brute-force

To‘liq perebor — barcha variantlarni tekshirib, mosini tanlash. Eng oddiy va eng ishonchli yechim: agar n kichik bo‘lsa (masalan, 10–20 gacha), ko‘pincha shuning o‘zi yetadi.

from itertools import combinations, permutations, product

best = max(sum(c) for c in combinations(nums, 3) if sum(c) <= limit)   # 3 tadan tanlash
for p in permutations(range(n)): ...                                    # barcha tartiblar
for bits in product([0, 1], repeat=n): ...                              # barcha qism to‘plamlar

Qachon ishlatiladi

1. Chegaralar kichik — to‘g‘ridan-to‘g‘ri yechim.
2. Tez yechimni tekshirish uchun: kichik testlarda ikkalasining javobini solishtiring (stress-test).
3. Naqsh izlash: kichik n lar uchun javoblarni chiqarib, formulani ko‘rish.

Avval variantlar sonini hisoblang: 2²⁰ ≈ 10⁶ — bemalol, 2⁴⁰ — yo‘q.