Question

I have an array / list of numbers. Each number has a certain priority / importance.

I need an algorithm that generate all combinations of numbers, but begin form numbers with the most importance.

e.g. [number, priority]: [1,1], [2,3], [3,2]. Highest priority is 1.

Combinations:

1, 3, 2, 1 1, 1 3, 3 3, 3 1, 1 2, 3 2, 2 1, 2 2, 1 1 1, 1 1 3, 1 3 1...

Any idea how to do this?
Of course, I want to generate a certain number of combinations.

Answer 1

I changed my answer to an example code, this way you don’t even need a recursion. You have to sort first the elements by the priority. The example is in Perl, which is not so far from Pseudocode

@numbers = (1, 3, 2, 4);

push(@result, @numbers);
push(@working_list, @numbers);
for ($i = 1; $i < @numbers; $i++) {  # We loop exactly for the length of the array (-1 because the first iteration is already inside)
    my @result_list;
    for $result (@working_list) { # get the result of the last iteration of $i
        for $number (@numbers) { # iterate the numbers
            push (@result_list, "$result $number");  # adding the numbers
        }
    }

    push(@result, @result_list); # push the last result to final result list
    undef @working_list;
    push(@working_list, @result_list); # use the last result as a start point for next $i iteration

}

print join(', ', @result);