Question

I am trying to have an array with n elements permute through like so:

permute(x,y,z)
permute(-x,y,z)
permute(x,-y,z)
permute(-x,-y,z)

It is like incrementing in binary (if the – signs represented 1s).
I am attempting to do that in code, and have noticed this:

    list[1] = -list[1];
        perm(list, k, m);
        list[1] = -list[1];
        list[2] = -list[2];
        perm(list, k, m);
        list[1] = -list[1];
        perm(list, k, m);
        list[1] = -list[1];
        list[2] = -list[2];
        list[3] = -list[3];
        perm(list, k, m);
        list[1] = -list[1];
        perm(list, k, m);
        list[1] = -list[1];
        list[2] = -list[2];
        perm(list, k, m);
        list[1] = -list[1];
        perm(list, k, m);
        list[1] = -list[1];
        list[2] = -list[2];
        list[3] = -list[3];
        list[4] = -list[4];
        perm(list, k, m);

I have noticed that some sections repeat. Is there a way to write this into a loop? Thanks.

Answer 1

This returns the kth permutation according to your scheme:

IEnumerable<int> Perm(IEnumerable<int> source, int k)
{
    return source.Select((x, i) => ((k >> i) & 1) == 1 ? -x : x);
}

Example:

var data = new[] { 1, 2, 3, 4 };

for (int k = 0; k < (1 << data.Length); k++)
{
    Console.WriteLine(string.Join(", ", Perm(data, k)));
}

Output:

1, 2, 3, 4
-1, 2, 3, 4
1, -2, 3, 4
-1, -2, 3, 4
1, 2, -3, 4
-1, 2, -3, 4
1, -2, -3, 4
-1, -2, -3, 4
1, 2, 3, -4
-1, 2, 3, -4
1, -2, 3, -4
-1, -2, 3, -4
1, 2, -3, -4
-1, 2, -3, -4
1, -2, -3, -4
-1, -2, -3, -4