Re: Using a list as a variable

*To*: mathgroup at smc.vnet.net*Subject*: [mg67087] Re: [mg67069] Using a list as a variable*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 9 Jun 2006 01:07:22 -0400 (EDT)*References*: <200606080854.EAA12414@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 8 Jun 2006, at 17:54, 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. > > Reduce solves (or "reduces" ) algebraic and some transcendental (e.g. trygonometric) equations and inequalities. Your problem is not of this kind. One way to solve it: SubsetSum[S_, x_] := Select[Subsets[S], Total[#] == x &] SubsetSum[{1, 3, 5, 2, 7, 100, 6}, 101] {{1, 100}} SubsetSum[{1, 3, 5, 2, 7, 100, 6}, 105] {{5, 100}, {3, 2, 100}} Andrzej Kozlowski Tokyo, Japan

**References**:**Using a list as a variable***From:*"Bonny Banerjee" <banerjee@cse.ohio-state.edu>