How to find the difference between two lists (opposite of union[]?)

• To: mathgroup at smc.vnet.net
• Subject: [mg119887] How to find the difference between two lists (opposite of union[]?)
• From: "McHale, Paul" <Paul.McHale at excelitas.com>
• Date: Tue, 28 Jun 2011 07:55:27 -0400 (EDT)

```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
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Paul.McHale at Excelitas.com<mailto:Paul.McHale at perkinelmer.com>
www.excelitas.com<http://www.excelitas.com>

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