any bytes?

factorial(11)*11*8
ans =
              3512678400

So roughly 3.5 gigabytes. Stored as uint8 is better of course, but then you would ask next how to compute all permutations of a vector of length 12. :)

[Elysi Cochin]

i tried A=perms(uint8(1:11)) still Out of memory

[Stephen23]

@Elysi Cochin: essentially you have two choices:

1. buy more memory for your computer.
2. change your algorithm.

As the other commenters have already told you, even though beginners often imagine that their computer has never-ending memory and processing capabilities, in practice it is very simple to define a few commands that far exceed any computer's abilities.

Your task (as the author of your algorithm) is to understand this and to get information on alternatives. One possibility is to use a permutation generator that generates each permutation at a time (not all at once). This will be slow, but it will avoid the memory problems. You will find several submissions on FEX that provide this functionality:

http://www.mathworks.com/matlabcentral/fileexchange/22692-nextperm

http://www.mathworks.com/matlabcentral/fileexchange/13101-recperms--recursive-permutations-

http://www.mathworks.com/matlabcentral/fileexchange/23067-oneperm

http://www.mathworks.com/matlabcentral/fileexchange/24459-next-combination-permutation

Ultimately however, you will just find that this takes too long, and you will then have to consider alternatives to your algorithm. Good luck!

Answer 2

[Jos (10584)]

I just submitted NEXTPERM http://uk.mathworks.com/matlabcentral/fileexchange/57429-nextperm