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2011-09-03T20:54:59.800
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2011-09-03T20:54:59.800
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<p>Here is one solution to the problem in Python. It is not optimized at all. I even check 2, 4 after I check 4,2, for example. But for showing how you can find a solution, I think it is good enough.</p> <pre><code>def all_but(lst, pos): return lst[0:pos]+lst[pos+1:] def find_sets_with_len(segs, l): for i in range(0, len(segs)): val = segs[i] if (val == l): yield [val], all_but(segs, i) if (val < l): for soln, rest in find_sets_with_len(all_but(segs, i), l - val): yield [val]+soln, rest def find_rect(segs, l1, l2): for side1, rest1 in find_sets_with_len(segs, l1): for side2, rest2 in find_sets_with_len(rest1, l1): for side3, rest3 in find_sets_with_len(rest2, l2): return [side1, side2, side3, rest3] def make_rect(segs): tot_len = sum(segs) if (tot_len %2) == 0: opt_len=tot_len/4 for l in range(opt_len, 0, -1): sides = find_rect(segs, l, tot_len/2-l) if sides is not None: print(sides) return sides print("Can't find any solution") make_rect([4,2,4,4,6,8]) </code></pre> <p>The idea is simple: first, calculate the optimal length (that is, the length to make a square), then search everything starting off with the optimal length, and go down to 1 for one side. For each length, enumerate all sets for one side of the claculated length, then enumerate all sets for the opposite side (of the same length), then if I can find one more set of the remaining length (that is <code>total_len/2</code> minus the side length I am looking at), then I've got the best solution. This happens in <code>find_rect()</code> function.</p>
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1. POConstruct the largest possible rectangle out of line segments of given lengths
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1. COthank you for the solution.
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