在 Python 中设置分区 [英] Set partitions in Python

问题描述

我有一个 [1,2,3]

我想使用数组的所有元素进行所有可能的组合:

I want to make all the possible combinations using all elements of the array:

结果:

[[1], [2], [3]]
[[1,2], [3]]
[[1], [2,3]]
[[1,3], [2]]
[[1,2,3]]

推荐答案

既然这个好问题已经复活，这里有一个新的答案.

Since this nice question has been brought back to life, here's a fresh answer.

问题递归解决:如果你已经有一个n-1个元素的分区，你如何用它来分区n个元素?将第 n 个元素放在现有子集之一中，或将其添加为新的单例子集.这就是全部；没有itertools，没有集合，没有重复的输出，总共只有n 次对partition() 的调用:

The problem is solved recursively: If you already have a partition of n-1 elements, how do you use it to partition n elements? Either place the n'th element in one of the existing subsets, or add it as a new, singleton subset. That's all it takes; no itertools, no sets, no repeated outputs, and a total of just n calls to partition():

def partition(collection):
    if len(collection) == 1:
        yield [ collection ]
        return

    first = collection[0]
    for smaller in partition(collection[1:]):
        # insert `first` in each of the subpartition's subsets
        for n, subset in enumerate(smaller):
            yield smaller[:n] + [[ first ] + subset]  + smaller[n+1:]
        # put `first` in its own subset 
        yield [ [ first ] ] + smaller


something = list(range(1,5))

for n, p in enumerate(partition(something), 1):
    print(n, sorted(p))

输出:

1 [[1, 2, 3, 4]]
2 [[1], [2, 3, 4]]
3 [[1, 2], [3, 4]]
4 [[1, 3, 4], [2]]
5 [[1], [2], [3, 4]]
6 [[1, 2, 3], [4]]
7 [[1, 4], [2, 3]]
8 [[1], [2, 3], [4]]
9 [[1, 3], [2, 4]]
10 [[1, 2, 4], [3]]
11 [[1], [2, 4], [3]]
12 [[1, 2], [3], [4]]
13 [[1, 3], [2], [4]]
14 [[1, 4], [2], [3]]
15 [[1], [2], [3], [4]]

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