1到$n^2$分成$n\times n$个，每组和相等，分法有几种

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A321230 Number of set partitions of [n^2] into n n-element subsets having the same sum.
$n=5$ Python 代码:

1. from itertools import permutations
2. for x in permutations(range(1, 26)):
3.     if all(
4.         sum(x) == 65 for x in zip(x[::5], x[1::5], x[2::5], x[3::5], x[4::5])
5.     ):
6.         print(x)

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改进后的代码:

1. from itertools import combinations
3. def find_partitions(total_sum, num_subsets, subset_size):
4.     # base case: only one subset remaining, generate it from the remaining numbers
5.     if num_subsets == 1:
6.         if total_sum == sum(range(26)):
7.             yield [range(1, 26)]
8.         return
10.     # generate the first subset and recursively search for the remaining ones
11.     for subset in combinations(range(1, 26), subset_size):
12.         if sum(subset) == total_sum:
13.             remaining = set(range(1, 26)) - set(subset)
14.             for partition in find_partitions(total_sum, num_subsets-1, subset_size):
15.                 partition.append(subset)
16.                 yield partition
18. # find all partitions with 5 subsets of size 5 and sum 65
19. for partition in find_partitions(65, 5, 5):
20.     print(partition)

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