2016 ACM ICPC Regionals Division 2 Problem 2

robot.hs

{-
Copyright (C) Freddy A Cubas "Superstar64" 2019

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--https://ser.cs.fit.edu/ser2016//problems/division_2/SER2016%20Problem%20Set%20-%20Division2.pdf
--Problem 2

--all type annotions are optional

import Prelude hiding(Left,Right)
import Data.List (elemIndex,findIndex,inits)
import Data.Maybe (isJust,fromJust,catMaybes)


data Direction = Left | Right | Up | Down deriving (Eq,Show)
data Box = Empty | Robot | Block | Exit deriving (Eq,Show)

replace :: [a] -> Int -> a -> [a]
replace list index element = let (h,_:t) = splitAt index list in h ++ (element : t)

remove :: [a] -> Int -> [a]
remove list index = let (h,_:t) = splitAt index list in h ++ t

insert :: [a] -> Int -> a -> [a]
insert list index element = let (h,t) = splitAt index list in h ++ (element : t)

findBox :: Eq a => a -> [[a]] -> (Int, Int)
findBox box grid = (x,y) where
 list = fmap (elemIndex box) grid
 x = head $ catMaybes $ list
 y = fromJust $ findIndex isJust list

findRobot :: [[Box]] -> (Int, Int)
findRobot = findBox Robot

findExit :: [[Box]] -> (Int, Int)
findExit = findBox Exit

applyDiretion :: (Int, Int) -> Direction -> (Int, Int)
applyDiretion (x,y) Left  = (x-1,y)
applyDiretion (x,y) Right = (x+1,y)
applyDiretion (x,y) Up = (x,y-1)
applyDiretion (x,y) Down = (x,y+1)

bound :: [[a]] -> (Int, Int) -> (Int, Int)
bound grid (x,y) = (fx x,fy y) where
 width = head $ fmap (length) grid
 height = length grid
 fx = max 0 . min (width - 1)
 fy = max 0 . min (height - 1)

index :: (Int, Int) -> [[a]] -> a
index (x,y) grid = grid !! y !! x

set :: (Int, Int) -> a -> [[a]] -> [[a]]
set (x,y) element grid = replace grid y (replace (grid !! y) x element)

move :: Direction -> [[Box]] -> [[Box]]
move direction grid = if valid then grid' else grid where
 (x,y) = findRobot grid
 (tx,ty) = bound grid $ applyDiretion (x,y) direction
 target = index (tx,ty) grid
 valid = target /= Block
 grid' = set (tx,ty) Robot $ set(x,y) Empty grid

applyInstructions :: [[Box]] -> [Direction] -> [[Box]]
applyInstructions grid instructions = foldr (flip (.)) id (fmap move instructions) grid

nextToExit :: [[Box]] -> Bool
nextToExit grid = any (== findRobot grid) $ fmap (applyDiretion $ findExit grid) [Left,Right,Up,Down] 

hitsExit :: [[Box]] -> [Direction] -> Bool
hitsExit grid instructions = any nextToExit $ fmap (applyInstructions grid) $ inits instructions 

searchCases :: [Direction] -> [[Direction]]
searchCases instructions = subCases ++ plusCases where
 subCases = [remove instructions x | x <- [0.. (length instructions) - 1] ]
 plusCases = [insert instructions x | x <- [0.. length instructions] ] <*> [Left,Right,Up,Down]

searchImpl :: [Direction] -> [[[Direction]]]
searchImpl instructions = next : (next >>= searchImpl) where
 next = searchCases instructions

search :: [Direction] -> [[[Direction]]]
search instructions = [instructions] : searchImpl instructions

convertGrid :: [[Char]] -> [[Box]]
convertGrid = fmap $ fmap convertBox

convertBox :: Char -> Box
convertBox '.' = Empty
convertBox 'R' = Robot
convertBox '#' = Block
convertBox 'E' = Exit

convertInstruction :: Char -> Direction
convertInstruction 'L' = Left
convertInstruction 'R' = Right
convertInstruction 'D' = Down
convertInstruction 'U' = Up

main :: IO ()
main = do
 [rows,columns] <- fmap (fmap read .words) getLine
 grid <- fmap convertGrid $ sequence $ replicate rows getLine
 instructions <- fmap (fmap convertInstruction) getLine
 print $ fst $ head $ filter snd $ zip [0..] $ fmap (any (hitsExit grid)) $ search instructions