module Exercise08 where

import Data.Bits
import Data.List
import Data.Ord
import System.Random (Random, mkStdGen, randomIO, randoms)

-- Player is either 1 or -1
type Player = Int

-- A field is just an Int value where the absolute gives the number of pieces on the field
-- and the sign corresponds to the player
-- e.g. -3 would mean there are three blobs in this field of player -1
type Field = Int

type Row = [Field]

type Column = [Field]

-- boards are rectangles represented as a list of rows
type Board = [Row]

-- A position on the board is represented as (row, column)
-- (0,0) is the top left corner, coordinate values increase towards the bottom right
type Pos = (Int, Int)

-- A size represented as (height,width)
type Size = (Int, Int)

-- A strategy takes the player who's move it is, optionally takes a list of double values
-- to allow for probabilistic strategies, takes the current board and gives back the position
-- of the move the player should do
type Strategy = [Double] -> Player -> Board -> Pos

-- A stateful strategy can additionally pass some object between invocations
type StatefulStrategyFunc a = a -> [Double] -> Player -> Board -> (Pos, a)

-- first value is the state object to pass to the first invocation of each game
type StatefulStrategy a = (a, StatefulStrategyFunc a)

defaultSize :: (Int, Int)
defaultSize = (9, 6)

-- Some useful helper functions
row :: Board -> Int -> Row
row = (!!)

column :: Board -> Int -> Column
column = row . transpose

width :: Board -> Int
width (x : _) = length x
width _ = 0

height :: Board -> Int
height = length

size :: Board -> Size
size b = (height b, width b)

getCell :: Pos -> Board -> Field
getCell (y, x) b = b !! y !! x

-- pretty print a single cell
showCell :: Field -> String
showCell c = "- +" !! succ (signum c) : show (abs c)

-- pretty print the given board
showBoard :: Board -> String
showBoard = unlines . map (unwords . map showCell)

-- print a board to the console
printBoard :: Board -> IO ()
printBoard = putStr . showBoard

-- check if a position is one a board of the given size
isValidPos :: Size -> Pos -> Bool
isValidPos (r, c) (y, x) = y >= 0 && y < r && x >= 0 && x < c

{- x.1 -}

-- Check if the given player can put an orb on the given position
canPlaceOrb :: Player -> Pos -> Board -> Bool
canPlaceOrb p pos b = let cell = getCell pos b in isValidPos (size b) pos && (cell == 0 || signum cell == p)

-- Check if the given player has won the game,
-- you can assume that the opponent has made at least one move before
hasWon :: Player -> Board -> Bool
hasWon p b = and [cell == 0 || signum cell == p | row <- b, cell <- row]

-- the list of neighbors of a cell
neighbors :: Size -> Pos -> [Pos]
neighbors size (y, x) = filter (isValidPos size) [(y, x + 1), (y, x - 1), (y + 1, x), (y - 1, x)]

-- update a single position on the board
-- f: function that modifies the number of orbs in the cell
-- p: player to whom the updated cell should belong
updatePos :: (Int -> Int) -> Player -> Pos -> Board -> Board
updatePos f p (0, x) (row : b) = updatePos' f p x row : b
  where
    updatePos' f p 0 (cell : row) = p * abs (f $ abs cell) : row
    updatePos' f p x (cell : row) = cell : updatePos' f p (x - 1) row
updatePos f p (y, x) (row : b) = row : updatePos f p (y - 1, x) b

{- x.2 -}

-- place an orb for the given player in the given cell
putOrb :: Player -> Pos -> Board -> Board
putOrb p pos b = putOrb' [pos] (updatePos (+ 1) p pos b) [b]
  where
    putOrb' [] b _ = b
    putOrb' positions board bs =
      let (b, newPos) = foldr update (board, []) positions
       in if b `elem` bs then b else putOrb' newPos b (b : bs)
      where
        update pos (board, newPos) =
          let c = abs $ getCell pos board
              ns = neighbors (size board) pos
              l = length ns
           in if c >= l
                then (foldr (updatePos (+ div c l) p) (updatePos (`mod` l) p pos board) ns, ns ++ newPos)
                else (board, newPos)

{- x.3 -}

{-WETT-}

putOrbOvs :: Player -> Pos -> Board -> (Board, Int)
putOrbOvs p pos b = putOrb' [pos] (updatePos (+ 1) p pos b) [b] 0
  where
    putOrb' [] b _ overflows = (b, overflows)
    putOrb' positions board bs overflows =
      let (b, newPos, ovs) = foldr update (board, [], overflows) positions
       in if b `elem` bs then (b, ovs) else putOrb' newPos b (b : bs) ovs
      where
        update pos (board, newPos, ovs) =
          let c = abs $ getCell pos board
              ns = neighbors (size board) pos
              l = length ns
           in if c >= l
                then (foldr (updatePos (+ div c l) p) (updatePos (`mod` l) p pos board) ns, ns ++ newPos, ovs + 1)
                else (board, newPos, ovs)

-- Your strategy
strategy :: Strategy
strategy _ p b =
  let ops = [(putOrbOvs p pos b, pos) | pos <- options p b]
   in let greatest = takeGreatestBy 5 (value p . fst) ops
       in snd $ maximumBy (comparing $ branches 5 (- p) . fst . fst) greatest
  where
    branches 0 p b = value p (b, 0)
    branches depth p b =
      if hasWon (- p) b
        then value (p * (-1) ^ mod depth 2) (b, 0) * (depth + 1)
        else
          let ops = [putOrbOvs p pos b | pos <- options p b]
           in let greatest =
                    map (branches (depth - 1) (- p) . fst) $
                      takeGreatestBy 5 (value p) ops
               in if even depth
                    then {- my turn -} maximum greatest
                    else {- opp's turn -} minimum greatest

    options p b =
      let (r, c) = size b
          capt = captured b (0, 0)
            where
              captured [] _ = []
              captured ([] : b) (y, x) = captured b (y + 1, 0)
              captured ((cell : row) : b) (y, x)
                | p == signum cell = (y, x) : (y, x + 1) : (y, x - 1) : (y + 1, x) : (y - 1, x) : captured (row : b) (y, x + 1)
                | otherwise = captured (row : b) (y, x + 1)
       in filter (flip (canPlaceOrb p) b) $
            nub $ [(0, 0), (0, c - 1), (r - 1, 0), (r - 1, c - 1)] ++ capt

    value p (b, overflows) = p * sum (map sum b) + overflows

    takeGreatestBy n p = takeGreatestBy' n . sortOn (Down . p)
      where
        takeGreatestBy' _ [] = []
        takeGreatestBy' 1 (v1 : v2 : vs)
          | v1 == v2 = v1 : takeGreatestBy' 1 (v2 : vs)
          | otherwise = [v1]
        takeGreatestBy' n (v : vs) = v : takeGreatestBy' (n - 1) vs

-- adds state to a strategy that doesn't use it
wrapStrategy :: Strategy -> StatefulStrategy Int
wrapStrategy strat = (0, \s r p b -> (strat r p b, succ s))

-- the actual strategy submissions
-- if you want to use state modify this instead of strategy
-- additionally you may change the Int in this type declaration to any type that is usefully for your strategy
strategyState :: StatefulStrategy Int
strategyState = wrapStrategy strategy

{-TTEW-}

-- Simulate a game between two strategies on a board of the given size and
-- returns the state of the board before each move together with the player that won the game
play :: [Int] -> Size -> StatefulStrategy a -> StatefulStrategy b -> [(Board, Pos)]
play rss (r, c) (isa, sa) (isb, sb) = go rss isa sa isb sb 1 0 (replicate r (replicate c 0))
  where
    -- type signature is necessary, inferred type is wrong!
    go :: [Int] -> a -> StatefulStrategyFunc a -> b -> StatefulStrategyFunc b -> Player -> Int -> Board -> [(Board, Pos)]
    go (rs : rss) stc sc stn sn p n b
      | won = []
      | valid = (b, m) : go rss stn sn st' sc (- p) (succ n) (putOrb p m b)
      | otherwise = []
      where
        won = n > 1 && hasWon (- p) b
        (m, st') = sc stc (mkRandoms rs) p b
        valid = isValidPos (size b) m && canPlaceOrb p m b

-- Play a game and print it to the console
playAndPrint :: Size -> StatefulStrategy a -> StatefulStrategy b -> IO ()
playAndPrint size sa sb = do
  seed <- randomIO
  -- let seed = 42
  let moves = play (mkRandoms seed) size sa sb
  putStr $
    unlines (zipWith showState moves $ cycle ['+', '-']) ++ "\n"
      ++ (case length moves `mod` 2 of 1 -> "Winner: +"; 0 -> "Winner: -")
      ++ "\n"
      ++ "View at https://vmnipkow16.in.tum.de/christmas2020/embed.html#i"
      ++ base64 (1 : t size ++ concatMap (t . snd) moves)
      ++ "\n"
  where
    showState (b, pos) p = showBoard b ++ p : " places at " ++ show pos ++ "\n"
    t (a, b) = [a, b]

mkRandoms :: Random a => Int -> [a]
mkRandoms = randoms . mkStdGen

base64 :: [Int] -> String
base64 xs = case xs of
  [] -> ""
  [a] -> f1 a : f2 a 0 : "=="
  [a, b] -> f1 a : f2 a b : f3 b 0 : "="
  a : b : c : d -> f1 a : f2 a b : f3 b c : f4 c : base64 d
  where
    alphabet = (!!) "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"
    f1 a = alphabet $ shiftR a 2
    f2 a b = alphabet $ shiftL (a .&. 3) 4 .|. shiftR b 4
    f3 b c = alphabet $ shiftL (b .&. 15) 2 .|. shiftR c 6
    f4 c = alphabet $ c .&. 63