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Re: How to find the difference between two lists (opposite of union[]?)
*To*: mathgroup at smc.vnet.net
*Subject*: [mg119909] Re: How to find the difference between two lists (opposite of union[]?)
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Wed, 29 Jun 2011 05:28:31 -0400 (EDT)
data = RandomInteger[{1, 1000}, 1000];
compl = Complement[r = Range[1000], Union[data]];
Union[data, compl] === r
True
Bob Hanlon
---- "McHale wrote:
=============
I have been working through a neat book called Mathematica(r): A Problem-Centered Approach<http://www.amazon.com/Mathematica%C2%AE-Problem-Centered-Approach-Undergraduate-Mathematics/dp/1849962502/ref=sr_1_2?ie=UTF8&qid=1309181549&sr=8-2>. I have a problem I would like to know if there is a more elegant solution. I would think involving set theory, but I can't seem to (embarrassingly) find it.
I want to generate 1000 random integers between 1 and 1000. Then find out what numbers between 1 and 1000 were not generated.
(* Generate random list of 1000 numbers with range 1-1000*)
mList=RandomInteger[{1,1000},1000] //Sort;
(* Find out what numbers were omitted in the range 1-1000*)
(* Make a list of numbers 1-1000 with position of each within original array *)
mList=Table[{i,Position[mList,i] //Flatten},{i,1,1000}];
(* select numbers with no position in original array (musical chairs) *)
Select[mList,Length[#[[2]]]==0&][[All,1]]
This works creating a lot of extra array in the process. Just wanted to ask what are the methods you guys would use to solve this?
A funny (non-working) way of stating the same thing would be:
(* Generate random list of 1000 numbers with range 1-1000*)
mList=RandomInteger[{1,1000},1000] //Sort;
Solve[ Join[mList,mDiff]==Range[1000],mDiff]
Thanks,
Paul
Paul McHale | Electrical Engineer, Energetics Systems | Excelitas Technologies Corp.
Phone: +1 937.865.3004 | Fax: +1 937.865.5170 | Mobile: +1 937.371.2828
1100 Vanguard Blvd, Miamisburg, Ohio 45342-0312 USA
Paul.McHale at Excelitas.com<mailto:Paul.McHale at perkinelmer.com>
www.excelitas.com<http://www.excelitas.com>
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