module Commons where

import Data.List.Utils (split)


data Race = Race { time :: Int, distance :: Int } deriving Show


parseRaces :: [Int] -> [Int] -> [Race]
parseRaces (th: tt) (dh: dt) = Race {time = th, distance = dh}: parseRaces tt dt
parseRaces [] [] = []

parseTimes :: [String] -> [Int]
parseTimes (('T': _): t) = parseTimes t
parseTimes ([]: t) = parseTimes t
parseTimes (h: t) = read h: parseTimes t
parseTimes [] = []

parseDistances :: [String] -> [Int]
parseDistances (('D': _): t) = parseDistances t
parseDistances ([]: t) = parseDistances t
parseDistances (h: t) = read h: parseDistances t
parseDistances [] = []

parse :: IO [Race]
parse = do rawTimes <- getLine
           let times = parseTimes $ split " " rawTimes
           rawDistances <- getLine
           let distances = parseDistances $ split " " rawDistances
           return $ parseRaces times distances


getDistance :: Int -> Int -> Int
getDistance holdTime totalTime = (totalTime - holdTime) * holdTime

getMinimalHoldTime :: Race -> Int -> Int
getMinimalHoldTime race holdTime | getDistance holdTime (time race) > distance race = holdTime
                                 | otherwise = getMinimalHoldTime race (holdTime + 1)

getRaceRange :: Race -> Int
getRaceRange race = time race + 1 - 2 * getMinimalHoldTime race 0