Re: Re: distance function

• To: mathgroup at smc.vnet.net
• Subject: [mg68805] Re: [mg68772] Re: distance function
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 19 Aug 2006 00:41:08 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200608160736.DAA06170@smc.vnet.net> <ec1aub\$ou9\$1@smc.vnet.net> <200608180712.DAA02070@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Yes, I KNOW that I'm computing the distances twice in my solution:
that's why I said it's an "extravagant" solution!

Jens-Peer Kuska wrote:
> Hi Murray,
>
> at least you should compute the distances not twice
> because the matrix is symmetric with zero diagonal ...
>
> d[{p_,p_}]:=0.0
> d[{q_,p_}]/; OrderedQ[{q,p}]:=d[{q,p}]= Norm[p - q]
> d[{q_,p_}]:=d[{p,q}]
>
> Regards
>    Jens
>
>
> Murray Eisenberg wrote:
>> If you don't mind an "extravagant" solution -- one that is conceptually
>> simple and short but is probably inefficient due to redundant
>> calculations -- then this works, I believe:
>>
>>    d[{p_, q_}] := Norm[p - q]
>>    allDistances[pts_] := Union[Flatten[Outer[d, pts, pts]]]
>>
>>
>>
>> dimmechan at yahoo.com wrote:
>>> In the book of Gaylord et al. (1996) there is one exercise which asks
>>> (see page 113)
>>>
>>> "Given a list of points in the plane, write a function that finds the
>>> set of all distances
>>> between the points."
>>>
>>> Although there is one solution, that solution makes use of the Table
>>> and Length commands.
>>>
>>> Is it a way to define the same function using Higher-Order functions
>>>
>>> Thanks in advance for any help.
>>>
>>>
>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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