什么函数可以输出一个集合所有元素的不同排列

ggggwhw

有没有什么函数可以直接输出一个集合的所有元素的不同排列,
比如原集合为arr={1,2,3,4},要求输出的结果类似于
{{1,2,3,4},
{1,2,4,3},
{1,3,2,4},
{1,3,4,2},
{1,4,2,3},
{1,4,3,2},
{2,1,3,4},
{2,1,4,3},
{2,3,1,4},
{2,3,4,1},
{2,4,1,3},
{2,4,3,1},
{3,1,2,4},
{3,1,4,2},
{3,2,1,4},
{3,2,4,1},
{3,4,1,2},
{3,4,2,1},
{4,1,2,3},
{4,1,3,2},
{4,2,1,3},
{4,2,3,1},
{4,3,1,2},
{4,3,2,1}}
要求效率相对高些,但是内存占有量不能太高,两者出现矛盾时,首先考虑内存不能太高:比如下面的代码是我现在不喜欢但是不得不用的,我想改变这种状况.

1. 
   
2. 
   
3. [code]In[1]:= arr = Range[4];
   
4. 
   
5. n = Length@arr;
   
6. 
   
7. Union@Select[Tuples[arr, n], Sort@# == arr &]
   
8. 
   
9. Out[3]= {{1, 2, 3, 4}, {1, 2, 4, 3}, {1, 3, 2, 4}, {1, 3, 4, 2}, {1,
   
10. 4, 2, 3}, {1, 4, 3, 2}, {2, 1, 3, 4}, {2, 1, 4, 3}, {2, 3, 1,
    
11. 4}, {2, 3, 4, 1}, {2, 4, 1, 3}, {2, 4, 3, 1}, {3, 1, 2, 4}, {3, 1,
    
12. 4, 2}, {3, 2, 1, 4}, {3, 2, 4, 1}, {3, 4, 1, 2}, {3, 4, 2, 1}, {4,
    
13. 1, 2, 3}, {4, 1, 3, 2}, {4, 2, 1, 3}, {4, 2, 3, 1}, {4, 3, 1,
    
14. 2}, {4, 3, 2, 1}}

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ggggwhw

下面的情况来验证你的代码还正确吗?
arr={1,1,2,3}时,
要求输出结果类似于:
{{1, 1, 2, 3}, {1, 1, 3, 2}, {1, 2, 1, 3}, {1, 2, 3, 1}, {1, 3, 1,
  2}, {1, 3, 2, 1}, {2, 1, 1, 3}, {2, 1, 3, 1}, {2, 3, 1, 1}, {3, 1,
  1, 2}, {3, 1, 2, 1}, {3, 2, 1, 1}}
参考代码:

1. In[30]:=
   
2. arr = {1, 1, 2, 3};
   
3. n = Length@arr;
   
4. Union@Select[Tuples[arr, n], Sort@# == arr &]
   
5. 
   
6. Out[32]= {{1, 1, 2, 3}, {1, 1, 3, 2}, {1, 2, 1, 3}, {1, 2, 3, 1}, {1,
   
7.   3, 1, 2}, {1, 3, 2, 1}, {2, 1, 1, 3}, {2, 1, 3, 1}, {2, 3, 1,
   
8.   1}, {3, 1, 1, 2}, {3, 1, 2, 1}, {3, 2, 1, 1}}

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FreddyMusic

排列

1. 
   
2. Permutations[Range[4]]
   

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ggggwhw

FreddyMusic 三楼给的代码好像是我想要的Mathematica 专为排列给出的函数,但是Permutations只能用在最多10个不同元素上,好像有些少哦.而且也是很占内存的.
而我给出的代码好像只能给出6至7个元素的情况,而且我的代码在占用内存方面是不区分元素是否相同的.就这一点而言Permutations相对好些,但是我觉得10个元素似乎有些少.

jimogsh

元素多了排列数肯定多，占内存多也是必然的啊

FreddyMusic

J is right for Permutations, but we can reorgnized the data into smaller group and feed the memory slowly.