Dividing a cell array into permutations of two column cell

Assume I have this cell array:

 in={'A' 'B' 'C'};

I would like to get possible \t separated permutations of in in two columns as:

   out=

    'A' 'B     C'

    'B' 'A     C'

    'C' 'A     B'

    'A    B'  'C'

    'A    C'  'B'

    'B    C'  'A'

For a cell in={'A' 'B' 'C' 'D'} of length 4, there should be 14 different rows in out e.g., 'A B' 'C D'. How to get out for any cell in of length n?

We suppose transposition in single element of a cell is not allowed. That is 'A' 'B C' is read in the same way as 'A' 'C B'. I also need the code can handle words (strings of any type) as the same as 'A' and 'B'. That is 'Alice_' '2John' can be taken in instead of 'A' or 'B' which a tab delimiter should be considered to separate them in output when located in the same cell element.

[Cedric Wannaz]

why 14?

[Guillaume]

Yes don't understand where the 14 comes from. For 4 elements you have 24 permutations, multiply that by 3 different columns where you can put your joining tab and you have 42 possibilities.

In your example with 3 elements, you're missing another 6 possibilities:

'A'  'C   B'
'B   A'  'C'
'B'  'C   A'
'C   A'  'B'
'C   B'  'A'
'C'  'B   A'

[folira 81]

@Guillamume In what I need to get, 'A' 'B C' is supposed to be the same as 'A' 'C B'.

[Cedric Wannaz]

How could we know that? What is the logic for defining what is equivalent to what? How does that works with four letters? Ok, I am starting to see that the irregularities in your example are not a mistake but there is some aggregation. Yet, what defines equivalences?

[folira 81]

@Cedric You are right. I revised the question. Please see the end.

Answer 1

[Cedric Wannaz]

EDIT 1:

Here it goes:

 words = {'A', 'B', 'C', 'D'} ;

 n = length( words ) ;
 wordIds = arrayfun( @(k) nchoosek( 1:n,k ), 1:n-1, 'UniformOutput', false ) ;
 wordIds = cellfun( @(m) mat2cell( m, ones(size(m, 1), 1), size(m, 2) ), wordIds, 'UniformOutput', false ) ;
 wordIds = vertcat( wordIds{:} ) ;
 output  = arrayfun( @(k){sprintf('%s\t', words{wordIds{k}}), sprintf('%s\t', words{wordIds{end-k+1}})}, ...
    (1:numel(wordIds)).', 'UniformOutput', false ) ;
 output = strtrim( vertcat( output{:} )) ;

with that you get (where the irregular spacing comes from tabs):

 output =
  14×2 cell array
    'A'            'B  C  D'
    'B'            'A  C  D'
    'C'            'A  B  D'
    'D'            'A  B  C'
    'A  B'        'C  D'    
    'A  C'        'B  D'    
    'A  D'        'B  C'    
    'B  C'        'A  D'    
    'B  D'        'A  C'    
    'C  D'        'A  B'    
    'A  B  C'    'D'        
    'A  B  D'    'C'        
    'A  C  D'    'B'        
    'B  C  D'    'A'

FORMER: I had misunderstood the question.

 >> in  = {'A', 'B', 'C'} ;
 >> out = in(perms(1:length(in)))
 out =
  6×3 cell array
    'C'    'B'    'A'
    'C'    'A'    'B'
    'B'    'C'    'A'
    'B'    'A'    'C'
    'A'    'C'    'B'
    'A'    'B'    'C'

[folira 81]

Appreciate your answer, the output needs to be in the form stated in problem. It should be in two columns and be able to handle any type of strings. `A` , `B` , etc, are examples of words and strings of any type.

[Cedric Wannaz]

See EDIT 1.

[folira 81]

Thanks, I am not sure why I get error "Function 'subsindex' is not defined for values of class 'cell'."

[Cedric Wannaz]

When you run my example as is (copy from the code box, paste in the command window), do you get an error? If so, which version of MATLAB are you using? If not, please copy an example that generates the error.

[Cedric Wannaz]

Did you find what the problem was on your system/content?