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.


fn make_change(coins: &[usize], cents: usize) -> usize {
    let size = cents + 1;
    let mut ways = vec![0; size];
    ways[0] = 1;
    for &coin in coins {
        for amount in coin..size {
            ways[amount] += ways[amount - coin];
        }
    }
    ways[cents]
}
 
fn main() {
    println!("{}", make_change(&[1,5,10,25], 100));
    println!("{}", make_change(&[1,5,10,25,50,100], 100_000));
}