Re: Sort a List, in a List of Lists of Lists

• To: mathgroup at smc.vnet.net
• Subject: [mg113803] Re: Sort a List, in a List of Lists of Lists
• From: Albert Retey <awnl at gmx-topmail.de>
• Date: Sun, 14 Nov 2010 06:06:35 -0500 (EST)
• References: <ibl9g2\$b8a\$1@smc.vnet.net>

```Am 13.11.2010 06:59, schrieb leigh.pascoe at inserm.fr:
> Dear Mathgroup,
>
> I have a lsit of Lists of Lists:
>
> {{{1,2},{2,1},{1,1}},{{1,1},{1,1},{1,2}},{{2,1},{2,2},{1,2}},{{2,2},{1,2},{2,2}},{{1,1},{2,1},{1,2}},{{1,2},{2,2},{2,2}}}
>
> I would like to sort the elements in the lowest level of brackets to give
>
> {{{1, 2}, {1, 2}, {1, 1}}, {{1, 1}, {1, 1}, {1, 2}}, {{1, 2}, {2,
>     2}, {1, 2}}, {{2, 2}, {1, 2}, {2, 2}}, {{1, 1}, {1, 2}, {1,
>     2}}, {{1, 2}, {2, 2}, {2, 2}}}
>
> i.e retaining the same structure with the paired elements in the
> original order. I can't seem to get the syntax right to do this apart
> from the obvious
>
> {{Sort[{1, 2}], Sort[{2, 1}], Sort[{1, 1}]}, {Sort[{1, 1}],
>    Sort[{1, 1}], Sort[{1, 2}]}, {Sort[{2, 1}], Sort[{2, 2}],
>    Sort[{1, 2}]}, {Sort[{2, 2}], Sort[{1, 2}],
>    Sort[{2, 2}]}, {Sort[{1, 1}], Sort[{2, 1}],
>    Sort[{1, 2}]}, {Sort[{1, 2}], Sort[{2, 2}], Sort[{2, 2}]}}
>
> I must have a blind spot for the correct command. Can someone please
> help me with what should be a straightforward sort. As I want to carry
> this out on several hundred thousand pairs I need a more efficient

here are three ways:

lst = {{{1, 2}, {2, 1}, {1, 1}}, {{1, 1}, {1, 1}, {1, 2}}, {{2,
1}, {2, 2}, {1, 2}}, {{2, 2}, {1, 2}, {2, 2}}, {{1, 1}, {2,
1}, {1, 2}}, {{1, 2}, {2, 2}, {2, 2}}}

goal = {{{1, 2}, {1, 2}, {1, 1}}, {{1, 1}, {1, 1}, {1, 2}}, {{1,
2}, {2, 2}, {1, 2}}, {{2, 2}, {1, 2}, {2, 2}}, {{1, 1}, {1,
2}, {1, 2}}, {{1, 2}, {2, 2}, {2, 2}}}

In[86]:= res1 = Map[Sort, lst, {2}]

In[88]:= res2 = Map[Sort, lst, {-2}]

In[89]:= res3 = (lst /. (l:{__Integer}) :> Sort[l])

In[90]:= res1 == res2 == res3 == goal

Out[90]= True

hth,

albert

```

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