Question

Can somebody point me to some reading on some algorithm that given a set n, will place it’s elements in a bigger set m, evenly spaced (as much as possible). I plan to interpolate for the remaining values.

so I have a set of 3 elements which contains

    1 ,5 ,6 

and I want to distribute it in a dataframe of 10 slots as evely as possible with the 1st and last elements being 1st and last accordingly in the new set:

    1 [] [] [] 5 [] [] [] [] 6

Thanks in advance.

PS. I am trying to achieve this with R

Answer 1

I think you should use the term “vector” which, in R anyway, has the notion of positions and length which are needed for this problem. (Mathematical sets are unordered, so have no positional interpretation and R does have set operators and functions.)

# Make up an empty vector:
vec <- vector("numeric", length=10)
# create a vector of items to place
 items <- c(1,5,6)
#Put the first one in the first empty "slot" and the last in the last/
 vec[1] <- items[1]
 vec[length(vec)] <- items[length(items)]
#Now find a positions for the remaining element(s)
 seq(1,length(vec), by=length(vec)/(length(items)-1))[-c(1,length(items))]
#[1] 6
# And place them (or it in this case) ....
  vec[ seq(1,length(vec), by=length(vec)/(length(items)-1))[
                        -c(1,length(items))] ] <- 
                              items[ -c(1,length(items)) ] 
 vec
# [1] 1 0 0 0 0 5 0 0 0 6