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Re: List processing

  • To: mathgroup at
  • Subject: [mg37219] Re: List processing
  • From: tdelling at (Tim Dellinger)
  • Date: Thu, 17 Oct 2002 00:08:44 -0400 (EDT)
  • Organization: University of Illinois at Urbana-Champaign
  • References: <aokbp7$afv$>
  • Sender: owner-wri-mathgroup at

John Leary <leary at> writes:

>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.

If the numbers are all integers less than 401, as in your example,
then you could start with the list {1,2,3,...400} and compare each
number to every pair in your list-of-pairs.  If there exists no pair
that the given number falls between (inclusive), replace the number with zero.

Converting the resulting list to the output you want "is an exercise
for the reader" (clever replacement rules will do it easily).

Tim Dellinger                      
tdelling at

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