       Re: Algorithm Questions

• To: mathgroup at smc.vnet.net
• Subject: [mg29402] Re: Algorithm Questions
• From: Mark Fisher <mark at markfisher.net>
• Date: Sat, 16 Jun 2001 22:43:50 -0400 (EDT)
• References: <9gf01l\$7lj\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Try this:

SetAttributes[RandomWithoutReplacement, HoldFirst]

RandomWithoutReplacement[ran_, n_Integer?Positive] :=
Module[{list = {}, r},
While[Length[list] < n, If[FreeQ[list, r = ran], AppendTo[list, r]]];
list
]

Needs["DiscreteMath`Permutations`"]

RandomWithoutReplacement[RandomPartition, 100]

--Mark.

Hu Zhe wrote:
>
> Hi,
> I am wondering that if Mathematica has lazy-evaluation features. Say I
> am going to extract 100 lists from the permutation lists of {1,
> 2,...,100} (Permutation[Range]) randomly.
>
> If I program like this:
>
> largeList = Permutation[Range];
>
> indx = Table[Random[Integer, {1, 100!}], {100}];
>
> Part[largeList, indx]
>
> the program is very slow, since it works out all the 100! elements for
> the largeList, while I only need 100 items from it.
>
> Can I program like this ? Say,
>
> take 100 (somePermutationFunction 100)
>
> so that the permutation stops after 100 lists were taken. (I learned
> that it's called lazy-evaluation from Haskell.)
>
> The second question is that:
>
> I want the 100 lists randomly taken to be all different.
>
> So I program this way:
>
>  While[Length[a] != 100,
>       a = (Table[Random[Integer, {1, n!}], {100}] // Union)];
>
> there must be more efficient solutions, especially to combine the
> solution with the first question?
>
> So my slow program is like this, deeply welcome suggestions to improve
> it:
>
> randomList[n_, k_] :=
>   Module[{a},
>     While[Length[a] != k,
>       a = (Table[Random[Integer, {1, n!}], {k}] // Union)];
>     Part[Permutations[Range[n]], a]]
>
> Sincerely,
> Hu Zhe

```

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