R Bridge - Week 2 Assignment:

Implement code to calculate \(\binom{n}{r} = \frac{n!}{(n-r)!-r!}\)

n_choose_r

The function checks that n and r are positive integers and that n > r. Outside of structuring the equation and checking for erroneous inputs, calc_fact will do most of the heavy lifting.

n_choose_r <- function(n = 0, r = 0) {
    if (n != round(n) || r != round(r) || r < 0 || n < 0 || r > n) {
        return("Undefined: n & r must be positive integers and n must be greater than r")
    } else {
        return(calc_fact(n)/(calc_fact(n - r) * calc_fact(r)))
    }
}

calc_fact

The funciton uses recursion to calcualte the factorial of “n”. Ideally, this should be a private funciton as it is assumed that n_choose_r is the one having access to it after having checked for possible errors in the input.

calc_fact <- function(n) {
    if (n < 2) {
        return (1)
    } else {
        return (n * calc_fact(n - 1))
    }
}

Examples:

# --------- Test Cases ---------
# r > n
n <- 3
r <- 52
sprintf("%s!/((%s-%s)!*%s!) = %s.", n, n, r, r, n_choose_r(n,r))

## [1] "3!/((3-52)!*52!) = Undefined: n & r must be positive integers and n must be greater than r."

# n < 0
n <- -52
r <- 3
sprintf("%s!/((%s-%s)!*%s!) = %s.", n, n, r, r, n_choose_r(n,r))

## [1] "-52!/((-52-3)!*3!) = Undefined: n & r must be positive integers and n must be greater than r."

# Combos of a five card hand
n <- 52
r <- 5
sprintf("%s!/((%s-%s)!*%s!) = %s.", n, n, r, r, n_choose_r(n,r))

## [1] "52!/((52-5)!*5!) = 2598960."

# Combos of creating a group of 5 out of 12 people
n <- 12
r <- 5
sprintf("%s!/((%s-%s)!*%s!) = %s.", n, n, r, r, n_choose_r(n,r))

## [1] "12!/((12-5)!*5!) = 792."