Dealing with recursion depth limitation in R - r

Question

The algorithm is from https://www.math.upenn.edu/~wilf/eastwest.pdf page 16 RandomKSubsets
RandomKSubsets = function(n, k){
if (n<0 | k<0 | k<n){
return()
}
else {
if (n==0 && k==0){
return(c())
}
else {
rno = runif(1)
if (rno < n/k){
east = RandomKSubsets(n-1,k-1)
return (c(east, k))
}
else{
west = RandomKSubsets(n,k-1)
return(west)
}
}
}
}
Running the program with k=4000 and n=1200 I run into recursion depth limit. I tried options(expressions=500000) but it's not enough for the algorithm. How can I run this code for my variables?

Answer 1

This is close to tail recursion: the only recursive calls are in the return statements. This blog: http://blog.moertel.com/posts/2013-05-11-recursive-to-iterative.html describes how to change such functions into loops. I followed the mostly mechanical process described there, and came up with this version:
RandomKSubsetsLoop = function(n, k) {
acc <- NULL
while (TRUE) {
if (n<0 | k<0 | k<n){
return(acc)
}
else {
if (n==0 && k==0){
return(acc)
}
else {
rno = runif(1)
if (rno < n/k){
acc <- c(k, acc)
k <- k - 1
n <- n - 1
next
}
else{
k <- k - 1
next
}
}
}
break
}
}
I haven't tested it extensively, but it produces the same result as the original in this test:
set.seed(1)
RandomKSubsets(5, 10)
# [1] 1 3 6 9 10
set.seed(1)
RandomKSubsetsLoop(5, 10)
# [1] 1 3 6 9 10
You'll probably want to do more extensive testing, and read the blog to make sure I've done things as it describes.
By the way, there are other algorithms to do this sampling, e.g. the one described in
AUTHOR="McLeod, A.I. and Bellhouse, D.R. ",
YEAR = 1983,
TITLE="A convenient algorithm for drawing a simple random sample",
JOURNAL="Applied Statistics",
VOLUME="32",
PAGES="182-184"
That one is based on a loop by design, and has the advantage that you don't need to know the population size (k in your notation) in advance: you just keep updating your sample until there are no more items to process.