Posts Tagged ‘chess’

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

Programming Praxis – N-Queens

June 11, 2010

In today’s Programming Praxis we have to solve the classic n-queens problem. The provided Scheme solution has 13 lines. Let’s see if we can do any better.

A quick import:

import Data.List

The wikipedia page for the algorithm mentions a simple algorithm where you take the permutations of 1 through n as the column positions for the n consecutive rows and removing the illegal ones. So let’s see if that works.

queens :: Int -> [[Int]]
queens n = filter (safe . zip [1..]) $ permutations [1..n]

Since the algorithm guarantees that no two queens will be on the same row or column, we only need to check the diagonals.

safe :: [(Int, Int)] -> Bool
safe []     = True
safe (x:xs) = all (safe' x) xs && safe xs where
    safe' (x1,y1) (x2,y2) = x1+y1 /= x2+y2 && x1-y1 /= x2-y2

A quick test produces the same results as the Scheme solution, and the correct amount according to Wikipedia. At four lines, that will do nicely (you can make it 3 by expressing safe as safe xs = and . zipWith (all . safe’) xs . tail $ tails xs, but I find that version to be less clear than the current one).

main :: IO ()
main = mapM_ print $ queens 5