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Re: Golf: Grocery Baggingby grinder (Bishop) 
on May 23, 2001 at 20:04 UTC ( [id://82599] : note . print w/replies, xml )  Need Help?? 
I'm not even going to attempt to write any code for this because it's pointless. For positive numbers, the problem is already NPcomplete. When you mix in negative numbers, it becomes worse. The only feasible way to proceed is to generate all possible groupings and bruteforce your way through them. For three elements, it's easy: abc, ab c, ac b, bc a. For four elements there is already an explosion of combinations: abcd, abc d, abd c, acd b, bcd a, ab cd, ac db, ad cb, ab c d, ac b d, ad b c, bc a d, bd a c, cd a b, a b c d. I won't even post what the results of 5 gives, and I doubt this server has enough disk space available to store all the possible enumerations of 10 elements. One could start to develop heuristics that paid special attention to groups of elements whose sigma matches the container size, but then that's going against the spirit of golf. Noodling around some code here, it looks like the complexity of the algorithm is O(n!). Which means that it's going to be quite... slow.  g r i n d e r
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