Get combinations of digits in a sequence

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  • Posted by jmduro Aug 17, 2017
  • 1570 views

Here are 2 recursive functions that give all combinations of digits in a sequence. 

sequence combinations 
 
procedure get_all_combinations(sequence s, sequence used, integer n) 
  integer lg 
   
  lg = length(s) 
  if n = lg then 
    combinations = append(combinations, used) 
    return 
  end if 
  n += 1 
  for d = 1 to length(s[n]) do 
    get_all_combinations(s, used&s[n][d], n) 
  end for 
end procedure 
 
------------------------------------------------------------------------------ 
 
procedure get_unique_combinations(sequence s, sequence used, integer n) 
  integer lg 
   
  lg = length(s) 
  if n = lg then 
    combinations = append(combinations, used) 
    return 
  end if 
  n += 1 
  for d = 1 to length(s[n]) do 
    if not find(s[n][d], used) then 
      get_unique_combinations(s, used&s[n][d], n) 
    end if 
  end for 
end procedure

And here is an example of usage: 

constant 
  SEQ = {{4,8,9}, {1,2,4}, {1,4,5,6}} 
 
combinations = {} 
get_all_combinations(SEQ, {}, 0) 
pretty_print(1, combinations, {}) 
puts(1, "\n") 
 
combinations = {} 
get_unique_combinations(SEQ, {}, 0) 
pretty_print(1, combinations, {}) 
puts(1, "\n")

Here is the result: get_all_combinations allows duplicate digits, get_unique_combinations does not. 

{ 
  {4,1,1},  {4,1,4},  {4,1,5},  {4,1,6},  {4,2,1},  {4,2,4}, 
  {4,2,5},  {4,2,6},  {4,4,1},  {4,4,4},  {4,4,5},  {4,4,6}, 
  {8,1,1},  {8,1,4},  {8,1,5},  {8,1,6},  {8,2,1},  {8,2,4}, 
  {8,2,5},  {8,2,6},  {8,4,1},  {8,4,4},  {8,4,5},  {8,4,6}, 
  {9,1,1},  {9,1,4},  {9,1,5},  {9,1,6},  {9,2,1},  {9,2,4}, 
  {9,2,5},  {9,2,6},  {9,4,1},  {9,4,4},  {9,4,5},  {9,4,6} 
} 
{ 
  {4,1,5},  {4,1,6},  {4,2,1},  {4,2,5},  {4,2,6},  {8,1,4}, 
  {8,1,5},  {8,1,6},  {8,2,1},  {8,2,4},  {8,2,5},  {8,2,6}, 
  {8,4,1},  {8,4,5},  {8,4,6},  {9,1,4},  {9,1,5},  {9,1,6}, 
  {9,2,1},  {9,2,4},  {9,2,5},  {9,2,6},  {9,4,1},  {9,4,5}, 
  {9,4,6} 
}

Jean-Marc

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