Generate all possible array combinations in C - Optimal Graph Colouring

问题

I need to generate arrays with all possible combinations, like this question I've found here:

Combinatorics: generate all "states" - array combinations

I'm doing a simple work of optimal Graph Coloring, so, I'm trying to generate all possible color combinations (the array represents the color for each node). This code is working but, is also doing unnecessary work. In this situation, [1, 1, 2] is the same thing of [2, 2, 1], I don't need to test if this is a valid graph again.

I can't think of anything, but first I would like to know if there's a simple code for doing what I want to.

For now, my code is something like this:

void generatearray(int array[], int array_size, int idx){

    int i;

    if(idx == array_size){
        putchar('\n');
        for(i = 0; i < array_size; i++) printf("%i ", array[i]);

    }
    else for(i = 0; i <= 3; i++){
        array[idx] = i;
        generatearray(array, array_size, idx+1);
    }

}

And it will print:

    [0, 0, 0]
    [0, 0, 1]
    [0, 0, 2]
    [0, 0, 3]
    [0, 1, 0]
    [0, 1, 1]
    ...
    [3, 3, 0]
    [3, 3, 1]
    [3, 3, 2]
    [3, 3, 3]

回答1:

Try this:

void generatearray( int array[], int array_size, int idx = 0, int fixed = 0 )
{
   int i;

   if ( idx == array_size )
   {
       putchar('\n');
       for( i = 0; i < array_size; i++ ) printf( "%i ", array[i] );

   } else {

       for( i = 0; i <= 3; i++ )
       {
          if ( fixed == i )
          {
             fixed++;
             array[idx] = i;
             return generatearray( array, array_size, idx + 1, fixed );
          }
          array[idx] = i;
          generatearray( array, array_size, idx + 1, fixed );
       }
   }
}

int arr[6];
generatearray( arr, 6 );

Old broken answer:

void generatearray(int array[], int array_size, int idx){

   int i;

   if(idx == array_size){
       putchar('\n');
       for(i = 0; i < array_size; i++) printf("%i ", array[i]);

   }
   else if ( idx == 0 ) {
       array[idx] = 0;
       generatearray(array, array_size, idx+1);
   } else {
       for(i = 0; i <= 3; i++){
       array[idx] = i;
       generatearray(array, array_size, idx+1);
       }

   }
}

来源：https://stackoverflow.com/questions/16444084/generate-all-possible-array-combinations-in-c-optimal-graph-colouring

标签

combinatorics