There are four types of common coins in   US   currency:

   quarters   (25 cents)
   dimes   (10 cents)
   nickels   (5 cents),   and 
   pennies   (1 cent) 


There are six ways to make change for 15 cents:

   A dime and a nickel 
   A dime and 5 pennies
   3 nickels
   2 nickels and 5 pennies
   A nickel and 10 pennies
   15 pennies


Task

How many ways are there to make change for a dollar using these common coins?     (1 dollar = 100 cents).



Optional

Less common are dollar coins (100 cents);   and very rare are half dollars (50 cents).   With the addition of these two coins, how many ways are there to make change for $1000?

(Note:   the answer is larger than   232).



References

 an algorithm from the book Structure and Interpretation of Computer Programs.
 an article in the algorithmist.
 Change-making problem on Wikipedia.


func countCoins(coins, n) {
    var xs = Array.Empty(n + 1, 0)
    xs[0] = 1
    for c in coins {
        var cj = c
        while cj <= n {
            xs[cj] += xs[cj - c]
            cj += 1
        }
    }
    return xs[n]
}
 
var coins = [1, 5, 10, 25]
print(countCoins(coins, 100))