Algorithm of N queens

Question

Algorithm NQueens ( k, n) //Prints all Solution to the n-queens problem
{
    for i := 1 to n do
    {
        if Place (k, i) then
        {
            x[k] := i;
         


        

Answer 1

I have code for this without using backtracking, but the nice thing is, it is giving time complexity of big-oh(n).

// when n is even...
for(j=1;j<=n/2;j++)
{
    x[j]=2*j;
};
i=1;
for(j=n/2 +1 ;j<=n;j++)
{
    x[j] =i;
    i=(2*i)+1;
}

// when n is odd..
i=0;
for(j=1;j<=(n/2+1);j++)
{
    x[i] = (2*i)+1;
    i++;
}
i=1;
for(j=(n/2+2);j<=n;j++)
{
    x[j] = 2*i;
    i++;
}

This code works well and gives one solution, but now I am in search of getting all possible solutions using this algorithm.