python - 如何获得列表元素的所有可能组合？

Question

我有一个包含 15 个数字的列表，我需要编写一些代码来生成这些数字的所有 32,768 个组合。

我发现一些代码（通过谷歌搜索）显然可以满足我的要求，但我发现代码相当不透明并且对使用它持谨慎态度。另外，我觉得必须有一个更优雅的解决方案。

我唯一想到的就是循环遍历十进制整数 1-32768 并将它们转换为二进制，然后使用二进制表示作为过滤器来挑选出适当的数字。

有人知道更好的方法吗？使用map()，也许？

score 742 · Accepted Answer

这个答案错过了一个方面：OP要求所有组合......不仅仅是长度“r”的组合。

所以你要么必须遍历所有长度“L”：

import itertools

stuff = [1, 2, 3]
for L in range(0, len(stuff)+1):
    for subset in itertools.combinations(stuff, L):
        print(subset)

或者——如果你想变得时髦（或者让阅读你代码的人的大脑弯曲）——你可以生成“combinations()”生成器链，并遍历它：

from itertools import chain, combinations
def all_subsets(ss):
    return chain(*map(lambda x: combinations(ss, x), range(0, len(ss)+1)))

for subset in all_subsets(stuff):
    print(subset)

score 618 · Accepted Answer

看看itertools.combinations：

itertools.combinations(iterable, r)
从输入可迭代中返回 r 个长度的元素子序列。

组合按字典排序顺序发出。因此，如果输入的可迭代对象已排序，则组合元组将按排序顺序生成。

从 2.6 开始，包括电池！

score 60 · Accepted Answer

这是一个懒惰的单线，也使用 itertools：

from itertools import compress, product

def combinations(items):
    return ( set(compress(items,mask)) for mask in product(*[[0,1]]*len(items)) )
    # alternative:                      ...in product([0,1], repeat=len(items)) )

这个答案背后的主要思想：有 2^N 组合 - 与长度为 N 的二进制字符串的数量相同。对于每个二进制字符串，您选择与“1”相对应的所有元素。

items=abc * mask=###
 |
 V
000 -> 
001 ->   c
010 ->  b
011 ->  bc
100 -> a
101 -> a c
110 -> ab
111 -> abc

需要考虑的事项：

这要求您可以调用len(...)（items解决方法：如果items类似于生成器之类的可迭代对象，请先将其转换为列表items=list(_itemsArg)）
这要求迭代的顺序items不是随机的（解决方法：不要发疯）
这要求这些项目是唯一的，否则它们{2,2,1}都{2,1,1}将折叠到{2,1}（解决方法：collections.Counter用作的替代品；它基本上是一个多重集......尽管如果您需要它是可散列set的，您可能需要稍后使用）tuple(sorted(Counter(...).elements()))

演示

>>> list(combinations(range(4)))
[set(), {3}, {2}, {2, 3}, {1}, {1, 3}, {1, 2}, {1, 2, 3}, {0}, {0, 3}, {0, 2}, {0, 2, 3}, {0, 1}, {0, 1, 3}, {0, 1, 2}, {0, 1, 2, 3}]

>>> list(combinations('abcd'))
[set(), {'d'}, {'c'}, {'c', 'd'}, {'b'}, {'b', 'd'}, {'c', 'b'}, {'c', 'b', 'd'}, {'a'}, {'a', 'd'}, {'a', 'c'}, {'a', 'c', 'd'}, {'a', 'b'}, {'a', 'b', 'd'}, {'a', 'c', 'b'}, {'a', 'c', 'b', 'd'}]

score 57 · Accepted Answer

在@Dan H 高度赞成的回答下的评论中，提到了文档powerset()中的配方——包括Dan 自己的配方。但是，到目前为止，没有人将其发布为答案。由于它可能是解决问题的最佳方法之一，如果不是最好的方法，并且得到另一位评论者的一点鼓励，如下所示。该函数生成每个可能长度的列表元素的所有唯一组合（包括那些包含零和所有元素的组合）。itertools

注意：如果略有不同，目标是仅获得唯一元素的组合，请更改行s = list(iterable)以s = list(set(iterable))消除任何重复元素。无论如何，iterable最终变成了一种list可以与生成器一起使用的方法这一事实（与其他几个答案不同）。

from itertools import chain, combinations

def powerset(iterable):
    "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
    s = list(iterable)  # allows duplicate elements
    return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))

stuff = [1, 2, 3]
for i, combo in enumerate(powerset(stuff), 1):
    print('combo #{}: {}'.format(i, combo))

输出：

combo #1: ()
combo #2: (1,)
combo #3: (2,)
combo #4: (3,)
combo #5: (1, 2)
combo #6: (1, 3)
combo #7: (2, 3)
combo #8: (1, 2, 3)

score 43 · Accepted Answer

这个单线为您提供所有组合（如果原始列表/集合包含不同的元素，则为项目之间的0和项目）并使用本机方法：nnitertools.combinations

蟒蛇2

from itertools import combinations

input = ['a', 'b', 'c', 'd']

output = sum([map(list, combinations(input, i)) for i in range(len(input) + 1)], [])

蟒蛇 3

from itertools import combinations

input = ['a', 'b', 'c', 'd']

output = sum([list(map(list, combinations(input, i))) for i in range(len(input) + 1)], [])

输出将是：

[[],
 ['a'],
 ['b'],
 ['c'],
 ['d'],
 ['a', 'b'],
 ['a', 'c'],
 ['a', 'd'],
 ['b', 'c'],
 ['b', 'd'],
 ['c', 'd'],
 ['a', 'b', 'c'],
 ['a', 'b', 'd'],
 ['a', 'c', 'd'],
 ['b', 'c', 'd'],
 ['a', 'b', 'c', 'd']]

在线尝试：

http://ideone.com/COghfX

score 42 · Accepted Answer

这是一个使用递归的例子：

>>> import copy
>>> def combinations(target,data):
...     for i in range(len(data)):
...         new_target = copy.copy(target)
...         new_data = copy.copy(data)
...         new_target.append(data[i])
...         new_data = data[i+1:]
...         print new_target
...         combinations(new_target,
...                      new_data)
...                      
... 
>>> target = []
>>> data = ['a','b','c','d']
>>> 
>>> combinations(target,data)
['a']
['a', 'b']
['a', 'b', 'c']
['a', 'b', 'c', 'd']
['a', 'b', 'd']
['a', 'c']
['a', 'c', 'd']
['a', 'd']
['b']
['b', 'c']
['b', 'c', 'd']
['b', 'd']
['c']
['c', 'd']
['d']

score 42 · Accepted Answer

这是一种可以很容易地转移到所有支持递归的编程语言（没有 itertools，没有 yield，没有列表理解）的方法：

def combs(a):
    if len(a) == 0:
        return [[]]
    cs = []
    for c in combs(a[1:]):
        cs += [c, c+[a[0]]]
    return cs

>>> combs([1,2,3,4,5])
[[], [1], [2], [2, 1], [3], [3, 1], [3, 2], ..., [5, 4, 3, 2, 1]]

score 28 · Accepted Answer

您可以使用以下简单代码在 Python 中生成列表的所有组合：

import itertools

a = [1,2,3,4]
for i in xrange(0,len(a)+1):
   print list(itertools.combinations(a,i))

结果将是：

[()]
[(1,), (2,), (3,), (4,)]
[(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
[(1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4)]
[(1, 2, 3, 4)]

score 22 · Accepted Answer

我同意 Dan H 的观点，Ben 确实要求所有组合。itertools.combinations()没有给出所有组合。

另一个问题是，如果输入迭代很大，最好返回一个生成器而不是列表中的所有内容：

iterable = range(10)
for s in xrange(len(iterable)+1):
  for comb in itertools.combinations(iterable, s):
    yield comb

score 20 · Accepted Answer

我想我会为那些在不导入 itertools 或任何其他额外库的情况下寻求答案的人添加此功能。

def powerSet(items):
    """
    Power set generator: get all possible combinations of a list’s elements

    Input:
        items is a list
    Output:
        returns 2**n combination lists one at a time using a generator 

    Reference: edx.org 6.00.2x Lecture 2 - Decision Trees and dynamic programming
    """

    N = len(items)
    # enumerate the 2**N possible combinations
    for i in range(2**N):
        combo = []
        for j in range(N):
            # test bit jth of integer i
            if (i >> j) % 2 == 1:
                combo.append(items[j])
        yield combo

简单的产量发生器用法：

for i in powerSet([1,2,3,4]):
    print (i, ", ",  end="")

上面使用示例的输出：

[] , [1] , [2] , [1, 2] , [3] , [1, 3] , [2, 3] , [1, 2, 3] , [4] , [1, 4] , [2, 4] , [1, 2, 4] , [3, 4] , [1, 3, 4] , [2, 3, 4] , [1, 2, 3, 4] ,

score 9 · Accepted Answer

这是另一个解决方案（单线），涉及使用itertools.combinations函数，但这里我们使用双列表推导（而不是 for 循环或求和）：

def combs(x):
    return [c for i in range(len(x)+1) for c in combinations(x,i)]

演示：

>>> combs([1,2,3,4])
[(), 
 (1,), (2,), (3,), (4,), 
 (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4), 
 (1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4), 
 (1, 2, 3, 4)]

score 9 · Accepted Answer

3个功能：

n 个元素的所有组合列表
n 元素列表的所有组合，其中顺序不明确
所有排列

import sys

def permutations(a):
    return combinations(a, len(a))

def combinations(a, n):
    if n == 1:
        for x in a:
            yield [x]
    else:
        for i in range(len(a)):
            for x in combinations(a[:i] + a[i+1:], n-1):
                yield [a[i]] + x

def combinationsNoOrder(a, n):
    if n == 1:
        for x in a:
            yield [x]
    else:
        for i in range(len(a)):
            for x in combinationsNoOrder(a[:i], n-1):
                yield [a[i]] + x
    
if __name__ == "__main__":
    for s in combinations(list(map(int, sys.argv[2:])), int(sys.argv[1])):
        print(s)

score 8 · Accepted Answer

from itertools import permutations, combinations


features = ['A', 'B', 'C']
tmp = []
for i in range(len(features)):
    oc = combinations(features, i + 1)
    for c in oc:
        tmp.append(list(c))

输出

[
 ['A'],
 ['B'],
 ['C'],
 ['A', 'B'],
 ['A', 'C'],
 ['B', 'C'],
 ['A', 'B', 'C']
]

score 8 · Accepted Answer

您还可以使用优秀软件包中的powerset功能。more_itertools

from more_itertools import powerset

l = [1,2,3]
list(powerset(l))

# [(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)]

我们还可以验证它是否符合 OP 的要求

from more_itertools import ilen

assert ilen(powerset(range(15))) == 32_768

score 6 · Accepted Answer

以下是“标准递归答案”，类似于其他类似答案https://stackoverflow.com/a/23743696/711085。（我们实际上不必担心堆栈空间用完，因为我们无法处理所有 N! 排列。）

它依次访问每个元素，要么取走它，要么离开它（我们可以直接从这个算法中看到 2^N 基数）。

def combs(xs, i=0):
    if i==len(xs):
        yield ()
        return
    for c in combs(xs,i+1):
        yield c
        yield c+(xs[i],)

演示：

>>> list( combs(range(5)) )
[(), (0,), (1,), (1, 0), (2,), (2, 0), (2, 1), (2, 1, 0), (3,), (3, 0), (3, 1), (3, 1, 0), (3, 2), (3, 2, 0), (3, 2, 1), (3, 2, 1, 0), (4,), (4, 0), (4, 1), (4, 1, 0), (4, 2), (4, 2, 0), (4, 2, 1), (4, 2, 1, 0), (4, 3), (4, 3, 0), (4, 3, 1), (4, 3, 1, 0), (4, 3, 2), (4, 3, 2, 0), (4, 3, 2, 1), (4, 3, 2, 1, 0)]

>>> list(sorted( combs(range(5)), key=len))
[(), 
 (0,), (1,), (2,), (3,), (4,), 
 (1, 0), (2, 0), (2, 1), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2), (4, 3), 
 (2, 1, 0), (3, 1, 0), (3, 2, 0), (3, 2, 1), (4, 1, 0), (4, 2, 0), (4, 2, 1), (4, 3, 0), (4, 3, 1), (4, 3, 2), 
 (3, 2, 1, 0), (4, 2, 1, 0), (4, 3, 1, 0), (4, 3, 2, 0), (4, 3, 2, 1), 
 (4, 3, 2, 1, 0)]

>>> len(set(combs(range(5))))
32

score 4 · Accepted Answer

我知道使用 itertools 来获取所有组合要实用得多，但是如果你碰巧想要编写很多代码，你可以部分地通过列表理解来实现这一点

对于两对的组合：

lambda l: [(a, b) for i, a in enumerate(l) for b in l[i+1:]]

而且，对于三对的组合，就这么简单：

lambda l: [(a, b, c) for i, a in enumerate(l) for ii, b in enumerate(l[i+1:]) for c in l[i+ii+2:]]

结果与使用 itertools.combinations 相同：

import itertools
combs_3 = lambda l: [
    (a, b, c) for i, a in enumerate(l) 
    for ii, b in enumerate(l[i+1:]) 
    for c in l[i+ii+2:]
]
data = ((1, 2), 5, "a", None)
print("A:", list(itertools.combinations(data, 3)))
print("B:", combs_3(data))
# A: [((1, 2), 5, 'a'), ((1, 2), 5, None), ((1, 2), 'a', None), (5, 'a', None)]
# B: [((1, 2), 5, 'a'), ((1, 2), 5, None), ((1, 2), 'a', None), (5, 'a', None)]

score 3 · Accepted Answer

这里有两个实现itertools.combinations

一个返回列表的

def combinations(lst, depth, start=0, items=[]):
    if depth <= 0:
        return [items]
    out = []
    for i in range(start, len(lst)):
        out += combinations(lst, depth - 1, i + 1, items + [lst[i]])
    return out

一个返回一个生成器

def combinations(lst, depth, start=0, prepend=[]):
    if depth <= 0:
        yield prepend
    else:
        for i in range(start, len(lst)):
            for c in combinations(lst, depth - 1, i + 1, prepend + [lst[i]]):
                yield c

请注意，建议为那些提供帮助函数，因为 prepend 参数是静态的，并且不会随着每次调用而改变

print([c for c in combinations([1, 2, 3, 4], 3)])
# [[1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4]]

# get a hold of prepend
prepend = [c for c in combinations([], -1)][0]
prepend.append(None)

print([c for c in combinations([1, 2, 3, 4], 3)])
# [[None, 1, 2, 3], [None, 1, 2, 4], [None, 1, 3, 4], [None, 2, 3, 4]]

这是一个非常肤浅的案例，但最好是安全而不是抱歉

score 3 · Accepted Answer

这个怎么样..使用字符串而不是列表，但同样的事情..字符串可以被视为Python中的列表：

def comb(s, res):
    if not s: return
    res.add(s)
    for i in range(0, len(s)):
        t = s[0:i] + s[i + 1:]
        comb(t, res)

res = set()
comb('game', res) 

print(res)

score 3 · Accepted Answer

来自 itertools 的组合

import itertools
col_names = ["aa","bb", "cc", "dd"]
all_combinations = itertools.chain(*[itertools.combinations(col_names,i+1) for i,_ in enumerate(col_names)])
print(list(all_combinations))

score 3 · Accepted Answer

如果没有 itertoolsPython 3，您可以执行以下操作：

def combinations(arr, carry):
    for i in range(len(arr)):
        yield carry + arr[i]
        yield from combinations(arr[i + 1:], carry + arr[i])

最初在哪里carry = "".

score 2 · Accepted Answer

这段代码采用了一个简单的算法和嵌套列表......

# FUNCTION getCombos: To generate all combos of an input list, consider the following sets of nested lists...
#
#           [ [ [] ] ]
#           [ [ [] ], [ [A] ] ]
#           [ [ [] ], [ [A],[B] ],         [ [A,B] ] ]
#           [ [ [] ], [ [A],[B],[C] ],     [ [A,B],[A,C],[B,C] ],                   [ [A,B,C] ] ]
#           [ [ [] ], [ [A],[B],[C],[D] ], [ [A,B],[A,C],[B,C],[A,D],[B,D],[C,D] ], [ [A,B,C],[A,B,D],[A,C,D],[B,C,D] ], [ [A,B,C,D] ] ]
#
#  There is a set of lists for each number of items that will occur in a combo (including an empty set).
#  For each additional item, begin at the back of the list by adding an empty list, then taking the set of
#  lists in the previous column (e.g., in the last list, for sets of 3 items you take the existing set of
#  3-item lists and append to it additional lists created by appending the item (4) to the lists in the
#  next smallest item count set. In this case, for the three sets of 2-items in the previous list. Repeat
#  for each set of lists back to the initial list containing just the empty list.
#

def getCombos(listIn = ['A','B','C','D','E','F'] ):
    listCombos = [ [ [] ] ]     # list of lists of combos, seeded with a list containing only the empty list
    listSimple = []             # list to contain the final returned list of items (e.g., characters)

    for item in listIn:
        listCombos.append([])   # append an emtpy list to the end for each new item added
        for index in xrange(len(listCombos)-1, 0, -1):  # set the index range to work through the list
            for listPrev in listCombos[index-1]:        # retrieve the lists from the previous column
                listCur = listPrev[:]                   # create a new temporary list object to update
                listCur.append(item)                    # add the item to the previous list to make it current
                listCombos[index].append(listCur)       # list length and append it to the current list

                itemCombo = ''                          # Create a str to concatenate list items into a str
                for item in listCur:                    # concatenate the members of the lists to create
                    itemCombo += item                   # create a string of items
                listSimple.append(itemCombo)            # add to the final output list

    return [listSimple, listCombos]
# END getCombos()

score 2 · Accepted Answer

这是我的实现

def get_combinations(list_of_things):
"""gets every combination of things in a list returned as a list of lists

Should be read : add all combinations of a certain size to the end of a list for every possible size in the
the list_of_things.

"""
list_of_combinations = [list(combinations_of_a_certain_size)
                        for possible_size_of_combinations in range(1,  len(list_of_things))
                        for combinations_of_a_certain_size in itertools.combinations(list_of_things,
                                                                                     possible_size_of_combinations)]
return list_of_combinations

score 2 · Accepted Answer

不使用 itertools：

def combine(inp):
    return combine_helper(inp, [], [])


def combine_helper(inp, temp, ans):
    for i in range(len(inp)):
        current = inp[i]
        remaining = inp[i + 1:]
        temp.append(current)
        ans.append(tuple(temp))
        combine_helper(remaining, temp, ans)
        temp.pop()
    return ans


print(combine(['a', 'b', 'c', 'd']))

score 1 · Accepted Answer

使用列表理解：

def selfCombine( list2Combine, length ):
    listCombined = str( ['list2Combine[i' + str( i ) + ']' for i in range( length )] ).replace( "'", '' ) \
                     + 'for i0 in range(len( list2Combine ) )'
    if length > 1:
        listCombined += str( [' for i' + str( i ) + ' in range( i' + str( i - 1 ) + ', len( list2Combine ) )' for i in range( 1, length )] )\
            .replace( "', '", ' ' )\
            .replace( "['", '' )\
            .replace( "']", '' )

    listCombined = '[' + listCombined + ']'
    listCombined = eval( listCombined )

    return listCombined

list2Combine = ['A', 'B', 'C']
listCombined = selfCombine( list2Combine, 2 )

输出将是：

['A', 'A']
['A', 'B']
['A', 'C']
['B', 'B']
['B', 'C']
['C', 'C']

score 1 · Accepted Answer

我迟到了，但想分享我找到的解决同一问题的解决方案：具体来说，我正在寻找顺序组合，所以对于“STAR”，我想要“STAR”、“TA”、“AR”，但不是“SR”。

lst = [S, T, A, R]
lstCombos = []
for Length in range(0,len(lst)+1):
    for i in lst:
        lstCombos.append(lst[lst.index(i):lst.index(i)+Length])

可以通过在最后一行之前添加额外的 if 来过滤重复项：

lst = [S, T, A, R]
lstCombos = []
for Length in range(0,len(lst)+1):
    for i in lst:
         if not lst[lst.index(i):lst.index(i)+Length]) in lstCombos:
             lstCombos.append(lst[lst.index(i):lst.index(i)+Length])

如果由于某种原因这会在输出中返回空白列表，这发生在我身上，我补充说：

for subList in lstCombos:
    if subList = '':
         lstCombos.remove(subList)

score 0 · Accepted Answer

如文档中所述

def combinations(iterable, r):
    # combinations('ABCD', 2) --> AB AC AD BC BD CD
    # combinations(range(4), 3) --> 012 013 023 123
    pool = tuple(iterable)
    n = len(pool)
    if r > n:
        return
    indices = list(range(r))
    yield tuple(pool[i] for i in indices)
    while True:
        for i in reversed(range(r)):
            if indices[i] != i + n - r:
                break
        else:
            return
        indices[i] += 1
        for j in range(i+1, r):
            indices[j] = indices[j-1] + 1
        yield tuple(pool[i] for i in indices)


x = [2, 3, 4, 5, 1, 6, 4, 7, 8, 3, 9]
for i in combinations(x, 2):
    print i

score 0 · Accepted Answer

如果有人正在寻找一个反向列表，就像我一样：

stuff = [1, 2, 3, 4]

def reverse(bla, y):
    for subset in itertools.combinations(bla, len(bla)-y):
        print list(subset)
    if y != len(bla):
        y += 1
        reverse(bla, y)

reverse(stuff, 1)

score 0 · Accepted Answer

flag = 0
requiredCals =12
from itertools import chain, combinations

def powerset(iterable):
    s = list(iterable)  # allows duplicate elements
    return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))

stuff = [2,9,5,1,6]
for i, combo in enumerate(powerset(stuff), 1):
    if(len(combo)>0):
        #print(combo , sum(combo))
        if(sum(combo)== requiredCals):
            flag = 1
            break
if(flag==1):
    print('True')
else:
    print('else')

score 0 · Accepted Answer

如果您不想使用组合库，这里是解决方案：

nums = [1,2,3]
p = [[]]
fnl = [[],nums]

for i in range(len(nums)):
    for j in range(i+1,len(nums)):
        p[-1].append([i,j])

for i in range(len(nums)-3):
    p.append([])
    for m in p[-2]:
        p[-1].append(m+[m[-1]+1])

for i in p:
    for j in i:
        n = []
        for m in j:
            if m < len(nums):
                n.append(nums[m])
        if n not in fnl:
            fnl.append(n)

for i in nums:
    if [i] not in fnl:
        fnl.append([i])

print(fnl)

输出：

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

score 0 · Accepted Answer

在组合大小上递归的另一种解决方案：

def _comb(items, i, res, pos):
    if len(items) == i:
        return

    res += [r + [c] for c in items for r in res[pos:]]
    # Combinations are like a tree, and "pos" is the leaves index
    # where we build the new sub tree 
    _comb(items,i+1, res, len(items)**i+pos)

def comb(items):
    l = [[]]
    _comb(items, 0, l, 0)
    return l

python - 如何获得列表元素的所有可能组合？

30 回答 30

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