# 15 How to put n things in m boxes

How to put n things randomly and uniformly into m boxes, this is an interesting problem and its solution is useful for our work. There are probably many ways to solve this problem; here is my way—I will use gtools::rdirichlet() (For details about the Dirichlet distribution, see https://en.wikipedia.org/wiki/Dirichlet_distribution)

R code:

split_n <- function(n, m)
{n <- as.integer(abs(n))
m <- as.integer(abs(m))

if(n == 0L | m < 2L) print("n must be postive and m must be larger than 2.")
else
{the_weights <- gtools::rdirichlet(1, rep(1, m))
# Sometimes the following weighting is useful
# the_weights <- gtools::rdirichlet(1, abs(rnorm(m)))
the_weights <- as.vector(the_weights)
the_split <- floor(n * the_weights) # always rounding down
left_number <- n - sum(the_split)
# randomly choose the positions where extra 1 will be added to the_split
the_position <- sample(1:m, left_number)
the_split[the_position] <- the_split[the_position] + 1
return(the_split)
}
}

(split_n(10, 4))
## [1] 1 1 5 3