Exercise 1: n!

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. 0! = 1, by definition.

A naive approach, without the use of a recurrence relation, may use a for-loop or a while-loop:

f_naive <- function(n) {
    
  result <- 1
  for (i in 0:n) {
    if (0 < i)
      result <- result * i
  }

  return(result)
}

After pasting the code in R, you can test it e.g. byf_naive(3), which should return 6.

The goal is to write a recursive function f(n) that implements the factorial function n!. You can start using the following template.

Task

f <- function(n) {
  if ("Task-0" == "Put base case here")
    return(1)
  else
    return("Task-1: put recursion here")
}

# Test your solution
f(0) # Should return 1
f(3) # Should return 6
if (f_naive(7) == f(7)) cat("Good job!") else cat("Some work to do.")

Solution

f <- function(n) {
  if (0 == n)
    return(1)
  else
    return(n * f(n-1))
}

# Test your solution
f(0) # Should return 1
f(3) # Should return 6
if (f_naive(7) == f(7)) cat("Good job!") else cat("Some work to do.")

One may argue that the recursive implementation is more intuitive. Don't you think so?