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Re: Using a list as a variable
*To*: mathgroup at smc.vnet.net
*Subject*: [mg67082] Re: Using a list as a variable
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Fri, 9 Jun 2006 01:06:52 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, UK
*References*: <e68qc9$d2i$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Bonny Banerjee wrote:
> I would like to use a list (or set) as a variable. I am working on the
> Subset-Sum problem. Given a set S of integers, the goal is to find a subset
> of S (say Q) whose elements add to a given integer x. This is how I would
> like to define the function:
>
> SubsetSum(S, x) := {Q such that Q is a subset of S and sum of the elements
> of Q is x}
>
> In Mathematica functional programming language, this would look like:
>
> SubsetSum[S_, x_] := Reduce[Q \[Element] Subsets[S] && Sum[Q,
> {i,1,Length[Q]}]==x, Q, Reals]
>
> Now when I try to evaluate SubsetSum[{1, 3, 5, 2, 7, 100, 6}, 101], the
> output is as follows:
>
> Reduce : : naqs :
> \[Exists]{Q} Q is not a quantified system of equations and
> inequalities. More ...
>
> Out[365]= Reduce[Q, False, Q, Reals]
>
>
> I guess, Mathematica is not being able to understand from my statement that
> the variable Q is not an atom but a list. But it should since I stated that
> Q is an element of the power set of S.
>
> Note that I know how to write a function for Subset-Sum using a Module. But
> I am interested in functional programming, similar to the format shown
> above.
>
> Any help would be appreciated.
>
> Thanks much,
> Bonny.
>
>
Hi Bonny,
What about the following function (see In[1])? You wanted functional
programming, you've got it :-)]
In[1]:=
subsetSum[S_,x_]:=Extract[#,Position[Plus@@@#,x]]&@Rest@Subsets@Union@S
In[2]:=
subsetSum[{1,3,5,2,7,100,6},101]
Out[2]=
{{1,100}}
In[3]:=
mySet=Range[3]
Out[3]=
{1,2,3}
In[4]:=
subsetSum[mySet,3]
Out[4]=
{{3},{1,2}}
In[5]:=
subsetSum[mySet,12]
Out[5]=
{}
In[6]:=
subsetSum[mySet,0]
Out[6]=
{}
In[7]:=
mySet=Table[Random[Integer,{1,4}],{10}]
Out[7]=
{2,1,4,2,1,3,2,3,2,3}
In[8]:=
Subsets[mySet]//Length
Out[8]=
1024
In[9]:=
subsetSum[mySet,6]
Out[9]=
{{2,4},{1,2,3}}
By the way, I might be pessimistic but I do not believe that Reduce is
capable of doing what you are looking for.
Best regards,
Jean-Marc
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