On Sat, Feb 04, 2012 at 08:45:20AM +0100, Marc Girondot wrote:
> 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
Hi.
The number of these placements is choose(n+k-1, k-1), which follows
from the representation of each placement by a sequence of balls and
boundaries between boxes, where "o" is a ball and "|" is a boundary.
For example (2, 0, 0) corresponds to "oo||" and
(1, 0, 1) is "o||o". Since this is a bijection, we can use it
for counting and also for generation.
n <- 2
k <- 3
# generate all possible positions of the boundaries
x <- combn(n+k-1, k-1)
# compute the number of balls in each box
a <- cbind(0, diag(k)) - cbind(diag(k), 0)
t(a %*% rbind(0, x, n+k) - 1)
[,1] [,2] [,3]
[1,] 0 0 2
[2,] 0 1 1
[3,] 0 2 0
[4,] 1 0 1
[5,] 1 1 0
[6,] 2 0 0
Hope this helps.
Petr Savicky.
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
