我如何找到所有可能的方法，我可以將一個數組安裝到 4 個插槽中，並且數組可能有更多/少於 4 個數字？

Question

假設我有 4 個桶和一組數字，例如[1,2,3,4,5]

|  ||  ||  ||  |
|__||__||__||__|
 1   2   3   4
 5   2   3   4
 1   5   3   4     
 etc...

我也可以有少於 4 個數字，例如[1, 2, 3]

|  ||  ||  ||  |
|__||__||__||__|
 1   2   3   
 1   3   2   
     1   2   3     
 etc...

如何找到桶中數字的所有可能組合（如[1,2,3,4]如果長度 >= 4 或[1,2,None,None]如果長度 < 4）？

Answer 1

您可以使用遞歸生成器 function：

def combos(nums, buckets, c = []):
  if len(c) == buckets:
    yield c
  else:
    if len(c) + len(nums) < buckets:
      yield from combos(nums, buckets, c+[None])
    for i, a in enumerate(nums):
      yield from combos(nums[:i]+nums[i+1:], buckets, c+[a])

print(list(combos([1, 2, 3, 4, 5], 4)))
print(list(combos([1, 2, 3], 4)))

Output：

[[1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 4, 3], [1, 2, 4, 5], [1, 2, 5, 3], [1, 2, 5, 4], [1, 3, 2, 4], [1, 3, 2, 5], [1, 3, 4, 2], [1, 3, 4, 5], [1, 3, 5, 2], [1, 3, 5, 4], [1, 4, 2, 3], [1, 4, 2, 5], [1, 4, 3, 2], [1, 4, 3, 5], [1, 4, 5, 2], [1, 4, 5, 3], [1, 5, 2, 3], [1, 5, 2, 4], [1, 5, 3, 2], [1, 5, 3, 4], [1, 5, 4, 2], [1, 5, 4, 3], [2, 1, 3, 4], [2, 1, 3, 5], [2, 1, 4, 3], [2, 1, 4, 5], [2, 1, 5, 3], [2, 1, 5, 4], [2, 3, 1, 4], [2, 3, 1, 5], [2, 3, 4, 1], [2, 3, 4, 5], [2, 3, 5, 1], [2, 3, 5, 4], [2, 4, 1, 3], [2, 4, 1, 5], [2, 4, 3, 1], [2, 4, 3, 5], [2, 4, 5, 1], [2, 4, 5, 3], [2, 5, 1, 3], [2, 5, 1, 4], [2, 5, 3, 1], [2, 5, 3, 4], [2, 5, 4, 1], [2, 5, 4, 3], [3, 1, 2, 4], [3, 1, 2, 5], [3, 1, 4, 2], [3, 1, 4, 5], [3, 1, 5, 2], [3, 1, 5, 4], [3, 2, 1, 4], [3, 2, 1, 5], [3, 2, 4, 1], [3, 2, 4, 5], [3, 2, 5, 1], [3, 2, 5, 4], [3, 4, 1, 2], [3, 4, 1, 5], [3, 4, 2, 1], [3, 4, 2, 5], [3, 4, 5, 1], [3, 4, 5, 2], [3, 5, 1, 2], [3, 5, 1, 4], [3, 5, 2, 1], [3, 5, 2, 4], [3, 5, 4, 1], [3, 5, 4, 2], [4, 1, 2, 3], [4, 1, 2, 5], [4, 1, 3, 2], [4, 1, 3, 5], [4, 1, 5, 2], [4, 1, 5, 3], [4, 2, 1, 3], [4, 2, 1, 5], [4, 2, 3, 1], [4, 2, 3, 5], [4, 2, 5, 1], [4, 2, 5, 3], [4, 3, 1, 2], [4, 3, 1, 5], [4, 3, 2, 1], [4, 3, 2, 5], [4, 3, 5, 1], [4, 3, 5, 2], [4, 5, 1, 2], [4, 5, 1, 3], [4, 5, 2, 1], [4, 5, 2, 3], [4, 5, 3, 1], [4, 5, 3, 2], [5, 1, 2, 3], [5, 1, 2, 4], [5, 1, 3, 2], [5, 1, 3, 4], [5, 1, 4, 2], [5, 1, 4, 3], [5, 2, 1, 3], [5, 2, 1, 4], [5, 2, 3, 1], [5, 2, 3, 4], [5, 2, 4, 1], [5, 2, 4, 3], [5, 3, 1, 2], [5, 3, 1, 4], [5, 3, 2, 1], [5, 3, 2, 4], [5, 3, 4, 1], [5, 3, 4, 2], [5, 4, 1, 2], [5, 4, 1, 3], [5, 4, 2, 1], [5, 4, 2, 3], [5, 4, 3, 1], [5, 4, 3, 2]]
[[None, 1, 2, 3], [None, 1, 3, 2], [None, 2, 1, 3], [None, 2, 3, 1], [None, 3, 1, 2], [None, 3, 2, 1], [1, None, 2, 3], [1, None, 3, 2], [1, 2, None, 3], [1, 2, 3, None], [1, 3, None, 2], [1, 3, 2, None], [2, None, 1, 3], [2, None, 3, 1], [2, 1, None, 3], [2, 1, 3, None], [2, 3, None, 1], [2, 3, 1, None], [3, None, 1, 2], [3, None, 2, 1], [3, 1, None, 2], [3, 1, 2, None], [3, 2, None, 1], [3, 2, 1, None]]

在每次遞歸調用中，如果還沒有形成組合，代碼會做兩件事：

1. 檢查指定的桶數是否大於輸入數列表。 如果是這樣，那么 output 用None填充。
2. 對剩余的數列表進行迭代，將每個迭代值加到運行結果中，繼續遞歸。

Answer 2

使用內置的 function itertools.permutations 。

import itertools


def func(arr: list, slot_count=4):
    if (v := slot_count - len(arr)) > 0:
        arr.extend([None for _ in range(v)])
    return itertools.permutations(arr, slot_count)


print(list(func([1, 2, 3])))

print(list(func([1, 2, 3, 4, 5])))

[(1, 2, 3, None), (1, 2, None, 3), (1, 3, 2, None), (1, 3, None, 2), (1, None, 2, 3), (1, None, 3, 2), (2, 1, 3, None), (2, 1, None, 3), (2, 3, 1, None), (2, 3, None, 1), (2, None, 1, 3), (2, None, 3, 1), (3, 1, 2, None), (3, 1, None, 2), (3, 2, 1, None), (3, 2, None, 1), (3, None, 1, 2), (3, None, 2, 1), (None, 1, 2, 3), (None, 1, 3, 2), (None, 2, 1, 3), (None, 2, 3, 1), (None, 3, 1, 2), (None, 3, 2, 1)]
[(1, 2, 3, 4), (1, 2, 3, 5), (1, 2, 4, 3), (1, 2, 4, 5), (1, 2, 5, 3), (1, 2, 5, 4), (1, 3, 2, 4), (1, 3, 2, 5), (1, 3, 4, 2), (1, 3, 4, 5), (1, 3, 5, 2), (1, 3, 5, 4), (1, 4, 2, 3), (1, 4, 2, 5), (1, 4, 3, 2), (1, 4, 3, 5), (1, 4, 5, 2), (1, 4, 5, 3), (1, 5, 2, 3), (1, 5, 2, 4), (1, 5, 3, 2), (1, 5, 3, 4), (1, 5, 4, 2), (1, 5, 4, 3), (2, 1, 3, 4), (2, 1, 3, 5), (2, 1, 4, 3), (2, 1, 4, 5), (2, 1, 5, 3), (2, 1, 5, 4), (2, 3, 1, 4), (2, 3, 1, 5), (2, 3, 4, 1), (2, 3, 4, 5), (2, 3, 5, 1), (2, 3, 5, 4), (2, 4, 1, 3), (2, 4, 1, 5), (2, 4, 3, 1), (2, 4, 3, 5), (2, 4, 5, 1), (2, 4, 5, 3), (2, 5, 1, 3), (2, 5, 1, 4), (2, 5, 3, 1), (2, 5, 3, 4), (2, 5, 4, 1), (2, 5, 4, 3), (3, 1, 2, 4), (3, 1, 2, 5), (3, 1, 4, 2), (3, 1, 4, 5), (3, 1, 5, 2), (3, 1, 5, 4), (3, 2, 1, 4), (3, 2, 1, 5), (3, 2, 4, 1), (3, 2, 4, 5), (3, 2, 5, 1), (3, 2, 5, 4), (3, 4, 1, 2), (3, 4, 1, 5), (3, 4, 2, 1), (3, 4, 2, 5), (3, 4, 5, 1), (3, 4, 5, 2), (3, 5, 1, 2), (3, 5, 1, 4), (3, 5, 2, 1), (3, 5, 2, 4), (3, 5, 4, 1), (3, 5, 4, 2), (4, 1, 2, 3), (4, 1, 2, 5), (4, 1, 3, 2), (4, 1, 3, 5), (4, 1, 5, 2), (4, 1, 5, 3), (4, 2, 1, 3), (4, 2, 1, 5), (4, 2, 3, 1), (4, 2, 3, 5), (4, 2, 5, 1), (4, 2, 5, 3), (4, 3, 1, 2), (4, 3, 1, 5), (4, 3, 2, 1), (4, 3, 2, 5), (4, 3, 5, 1), (4, 3, 5, 2), (4, 5, 1, 2), (4, 5, 1, 3), (4, 5, 2, 1), (4, 5, 2, 3), (4, 5, 3, 1), (4, 5, 3, 2), (5, 1, 2, 3), (5, 1, 2, 4), (5, 1, 3, 2), (5, 1, 3, 4), (5, 1, 4, 2), (5, 1, 4, 3), (5, 2, 1, 3), (5, 2, 1, 4), (5, 2, 3, 1), (5, 2, 3, 4), (5, 2, 4, 1), (5, 2, 4, 3), (5, 3, 1, 2), (5, 3, 1, 4), (5, 3, 2, 1), (5, 3, 2, 4), (5, 3, 4, 1), (5, 3, 4, 2), (5, 4, 1, 2), (5, 4, 1, 3), (5, 4, 2, 1), (5, 4, 2, 3), (5, 4, 3, 1), (5, 4, 3, 2)]