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

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  • Subject: [mg119900] Re: How to find the difference between two lists (opposite of union[]?)
  • From: "W. Craig Carter" <ccarter at mit.edu>
  • Date: Wed, 29 Jun 2011 05:26:54 -0400 (EDT)
  • References: <201106281155.HAA21477@smc.vnet.net>

Hello Paul,
You may get other responses, but this should work for you:

numbers = RandomInteger[{1, 1000}, {1000}];
Complement[Range[1000], numbers]

This may be interesting to you as well:

Histogram[Length /@ (Union /@ RandomInteger[{1, 1000}, {1000, 1000}])]

On 28 Jun,   2011, at 7:55 AM, McHale, Paul 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.
>
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>
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