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
以下代码是给定列表的就地排列,作为生成器实现。由于它只返回对列表的引用,因此不应在生成器外部修改列表。该解决方案是非递归的,因此使用了低内存。还可以很好地处理输入列表中元素的多个副本。
def permute_in_place(a):
a.sort()
yield list(a)
if len(a) <= 1:
return
first = 0
last = len(a)
while 1:
i = last - 1
while 1:
i = i - 1
if a[i] < a[i+1]:
j = last - 1
while not (a[i] < a[j]):
j = j - 1
a[i], a[j] = a[j], a[i] # swap the values
r = a[i+1:last]
r.reverse()
a[i+1:last] = r
yield list(a)
break
if i == first:
a.reverse()
return
if __name__ == '__main__':
for n in range(5):
for a in permute_in_place(range(1, n+1)):
print a
print
for a in permute_in_place([0, 0, 1, 1, 1]):
print a
print
其他回答
这里有一个算法,它在不创建新的中间列表的情况下处理列表,类似于Ber在https://stackoverflow.com/a/108651/184528.
def permute(xs, low=0):
if low + 1 >= len(xs):
yield xs
else:
for p in permute(xs, low + 1):
yield p
for i in range(low + 1, len(xs)):
xs[low], xs[i] = xs[i], xs[low]
for p in permute(xs, low + 1):
yield p
xs[low], xs[i] = xs[i], xs[low]
for p in permute([1, 2, 3, 4]):
print p
您可以在这里亲自尝试代码:http://repl.it/J9v
from __future__ import print_function
def perm(n):
p = []
for i in range(0,n+1):
p.append(i)
while True:
for i in range(1,n+1):
print(p[i], end=' ')
print("")
i = n - 1
found = 0
while (not found and i>0):
if p[i]<p[i+1]:
found = 1
else:
i = i - 1
k = n
while p[i]>p[k]:
k = k - 1
aux = p[i]
p[i] = p[k]
p[k] = aux
for j in range(1,(n-i)/2+1):
aux = p[i+j]
p[i+j] = p[n-j+1]
p[n-j+1] = aux
if not found:
break
perm(5)
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)
使用计数器
from collections import Counter
def permutations(nums):
ans = [[]]
cache = Counter(nums)
for idx, x in enumerate(nums):
result = []
for items in ans:
cache1 = Counter(items)
for id, n in enumerate(nums):
if cache[n] != cache1[n] and items + [n] not in result:
result.append(items + [n])
ans = result
return ans
permutations([1, 2, 2])
> [[1, 2, 2], [2, 1, 2], [2, 2, 1]]
对于Python,我们可以使用itertools并导入排列和组合来解决问题
from itertools import product, permutations
A = ([1,2,3])
print (list(permutations(sorted(A),2)))