将彩球放入箱子的所有可能方法
All possible ways to place colored balls into bins
我有很多垃圾箱。每个箱子只能容纳一个球。
比方说，我有
Na 个红球
Nb个蓝球
Nc绿球数
等等。
我想找出将球放入长度为 (Na+Nb+Nc) 的容器中的所有可能方法。
例如，假设我只有两个红球和两个蓝球。我想将它们放入 4 个箱子中。可能的排列方式有：
R R B B
R B R B
R B B R
B R R B
B R B R
B B R R
(希望没有漏掉任何一个组合)
有什么简单的方法可以为不同的颜色生成索引，例如：
First row is : R=(0,1) B=(2,3)
Second row is : R=(0,2) B=(1,3)
有没有一种简单的方法可以在 numpy 中生成它？
垃圾箱实际上有不同的重量，例如：
[0.1, 0.3, 0.2, 0.5]
因此，对于表示为 R at (0,1) and B at (2,3) 的组合 R R B B ，R 的总权重为 0.1+0.3=0.4，B 的总权重为 0.2+0.5=0.7
我最终对不同排列中每种颜色的总权重感兴趣，并想从另一个成本函数 f(total_weight(R), total_weight(B) 中选择最好的一个).如果总重量的生成可以在 numpy 中以不同的简单方式完成，有什么意见吗？
生成排列并删除重复项。
>>> import itertools
>>> Na = 2
>>> Nb = 2
>>> p = itertools.permutations(['R']*Na + ['B']*Nb)
>>> for perm in sorted(list(set(p)), reverse=True):
... print perm
...
('R', 'R', 'B', 'B')
('R', 'B', 'R', 'B')
('R', 'B', 'B', 'R')
('B', 'R', 'R', 'B')
('B', 'R', 'B', 'R')
('B', 'B', 'R', 'R')
你可以用 itertools 解决这个问题：
import itertools
last = None
result = []
for v in itertools.permutations(['A','A','B','B']):
key = "".join(v)
if key == last: continue
last = key
result.append(v)
print result
这是一个不需要消除重复排列的 "multi-combinations" 实现。第一个参数 n 是列表 [Na, Nb, Nc, ...]。
它是作为递归生成器实现的，因此您可以遍历组合，而无需一次将它们全部存储在内存中。您在评论中说 Na + Nb + ... 通常在 20 左右，但可能高达 50 或 100。这意味着您几乎肯定不想将所有组合存储在内存中。考虑一个有四个 "colors" 的例子，其中 Na = Nb = Nc = Nd = 5。组合的数量是 choose(20, 5) * choose(15, 5) * choose(10, 5) = 11732745024，其中 choose(n, k) 是 binomial coefficient。我的计算机只有 16 GB 的 RAM，因此组合数量所需的存储空间将远远超过我计算机的内存。
from itertools import combinations
def multicombinations(n, bins=None):
if bins is None:
bins = set(range(sum(n)))
if len(n) == 0:
yield []
else:
for c in combinations(bins, n[0]):
for t in multicombinations(n[1:], bins - set(c)):
yield [c] + t
它生成一个元组列表。也就是说，如果您对第一行的描述是 "First row is : R=(0,1) B=(2,3)"，则 multicombinations([2, 2]) 生成的第一个值是 [(0, 1), (2, 3)]。 （考虑到您接下来要进行的权重计算的描述，这可能不是结果的最佳格式。）
一些例子：
In [74]: list(multicombinations([2, 2]))
Out[74]:
[[(0, 1), (2, 3)],
[(0, 2), (1, 3)],
[(0, 3), (1, 2)],
[(1, 2), (0, 3)],
[(1, 3), (0, 2)],
[(2, 3), (0, 1)]]
In [75]: list(multicombinations([3, 2]))
Out[75]:
[[(0, 1, 2), (3, 4)],
[(0, 1, 3), (2, 4)],
[(0, 1, 4), (2, 3)],
[(0, 2, 3), (1, 4)],
[(0, 2, 4), (1, 3)],
[(0, 3, 4), (1, 2)],
[(1, 2, 3), (0, 4)],
[(1, 2, 4), (0, 3)],
[(1, 3, 4), (0, 2)],
[(2, 3, 4), (0, 1)]]
In [76]: list(multicombinations([2, 3, 2]))
Out[76]:
[[(0, 1), (2, 3, 4), (5, 6)],
[(0, 1), (2, 3, 5), (4, 6)],
[(0, 1), (2, 3, 6), (4, 5)],
[(0, 1), (2, 4, 5), (3, 6)],
[(0, 1), (2, 4, 6), (3, 5)],
[(0, 1), (2, 5, 6), (3, 4)],
[(0, 1), (3, 4, 5), (2, 6)],
[(0, 1), (3, 4, 6), (2, 5)],
[(0, 1), (3, 5, 6), (2, 4)],
[(0, 1), (4, 5, 6), (2, 3)],
[(0, 2), (1, 3, 4), (5, 6)],
[(0, 2), (1, 3, 5), (4, 6)],
[(0, 2), (1, 3, 6), (4, 5)],
[(0, 2), (1, 4, 5), (3, 6)],
[(0, 2), (1, 4, 6), (3, 5)],
[(0, 2), (1, 5, 6), (3, 4)],
[(0, 2), (3, 4, 5), (1, 6)],
[(0, 2), (3, 4, 6), (1, 5)],
[(0, 2), (3, 5, 6), (1, 4)],
[(0, 2), (4, 5, 6), (1, 3)],
[(0, 3), (1, 2, 4), (5, 6)],
[(0, 3), (1, 2, 5), (4, 6)],
[(0, 3), (1, 2, 6), (4, 5)],
[(0, 3), (1, 4, 5), (2, 6)],
[(0, 3), (1, 4, 6), (2, 5)],
[(0, 3), (1, 5, 6), (2, 4)],
[(0, 3), (2, 4, 5), (1, 6)],
[(0, 3), (2, 4, 6), (1, 5)],
[(0, 3), (2, 5, 6), (1, 4)],
[(0, 3), (4, 5, 6), (1, 2)],
[(0, 4), (1, 2, 3), (5, 6)],
[(0, 4), (1, 2, 5), (3, 6)],
[(0, 4), (1, 2, 6), (3, 5)],
[(0, 4), (1, 3, 5), (2, 6)],
[(0, 4), (1, 3, 6), (2, 5)],
[(0, 4), (1, 5, 6), (2, 3)],
[(0, 4), (2, 3, 5), (1, 6)],
[(0, 4), (2, 3, 6), (1, 5)],
[(0, 4), (2, 5, 6), (1, 3)],
[(0, 4), (3, 5, 6), (1, 2)],
[(0, 5), (1, 2, 3), (4, 6)],
[(0, 5), (1, 2, 4), (3, 6)],
[(0, 5), (1, 2, 6), (3, 4)],
[(0, 5), (1, 3, 4), (2, 6)],
[(0, 5), (1, 3, 6), (2, 4)],
[(0, 5), (1, 4, 6), (2, 3)],
[(0, 5), (2, 3, 4), (1, 6)],
[(0, 5), (2, 3, 6), (1, 4)],
[(0, 5), (2, 4, 6), (1, 3)],
[(0, 5), (3, 4, 6), (1, 2)],
[(0, 6), (1, 2, 3), (4, 5)],
[(0, 6), (1, 2, 4), (3, 5)],
[(0, 6), (1, 2, 5), (3, 4)],
[(0, 6), (1, 3, 4), (2, 5)],
[(0, 6), (1, 3, 5), (2, 4)],
[(0, 6), (1, 4, 5), (2, 3)],
[(0, 6), (2, 3, 4), (1, 5)],
[(0, 6), (2, 3, 5), (1, 4)],
[(0, 6), (2, 4, 5), (1, 3)],
[(0, 6), (3, 4, 5), (1, 2)],
[(1, 2), (0, 3, 4), (5, 6)],
[(1, 2), (0, 3, 5), (4, 6)],
[(1, 2), (0, 3, 6), (4, 5)],
[(1, 2), (0, 4, 5), (3, 6)],
[(1, 2), (0, 4, 6), (3, 5)],
[(1, 2), (0, 5, 6), (3, 4)],
[(1, 2), (3, 4, 5), (0, 6)],
[(1, 2), (3, 4, 6), (0, 5)],
[(1, 2), (3, 5, 6), (0, 4)],
[(1, 2), (4, 5, 6), (0, 3)],
[(1, 3), (0, 2, 4), (5, 6)],
[(1, 3), (0, 2, 5), (4, 6)],
[(1, 3), (0, 2, 6), (4, 5)],
[(1, 3), (0, 4, 5), (2, 6)],
[(1, 3), (0, 4, 6), (2, 5)],
[(1, 3), (0, 5, 6), (2, 4)],
[(1, 3), (2, 4, 5), (0, 6)],
[(1, 3), (2, 4, 6), (0, 5)],
[(1, 3), (2, 5, 6), (0, 4)],
[(1, 3), (4, 5, 6), (0, 2)],
[(1, 4), (0, 2, 3), (5, 6)],
[(1, 4), (0, 2, 5), (3, 6)],
[(1, 4), (0, 2, 6), (3, 5)],
[(1, 4), (0, 3, 5), (2, 6)],
[(1, 4), (0, 3, 6), (2, 5)],
[(1, 4), (0, 5, 6), (2, 3)],
[(1, 4), (2, 3, 5), (0, 6)],
[(1, 4), (2, 3, 6), (0, 5)],
[(1, 4), (2, 5, 6), (0, 3)],
[(1, 4), (3, 5, 6), (0, 2)],
[(1, 5), (0, 2, 3), (4, 6)],
[(1, 5), (0, 2, 4), (3, 6)],
[(1, 5), (0, 2, 6), (3, 4)],
[(1, 5), (0, 3, 4), (2, 6)],
[(1, 5), (0, 3, 6), (2, 4)],
[(1, 5), (0, 4, 6), (2, 3)],
[(1, 5), (2, 3, 4), (0, 6)],
[(1, 5), (2, 3, 6), (0, 4)],
[(1, 5), (2, 4, 6), (0, 3)],
[(1, 5), (3, 4, 6), (0, 2)],
[(1, 6), (0, 2, 3), (4, 5)],
[(1, 6), (0, 2, 4), (3, 5)],
[(1, 6), (0, 2, 5), (3, 4)],
[(1, 6), (0, 3, 4), (2, 5)],
[(1, 6), (0, 3, 5), (2, 4)],
[(1, 6), (0, 4, 5), (2, 3)],
[(1, 6), (2, 3, 4), (0, 5)],
[(1, 6), (2, 3, 5), (0, 4)],
[(1, 6), (2, 4, 5), (0, 3)],
[(1, 6), (3, 4, 5), (0, 2)],
[(2, 3), (0, 1, 4), (5, 6)],
[(2, 3), (0, 1, 5), (4, 6)],
[(2, 3), (0, 1, 6), (4, 5)],
[(2, 3), (0, 4, 5), (1, 6)],
[(2, 3), (0, 4, 6), (1, 5)],
[(2, 3), (0, 5, 6), (1, 4)],
[(2, 3), (1, 4, 5), (0, 6)],
[(2, 3), (1, 4, 6), (0, 5)],
[(2, 3), (1, 5, 6), (0, 4)],
[(2, 3), (4, 5, 6), (0, 1)],
[(2, 4), (0, 1, 3), (5, 6)],
[(2, 4), (0, 1, 5), (3, 6)],
[(2, 4), (0, 1, 6), (3, 5)],
[(2, 4), (0, 3, 5), (1, 6)],
[(2, 4), (0, 3, 6), (1, 5)],
[(2, 4), (0, 5, 6), (1, 3)],
[(2, 4), (1, 3, 5), (0, 6)],
[(2, 4), (1, 3, 6), (0, 5)],
[(2, 4), (1, 5, 6), (0, 3)],
[(2, 4), (3, 5, 6), (0, 1)],
[(2, 5), (0, 1, 3), (4, 6)],
[(2, 5), (0, 1, 4), (3, 6)],
[(2, 5), (0, 1, 6), (3, 4)],
[(2, 5), (0, 3, 4), (1, 6)],
[(2, 5), (0, 3, 6), (1, 4)],
[(2, 5), (0, 4, 6), (1, 3)],
[(2, 5), (1, 3, 4), (0, 6)],
[(2, 5), (1, 3, 6), (0, 4)],
[(2, 5), (1, 4, 6), (0, 3)],
[(2, 5), (3, 4, 6), (0, 1)],
[(2, 6), (0, 1, 3), (4, 5)],
[(2, 6), (0, 1, 4), (3, 5)],
[(2, 6), (0, 1, 5), (3, 4)],
[(2, 6), (0, 3, 4), (1, 5)],
[(2, 6), (0, 3, 5), (1, 4)],
[(2, 6), (0, 4, 5), (1, 3)],
[(2, 6), (1, 3, 4), (0, 5)],
[(2, 6), (1, 3, 5), (0, 4)],
[(2, 6), (1, 4, 5), (0, 3)],
[(2, 6), (3, 4, 5), (0, 1)],
[(3, 4), (0, 1, 2), (5, 6)],
[(3, 4), (0, 1, 5), (2, 6)],
[(3, 4), (0, 1, 6), (2, 5)],
[(3, 4), (0, 2, 5), (1, 6)],
[(3, 4), (0, 2, 6), (1, 5)],
[(3, 4), (0, 5, 6), (1, 2)],
[(3, 4), (1, 2, 5), (0, 6)],
[(3, 4), (1, 2, 6), (0, 5)],
[(3, 4), (1, 5, 6), (0, 2)],
[(3, 4), (2, 5, 6), (0, 1)],
[(3, 5), (0, 1, 2), (4, 6)],
[(3, 5), (0, 1, 4), (2, 6)],
[(3, 5), (0, 1, 6), (2, 4)],
[(3, 5), (0, 2, 4), (1, 6)],
[(3, 5), (0, 2, 6), (1, 4)],
[(3, 5), (0, 4, 6), (1, 2)],
[(3, 5), (1, 2, 4), (0, 6)],
[(3, 5), (1, 2, 6), (0, 4)],
[(3, 5), (1, 4, 6), (0, 2)],
[(3, 5), (2, 4, 6), (0, 1)],
[(3, 6), (0, 1, 2), (4, 5)],
[(3, 6), (0, 1, 4), (2, 5)],
[(3, 6), (0, 1, 5), (2, 4)],
[(3, 6), (0, 2, 4), (1, 5)],
[(3, 6), (0, 2, 5), (1, 4)],
[(3, 6), (0, 4, 5), (1, 2)],
[(3, 6), (1, 2, 4), (0, 5)],
[(3, 6), (1, 2, 5), (0, 4)],
[(3, 6), (1, 4, 5), (0, 2)],
[(3, 6), (2, 4, 5), (0, 1)],
[(4, 5), (0, 1, 2), (3, 6)],
[(4, 5), (0, 1, 3), (2, 6)],
[(4, 5), (0, 1, 6), (2, 3)],
[(4, 5), (0, 2, 3), (1, 6)],
[(4, 5), (0, 2, 6), (1, 3)],
[(4, 5), (0, 3, 6), (1, 2)],
[(4, 5), (1, 2, 3), (0, 6)],
[(4, 5), (1, 2, 6), (0, 3)],
[(4, 5), (1, 3, 6), (0, 2)],
[(4, 5), (2, 3, 6), (0, 1)],
[(4, 6), (0, 1, 2), (3, 5)],
[(4, 6), (0, 1, 3), (2, 5)],
[(4, 6), (0, 1, 5), (2, 3)],
[(4, 6), (0, 2, 3), (1, 5)],
[(4, 6), (0, 2, 5), (1, 3)],
[(4, 6), (0, 3, 5), (1, 2)],
[(4, 6), (1, 2, 3), (0, 5)],
[(4, 6), (1, 2, 5), (0, 3)],
[(4, 6), (1, 3, 5), (0, 2)],
[(4, 6), (2, 3, 5), (0, 1)],
[(5, 6), (0, 1, 2), (3, 4)],
[(5, 6), (0, 1, 3), (2, 4)],
[(5, 6), (0, 1, 4), (2, 3)],
[(5, 6), (0, 2, 3), (1, 4)],
[(5, 6), (0, 2, 4), (1, 3)],
[(5, 6), (0, 3, 4), (1, 2)],
[(5, 6), (1, 2, 3), (0, 4)],
[(5, 6), (1, 2, 4), (0, 3)],
[(5, 6), (1, 3, 4), (0, 2)],
[(5, 6), (2, 3, 4), (0, 1)]]
这是一种可能的实施方式：
def permutations(colors, l):
if l == 0:
yield []
else:
for i in range(len(colors)):
if colors[i]:
la = colors[:i]
lb = [colors[i][1:]]
lc = colors[i + 1:]
choice = colors[i][0]
for rest in permutations(la + lb + lc, l - 1):
yield [choice] + rest
用法：
for choice in permutations([['R'] * 2, ['B'] * 2], 4):
print(choice)
['R', 'R', 'B', 'B']
['R', 'B', 'R', 'B']
['R', 'B', 'B', 'R']
['B', 'R', 'R', 'B']
['B', 'R', 'B', 'R']
['B', 'B', 'R', 'R']
我有很多垃圾箱。每个箱子只能容纳一个球。
比方说，我有
Na 个红球
Nb个蓝球
Nc绿球数
等等。
我想找出将球放入长度为 (Na+Nb+Nc) 的容器中的所有可能方法。
例如，假设我只有两个红球和两个蓝球。我想将它们放入 4 个箱子中。可能的排列方式有：
R R B B
R B R B
R B B R
B R R B
B R B R
B B R R
(希望没有漏掉任何一个组合)
有什么简单的方法可以为不同的颜色生成索引，例如：
First row is : R=(0,1) B=(2,3)
Second row is : R=(0,2) B=(1,3)
有没有一种简单的方法可以在 numpy 中生成它？
垃圾箱实际上有不同的重量，例如：
[0.1, 0.3, 0.2, 0.5]
因此，对于表示为 R at (0,1) and B at (2,3) 的组合 R R B B ，R 的总权重为 0.1+0.3=0.4，B 的总权重为 0.2+0.5=0.7
我最终对不同排列中每种颜色的总权重感兴趣，并想从另一个成本函数 f(total_weight(R), total_weight(B) 中选择最好的一个).如果总重量的生成可以在 numpy 中以不同的简单方式完成，有什么意见吗？
生成排列并删除重复项。
>>> import itertools
>>> Na = 2
>>> Nb = 2
>>> p = itertools.permutations(['R']*Na + ['B']*Nb)
>>> for perm in sorted(list(set(p)), reverse=True):
... print perm
...
('R', 'R', 'B', 'B')
('R', 'B', 'R', 'B')
('R', 'B', 'B', 'R')
('B', 'R', 'R', 'B')
('B', 'R', 'B', 'R')
('B', 'B', 'R', 'R')
你可以用 itertools 解决这个问题：
import itertools
last = None
result = []
for v in itertools.permutations(['A','A','B','B']):
key = "".join(v)
if key == last: continue
last = key
result.append(v)
print result
这是一个不需要消除重复排列的 "multi-combinations" 实现。第一个参数 n 是列表 [Na, Nb, Nc, ...]。
它是作为递归生成器实现的，因此您可以遍历组合，而无需一次将它们全部存储在内存中。您在评论中说 Na + Nb + ... 通常在 20 左右，但可能高达 50 或 100。这意味着您几乎肯定不想将所有组合存储在内存中。考虑一个有四个 "colors" 的例子，其中 Na = Nb = Nc = Nd = 5。组合的数量是 choose(20, 5) * choose(15, 5) * choose(10, 5) = 11732745024，其中 choose(n, k) 是 binomial coefficient。我的计算机只有 16 GB 的 RAM，因此组合数量所需的存储空间将远远超过我计算机的内存。
from itertools import combinations
def multicombinations(n, bins=None):
if bins is None:
bins = set(range(sum(n)))
if len(n) == 0:
yield []
else:
for c in combinations(bins, n[0]):
for t in multicombinations(n[1:], bins - set(c)):
yield [c] + t
它生成一个元组列表。也就是说，如果您对第一行的描述是 "First row is : R=(0,1) B=(2,3)"，则 multicombinations([2, 2]) 生成的第一个值是 [(0, 1), (2, 3)]。 （考虑到您接下来要进行的权重计算的描述，这可能不是结果的最佳格式。）
一些例子：
In [74]: list(multicombinations([2, 2]))
Out[74]:
[[(0, 1), (2, 3)],
[(0, 2), (1, 3)],
[(0, 3), (1, 2)],
[(1, 2), (0, 3)],
[(1, 3), (0, 2)],
[(2, 3), (0, 1)]]
In [75]: list(multicombinations([3, 2]))
Out[75]:
[[(0, 1, 2), (3, 4)],
[(0, 1, 3), (2, 4)],
[(0, 1, 4), (2, 3)],
[(0, 2, 3), (1, 4)],
[(0, 2, 4), (1, 3)],
[(0, 3, 4), (1, 2)],
[(1, 2, 3), (0, 4)],
[(1, 2, 4), (0, 3)],
[(1, 3, 4), (0, 2)],
[(2, 3, 4), (0, 1)]]
In [76]: list(multicombinations([2, 3, 2]))
Out[76]:
[[(0, 1), (2, 3, 4), (5, 6)],
[(0, 1), (2, 3, 5), (4, 6)],
[(0, 1), (2, 3, 6), (4, 5)],
[(0, 1), (2, 4, 5), (3, 6)],
[(0, 1), (2, 4, 6), (3, 5)],
[(0, 1), (2, 5, 6), (3, 4)],
[(0, 1), (3, 4, 5), (2, 6)],
[(0, 1), (3, 4, 6), (2, 5)],
[(0, 1), (3, 5, 6), (2, 4)],
[(0, 1), (4, 5, 6), (2, 3)],
[(0, 2), (1, 3, 4), (5, 6)],
[(0, 2), (1, 3, 5), (4, 6)],
[(0, 2), (1, 3, 6), (4, 5)],
[(0, 2), (1, 4, 5), (3, 6)],
[(0, 2), (1, 4, 6), (3, 5)],
[(0, 2), (1, 5, 6), (3, 4)],
[(0, 2), (3, 4, 5), (1, 6)],
[(0, 2), (3, 4, 6), (1, 5)],
[(0, 2), (3, 5, 6), (1, 4)],
[(0, 2), (4, 5, 6), (1, 3)],
[(0, 3), (1, 2, 4), (5, 6)],
[(0, 3), (1, 2, 5), (4, 6)],
[(0, 3), (1, 2, 6), (4, 5)],
[(0, 3), (1, 4, 5), (2, 6)],
[(0, 3), (1, 4, 6), (2, 5)],
[(0, 3), (1, 5, 6), (2, 4)],
[(0, 3), (2, 4, 5), (1, 6)],
[(0, 3), (2, 4, 6), (1, 5)],
[(0, 3), (2, 5, 6), (1, 4)],
[(0, 3), (4, 5, 6), (1, 2)],
[(0, 4), (1, 2, 3), (5, 6)],
[(0, 4), (1, 2, 5), (3, 6)],
[(0, 4), (1, 2, 6), (3, 5)],
[(0, 4), (1, 3, 5), (2, 6)],
[(0, 4), (1, 3, 6), (2, 5)],
[(0, 4), (1, 5, 6), (2, 3)],
[(0, 4), (2, 3, 5), (1, 6)],
[(0, 4), (2, 3, 6), (1, 5)],
[(0, 4), (2, 5, 6), (1, 3)],
[(0, 4), (3, 5, 6), (1, 2)],
[(0, 5), (1, 2, 3), (4, 6)],
[(0, 5), (1, 2, 4), (3, 6)],
[(0, 5), (1, 2, 6), (3, 4)],
[(0, 5), (1, 3, 4), (2, 6)],
[(0, 5), (1, 3, 6), (2, 4)],
[(0, 5), (1, 4, 6), (2, 3)],
[(0, 5), (2, 3, 4), (1, 6)],
[(0, 5), (2, 3, 6), (1, 4)],
[(0, 5), (2, 4, 6), (1, 3)],
[(0, 5), (3, 4, 6), (1, 2)],
[(0, 6), (1, 2, 3), (4, 5)],
[(0, 6), (1, 2, 4), (3, 5)],
[(0, 6), (1, 2, 5), (3, 4)],
[(0, 6), (1, 3, 4), (2, 5)],
[(0, 6), (1, 3, 5), (2, 4)],
[(0, 6), (1, 4, 5), (2, 3)],
[(0, 6), (2, 3, 4), (1, 5)],
[(0, 6), (2, 3, 5), (1, 4)],
[(0, 6), (2, 4, 5), (1, 3)],
[(0, 6), (3, 4, 5), (1, 2)],
[(1, 2), (0, 3, 4), (5, 6)],
[(1, 2), (0, 3, 5), (4, 6)],
[(1, 2), (0, 3, 6), (4, 5)],
[(1, 2), (0, 4, 5), (3, 6)],
[(1, 2), (0, 4, 6), (3, 5)],
[(1, 2), (0, 5, 6), (3, 4)],
[(1, 2), (3, 4, 5), (0, 6)],
[(1, 2), (3, 4, 6), (0, 5)],
[(1, 2), (3, 5, 6), (0, 4)],
[(1, 2), (4, 5, 6), (0, 3)],
[(1, 3), (0, 2, 4), (5, 6)],
[(1, 3), (0, 2, 5), (4, 6)],
[(1, 3), (0, 2, 6), (4, 5)],
[(1, 3), (0, 4, 5), (2, 6)],
[(1, 3), (0, 4, 6), (2, 5)],
[(1, 3), (0, 5, 6), (2, 4)],
[(1, 3), (2, 4, 5), (0, 6)],
[(1, 3), (2, 4, 6), (0, 5)],
[(1, 3), (2, 5, 6), (0, 4)],
[(1, 3), (4, 5, 6), (0, 2)],
[(1, 4), (0, 2, 3), (5, 6)],
[(1, 4), (0, 2, 5), (3, 6)],
[(1, 4), (0, 2, 6), (3, 5)],
[(1, 4), (0, 3, 5), (2, 6)],
[(1, 4), (0, 3, 6), (2, 5)],
[(1, 4), (0, 5, 6), (2, 3)],
[(1, 4), (2, 3, 5), (0, 6)],
[(1, 4), (2, 3, 6), (0, 5)],
[(1, 4), (2, 5, 6), (0, 3)],
[(1, 4), (3, 5, 6), (0, 2)],
[(1, 5), (0, 2, 3), (4, 6)],
[(1, 5), (0, 2, 4), (3, 6)],
[(1, 5), (0, 2, 6), (3, 4)],
[(1, 5), (0, 3, 4), (2, 6)],
[(1, 5), (0, 3, 6), (2, 4)],
[(1, 5), (0, 4, 6), (2, 3)],
[(1, 5), (2, 3, 4), (0, 6)],
[(1, 5), (2, 3, 6), (0, 4)],
[(1, 5), (2, 4, 6), (0, 3)],
[(1, 5), (3, 4, 6), (0, 2)],
[(1, 6), (0, 2, 3), (4, 5)],
[(1, 6), (0, 2, 4), (3, 5)],
[(1, 6), (0, 2, 5), (3, 4)],
[(1, 6), (0, 3, 4), (2, 5)],
[(1, 6), (0, 3, 5), (2, 4)],
[(1, 6), (0, 4, 5), (2, 3)],
[(1, 6), (2, 3, 4), (0, 5)],
[(1, 6), (2, 3, 5), (0, 4)],
[(1, 6), (2, 4, 5), (0, 3)],
[(1, 6), (3, 4, 5), (0, 2)],
[(2, 3), (0, 1, 4), (5, 6)],
[(2, 3), (0, 1, 5), (4, 6)],
[(2, 3), (0, 1, 6), (4, 5)],
[(2, 3), (0, 4, 5), (1, 6)],
[(2, 3), (0, 4, 6), (1, 5)],
[(2, 3), (0, 5, 6), (1, 4)],
[(2, 3), (1, 4, 5), (0, 6)],
[(2, 3), (1, 4, 6), (0, 5)],
[(2, 3), (1, 5, 6), (0, 4)],
[(2, 3), (4, 5, 6), (0, 1)],
[(2, 4), (0, 1, 3), (5, 6)],
[(2, 4), (0, 1, 5), (3, 6)],
[(2, 4), (0, 1, 6), (3, 5)],
[(2, 4), (0, 3, 5), (1, 6)],
[(2, 4), (0, 3, 6), (1, 5)],
[(2, 4), (0, 5, 6), (1, 3)],
[(2, 4), (1, 3, 5), (0, 6)],
[(2, 4), (1, 3, 6), (0, 5)],
[(2, 4), (1, 5, 6), (0, 3)],
[(2, 4), (3, 5, 6), (0, 1)],
[(2, 5), (0, 1, 3), (4, 6)],
[(2, 5), (0, 1, 4), (3, 6)],
[(2, 5), (0, 1, 6), (3, 4)],
[(2, 5), (0, 3, 4), (1, 6)],
[(2, 5), (0, 3, 6), (1, 4)],
[(2, 5), (0, 4, 6), (1, 3)],
[(2, 5), (1, 3, 4), (0, 6)],
[(2, 5), (1, 3, 6), (0, 4)],
[(2, 5), (1, 4, 6), (0, 3)],
[(2, 5), (3, 4, 6), (0, 1)],
[(2, 6), (0, 1, 3), (4, 5)],
[(2, 6), (0, 1, 4), (3, 5)],
[(2, 6), (0, 1, 5), (3, 4)],
[(2, 6), (0, 3, 4), (1, 5)],
[(2, 6), (0, 3, 5), (1, 4)],
[(2, 6), (0, 4, 5), (1, 3)],
[(2, 6), (1, 3, 4), (0, 5)],
[(2, 6), (1, 3, 5), (0, 4)],
[(2, 6), (1, 4, 5), (0, 3)],
[(2, 6), (3, 4, 5), (0, 1)],
[(3, 4), (0, 1, 2), (5, 6)],
[(3, 4), (0, 1, 5), (2, 6)],
[(3, 4), (0, 1, 6), (2, 5)],
[(3, 4), (0, 2, 5), (1, 6)],
[(3, 4), (0, 2, 6), (1, 5)],
[(3, 4), (0, 5, 6), (1, 2)],
[(3, 4), (1, 2, 5), (0, 6)],
[(3, 4), (1, 2, 6), (0, 5)],
[(3, 4), (1, 5, 6), (0, 2)],
[(3, 4), (2, 5, 6), (0, 1)],
[(3, 5), (0, 1, 2), (4, 6)],
[(3, 5), (0, 1, 4), (2, 6)],
[(3, 5), (0, 1, 6), (2, 4)],
[(3, 5), (0, 2, 4), (1, 6)],
[(3, 5), (0, 2, 6), (1, 4)],
[(3, 5), (0, 4, 6), (1, 2)],
[(3, 5), (1, 2, 4), (0, 6)],
[(3, 5), (1, 2, 6), (0, 4)],
[(3, 5), (1, 4, 6), (0, 2)],
[(3, 5), (2, 4, 6), (0, 1)],
[(3, 6), (0, 1, 2), (4, 5)],
[(3, 6), (0, 1, 4), (2, 5)],
[(3, 6), (0, 1, 5), (2, 4)],
[(3, 6), (0, 2, 4), (1, 5)],
[(3, 6), (0, 2, 5), (1, 4)],
[(3, 6), (0, 4, 5), (1, 2)],
[(3, 6), (1, 2, 4), (0, 5)],
[(3, 6), (1, 2, 5), (0, 4)],
[(3, 6), (1, 4, 5), (0, 2)],
[(3, 6), (2, 4, 5), (0, 1)],
[(4, 5), (0, 1, 2), (3, 6)],
[(4, 5), (0, 1, 3), (2, 6)],
[(4, 5), (0, 1, 6), (2, 3)],
[(4, 5), (0, 2, 3), (1, 6)],
[(4, 5), (0, 2, 6), (1, 3)],
[(4, 5), (0, 3, 6), (1, 2)],
[(4, 5), (1, 2, 3), (0, 6)],
[(4, 5), (1, 2, 6), (0, 3)],
[(4, 5), (1, 3, 6), (0, 2)],
[(4, 5), (2, 3, 6), (0, 1)],
[(4, 6), (0, 1, 2), (3, 5)],
[(4, 6), (0, 1, 3), (2, 5)],
[(4, 6), (0, 1, 5), (2, 3)],
[(4, 6), (0, 2, 3), (1, 5)],
[(4, 6), (0, 2, 5), (1, 3)],
[(4, 6), (0, 3, 5), (1, 2)],
[(4, 6), (1, 2, 3), (0, 5)],
[(4, 6), (1, 2, 5), (0, 3)],
[(4, 6), (1, 3, 5), (0, 2)],
[(4, 6), (2, 3, 5), (0, 1)],
[(5, 6), (0, 1, 2), (3, 4)],
[(5, 6), (0, 1, 3), (2, 4)],
[(5, 6), (0, 1, 4), (2, 3)],
[(5, 6), (0, 2, 3), (1, 4)],
[(5, 6), (0, 2, 4), (1, 3)],
[(5, 6), (0, 3, 4), (1, 2)],
[(5, 6), (1, 2, 3), (0, 4)],
[(5, 6), (1, 2, 4), (0, 3)],
[(5, 6), (1, 3, 4), (0, 2)],
[(5, 6), (2, 3, 4), (0, 1)]]
这是一种可能的实施方式：
def permutations(colors, l):
if l == 0:
yield []
else:
for i in range(len(colors)):
if colors[i]:
la = colors[:i]
lb = [colors[i][1:]]
lc = colors[i + 1:]
choice = colors[i][0]
for rest in permutations(la + lb + lc, l - 1):
yield [choice] + rest
用法：
for choice in permutations([['R'] * 2, ['B'] * 2], 4):
print(choice)
['R', 'R', 'B', 'B']
['R', 'B', 'R', 'B']
['R', 'B', 'B', 'R']
['B', 'R', 'R', 'B']
['B', 'R', 'B', 'R']
['B', 'B', 'R', 'R']