如何生成列表的所有排列?例如:
permutations([])
[]
permutations([1])
[1]
permutations([1, 2])
[1, 2]
[2, 1]
permutations([1, 2, 3])
[1, 2, 3]
[1, 3, 2]
[2, 1, 3]
[2, 3, 1]
[3, 1, 2]
[3, 2, 1]
如何生成列表的所有排列?例如:
permutations([])
[]
permutations([1])
[1]
permutations([1, 2])
[1, 2]
[2, 1]
permutations([1, 2, 3])
[1, 2, 3]
[1, 3, 2]
[2, 1, 3]
[2, 3, 1]
[3, 1, 2]
[3, 2, 1]
当前回答
人们确实可以对每个排列的第一个元素进行迭代,正如tzwen的答案。然而,这样编写此解决方案更有效:
def all_perms(elements):
if len(elements) <= 1:
yield elements # Only permutation possible = no permutation
else:
# Iteration over the first element in the result permutation:
for (index, first_elmt) in enumerate(elements):
other_elmts = elements[:index]+elements[index+1:]
for permutation in all_perms(other_elmts):
yield [first_elmt] + permutation
这个解决方案大约快了30%,显然是因为递归以len(元素)<=1而不是0结尾。它的内存效率也高得多,因为它使用了一个生成器函数(通过yield),就像Riccardo Reyes的解决方案一样。
其他回答
该算法是最有效的算法,它避免了递归调用中的数组传递和操作,适用于Python 2、3:
def permute(items):
length = len(items)
def inner(ix=[]):
do_yield = len(ix) == length - 1
for i in range(0, length):
if i in ix: #avoid duplicates
continue
if do_yield:
yield tuple([items[y] for y in ix + [i]])
else:
for p in inner(ix + [i]):
yield p
return inner()
用法:
for p in permute((1,2,3)):
print(p)
(1, 2, 3)
(1, 3, 2)
(2, 1, 3)
(2, 3, 1)
(3, 1, 2)
(3, 2, 1)
def permutations(head, tail=''):
if len(head) == 0:
print(tail)
else:
for i in range(len(head)):
permutations(head[:i] + head[i+1:], tail + head[i])
称为:
permutations('abc')
list2Perm = [1, 2.0, 'three']
listPerm = [[a, b, c]
for a in list2Perm
for b in list2Perm
for c in list2Perm
if ( a != b and b != c and a != c )
]
print listPerm
输出:
[
[1, 2.0, 'three'],
[1, 'three', 2.0],
[2.0, 1, 'three'],
[2.0, 'three', 1],
['three', 1, 2.0],
['three', 2.0, 1]
]
def pzip(c, seq):
result = []
for item in seq:
for i in range(len(item)+1):
result.append(item[i:]+c+item[:i])
return result
def perm(line):
seq = [c for c in line]
if len(seq) <=1 :
return seq
else:
return pzip(seq[0], perm(seq[1:]))
另一种解决方案:
def permutation(flag, k =1 ):
N = len(flag)
for i in xrange(0, N):
if flag[i] != 0:
continue
flag[i] = k
if k == N:
print flag
permutation(flag, k+1)
flag[i] = 0
permutation([0, 0, 0])