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

• To: mathgroup at smc.vnet.net
• Subject: [mg113831] Re: Sort a List, in a List of Lists of Lists
• From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
• Date: Sun, 14 Nov 2010 06:11:52 -0500 (EST)

```On Sat, 13 Nov 2010, leigh.pascoe at inserm.fr wrote:

> 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
>
> LP
>
> ----------------------------------------------------------------
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>
>
>
>

Hi,

you could use

data = {{{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}}};

Map[f, data, {2}]

{{f[{1, 2}], f[{2, 1}], f[{1, 1}]}, {f[{1, 1}], f[{1, 1}],
f[{1, 2}]}, {f[{2, 1}], f[{2, 2}], f[{1, 2}]}, {f[{2, 2}],
f[{1, 2}], f[{2, 2}]}, {f[{1, 1}], f[{2, 1}],
f[{1, 2}]}, {f[{1, 2}], f[{2, 2}], f[{2, 2}]}}

Map[Sort, data, {2}]

{{{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}}}

HTH,
Oliver

```

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