Re: List processing

• To: mathgroup at smc.vnet.net
• Subject: [mg37239] Re: List processing
• From: daiyanh at earthlink.net (Daitaro Hagihara)
• Date: Fri, 18 Oct 2002 05:16:57 -0400 (EDT)
• References: <aokbp7\$afv\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <aokbp7\$afv\$1 at smc.vnet.net>, John Leary <leary at paradise.net.nz>
wrote:

>Greetings
>
>This problem can be solved by conventional programming, but I wonder if
>there is an elegant Mathematica solution ?
>
>A list contains pairs of values, with each pair representing the lower and
>upper edge of a sub-range.  Some of the sub-ranges partially overlap, some
>fully overlap, others don't overlap at all.  The problem is to produce a
>second list that contains the overall upper and lower edges of the
>overlapping sub-ranges.
>
>A simple example :  {{100,200},{150,250},{120,270},{300,400}}  would result
>in {{100,270},{300,400}}.
>
>In the real case, the input list has several hundred elements and the
>output list typically has five elements.
>
>I have a working solution based on loops, but there must be a more elegant
>one.  I would be very grateful for any suggestions.

Block[{data = {{100,200},{150,250},{120,270},
{300,400}}},
data = Sort[data,#[[1]]<#2[[1]]&];
{{data[[1,1]],
Fold[If[#<#2[[1]],#,Max[#,#2[[2]]]]&,
data[[1,2]],Rest[data]]},
{Fold[If[#>#2[[2]],#,Min[#,#2[[1]]]]&,
(data=Reverse@data)[[1,1]],Rest[data]],
data[[1,2]]}}]

-->
{{100, 270}, {300, 400}}

I haven't tested too extensively.  The so-called
"Mathematica way" is illustrated by the use of
Fold function to process data, without which you
must resort to conventional looping.

DH

```

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