compiler error message when using State monad for memoization - scala

Question

I have a problem to make a working version of the Euler project problem 31 with the use of State trait (inspired from scalaz)
First, I have a solution with a mutable HashMap for memoization. It works but i would like to use the State monad, to understand it and to improve my skills.
I have used it with the fibonacci example, but when i attempt to apply the same technique to my case, i have a compiler error that i don't understand.
I use this implementation for State :
trait State[S, A] {
val run: S => (S, A)
def apply(s: S): (S, A) = run(s)
def eval(s: S): A = run(s)._2
def map[B](f: A => B): State[S, B] =
State { s: S =>
val (s1, a) = run(s)
(s1, f(a))
}
def flatMap[B](f: A => State[S, B]): State[S, B] =
State { s: S =>
val (s1, a) = run(s)
f(a)(s1)
}
}
object State {
def apply[S, A](f: S => (S, A)): State[S, A] = new State[S, A] {
final val run = f
}
def init[S, A](a: A) = State { s: S => (s, a) }
def update[S, A](f: S => S): State[S, Unit] = State { s: S => (f(s), ()) }
def gets[S, A](f: S => A): State[S, A] = State { s: S => (s, f(s)) }
}
my attempt to use it is here :
val coins = List(1, 2, 5, 10, 20, 50, 100, 200)
type MemoKey = (List[Int], Int)
type MemoType = Map[MemoKey, Int]
def ways(listCoins: List[Int], amount: Int): Int = {
def ways_impl(coins: List[Int], sum: Int): State[MemoType, Int] = (coins, sum) match {
case (Nil, 0) => State.init(1)
case (Nil, _) => State.init(0)
case (c :: cs, _) =>
for {
memoed <- State.gets { m: MemoType => m.get((coins, sum)) }
res <- memoed match {
case Some(way) => State.init[MemoType, Int](way)
case None =>
(for {
i <- 0 to sum / c
r <- ways_impl(cs, sum - i * c)
_ <- State.update { m: MemoType => m + ((coins, sum) -> r) }
} yield r).sum
}
} yield res
}
ways_impl(listCoins, amount) eval (Map())
I have a compiler error at this line :
r <- ways_impl(cs, sum - i * c)
The compiler said :
type mismatch; found : State[MemoType,Int] (which expands to) State[scala.collection.immutable.Map[(List[Int], Int),Int],Int] required: scala.collection.GenTraversableOnce[?]
For information, here is my first version with mutable map :
import scala.collection.mutable._
val memo = HashMap[(List[Int], Int), Int]()
val coins = List(1, 2, 5, 10, 20, 50, 100, 200)
def memoWays(coins: List[Int], sum: Int): Int = {
memo.getOrElse((coins, sum), {
val y = ways(coins, sum)
memo += ((coins, sum) -> y)
y
})
}
// brute force method with memoization
def ways(coins: List[Int], sum: Int): Int = (coins, sum) match {
case (Nil, 0) => 1
case (Nil, _) => 0
case (c :: cs, n) =>
(for {
i <- 0 to n / c
r = memoWays(cs, n - i * c)
} yield r).sum
}
println(s"result=${Mesure(ways(coins, 200))}")
What does that error mean ? Why the compiler want a GenTraversableOnce instead of State ?
What kind of thing i don't understand on State monad ?
And, if i may, I have an optional question :
Is my way to memoize with State Monad, is a good choice, or my first implementation with mutable map is better anyway ?

Answer 1

The problem is that your for comprehension is attempting to flatMap two unrelated types: a Range and a State. You're going to have to refactor, although off the top of my head, it's not clear to me how you'll be able to leverage State in a simple way. I'd probably use an immutable Map for the memo, a List to represent the future iterations to be tried, and simple recursion to iterate.