All possible combinations of a set that sum to a target value

Question

I have an input vector such as:

weights <- seq(0, 1, by = 0.2)

I would like to generate all the combinations of weights (repeats allowed

Answer 1

If you are planning to implement it using base R only, then an alternative approach is the recursion.

Assuming x <- c(1,2,4,8), and s <- 9 denotes the target sum, then the following function can get you there:

f <- function(s, x, xhead = head(x,1), r = c()) {
  if (s == 0) {
    return(list(r))
  } else {
    x <- sort(x,decreasing = T)
    return(unlist(lapply(x[x<=min(xhead,s)], function(k) f(round(s-k,10), x[x<= round(s-k,10)], min(k,head(x[x<=round(s-k,10)],1)), c(r,k))),recursive = F)) 
  }
}

which f(s,x) gives:

[[1]]
[1] 8 1

[[2]]
[1] 4 4 1

[[3]]
[1] 4 2 2 1

[[4]]
[1] 4 2 1 1 1

[[5]]
[1] 4 1 1 1 1 1

[[6]]
[1] 2 2 2 2 1

[[7]]
[1] 2 2 2 1 1 1

[[8]]
[1] 2 2 1 1 1 1 1

[[9]]
[1] 2 1 1 1 1 1 1 1

[[10]]
[1] 1 1 1 1 1 1 1 1 1

Note: round(*,digits=10) is used to take care of floating-point numbers, where digits should adapt to decimals of input.