更新时间:2023-02-10 11:29:34
是的,需要递归.基本逻辑是将一个部分分为一部分和其余部分,然后以所有可能的方式递归拆分其余部分.我已经按照你的假设假设一切都是可区分的,这会产生很多可能性,可能太多而无法一一列举.尽管如此:
Yes, recursion is called for. The basic logic is to do a bipartition into one part and the rest and then recursively split the rest in all possible ways. I've followed your lead in assuming that everything is distinguishable, which creates a lot of possibilities, possibly too many to enumerate. Nevertheless:
import itertools
def totals_from_ratios(sum_numbers, ratios):
sum_ratios = sum(ratios)
totals = [(sum_numbers * ratio) // sum_ratios for ratio in ratios]
residues = [(sum_numbers * ratio) % sum_ratios for ratio in ratios]
for i in sorted(
range(len(ratios)), key=lambda i: residues[i] * ratios[i], reverse=True
)[: sum_numbers - sum(totals)]:
totals[i] += 1
return totals
def bipartitions(numbers, total):
n = len(numbers)
for k in range(n + 1):
for combo in itertools.combinations(range(n), k):
if sum(numbers[i] for i in combo) == total:
set_combo = set(combo)
yield sorted(numbers[i] for i in combo), sorted(
numbers[i] for i in range(n) if i not in set_combo
)
def partitions_into_totals(numbers, totals):
assert totals
if len(totals) == 1:
yield [numbers]
else:
for first, remaining_numbers in bipartitions(numbers, totals[0]):
for rest in partitions_into_totals(remaining_numbers, totals[1:]):
yield [first] + rest
def partitions_into_ratios(numbers, ratios):
totals = totals_from_ratios(sum(numbers), ratios)
yield from partitions_into_totals(numbers, totals)
lst = [2, 0, 1, 7, 2, 4, 9, 7, 6, 0, 5, 4, 7, 4, 5, 0, 4, 5, 2, 3]
for part in partitions_into_ratios(lst, [4, 3, 3]):
print(part)