Combining vectorization and recursion in R?

Question

I am trying to combine vectorization and recursion in this implementation of the factorial function:

fac <- function(n) {
  ifelse(n == 1, 1, n * fac(n-1))
}

fac(6)      #720
fac(c(6,7)) #Error: evaluation nested too deeply: infinite recursion / options(expressions=)?
            #Error during wrapup: evaluation nested too deeply: infinite recursion / options(expressions=)?

Although ifelse is the vectorized version of if this doesn't work (see errors).

My question
1. Why doesn't it work?
2. How can I make it work?

Edit: I don't really see the connection to the proposed duplicate because the above function doesn't even work for a vector of two!

Answer 1

Let's look what happens:

fac <- function(n) {
  ifelse(n == 1, 1, {message(paste(n-1, collapse = ",")); 
                     stopifnot(n > 0); n * fac(n-1)})
}

fac(4:5)
#3,4
#2,3
#1,2
#0,1
#-1,0
# Show Traceback
# 
# Rerun with Debug
# Error: n > 0 are not all TRUE 

As you see, the condition is never TRUE for all elements of n and thus, recursion never stops.

If all elements of n are equal, it works:

fac(c(5,5))
#4,4
#3,3
#2,2
#1,1
#[1] 120 120

With a small adjustment your function can work for unequal elements of n, too:

fac <- function(n) {
  ifelse(n <= 1, 1, n * fac(n-1))
}
fac(1:5)
#[1]   1   2   6  24 120