Subset sum problem
Implement a function/procedure/method/subroutine that takes a set/array/list/stream/table/collection of words with integer weights, and identifies a non-empty subset of them whose weights sum to zero (cf. the Dropbox Diet candidate screening exercise and the Subset sum problem Wikipedia article).
For example, for this set of weighted words, one solution would be the set of words {elysee, efferent, deploy, departure, centipede, bonnet, balm, archbishop}, because their respective weights of -326, 54, 44, 952, -658, 452, 397, and -915 sum to zero.
word | weight |
---|---|
alliance | -624 |
archbishop | -915 |
balm | 397 |
bonnet | 452 |
brute | 870 |
centipede | -658 |
cobol | 362 |
covariate | 590 |
departure | 952 |
deploy | 44 |
diophantine | 645 |
efferent | 54 |
elysee | -326 |
eradicate | 376 |
escritoire | 856 |
exorcism | -983 |
fiat | 170 |
filmy | -874 |
flatworm | 503 |
gestapo | 915 |
infra | -847 |
isis | -982 |
lindholm | 999 |
markham | 475 |
mincemeat | -880 |
moresby | 756 |
mycenae | 183 |
plugging | -266 |
smokescreen | 423 |
speakeasy | -745 |
vein | 813 |
Another solution would be the set of words {flatworm, gestapo, infra, isis, lindholm, plugging, smokescreen, speakeasy}, because their respective weights of 503, 915, -847, -982, 999, -266, 423, and -745 also sum to zero.
You may assume the weights range from -1000 to 1000. If there are multiple solutions, only one needs to be found. Use any algorithm you want and demonstrate it on a set of at least 30 weighted words with the results shown in a human readable form. Note that an implementation that depends on enumerating all possible subsets is likely to be infeasible.
Ursala
This solution scans the set sequentially while maintaining a record of all distinct sums obtainable by words encountered thus far, and stops when a zero sum is found. <lang Ursala>#import std
- import int
weights =
{
'alliance': -624, 'archbishop': -915, 'balm': 397, 'bonnet': 452, 'brute': 870, 'centipede': -658, 'cobol': 362, 'covariate': 590, 'departure': 952, 'deploy': 44, 'diophantine': 645, 'efferent': 54, 'elysee': -326, 'eradicate': 376, 'escritoire': 856, 'exorcism': -983, 'fiat': 170, 'filmy': -874, 'flatworm': 503, 'gestapo': 915, 'infra': -847, 'isis': -982, 'lindholm': 999, 'markham': 475, 'mincemeat': -880, 'moresby': 756, 'mycenae': 183, 'plugging': -266, 'smokescreen': 423, 'speakeasy': -745, 'vein': 813}
nullset = ~&nZFihmPB+ =><> ~&ng?r\~&r ^TnK2hS\~&r ^C/~&lmPlNCX *D ^A/sum@lmPrnPX ~&lrmPC
- cast %zm
main = nullset weights</lang> output:
< 'flatworm': 503, 'gestapo': 915, 'infra': -847, 'isis': -982, 'lindholm': 999, 'plugging': -266, 'smokescreen': 423, 'speakeasy': -745>