from itertools import combinations
import clingo

nhan = {"a", "b", "c"}
xung_dot = [{"a", "b"}, {"b", "c"}]
tap_sua = [
    set(chon)
    for co in range(4)
    for chon in combinations(sorted(nhan), co)
    if all(set(chon) & nhom for nhom in xung_dot)
]
toi_tieu = [chon for chon in tap_sua if not any(khac < chon for khac in tap_sua)]
assert sorted(map(sorted, toi_tieu)) == [["a", "c"], ["b"]]

ctl = clingo.Control(["0"])
ctl.add("base", [], """
nhan(a;b;c).
gia(a,1). gia(b,5). gia(c,1).
{ bo(X) } :- nhan(X).
:- not bo(a), not bo(b).
:- not bo(b), not bo(c).
#minimize { W,X : bo(X), gia(X,W) }.
#show bo/1.
""")
ctl.ground([("base", [])])
nghiem = []
ctl.solve(on_model=lambda m: nghiem.append((set(map(str, m.symbols(shown=True))), list(m.cost))))
assert nghiem[-1] == ({"bo(a)", "bo(c)"}, [2])
print("Theo bao hàm", sorted(map(sorted, toi_tieu)), "| Theo chi phí", nghiem[-1])