# Haskell Quiz/Word Search/Solution Sjanssen

### From HaskellWiki

## 1 A trie structure

A prefix oriented structure is ideal for the word search algorithm.

module Trie where import qualified Data.Map as Map data Trie = Trie Bool (Map.Map Char Trie) deriving (Show) empty = Trie False Map.empty insert [] (Trie b m) = Trie True m insert (x:xs) (Trie b m) = Trie b $ Map.alter (maybe (Just $ fromString xs) (Just . insert xs)) x m fromString = foldr (\x xs -> Trie False (Map.singleton x xs)) (Trie True Map.empty) fromList = foldr insert empty

## 2 Initial solution

import Data.Array import Data.Char import qualified Data.Map as Map import Trie type Grid = Array (Int, Int) Char -- | Given a grid and a trie, produce a list of matched words as well as the -- location of the match. The algorithm differs slightly from the example, -- if a word appears several times a match is produced for each location. match :: Grid -> Trie -> [(String, [(Int, Int)])] match g t = concatMap (flip go t) paths where bs = bounds g paths = concatMap dirs (range bs) dirs x = [takeWhile (inRange bs) $ iterate (next (i, j)) x | i <- [-1 .. 1], j <- [-1 .. 1], i /= 0 || j /= 0] go xs (Trie b m) = (if b then [([], [])] else []) ++ do (x:xs) <- return xs let c = g ! x t <- Map.lookup c m (s, is) <- go xs t return (c:s, x:is) next (x, y) (i, j) = (i + x, j + y) readBoard = do l <- getLine if null l then return [] else fmap (l:) readBoard csv [] = [] csv xs = l : csv (dropWhile (\x -> isSpace x || x == ',') r) where (l, r) = span (/= ',') xs output g ms = sequence_ [putStrLn [g' ! (i, j) | j <- [1..c]] | i <- [1..r]] where g' = listArray ((1, 1), (r, c)) (repeat '+') // (map (\x -> (x, g ! x)) $ concatMap snd ms) ((1, 1), (r, c)) = bounds g main = do b <- readBoard let r = length b c = length (head b) g = listArray ((1, 1), (r, c)) . map toUpper . concat $ b l <- getLine let ws = map (map toUpper) $ csv l t = fromList ws ms = match g t output g ms

## 3 Extra credit

For extra credit, I extended the program to support wildcards (*) in the board. This only required changing two lines and adding another.

import Data.Array import Data.Char import qualified Data.Map as Map import Trie type Grid = Array (Int, Int) Char -- | Given a grid and a trie, produce a list of matched words as well as the -- location of the match. The algorithm differs slightly from the example, -- if a word appears several times a match is produced for each location. match :: Grid -> Trie -> [(String, [(Int, Int)])] match g t = concatMap (flip go t) paths where bs = bounds g paths = concatMap dirs (range bs) dirs x = [takeWhile (inRange bs) $ iterate (next (i, j)) x | i <- [-1 .. 1], j <- [-1 .. 1], i /= 0 || j /= 0] go xs (Trie b m) = (if b then [([], [])] else []) ++ do (x:xs) <- return xs (c, t) <- case g ! x of '*' -> Map.assocs m c -> fmap ((,) c) (Map.lookup c m) (s, is) <- go xs t return (c:s, x:is) next (x, y) (i, j) = (i + x, j + y) readBoard = do l <- getLine if null l then return [] else fmap (l:) readBoard csv [] = [] csv xs = l : csv (dropWhile (\x -> isSpace x || x == ',') r) where (l, r) = span (/= ',') xs output g ms = sequence_ [putStrLn [g' ! (i, j) | j <- [1..c]] | i <- [1..r]] where g' = listArray ((1, 1), (r, c)) (repeat '+') // (map (\x -> (x, g ! x)) $ concatMap snd ms) ((1, 1), (r, c)) = bounds g main = do b <- readBoard let r = length b c = length (head b) g = listArray ((1, 1), (r, c)) . map toUpper . concat $ b l <- getLine let ws = map (map toUpper) $ csv l t = fromList ws ms = match g t output g ms