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(Othello (Reversi). Manuel Hernández, April 2011.)
(Othello (Reversi). Manuel Hernández, April 2011.)
Line 193: Line 193:
 
ls = (map transTree (a:bs))
 
ls = (map transTree (a:bs))
 
nm = length (allNum n pos)
 
nm = length (allNum n pos)
--Simple minimax: To do, alpha-beta pruning.
+
--Simple minimax: alpha-beta pruning, see below...
 
minimax (T4 (n,[mov],(numberOfxs,numberOfos,nm)) [])
 
minimax (T4 (n,[mov],(numberOfxs,numberOfos,nm)) [])
 
|nm==0 = ([mov],-70) -- -70 o 70?
 
|nm==0 = ([mov],-70) -- -70 o 70?
Line 273: Line 273:
 
# Special turns (like to put a token over an arbitrary square)
 
# Special turns (like to put a token over an arbitrary square)
 
# Hexa "squares"
 
# Hexa "squares"
  +
  +
The alpha-beta pruning process is:
  +
<haskell>
  +
  +
bmx alpha beta (T4 (n,[mov],(numberOfxs,numberOfos,nm)) []) =
  +
([mov],max alpha (min numberOfxs beta))
  +
bmx alpha beta (T4 (n,ls,(numberOfxs,numberOfos,nm)) (b:bs)) =
  +
(ls++mvT,val)
  +
where
  +
(mvT,val) = cmx alpha beta (b:bs)
  +
  +
-- ...following Bird and Wadler...
  +
  +
cmx alpha beta [] = ([],alpha)
  +
cmx alpha beta (b:bs)
  +
| alpha'== beta = ([],alpha')
  +
| otherwise = (ls++mvs,val)
  +
where
  +
(ls,val) = cmx alpha' beta bs
  +
(mvs,alpha') = negP (bmx (-beta) (-alpha) b)
  +
  +
-- Use the following "best move" instead of bestMv
  +
  +
bestMv' player pos level =
  +
bmx (-70) 70 (transTree (last (genTree player pos level)))
  +
</haskell>

Revision as of 21:43, 5 April 2011

Othello (Reversi). Manuel Hernández, April 2011.

import Random
import List
 
data Element = O | X | E | L deriving (Eq,Show)
data ArbolG = T Board [ArbolG] deriving Show
type Board = [Element]
data ArbolG1 = T1 (Element,Integer,Board,Int,Int) [ArbolG1] deriving Show
--Bug? Hugs does not accept "vectors" from size > 5 to show
-- T1 (Int,Int,Int,Int,Int) is not shown...
data ArbolG3 = T3 (Element, -- Player
                   Integer, -- Mov
                   Board, -- Position
                   (Int,Int,Int) -- (num Xs, num Os, num Movs) 
                   ) [ArbolG3] deriving Show
 
data ArbolG4 = T4 (Element, -- Player
                   [Integer], -- Mov
                   (Int,Int,Int) -- (num Xs, num Os, num Movs) 
                   ) [ArbolG4] deriving Show
 
data MvVal = MvVal {mov::Integer, xs :: Int, os :: Int} deriving Show
 
lcoords = concat [[(x+1)..(x+8)]| x<-[10,20..80]]
 
coords pos = zipWith (\x y -> (x,y)) lcoords pos
 
expandx pos ((ini,X),(cand, O)) = 
        let (delta,av) = (cand-ini,cand+delta)
            es = findCoords av (coords pos)
            in if null es then [] else 
                 let h = snd (head es) in
                    case h of 
                     X -> []
                     E -> [(cand,O),(av,E)]
                     O ->  let rest = expandoX pos delta (av, O) in
                             if null rest then [] else (cand, O):rest 
 
expandoX pos delta (av, O) = 
             let av1 = av + delta
                 es = findCoords av1 (coords pos)
                  in if null es then [] else
                    let h = snd (head es) in 
                      case h of 
                        X -> [] 
                        E -> [(av, O),(av1, E)]
                        O -> let rest= expandoX pos delta (av1, O) in
                               if null rest then [] else (av, O):rest
 
expando pos ((ini,O),(cand, X)) = 
        let
           (delta,av) = (cand-ini,cand+delta)
           es = findCoords av (coords pos)
           in 
            if null es  then [] else 
                 let h = snd (head es) in
                    case h of 
                     O -> []
                     E -> [(cand, X),(av, E)]
                     X ->  let rest = expandxO pos delta (av, X) in
                             if null rest then [] else  (cand, X):rest 
 
expandxO pos delta (av, X) = let
                 av1 = av + delta
                 es = findCoords av1 (coords pos) in
                   if null es then [] else
                        let h = snd (head es) in 
                          case h of 
                           O -> [] 
                           E -> [(av, X),(av1, E)]
                           X -> let rest= expandxO pos delta (av1, X) in
                                    if null rest then [] else  (av, X):rest
 
allNum player pos = (nub . sort) 
              (map (fst) (validMoves player pos))
 
validMoves player pos = map last (allMoves player pos)
 
allMoves player pos = filter (/=[]) (movs player pos) 
 
movs player pos = if player==X then 
        map (expandx pos) (concat (onlyNBos X pos))
               else
        map (expando pos) (concat (onlyNBos O pos))
 
candidates (init, ls) = zip (repeat init) ls
 
findF e coors = (filter (\x -> (snd x)==e) coors) 
 
findCoords m coors = (filter (\x -> (fst x) == m) coors) 
 
neighbs e1 pos (n, e) = ((n, e),(only e1 
                                 (concat 
                                   [findCoords x (coords pos)| x<-dirs n])))
-- To find the neighborhoods...
onlyNBos player pos =  map (candidates . (neighbs (change player) pos)) 
                                     (findF player (coords pos))
 
only e ls = filter (\x -> (snd x)==e) ls
 
dirs n | elem n ([22..27]++[32..37]++[42..47]++[52..57]++[62..67]++[72..77])
                         =  map (+n) [-11,-10,-9,-1,1,9,10,11]
       | elem n [12..17] = map (+n) [-1,1,9,10,11]
       | elem n [82..87] = map (+n) [-1,1,-9,-10,-11]
       | elem n [21,31..71] = map (+n) [-10,-9,1,10,11]
       | elem n [28,38..78] = map (+n) [-11,-10,-1,9,10]
       | elem n [11] = [12,22,21]
       | elem n [88] = [87,77,78]
       | elem n [81] = [71,72,82]
       | elem n [18] = [17,27,28]
 
numTTT::Int
numTTT= 64
 
part8 [] = []
part8 (a:bs) = (take 8 (a:bs)):(part8 (drop 8 (a:bs)))
 
posIni::[Element]
posIni =  (take 24 (repeat E))++[E,E,E,X,O,E,E,E,
                                 E,E,E,O,X,E,E,E]++(take 24 (repeat E))
 
to a = snd (head (filter (\x -> a==fst x) (zip lcoords [1..64])))
 
maxV (MvVal n1 a1 b1) (MvVal n2 a2 b2) | a1<=a2 = MvVal n2 a2 b2
                                       | otherwise = MvVal n1 a1 b1
 
findMaxV ls = foldr (maxV) (MvVal 0 (-1000) 0) ls 
 
showB [] = ""
showB (a:bs) = (show a)++"\n"++(showB bs)
 
showBoard pos = putStr (" _ _ _ _ _ _ _ _ \n"
                ++[xchange x|x<-(showB (part8 pos))])
 
xchange x | x==',' = '|' 
          | x=='E' = '_'
          | otherwise = x
 
count player pos = length (filter (==player) pos)
 
validCoord player pos = nub (strip (validMoves player pos))
 
strip [] = []
strip ((n, x):ls) = fst (n, x):strip ls
------------------------------begin wrt X---------------------
allVBasic player g pos = 
           T1 (player,g,pos,count X pos,count O pos) ls
            where 
            ls = [T1 (mMoveVirtual player k pos) [] | k <- (allNum player pos)]
 
barrer player (T1 (p,m,pos,n1,n2) []) = allVBasic player m pos
barrer player (T1 (p,m,pos,n1,n2) (c:cs)) = 
           T1 (player,m,pos,count X pos,count O pos) 
                 (map (barrer (change player)) (c:cs))
 
genTree player pos n = take n (iterate (barrer player) (T1 (X,0,pos,2,2) []))
--Realmente sólo se utilizan jugador=X y posición=pos
 
mMoveVirtual player n pos = 
            let newpos = (applyMove 
                    (apply player (nub (concat 
                      (filter (\x->fst (head x)==n) 
                        (map reverse 
                               (allMoves player pos)))))) pos)
             in (player, n, newpos, count X newpos, count O newpos)
--Dato: (player, movement, position, howmanyX, howmanyO)
 
sortby [] = []
sortby ((a1,b1):bs) = sortby [x | x<- bs, snd x < b1]++[(a1,b1)]++ 
                      sortby [x | x<- bs, snd x >= b1] 
newPos player n pos = 
            applyMove
                    (apply player (nub (concat 
                      (filter (\x->fst (head x)==n) 
                        (map reverse 
                               (allMoves player pos)))))) pos
mMvVirtual player n pos = 
            let newpos = (applyMove
                    (apply player (nub (concat 
                      (filter (\x->fst (head x)==n) 
                        (map reverse 
                               (allMoves player pos)))))) pos)
                          in MvVal n (count X newpos) (count O newpos)
 
transTree (T1 (n,mov,pos,xs,os) []) = T4 (n,[mov],(xs-os,os,nm)) []
                                     where
                                       nm = length (allNum n pos)
transTree (T1 (n,mov,pos,xs,os) (a:bs)) = T4 (n,[mov],(xs,os,nm)) ls 
                             where 
                               ls =  (map transTree (a:bs))
                               nm = length (allNum n pos)
--Simple minimax: alpha-beta pruning, see below...
minimax (T4 (n,[mov],(numberOfxs,numberOfos,nm)) [])  
                        |nm==0 = ([mov],-70) -- -70 o 70?
minimax (T4 (n,[mov],(numberOfxs,numberOfos,nm)) [])
                        |nm>0 = ([mov],-numberOfxs) -- positive, it is "greedy" 
minimax (T4 (n,[mov],(numberOfxs,numberOfos,nm)) (a:bs)) = (ms,n)
           where
             ls = (negP (minList' (map minimax (a:bs))))
             (mvT,val) = ls 
             ms = (mov:mvT) -- ++[mov]
             n  = val
 
app ls (ms,t) = (ls++ms,t)
negP (a,b) = (a,-b)
 
bestMv player pos n = 
               minimax (transTree (last (genTree player pos n)))
 
minList ls = foldr (min) (1000) ls
minP (a1,b1) (a2,b2) = if b1<b2 then (a1,b1) else (a2,b2)
minList' ls = foldr (minP) ([],1000) ls
 
mMove player n pos = showBoard (applyMove
                  (apply player (nub (concat 
                      (filter (\x->fst (head x)==n) 
                        (map reverse 
                               (allMoves player pos)))))) pos)
---------------------------end wrt X-----------------------------
apply player [] = []
apply player ((n,e):ls) = (n,player):apply player ls 
 
applyMove [] pos = pos
applyMove ((n,player):ls) pos = applyMove ls (sustn player (to n) pos)     
 
sustn :: (Num a, Ord a) => b -> a -> [b] -> [b]
sustn a 1 (c:cs) = (a:cs) 
sustn a n (c:cs) | n>1 =  c:(sustn a (n-1) cs)
 
change X = O
change O = X
 
-- The strength of playing depends on the eval function. 
 
calcMov :: Board -> IO()
calcMov pos = do
        --Report winner..., missing
        let 
          bm = head (tail (fst (bestMv X pos 3))) -- Empty list..., missing
          newpos1 = newPos X bm pos
        mMove X bm  pos
        putStr $ show bm
        putStr $ "\n"
        putStrLn $ "Black: " ++ (show (count X newpos1))
        putStrLn $ "White: " ++ (show (count O newpos1))
        putStrLn $ (show (allNum O newpos1))++"\n"
        putStr "Your move: "
        input <- getLine
        let square = (read input) :: Integer
--        putStr (show square)
        let 
          newpos2 = newPos O square newpos1
        mMove O square newpos1  
        putStrLn $ "Black: "++ (show (count X newpos2))                
        putStrLn $ "White: "++ (show (count O newpos2))                
        calcMov (newPos O square newpos2)          
 
main = calcMov posIni

--Variants:

  1. Three players (or more)
  2. Scattering pieces over the board
  3. Boards with obstacles (squares, or diamonds, for example)
  4. Boards with distinct geometrical forms.
  5. Boards with distinct square geometry.
  6. Random static token
  7. Factor number betrayed
  8. ¿Dimensions? I am thinking... 3D Othello.
  9. Special turns (like to put a token over an arbitrary square)
  10. Hexa "squares"

The alpha-beta pruning process is:

bmx alpha beta (T4 (n,[mov],(numberOfxs,numberOfos,nm)) []) =
                      ([mov],max alpha (min numberOfxs beta))
bmx alpha beta (T4 (n,ls,(numberOfxs,numberOfos,nm)) (b:bs)) =
                        (ls++mvT,val)
                      where 
                        (mvT,val) = cmx alpha beta (b:bs)
 
-- ...following Bird and Wadler...
 
cmx alpha beta [] = ([],alpha)
cmx alpha beta (b:bs) 
     | alpha'== beta = ([],alpha')
     | otherwise = (ls++mvs,val)
        where  
           (ls,val) = cmx alpha' beta bs
           (mvs,alpha') = negP (bmx (-beta) (-alpha) b)
 
-- Use the following "best move" instead of bestMv
 
bestMv' player pos level = 
               bmx (-70) 70 (transTree (last (genTree player pos level)))