Hi "the list" !
I would like to create a dataframe that answer to : "all the
combinations of the different way to distribute n indistinguishable
balls into k distinguishable boxes". Let take an example: 2 balls in 3
boxes:
Box1 Box2 Box3
2 0 0
1 1 0
1 0 1
0 2 0
0 1 1
0 0 2
I have made a script (see script below) using expand.grid but it
generates huge number of unnecessary solutions that I must filter. And
when the number of balls or box is large, the size of the dataframe can
be huge.
Has someone a solution for this problem ?
Thanks a lot
(I don't play with balls and box... it is a way to manage uncertainty. I
know that 2 events have occured during a period of 3 days but I don't
know when exactly)
Marc
Nballs<-2
nbbox<-3
# The number of different ways to distribute n indistinguishable balls
# into k distinguishable boxes is C(n+k-1,k-1).
# nb<-choose(Nballs+nbbox-1,nbbox-1)=dim(tb)[1]
if (Nballs==0) {
tb<-as.data.frame(matrix(rep(0, nbbox), ncol=nbbox))
} else {
es<-list(0:(Nballs-1))
es<-rep(es, nbbox)
tb<-expand.grid(es)
tb<-tb[apply(tb, 1, sum)==Nballs,1:nbbox]
# trick to have smaller tb after expand.grid
tbfull<- as.data.frame(matrix(rep(0, nbbox*nbbox), ncol=nbbox,
dimnames=list(NULL, names(tb))))
for(i in 1:nbbox) {tbfull[i, i]<-Nballs}
tb<-rbind(tb, tbfull)
}
Result:
> tb
Var1 Var2 Var3
4 1 1 0
6 1 0 1
7 0 1 1
41 2 0 0
5 0 2 0
61 0 0 2
--
__________________________________________________________
Marc Girondot, Pr
Laboratoire Ecologie, Systématique et Evolution
Equipe de Conservation des Populations et des Communautés
CNRS, AgroParisTech et Université Paris-Sud 11 , UMR 8079
Bâtiment 362
91405 Orsay Cedex, France
Tel: 33 1 (0)1.69.15.72.30 Fax: 33 1 (0)1.69.15.73.53
e-mail: marc.giron...@u-psud.fr
Web: http://www.ese.u-psud.fr/epc/conservation/Marc.html
Skype: girondot
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