#!/usr/bin/env python

import sys
from pulp import *
from itertools import chain

setcontents = [line.split() for line in open(sys.argv[1]).readlines()]
sets = range(len(setcontents))
elements = set(chain(*setcontents))

chosen = LpVariable.dicts('If chosen', sets, 0, 1, LpInteger)

model = LpProblem('Set cover', LpMinimize)

model += lpSum(chosen), "Chosen sets"
for j in elements:
    model += lpSum(chosen[i] for i in sets if j in setcontents[i]) >= 1, \
            "Element %s" % j

model.writeLP('setcover.lp')
pulp.CPLEX_CMD().solve(model)
print "\nNeed to use at least %d sets: " % model.objective.value()
for i in sets:
    if chosen[i].value() == 1:
        print setcontents[i]