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2010-06-20T20:01:02.743
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2010-06-20T20:01:02.743
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Ok, I'm sorry I never was able to clearly explain the problem, but here is a solution. We need two functions <code>combinations</code> and <code>runvector(v)</code>. <code>combinations(s,k)</code> generates the unique combinations of a multiset of a length <code>k</code>. For <code>s='xxyy'</code> these would be <code>['xx','xy','yy']</code>. <code>runvector(v)</code> transforms a multiset represented as a sorted vector into a more simple structure, the runvector. <code>runvector('cddeee')=[1,2,3]</code>. To solve the problem, we will use recursive generators. We run through all the combinations that fits in box1 and the recourse on the rest of the boxes, banning the values we already chose. To accomplish the banning, <code>combinations</code> will maintain a bitarray across of calls. In python the approach looks like this: <pre><code>def fillrest(banned,out,rv,b,i): if i == len(rv): yield None return for comb in combinations(b,rv[i],banned): out[i] = comb for rest in fillrest(banned,out,rv,b,i+1): yield None def balls(a,b): rv = runvector(a) banned = [False for _ in b] out = [None for _ in rv] for _ in fill(out,rv,0,b,banned): yield out[:] >>> print list(balls('abbccc','xyyzzz')) [['x', 'yy', 'zzz'], ['x', 'yz', 'yzz'], ['x', 'zz', 'yyz'], ['y', 'xy', 'zzz'], ['y', 'xz', 'yzz'], ['y', 'yz', 'xzz'], ['y', 'zz', 'xyz'], ['z', 'xy', 'yzz'], ['z', 'xz', 'yyz'], ['z', 'yy', 'xzz'], ['z', 'yz', 'xyz'], ['z', 'zz', 'xyy']] </code></pre> The output are in 'box' format, but can easily be merged back to simple strings: <code>'xyyzzzz'</code>, <code>'xyzyzz'</code>...
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1. POGenerating Balls in Boxes
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1. USThomas Ahle
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1. POGenerating Balls in Boxes
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1. COIf you're done with the question you should accept your own answer.
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 USGreg Kuperberg

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