get a combination of unique paths for given pair of numbers

I need to get combination of all unique paths. I have a path as follows:

107 111 354 371 326 375 145

pipe# 107 has 2 other pipes - 108 and 109

similarly, 354 has another 355

375 has 378 and 382

Desired output from [107/108/109], 111, [354 355], 371, 326, [375 378 382], 145 should be :

107 111 354 371 326 375 145

108 111 354 371 326 375 145

109 111 354 371 326 375 145

107 111 355 371 326 375 145

108 111 355 371 326 375 145

109 111 355 371 326 375 145

107 111 354 371 326 378 145

108 111 354 371 326 378 145

109 111 354 371 326 378 145

107 111 355 371 326 378 145

108 111 355 371 326 378 145

109 111 355 371 326 378 145

107 111 354 371 326 382 145

108 111 354 371 326 382 145

109 111 354 371 326 382 145

107 111 355 371 326 382 145

108 111 355 371 326 382 145

109 111 355 371 326 382 145

I would really appreciate if you could help me with the code or an idea. Thank you!!

Answer 1

[Walter Roberson]

This is easy to calculate using a code pattern that I call "odometer". Each cycle, move on to next valid entry in the last position, and when it reaches the maximum, "roll over" it and increment the second last... rolling it over as necessary. The general code pattern does not require that each position has the same number of possibilities.

https://www.mathworks.com/matlabcentral/answers/602395-different-number-of-for-loops#answer_502861

[ONKAR BHANDARE]

Hi Walter,

Thank you for responding. I went through the odometer code pattern but I still can't figure out how it applies to my question. Can you please help me with the code or give an idea how it would look like? I really appreciate all the help.

Thank you,

Onkar

[Walter Roberson]

The odometer utilities here do not assume that the values to be cycled through are all the same datatype.

The way the output is formatted for this particular example does assume that the entries are all integers.

pipes = {[107,108,109], 111, [354,355], 371, 326, [375, 378, 382], 145};

fmt = [repmat('%d ', 1, length(pipes)-1), '%d\n'];

[od_index, at_end] = odometer_init(pipes);
while ~at_end
    od_reading = odometer_fetch_reading(od_index, pipes);
    fprintf(fmt, cell2mat(od_reading));    
    [od_index, at_end] = odometer_next(od_index, pipes);
end

107 111 354 371 326 375 145
107 111 354 371 326 378 145
107 111 354 371 326 382 145
107 111 355 371 326 375 145
107 111 355 371 326 378 145
107 111 355 371 326 382 145
108 111 354 371 326 375 145
108 111 354 371 326 378 145
108 111 354 371 326 382 145
108 111 355 371 326 375 145
108 111 355 371 326 378 145
108 111 355 371 326 382 145
109 111 354 371 326 375 145
109 111 354 371 326 378 145
109 111 354 371 326 382 145
109 111 355 371 326 375 145
109 111 355 371 326 378 145
109 111 355 371 326 382 145

%these utilities do not permit empty positions.
function [od_index, at_end] = odometer_init(odvec)
   if isempty(odvec) || any(cellfun(@isempty, odvec))
       od_index = 0;
       at_end = true;
   else
       od_index = ones(1, length(odvec));
       at_end = false;
   end
end

function odreading = odometer_fetch_reading(od_index, odvec)
    odreading = cellfun(@(odcell, cellidx) odcell(cellidx), odvec, num2cell(od_index), 'uniform', 0);
end

function [od_index, at_end] = odometer_next(od_index, odvec)
  at_end = true;
  for vecidx = length(odvec) : -1 : 1
      if od_index(vecidx) == length(odvec{vecidx})
          od_index(vecidx) = 1;
      else
          od_index(vecidx) = od_index(vecidx) + 1;
          at_end = false;
          break;
      end
  end
end

[ONKAR BHANDARE]

Thanks a lot Walter! This helps a lot!