Create all combinations of 4 elements out of a larger list

Question

I want to create all possible combinations of 4 chemical elements out of a list of 9 and use them to create folders named after these combinations. The desired list looks something like this:

{Cr, Hf, Mo, Nb, Ta, Ti, V, W, Zr}

What I want to get out of it, would be:

CrHfMoNb

CrHfMoTa

CrHfMoTi

CrHfMoV

...

TiVWZr

and so on for all 126 possible arrangements, stored in a list or something similar so that I can use it as input for creating the folders. These combinations should be ordered alphabetically, so that Hf always comes after Cr and before Ti for example. I can use both Bash and Python, I prefer the simpler method. If the method could easily be adapted to a different number like combinations of 5 that's a big plus.

Answer 1

Python has "itertools" which includes a function to perform these kind of combinations for you.

combinations('ABCD', 2)  returns    AB AC AD BC BD CD

so you could do something like...

#!/usr/bin/python3.5
import itertools
output = []
for i in itertools.combinations(['Cr', 'Hf', 'Mo', 'Nb', 'Ta', 'Ti', 'V', 'W', 'Zr'], 4):
        output.append("".join(i))
print(sorted(output))

Which would produce all 126 combinations and sort them for you.

['CrHfMoNb', 'CrHfMoTa', 'CrHfMoTi', 'CrHfMoV', 'CrHfMoW', 'CrHfMoZr', 'CrHfNbTa', 'CrHfNbTi', 'CrHfNbV', 'CrHfNbW', 'CrHfNbZr', 'CrHfTaTi', 'CrHfTaV', 'CrHfTaW', 'CrHfTaZr', 'CrHfTiV', 'CrHfTiW', 'CrHfTiZr', 'CrHfVW', 'CrHfVZr', 'CrHfWZr', 'CrMoNbTa', 'CrMoNbTi', 'CrMoNbV', 'CrMoNbW', 'CrMoNbZr', 'CrMoTaTi', 'CrMoTaV', 'CrMoTaW', 'CrMoTaZr', 'CrMoTiV', 'CrMoTiW', 'CrMoTiZr', 'CrMoVW', 'CrMoVZr', 'CrMoWZr', 'CrNbTaTi', 'CrNbTaV', 'CrNbTaW', 'CrNbTaZr', 'CrNbTiV', 'CrNbTiW', 'CrNbTiZr', 'CrNbVW', 'CrNbVZr', 'CrNbWZr', 'CrTaTiV', 'CrTaTiW', 'CrTaTiZr', 'CrTaVW', 'CrTaVZr', 'CrTaWZr', 'CrTiVW', 'CrTiVZr', 'CrTiWZr', 'CrVWZr', 'HfMoNbTa', 'HfMoNbTi', 'HfMoNbV', 'HfMoNbW', 'HfMoNbZr', 'HfMoTaTi', 'HfMoTaV', 'HfMoTaW', 'HfMoTaZr', 'HfMoTiV', 'HfMoTiW', 'HfMoTiZr', 'HfMoVW', 'HfMoVZr', 'HfMoWZr', 'HfNbTaTi', 'HfNbTaV', 'HfNbTaW', 'HfNbTaZr', 'HfNbTiV', 'HfNbTiW', 'HfNbTiZr', 'HfNbVW', 'HfNbVZr', 'HfNbWZr', 'HfTaTiV', 'HfTaTiW', 'HfTaTiZr', 'HfTaVW', 'HfTaVZr', 'HfTaWZr', 'HfTiVW', 'HfTiVZr', 'HfTiWZr', 'HfVWZr', 'MoNbTaTi', 'MoNbTaV', 'MoNbTaW', 'MoNbTaZr', 'MoNbTiV', 'MoNbTiW', 'MoNbTiZr', 'MoNbVW', 'MoNbVZr', 'MoNbWZr', 'MoTaTiV', 'MoTaTiW', 'MoTaTiZr', 'MoTaVW', 'MoTaVZr', 'MoTaWZr', 'MoTiVW', 'MoTiVZr', 'MoTiWZr', 'MoVWZr', 'NbTaTiV', 'NbTaTiW', 'NbTaTiZr', 'NbTaVW', 'NbTaVZr', 'NbTaWZr', 'NbTiVW', 'NbTiVZr', 'NbTiWZr', 'NbVWZr', 'TaTiVW', 'TaTiVZr', 'TaTiWZr', 'TaVWZr', 'TiVWZr']

If you want them "neatly" just use...

#!/usr/bin/python3.5
import itertools
output = []
for i in itertools.combinations(['Cr', 'Hf', 'Mo', 'Nb', 'Ta', 'Ti', 'V', 'W', 'Zr'], 4):
        output.append("".join(i))

while output:
        print(output.pop(0))

which gives...

CrHfMoNb CrHfMoTa CrHfMoTi CrHfMoV CrHfMoW CrHfMoZr CrHfNbTa CrHfNbTi CrHfNbV CrHfNbW CrHfNbZr CrHfTaTi CrHfTaV CrHfTaW CrHfTaZr CrHfTiV CrHfTiW CrHfTiZr CrHfVW CrHfVZr CrHfWZr CrMoNbTa CrMoNbTi CrMoNbV CrMoNbW CrMoNbZr CrMoTaTi CrMoTaV CrMoTaW CrMoTaZr CrMoTiV CrMoTiW CrMoTiZr CrMoVW CrMoVZr CrMoWZr CrNbTaTi CrNbTaV CrNbTaW CrNbTaZr CrNbTiV CrNbTiW CrNbTiZr CrNbVW CrNbVZr CrNbWZr CrTaTiV CrTaTiW CrTaTiZr CrTaVW CrTaVZr CrTaWZr CrTiVW CrTiVZr CrTiWZr CrVWZr HfMoNbTa HfMoNbTi HfMoNbV HfMoNbW HfMoNbZr HfMoTaTi HfMoTaV HfMoTaW HfMoTaZr HfMoTiV HfMoTiW HfMoTiZr HfMoVW HfMoVZr HfMoWZr HfNbTaTi HfNbTaV HfNbTaW HfNbTaZr HfNbTiV HfNbTiW HfNbTiZr HfNbVW HfNbVZr HfNbWZr HfTaTiV HfTaTiW HfTaTiZr HfTaVW HfTaVZr HfTaWZr HfTiVW HfTiVZr HfTiWZr HfVWZr MoNbTaTi MoNbTaV MoNbTaW MoNbTaZr MoNbTiV MoNbTiW MoNbTiZr MoNbVW MoNbVZr MoNbWZr MoTaTiV MoTaTiW MoTaTiZr MoTaVW MoTaVZr MoTaWZr MoTiVW MoTiVZr MoTiWZr MoVWZr NbTaTiV NbTaTiW NbTaTiZr NbTaVW NbTaVZr NbTaWZr NbTiVW NbTiVZr NbTiWZr NbVWZr TaTiVW TaTiVZr TaTiWZr TaVWZr TiVWZr

Answer 2

Not as short as the python method, but still straightforward. Create a shell array and cycle through that in four for loops yielding the desired 126 lines:

ELARR=(Cr Hf Mo Nb Ta Ti V W Zr)
for ((i=0; i<${#ELARR[@]}; i++))
    do  for ((j=i+1; j<${#ELARR[@]}; j++))
          do    for ((k=j+1; k<${#ELARR[@]}; k++))
                  do    for ((l=k+1; l<${#ELARR[@]}; l++))
                          do    echo ${ELARR[i]}${ELARR[j]}${ELARR[k]}${ELARR[l]}
                          done
                  done
          done
    done
CrHfMoNb
CrHfMoTa
CrHfMoTi
CrHfMoV
CrHfMoW
.
.
.
TaTiWZr
TaVWZr
TiVWZr

Will be even shorter if you assign the array's element count to a variable, and use that, and mayhap use a shorter array name...