## Posts Tagged ‘moves’

### Programming Praxis – Knight Moves

March 8, 2013

In today’s Programming Praxis exercise, our goal is to list all the potential ways a knight on a chess board can get from one position to another. Let’s get started, shall we?

`import Data.Ix`

A knight can move to 8 positions, assuming they fit on the board. Each move is a combination of moving one square in one direction and two in the other.

```moves :: (Int, Int) -> [(Int, Int)]
moves (x,y) = [(x+dx,y+dy) | [dx,dy] <- combos [[-1,1],[-2,2]]
, inRange (1,8) (x+dx), inRange (1,8) (y+dy)]
where combos xs = sequence xs ++ sequence (reverse xs)```

To find the possible paths to the target square we simply generate all possible sequences of n moves and take the ones that end in the desired position.

```paths :: (Int, Int) -> (Int, Int) -> Int -> [[(Int, Int)]]
paths from to n = map reverse . filter (\(x:_) -> x == to) \$
iterate (>>= \(x:xs) -> map (:x:xs) \$ moves x) [[from]] !! n```

A test to see of everything is working properly:

```main :: IO ()
main = mapM_ print \$ paths (8,8) (1,1) 6```