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
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
其他回答
from typing import List
import time, random
def measure_time(func):
def wrapper_time(*args, **kwargs):
start_time = time.perf_counter()
res = func(*args, **kwargs)
end_time = time.perf_counter()
return res, end_time - start_time
return wrapper_time
class Solution:
def permute(self, nums: List[int], method: int = 1) -> List[List[int]]:
perms = []
perm = []
if method == 1:
_, time_perm = self._permute_recur(nums, 0, len(nums) - 1, perms)
elif method == 2:
_, time_perm = self._permute_recur_agian(nums, perm, perms)
print(perm)
return perms, time_perm
@measure_time
def _permute_recur(self, nums: List[int], l: int, r: int, perms: List[List[int]]):
# base case
if l == r:
perms.append(nums.copy())
for i in range(l, r + 1):
nums[l], nums[i] = nums[i], nums[l]
self._permute_recur(nums, l + 1, r , perms)
nums[l], nums[i] = nums[i], nums[l]
@measure_time
def _permute_recur_agian(self, nums: List[int], perm: List[int], perms_list: List[List[int]]):
"""
The idea is similar to nestedForLoops visualized as a recursion tree.
"""
if nums:
for i in range(len(nums)):
# perm.append(nums[i]) mistake, perm will be filled with all nums's elements.
# Method1 perm_copy = copy.deepcopy(perm)
# Method2 add in the parameter list using + (not in place)
# caveat: list.append is in-place , which is useful for operating on global element perms_list
# Note that:
# perms_list pass by reference. shallow copy
# perm + [nums[i]] pass by value instead of reference.
self._permute_recur_agian(nums[:i] + nums[i+1:], perm + [nums[i]], perms_list)
else:
# Arrive at the last loop, i.e. leaf of the recursion tree.
perms_list.append(perm)
if __name__ == "__main__":
array = [random.randint(-10, 10) for _ in range(3)]
sol = Solution()
# perms, time_perm = sol.permute(array, 1)
perms2, time_perm2 = sol.permute(array, 2)
print(perms2)
# print(perms, perms2)
# print(time_perm, time_perm2)
```
如果不想使用内置方法,例如:
import itertools
list(itertools.permutations([1, 2, 3]))
你可以自己实现permute函数
from collections.abc import Iterable
def permute(iterable: Iterable[str]) -> set[str]:
perms = set()
if len(iterable) == 1:
return {*iterable}
for index, char in enumerate(iterable):
perms.update([char + perm for perm in permute(iterable[:index] + iterable[index + 1:])])
return perms
if __name__ == '__main__':
print(permute('abc'))
# {'bca', 'abc', 'cab', 'acb', 'cba', 'bac'}
print(permute(['1', '2', '3']))
# {'123', '312', '132', '321', '213', '231'}
使用标准库中的itertools.permutations:
import itertools
list(itertools.permutations([1, 2, 3]))
从这里改编的是itertools.permutations如何实现的演示:
def permutations(elements):
if len(elements) <= 1:
yield elements
return
for perm in permutations(elements[1:]):
for i in range(len(elements)):
# nb elements[0:1] works in both string and list contexts
yield perm[:i] + elements[0:1] + perm[i:]
itertools.permutations文档中列出了两种替代方法
def permutations(iterable, r=None):
# permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC
# permutations(range(3)) --> 012 021 102 120 201 210
pool = tuple(iterable)
n = len(pool)
r = n if r is None else r
if r > n:
return
indices = range(n)
cycles = range(n, n-r, -1)
yield tuple(pool[i] for i in indices[:r])
while n:
for i in reversed(range(r)):
cycles[i] -= 1
if cycles[i] == 0:
indices[i:] = indices[i+1:] + indices[i:i+1]
cycles[i] = n - i
else:
j = cycles[i]
indices[i], indices[-j] = indices[-j], indices[i]
yield tuple(pool[i] for i in indices[:r])
break
else:
return
另一个基于itertools.product:
def permutations(iterable, r=None):
pool = tuple(iterable)
n = len(pool)
r = n if r is None else r
for indices in product(range(n), repeat=r):
if len(set(indices)) == r:
yield tuple(pool[i] for i in indices)
这是初始排序后生成排列的渐近最优方式O(n*n!)。
有n个!最多进行一次置换,且具有下一次置换(..),以O(n)时间复杂度运行
在3个步骤中,
找到最大的j,使a[j]可以增加以最小可行量增加a[j]找到扩展新a[0..j]的字典最少方法
'''
Lexicographic permutation generation
consider example array state of [1,5,6,4,3,2] for sorted [1,2,3,4,5,6]
after 56432(treat as number) ->nothing larger than 6432(using 6,4,3,2) beginning with 5
so 6 is next larger and 2345(least using numbers other than 6)
so [1, 6,2,3,4,5]
'''
def hasNextPermutation(array, len):
' Base Condition '
if(len ==1):
return False
'''
Set j = last-2 and find first j such that a[j] < a[j+1]
If no such j(j==-1) then we have visited all permutations
after this step a[j+1]>=..>=a[len-1] and a[j]<a[j+1]
a[j]=5 or j=1, 6>5>4>3>2
'''
j = len -2
while (j >= 0 and array[j] >= array[j + 1]):
j= j-1
if(j==-1):
return False
# print(f"After step 2 for j {j} {array}")
'''
decrease l (from n-1 to j) repeatedly until a[j]<a[l]
Then swap a[j], a[l]
a[l] is the smallest element > a[j] that can follow a[l]...a[j-1] in permutation
before swap we have a[j+1]>=..>=a[l-1]>=a[l]>a[j]>=a[l+1]>=..>=a[len-1]
after swap -> a[j+1]>=..>=a[l-1]>=a[j]>a[l]>=a[l+1]>=..>=a[len-1]
a[l]=6 or l=2, j=1 just before swap [1, 5, 6, 4, 3, 2]
after swap [1, 6, 5, 4, 3, 2] a[l]=5, a[j]=6
'''
l = len -1
while(array[j] >= array[l]):
l = l-1
# print(f"After step 3 for l={l}, j={j} before swap {array}")
array[j], array[l] = array[l], array[j]
# print(f"After step 3 for l={l} j={j} after swap {array}")
'''
Reverse a[j+1...len-1](both inclusive)
after reversing [1, 6, 2, 3, 4, 5]
'''
array[j+1:len] = reversed(array[j+1:len])
# print(f"After step 4 reversing {array}")
return True
array = [1,2,4,4,5]
array.sort()
len = len(array)
count =1
print(array)
'''
The algorithm visits every permutation in lexicographic order
generating one by one
'''
while(hasNextPermutation(array, len)):
print(array)
count = count +1
# The number of permutations will be n! if no duplicates are present, else less than that
# [1,4,3,3,2] -> 5!/2!=60
print(f"Number of permutations: {count}")
用递归求解,遍历元素,取第i个元素,然后问自己:“其余项目的排列是什么”,直到没有更多的元素。
我在这里解释了解决方案:https://www.youtube.com/watch?v=_7GE7psS2b4
class Solution:
def permute(self,nums:List[int])->List[List[int]]:
res=[]
def dfs(nums,path):
if len(nums)==0:
res.append(path)
for i in range(len(nums)):
dfs(nums[:i]+nums[i+1:],path+[nums[i]])
dfs(nums,[])
return res