Re: generating submultisets with repeated elements

• To: mathgroup at smc.vnet.net
• Subject: [mg103799] Re: generating submultisets with repeated elements
• From: Ray Koopman <koopman at sfu.ca>
• Date: Tue, 6 Oct 2009 08:02:38 -0400 (EDT)

```Here's some "roll your own nested loops" code.
It's faster than the "accumulator" approach.

subsets[n_,1] := Transpose@{Range@n};
subsets[n_,k_] := ToExpression["Flatten[Table["<>
StringTake[ToString@Table[Which[
j==0, "i"<>ToString@#& /@ Range@k,
j==1, {"i1",n},
True, {"i"<>ToString@j,"i"<>ToString[j-1],n}],
{j,0,k}],{2,-2}]<>"],"<>ToString[k-1]<>"]"]

coinsets[s_,k_] := s[[#]]& /@ Join@@(subsets[Length@s,#]&/@Range@k)

coinSets[s_,k_] := Flatten[Table[subMultiSets[s,i],{i,k}],1];
subMultiSets[s_,k_] := smsLoop[{},s,k];
smsLoop[{ts___},{x_},1] := {{ts,x}};
smsLoop[t:{ts___},{x_,xs___},1] := Prepend[smsLoop[t,{xs},1],{ts,x}];
smsLoop[{ts___},s:{x_},k_] := smsLoop[{ts,x},s,k-1];
smsLoop[t:{ts___},s:{x_,xs___},k_] := Join[smsLoop[{ts,x},s,k-1],
smsLoop[t,{xs},k]]

coinsets[{1,3,4,9},3]
% == coinSets[{1,3,4,9},3]

{{1},{3},{4},{9},{1,1},{1,3},{1,4},{1,9},{3,3},{3,4},{3,9},{4,4},
{4,9},{9,9},{1,1,1},{1,1,3},{1,1,4},{1,1,9},{1,3,3},{1,3,4},{1,3,9},
{1,4,4},{1,4,9},{1,9,9},{3,3,3},{3,3,4},{3,3,9},{3,4,4},{3,4,9},
{3,9,9},{4,4,4},{4,4,9},{4,9,9},{9,9,9}}
True

Timing@Length@coinsets[Range@20,7]
{6.69 Second,888029}

Timing@Length@coinSets[Range@20,7]
{11.03 Second,888029}

On Oct 5, 10:58 am, David Bevan <david.be... at pb.com> wrote:
>
> Thanks for the feedback.
>
> Here are some performance results:
>
> (* Dan *)
>
> Length[multiSetsUpToK[Range[20],7]]//Timing
>
> {18.14,888029}
>
>
>
> {9.516,888029}
>
> (* Kurt *)
>
> Length[coinSetsKurt[Range[20],7]]//Timing
>
> Subsets::toomany: The number of subsets (189407486533) indicated by Subsets=
> [{1,1,1,1,1,1,1,2,2,2,<<130>>},{1,7}] is too large; it must be a machine in=
> teger.
>
> And with my code:
>
> Length[coinSets[Range[20],7]]//Timing
>
> {5.063,888029}
>
> My 'accumulator' approach seems to be quite effective!
>
> However, I'm sure this can be improved significantly with the technique use=
> d for KSubsets without too much difficulty.
>
> David %^>

```

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