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Keep in mind that this is a weighted distribution: three categories with weight 10 are worth one category with weight 30 (so if N=2, you'd want 3/1 rather than 2/2).

This looks to me like a constrained (order must not change) variant on the bin packing problem. Bin packing is NP-complete in the general case (IIRC), but the order constraint makes this quite tractable (see merlyn's typesetting comment). This problem has a rather good (n lg n or n^2) solution via dynamic programming: the typesetting problem was on one of my assignments in an advanced algorithms class. (Hey, did Ovid just post a homework problem? ;-b) I'll dig through my old notes when I get home from work and see if I can find it. In the mean time, you (Ovid) might look at Text::Format for ideas.

Update: D'oh! Another constraint on the text formatting problem that isn't present here is a maximum on line length (bin size), which makes it hard to reject a bogus solution (too much in one bin) quickly. On the other hand, this solution is constrained by number of bins, which the text formatting solution isn't. Hmm.... (Great problem, Ovid!)

--
The hell with paco, vote for Erudil!
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In reply to Re(2): Puzzle: need a more general algorithm by FoxtrotUniform
in thread Puzzle: need a more general algorithm by Ovid

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