# Learn You Scala for Great Good! Part 6

Today I want to finish this long talk about Haskell and Scala.  The only thing that  stays in my to-do list is  “A knight’s quest”.

Please look at my previous posts:

Learn You Scala for Great Good!

Learn You Scala for Great Good! Part 2

Learn You Scala for Great Good! Part 3

Learn You Scala for Great Good! Part 4

Learn You Scala for Great Good! Part 5

### A knight’s quest

Here’s a problem that really lends itself to being solved with non-determinism. Say you have a chess board and only one knight piece on it. We want to find out if the knight can reach a certain position in three moves. We’ll just use a pair of numbers to represent the knight’s position on the chess board. The first number will determine the column he’s in and the second number will determine the row.

``````
type KnightPos = (Int,Int)
``````

Then the function `moveKnight` defines all possible moves for this position:

``````
moveKnight :: KnightPos -> [KnightPos]
moveKnight (c,r) = filter onBoard
[(c+2,r-1),(c+2,r+1),(c-2,r-1),(c-2,r+1)
,(c+1,r-2),(c+1,r+2),(c-1,r-2),(c-1,r+2)
]
where onBoard (c,r) = c `elem` [1..8] && r `elem` [1..8]
``````

And, at last, we can solve our problem:

``````

in3 :: KnightPos -> [KnightPos]
in3 start = do
first <- moveKnight start
second <- moveKnight first
moveKnight second

``````

OK! Let’s do the same in Scala. We can determine a case class `Position` and the companion object for this class. I’m used to use characters from ‘a’ to ‘h’ for chess rows, but not numbers. The method set will help me to define a knight position taking pairs `('a', 1)` or `('c', 4)`.

``````

case class Position (x: Int, y: Int) {
def getPos = (Position.xCoord(x - 1), y)
}

object Position {
private val xCoord = ('a' to 'h').toSeq
def set (x:Char, y: Int):Position = Position (xCoord.indexOf(x) + 1, y)
def move(p:Position):List[Position] = List(Position(p.x + 2, p.y - 1), Position(p.x + 2, p.y + 1),
Position(p.x - 2, p.y - 1), Position(p.x - 2, p.y + 1), Position(p.x + 1, p.y - 2), Position(p.x + 1, p.y +2),
Position(p.x - 1, p.y - 2), Position(p.x - 1, p.y + 2)
) filter onBoard

private def onBoard (p:Position) = 1 <= p.x && p.x <= 8 && 1 <= p.y && p.y <= 8

def canReachIn3(start:(Char, Int), end: (Char, Int)):Boolean = {
val s = Position.set(start._1, start._2)
val e = Position.set(end._1, end._2)
(for {
first <- Position move s
second <- Position move first
third <- Position move second
} yield third) contains e

}
}

``````

The method `canReachIn3` can tell us if the knight that is placed into the start position reaches the end position in three moves.

``````
val start = ('b', 5)
val end = ('a', 7)

println(Position.canReachIn3(start, end))
``````