Split number in random parts with constrain-CodePudding

I am trying to find a smart way for splitting a number (eg 50) into a number of random parts (e.g. 20) BUT under the constrain that each generated random value cannot be greater than a specific value (e.g. 4).

So for example in this case I would expect as an output a vector of 20 values of which sum is 50 but none of the 20 values is greater than 4 (e.g 2.5, 1.3, 3.9 etc..)

I had a look at similar questions but from what i see these are dealing with splitting a number into equal or random parts but none of them included the constrain, which is the bit i am stuck with! Any help would be higly appreciated!!

CodePudding user response：

set.seed(42)
repeat {
  vec <- runif(20)
  vec <- 50 * vec/sum(vec)
  if (all(vec <= 4)) break
} 
sum(vec)
# [1] 50
# [1] 50
vec
#  [1] 3.7299658 3.8207653 1.1666852 3.3860087 2.6166080 2.1165253 3.0033133 0.5490801 2.6787741 2.8747815 1.8663641
# [12] 2.9320577 3.8109668 1.0414675 1.8849202 3.8327490 3.9885516 0.4790347 1.9367197 2.2846613

Note: it is feasible with certain combinations that this could run "forever" (improbable to find a vector where all values are under 4). This works well here, but if you (say) change 20 to 10, it will never succeed (and will loop forever).

CodePudding user response：

Another possible solution (by limiting the range of the interval of the uniform distribution, it is more likely to get a solution):

set.seed(123)

x <- 50
n <- 20
threshold <- 4

gotit <- F
while (!gotit)
{  
  v <- round(runif(n, 0, x/(n/2)), 1)
  
  if (sum(v) == x & all(v <= threshold))
    gotit <- T
}

v

#>  [1] 2.2 3.0 2.2 3.0 3.0 0.5 2.4 2.5 2.7 4.0 1.0 1.7 1.2 2.8 2.9 3.3 2.9 3.0 3.0
#> [20] 2.7