3

I made a recursion function f(s,x) for the subset sum problem, which is able to produce all unique combinations that sum up to the target sum 's' when picking elements from the set of values x.

For example, assuming x <- c(2,4,8,10), and s <- 10 denotes the target sum, with the function f below

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(s-k, x[x<= s-k], min(k,head(x[x<=s-k],1)), c(r,k))),recursive = F)) 
  }
}

I can get all combinations for subset sum, i.e., 

> f(s,x)
[[1]]
[1] 10

[[2]]
[1] 8 2

[[3]]
[1] 4 4 2

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

[[5]]
[1] 2 2 2 2 2

The function above works well with integers for x and s. However, when I scaled down both x and s by 10, i.e., floating-point numbers for x and s, then the output becomes the undesired ones:

> f(s/10,x/10)
[[1]]
[1] 1

but the desired output should be like

> Map(function(v) v/10, f(s,x))
[[1]]
[1] 1

[[2]]
[1] 0.8 0.2

[[3]]
[1] 0.4 0.4 0.2

[[4]]
[1] 0.4 0.2 0.2 0.2

[[5]]
[1] 0.2 0.2 0.2 0.2 0.2

I suspect there must be some wring for my function f when dealing with floating-point numbers, but failed to fix it after several trials. Can anyone help me address this issue without big changes for the function f?

Appreciate any help in advance!

ThomasIsCoding
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1 Answers1

2

You can use round in your subtraction and set the decimal points 

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, 4), x[x<= round(s-k, 4)], min(k,head(x[x<= round(s-k, 4)],1)), c(r,k))),recursive = F)) 
  }
}

f(s/10,x/10)

Which returns the desired output:

[[1]]
[1] 1

[[2]]
[1] 0.8 0.2

[[3]]
[1] 0.4 0.4 0.2

[[4]]
[1] 0.4 0.2 0.2 0.2

[[5]]
[1] 0.2 0.2 0.2 0.2 0.2
Matt
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