Finding all non-conflicting combinations of values from multiple lists of values

Question

I have the following array which contains arrays of values:

$array = array(
    array(\'1\', \'2\'),
    array(\'a\', \'b\', \'c\'),
    array(\'x\', \'y\'),         


        

Answer 1

Look at it from a different angle: in order to compose a result row, you need to pick a value for each column. Each value should be picked from a different source row. The problem is know as "pick N out of M", or more mathematically, a Combination.

This means that a result row corresponds to an array of source-row indices.

You can build all possible pickings by starting to build an index-array like this (pseudo-code)

function combinations( $source ) {
  if( count( $source ) == 0 ) return $source;
  $result=array();
  // build one row
  foreach( $source as $index=>$value ) {
    $newsource = array_splice( $source, $index, 1 );

    $reduced_combinations=combinations( $newsource  );
    foreach( $reduced_combinations as $reduced_combi ) {
      $newrow=array_unshift( $reduced_combi, $value );
      $result[]=$newrow;
    }

  }
  return $result;
}

function retrieve_indices( $indices, $arrays ) {
   $result=array();
   foreach( $indices as $column=>$index ) {
     $result[]=$arrays[$index][$column];
   }
   return $result;
}

$source_arrays = array(
  array( "1", "2", "3" ),
  array( "a", "b", "c" ),
  array( "x", "y", "z" )
);

$index_combinations = combinations( range(0,2) );
$result=array();
foreach( $index_combinations as $combination ) {
  $result[]=retrieve_indices( $combination, $source_arrays );
}