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    <p><strong>New Solution</strong></p> <p>This is a breadth-first search with heuristics culling. The tree is limited to a depth of players/2. The player sum limit is totalscores/2. With a player pool of 100, it took approximately 10 seconds to solve.</p> <pre><code>def team(t): iterations = range(2, len(t)/2+1) totalscore = sum(t) halftotalscore = totalscore/2.0 oldmoves = {} for p in t: people_left = t[:] people_left.remove(p) oldmoves[p] = people_left if iterations == []: solution = min(map(lambda i: (abs(float(i)-halftotalscore), i), oldmoves.keys())) return (solution[1], sum(oldmoves[solution[1]]), oldmoves[solution[1]]) for n in iterations: newmoves = {} for total, roster in oldmoves.iteritems(): for p in roster: people_left = roster[:] people_left.remove(p) newtotal = total+p if newtotal &gt; halftotalscore: continue newmoves[newtotal] = people_left oldmoves = newmoves solution = min(map(lambda i: (abs(float(i)-halftotalscore), i), oldmoves.keys())) return (solution[1], sum(oldmoves[solution[1]]), oldmoves[solution[1]]) print team([90,200,100]) print team([2,3,10,5,8,9,7,3,5,2]) print team([1,1,1,1,1,1,1,1,1,9]) print team([87,100,28,67,68,41,67,1]) print team([1, 1, 50, 50, 50, 1000]) #output #(200, 190, [90, 100]) #(27, 27, [3, 9, 7, 3, 5]) #(5, 13, [1, 1, 1, 1, 9]) #(229, 230, [28, 67, 68, 67]) #(150, 1002, [1, 1, 1000]) </code></pre> <p>Also note that I attempted to solve this using GS's description, but it is impossible to get enough information simply by storing the running totals. And if you stored <strong>both</strong> the number of items and totals, then it would be the same as this solution except you kept needless data. Because you only need to keep the n-1 and n iterations up to numplayers/2.</p> <p>I had an old exhaustive one based on binomial coefficients (look in history). It solved the example problems of length 10 just fine, but then I saw that the competition had people of up to length 100.</p>
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    1. POAlgorithm to Divide a list of numbers into 2 equal sum lists
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    1. CO@becomingGuru, I implemented a solution that works correctly, take a look at it.
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    2. CO@tom10 actually your solution fails for [87,100,28,67,68,41,67,1]. It outputs 223 236. Nice try.
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    3. CO@tom10, no it is not. When your friend makes a mistake, do you simply tell him he's wrong? Or do you tell him how to solve it?
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