minimax solution and uebung06 presentation

Marius/uebung05/minimax_solution.pl

+% A Tic-Tac-Toe program in Prolog.   S. Tanimoto, May 11, 2003.
+% To play a game with the computer, type
+% playo.
+% To watch the computer play a game with itself, type
+% selfgame.
+%
+% original at https://courses.cs.washington.edu/courses/cse341/03sp/slides/PrologEx/tictactoe.pl.txt
+
+% Predicates that define the winning conditions:
+
+win(Board, Player) :- rowwin(Board, Player).
+win(Board, Player) :- colwin(Board, Player).
+win(Board, Player) :- diagwin(Board, Player).
+
+rowwin(Board, Player) :- Board = [Player,Player,Player,_,_,_,_,_,_].
+rowwin(Board, Player) :- Board = [_,_,_,Player,Player,Player,_,_,_].
+rowwin(Board, Player) :- Board = [_,_,_,_,_,_,Player,Player,Player].
+
+colwin(Board, Player) :- Board = [Player,_,_,Player,_,_,Player,_,_].
+colwin(Board, Player) :- Board = [_,Player,_,_,Player,_,_,Player,_].
+colwin(Board, Player) :- Board = [_,_,Player,_,_,Player,_,_,Player].
+
+diagwin(Board, Player) :- Board = [Player,_,_,_,Player,_,_,_,Player].
+diagwin(Board, Player) :- Board = [_,_,Player,_,Player,_,Player,_,_].
+
+% Helping predicate for alternating play in a "self" game:
+
+other(x,o).
+other(o,x).
+
+game(Board, Player) :- win(Board, Player), !, write([player, Player, wins]).
+game(Board, Player) :-
+  other(Player,Otherplayer),
+  move(Board,Player,Newboard),
+  !,
+  display(Newboard),
+  game(Newboard,Otherplayer).
+
+move([b,B,C,D,E,F,G,H,I], Player, [Player,B,C,D,E,F,G,H,I]).
+move([A,b,C,D,E,F,G,H,I], Player, [A,Player,C,D,E,F,G,H,I]).
+move([A,B,b,D,E,F,G,H,I], Player, [A,B,Player,D,E,F,G,H,I]).
+move([A,B,C,b,E,F,G,H,I], Player, [A,B,C,Player,E,F,G,H,I]).
+move([A,B,C,D,b,F,G,H,I], Player, [A,B,C,D,Player,F,G,H,I]).
+move([A,B,C,D,E,b,G,H,I], Player, [A,B,C,D,E,Player,G,H,I]).
+move([A,B,C,D,E,F,b,H,I], Player, [A,B,C,D,E,F,Player,H,I]).
+move([A,B,C,D,E,F,G,b,I], Player, [A,B,C,D,E,F,G,Player,I]).
+move([A,B,C,D,E,F,G,H,b], Player, [A,B,C,D,E,F,G,H,Player]).
+
+display([A,B,C,D,E,F,G,H,I]) :- write([A,B,C]),nl,write([D,E,F]),nl,
+ write([G,H,I]),nl,nl.
+
+selfgame :- game([b,b,b,b,b,b,b,b,b],x).
+
+% Predicates to support playing a game with the user:
+
+x_can_win_in_one(Board) :- move(Board, x, Newboard), win(Newboard, x).
+
+% The predicate orespond generates the computer's (playing o) reponse
+% from the current Board.
+
+% move and win
+orespond(Board,Newboard) :-
+  move(Board, o, Newboard),
+  win(Newboard, o),
+  !.
+
+% a draw occurs
+orespond(Board,Newboard) :-
+  not(member(b,Board)),
+  !,
+  write('Cats game!'), nl,
+  Newboard = Board.
+
+% minimax has to be calculated
+% this function computes the list of possible moves,
+% calculates the Utility value for each element in this list via minimap
+% and returns the board with the largest one (by sorting a List of Tuples (Utility,Board))
+orespond(Board,Newboard) :-
+  show_possiblemoves(Board,o,L),
+  maplist(minimaxwrap, L, ListofTuples),
+  predsort(sort_boards,ListofTuples,[(_,Newboard)|_]).
+
+% the wrapper for minimax, used to bind a board to an utilty value
+minimaxwrap(Board,(Utility, Board)):-
+  minimax(x,Board,Utility).
+
+% minimax(Player,Board,Utility value)
+% case: draw
+minimax(_,Board,0):-
+  not(win(Board,o)),
+  not(win(Board,x)),
+  not(member(b,Board)).
+
+% case: o wins
+minimax(_,Board,100):-
+  win(Board,o).
+
+% case: x wins
+minimax(_,Board,-100):-
+  win(Board,x).
+
+% case: o's turn
+minimax(o,Board,Utility):-
+  show_possiblemoves(Board,o,L),
+  maplist(minimax(x),L,Utilities),
+  max_list(Utilities,Utility).
+
+% case: x's turn
+minimax(x, Board,Utility):-
+  show_possiblemoves(Board,x,L),
+  maplist(minimax(o),L,Utilities),
+  min_list(Utilities,Utility).
+
+
+%% HELPER FUNCTIONS
+
+% compare function for a tuple (Utilty,Board)
+sort_boards(Delta, (C1,_),(C2,_)):-
+  C1==C2;
+  compare(Delta,C2,C1).
+
+%finds all possible moves for Player from Board and stores it into a ListOfBoards
+show_possiblemoves(Board, Player, ListOfBoards):-
+  findall(Newboard, move(Board,Player,Newboard),ListOfBoards).
+
+%% END HELPER FUNCTIONS
+
+
+% The following translates from an integer description
+% of x's move to a board transformation.
+
+xmove([b,B,C,D,E,F,G,H,I], 1, [x,B,C,D,E,F,G,H,I]).
+xmove([A,b,C,D,E,F,G,H,I], 2, [A,x,C,D,E,F,G,H,I]).
+xmove([A,B,b,D,E,F,G,H,I], 3, [A,B,x,D,E,F,G,H,I]).
+xmove([A,B,C,b,E,F,G,H,I], 4, [A,B,C,x,E,F,G,H,I]).
+xmove([A,B,C,D,b,F,G,H,I], 5, [A,B,C,D,x,F,G,H,I]).
+xmove([A,B,C,D,E,b,G,H,I], 6, [A,B,C,D,E,x,G,H,I]).
+xmove([A,B,C,D,E,F,b,H,I], 7, [A,B,C,D,E,F,x,H,I]).
+xmove([A,B,C,D,E,F,G,b,I], 8, [A,B,C,D,E,F,G,x,I]).
+xmove([A,B,C,D,E,F,G,H,b], 9, [A,B,C,D,E,F,G,H,x]).
+xmove(Board, _, Board) :- write('Illegal move.'), nl.
+
+% The 0-place predicate playo starts a game with the user.
+
+playo :- explain, playfrom([b,b,b,b,b,b,b,b,b]).
+
+explain :-
+  write('You play X by entering integer positions followed by a period.'),
+  nl,
+  display([1,2,3,4,5,6,7,8,9]).
+
+playfrom(Board) :- win(Board, x), write('You win!').
+playfrom(Board) :- win(Board, o), write('I win!').
+playfrom(Board) :- read(N),
+  xmove(Board, N, Newboard),
+  display(Newboard),
+  orespond(Newboard, Newnewboard),
+  display(Newnewboard),
+  playfrom(Newnewboard).
+
+% The 0-place predicate playo2 starts a game with the AI.
+playo2 :- explain, playfrom2([b,b,b,b,b,b,b,b,b]).
+
+playfrom2(Board) :- win(Board, x), write('You win!').
+playfrom2(Board) :- win(Board, o), write('I win!').
+playfrom2(Board) :-
+  orespond(Board, Newboard),
+  display(Newboard),
+  (not(member(b,Newboard)),
+  write('Cats game!');
+  win(Newboard, x),
+  write('You win!');
+  win(Newboard, o),
+  write('I win!');
+  read(N),
+  xmove(Newboard, N, Newnewboard),
+  display(Newnewboard),
+  playfrom2(Newnewboard)).