def f(ms: List[Int], n: Int): Int = ms match {
  case h :: t =>
    if (h > n) 0 else if (n == h) 1 else f(ms, n - h) + f(t, n)
  case _ => 0
}
val r = f(List(1, 2, 5, 10, 20, 50, 100, 200), 200)

final static int TOTAL = 200;

public static void main(String[] args) {
    int[] coins = {1, 2, 5, 10, 20, 50, 100, 200};
    int[] ways = new int[TOTAL + 1];
    ways[0] = 1;

    for (int coin : coins) {
        for (int j = coin; j <= TOTAL; j++) {
            ways[j] += ways[j - coin];
        }
    }

    System.out.println("Result: " + ways[TOTAL]);
}

class IterationForCoin(stream: Stream[Int], coin: Int) {
  val (lower, higher) = stream splitAt coin
  val next: Stream[Int] = lower #::: (higher zip next map { case (a, b) => a + b })
}
val coins = List(1, 2, 5, 10, 20, 50, 100, 200)
val result = coins.foldLeft(1 #:: Stream.fill(200)(0)) { (stream, coin) =>
  new IterationForCoin(stream, coin).next
} last

import scalaz._
import Scalaz._

val memo = immutableHashMapMemo[(List[Int], Int), Int]
def f(ms: List[Int], n: Int): Int = ms match {
  case h :: t =>
    if (h > n) 0 else if (n == h) 1 else memo((f _).tupled)(ms, n - h) + memo((f _).tupled)(t, n)
  case _ => 0
}
val r = f(List(1, 2, 5, 10, 20, 50, 100, 200), 200)