Subset sum problem

Implement a function/procedure/method/subroutine that takes a set of words with integer weights, and obtains 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.

Table of weighted words
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 the results shown in a human readable form.

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>