Array Packing Challenge

You are given n arrays A₁..A_n of n_k elements each, of which each element in A_n is either 0 or n. Your goal is to find an arrangement of the arrays such that no two nonzero elements of the arrays may share the same position, and the total length of the arrangement is minimised. For example, given the input file containing the lines

1010101
20002
303

One possible optimal arrangement is

121012303

Your program must read an input file of the form specified above from standard input and print out the optimal arrangement to standard output.

You have until 2012-07-01 00:00:00 4chan time.

>>28
the key to getting an efficient optimal algorithm will be to consider a number of choices that is polynomially bounded in terms of the lengths of the sequences and the number of sequences, and to do this in the worst case. It can be done if there are exploitable patterns in the sequences. But with no extra knowledge on the sequences, I'm not sure if it can be done. But maybe.

>>18

I don't see it. I see that decision problem exanding into a giant boolean formula, but I can't see how to use a solution to that formula to solve an arbitrary SAT.