% \iffalse \begingroup \def\tmp{plain} \expandafter \endgroup \csname if\ifx\tmp\fmtname false\else true\fi\endcsname \documentclass{article} \usepackage{shortvrb} \MakeShortVerb| \catcode`\%=9 \input \jobname.tex \fi % \fi % % \title{\texttt{reverxii.tex}\\ % Playing Reversi in \TeX{}} % \author{Bruno Le Floch} % \date{December 28, 2011} % \newcommand{\cs}[1]{\texttt{\char`\\ #1}} % \newcommand{\meta}[1]{$\langle \mathit{#1}\rangle$} % \newcommand{\enquote}[1]{``#1''} % \makeatletter % \def\verbatim{\@verbatim\frenchspacing\@vobeyspaces\catcode`\%=9 \@xverbatim} % \makeatother % \begin{document} % \maketitle % % \begin{abstract} % \texttt{reverxii.tex} is a $938$-byte long \TeX{} program % which lets you play Reversi against your favorite typestting engine. % To play, run plain \TeX{}, on the command line, in dvi-mode, % on the file \texttt{reverxii.tex}. In most distributions, % this should mean running \texttt{tex reverxii.tex} in a terminal. % To produce the documentation, run \LaTeX{} on the same file, % with any engine (\emph{e.g.}, \texttt{pdflatex reverxii.tex}). % \end{abstract} % % \section{The code} % % Line breaks can be removed, and the stripped down code takes $938$ % characters. % \begin{verbatim} \vsize5cm\hsize3cm\newlinechar`*\def~#1{\catcode`#113~} ~IJKLMNOPQRSTUVWXYZjqz@.[|](/+^'";:?,_)!*{ 13\def~#1#2{\let#1#2~} \def+{\count1}+1=2}*\cr[\ifnum(\ifcase|\or/\else]\fiN\number@\advance X\expandafter!\global?\message~\def.#1{@+1 1\countdef#1+1.} .IJKLPQRSTUVWYZ.-1P1T2+44P+55P+45T+54T ~j{[0Q[0J^/.]/.]/.]/.]} ~^{+NQNJ}~:#1{#11#12#13#14#15#16#17#18}~M#1{?{#1}#1} ~_#1#2{M#2:{\B#1}&M#2&M{*}}~\B#1#2{&M{(+#1#2 |-|0]}} ~q{?{Row and column? e.g. E6*}\read.to\EX\D\meaning\E ;} ~\D#1->#2#3#4;{Q`#2@Q-`@J`#3@J-`0)(V?{Invalid move #2#3.}q]} ~){V0 (jS1z1z0z.S0z1z.S.z1z0z.]}~;{@R(P|-]}~z#1{{K#1Z1{Y1,}(Z,]}} ~,{@QS@JK[j=T(Y!^P!;2]O,/[j=P!VV(I(Y/!Z0]]]]}~\A#1{Q#1:\C} ~\C#1{J#1)[0WWVUQLJ]]}~"#1{(#1|0|1|2|2|2|2|1|0]} ~O{Z"Q\multiplyZ3@Z"J@V(Z9|1|6|1|1|2|6|2|4] }~'{M :{&M}&M{*}} ~~{PXTXTNP\halign{&## *M{*}'_1A_2B_3C_4D_5E_6F_7G_8H'}\vfil\break I1W(W./0] :\AI0 [0R-/0] wins by N[0>R-]R].}X\end]~}~ % \end{verbatim} % % To play a two-player game, change |1=P| to |0=P| near the end: % this changes the computer player from $0$ to $1$, hence disabling it. % % \section{Explanation} % % \subsection{Some comments} % % The name \texttt{reverxii.tex} is of course a reference to the infamous % \texttt{xii.tex}, also on CTAN, which typesets the lyrics of the % \textit{Twelve days of Christmas} using code that very few can understand. % In my case, I aimed for the shortest possible code, rather than the % most obfuscated. In particular, I did not assign weird catcodes % other than making most characters active. % % Since I was aiming for short code, the text presented to the player % is concise, but hopefully enough to leave the game understandable % and usable. Despite aiming for short code, I thought it would be % neat to typeset a record of the game as it goes: after all, \TeX{} % is a typesetting program. This used up around $38$ characters, putting % me above the $900$ character line. % % One technique used to make the code shorter is to rename any primitive % used more than once into a single active character. Also, counters % holding the information about the board are accessed directly by number. % % A careful reader would notice that changing one of the remaining % one-character control sequences to active characters (|$| is still % unused) would gain one character. I didn't do it, because it messes % up the code-highlighting of my editor |:)|. Of course, I chose the % control sequences which are not active characters to be those appearing % the least, only twice each. % % \subsubsection{On with the code!} % % First set up the page dimensions. This would not be enough for pdf output. % \begin{verbatim} % \vsize5cm % \hsize3cm % \end{verbatim} % % Since plain \TeX{} does not provide the \cs{typeout} command, we are % using \cs{message}, hence need to setup a new line character. It is % arbitrarily chosen to be |*|, which will be made active and \cs{let} % to \cs{cr}. % \begin{verbatim} % \newlinechar`* % \end{verbatim} % % Then a first loop to make many characters active. The loop ends when % reaching the trailing brace group: there we make spaces active, then % redefine |~| for the next loop. We still have an annoying |13~| in % the input stream. Introduce a short-hand for count registers whose % number starts with |1|, then remove |13| by setting |\count11| to % |213| (this counter is used for allocation later on). The next loop % is triggered by the |~| which we left. % \begin{verbatim} % \def~#1{\catcode`#113~} % ~IJKLMNOPQRSTUVWXYZjqz@.[|](/+^'";:?,_)!* % { 13\def~#1#2{\let#1#2~}\def+{\count1}+1=2} % \end{verbatim} % % At this stage, |~| is defined to take two arguments, \cs{let} the % first to the second, and repeat. As announced |*| becomes \cs{cr}, % so that it will be a new line both in messages and in alignments. % We try to keep a relatively consistent naming scheme: opening % conditionals are left delimiters, \cs{or} and \cs{else} are % middle delimiters, and \cs{fi} is a right bracket. Other primitives % which are used a lot are also given short names. The loop ends by % redefining |~| to \cs{def}. % \begin{verbatim} % *\cr % [\ifnum % (\ifcase % |\or % /\else % ]\fi % N\number % @\advance % X\expandafter % !\global % ?\message % ~\def % \end{verbatim} % % It is time to allocate counters. Unfortunately, \cs{newcount} % is \cs{outer}, so it is unpractical to use. We have set |+1|, % \emph{aka.} |\count11| to $213$, and will allocate counters % starting from that number upwards. Repeatedly advance |+1| % by $1$ and define the next character to be the counter number |+1|, % then repeat. As always, the loop is interrupted by making it % redefine the looping macro |.| to be a counter. We use the trailing % dot to assign it the value $-1$, then assign a couple of counters: % starting player, other player, and the initial position: % the squares in rows and columns $4$ and $5$ are initially % filled in a cross pattern. % \begin{verbatim} % .#1{@+1 1\countdef#1+1.}.IJKLPQRSTUVWYZ.-1P1T2+44P+55P+45T+54T % \end{verbatim} % Let us summarize which counters are used where: % \begin{itemize} % \item [P] is the current player ($1$ for |-| or $2$ for |0|); % \item [T] is the other player; % \item [Q] is the row number; % \item [J] is the column number; % \item [S] is the step size in the row direction; % \item [K] is the step size in the column direction; % \item [R] is the score difference, positive when $0$ is winning; % \item [V] is used when computing the value of placing a piece at % the position (|Q|,|J|); % \item [W] is the value of the best possible move according to the AI, % also used to end the game if neither player can move; % \item [U] is the row number of the best move; % \item [L] is the column number of the best move; % \item [Y] is a boolean, true ($0$) most of the time, % it has to do with when we flip or not, but I don't % understand it now, help welcome; % \item [Z] is a temporary counter, used locally to compute % how much a given cell matters (\emph{i.e.} corners are important), % and used globally as a boolean to indicate whether to flip pieces % or not. % \end{itemize} % % The board is stored in counters |1|\meta{row}\meta{column}. % An empty square is has the value $0$, a square for player |-| % has value $1$, and player |0| corresponds to the value $2$. % The macro |j| retrieves that value, assuming that the row and % column numbers are stored as |Q| and |J|, and returns |.|, % that is, $-1$, if outside the board. Recall that |[| is \cs{ifnum}, % |/| is \cs{else}, and |]| is \cs{fi}. When |Q| and |J| are % within bounds, the value is retrieved by |^| as % |\count1|\meta{row}\meta{column}. Note that |j| and |^| are % only safe to use on the left-hand side of an \cs{ifnum} test % (because of expansion issues), and that |^| can be used % on the left-hand side of an assignment. % \begin{verbatim} % ~j{[0Q[0J^/.]/.]/.]/.]} % ~^{+NQNJ} % \end{verbatim} % % We often need to loop over numbers from $1$ to $8$; here is a macro. % \begin{verbatim} % ~:#1{#11#12#13#14#15#16#17#18} % \end{verbatim} % % The macros to print the board, both to the dvi and to the console. % |M| spews its argument as a \cs{message} (|?|), and directly typeset. % This is used rather directly to print the first and last lines (|'|), % which are simply alignment cells containing each number from $1$ to $8$, % with some care given to spaces and new lines. % The |_| macro receives a digit and the corresponding capital letter % as arguments, and outputs that row of the board. First place the % letter on the left of the board, then loop from $1$ to $8$, % typesetting and \cs{message}ing a space, |-| or |0|, depending on % the value of the relevant count register. Note the two spaces % in the definition: the first ends the counter's number, the second % is typeset (in plain \TeX{}, active spaces expand to a normal space). % \begin{verbatim} % ~M#1{?{#1}#1} % ~'{M :{&M}&M{*}} % ~_#1#2{M#2:{\B#1}&M#2&M{*}} % ~\B#1#2{&M{(+#1#2 |-|0]}} % \end{verbatim} % % The input is done by |q|, which queries the user until they give % a correct input, so that |Q| and |J| are in the range $[1,8]$. % Prompt the user with a small \cs{message}, giving an example % of what move he could do (only true at the start, but the hope % is that the player will understand what the input format is). % The code that follows is similar to \LaTeXe{}'s \cs{@onelevel@sanitize}. % We extract the two first characters from the the \cs{meaning} % of the user's input (remember, |X| is \cs{expandafter}), % as |#2| and |#3| of \cs{D}. Grab the character code of each, % relative to the characters |@| (row) or |0| (column). % The closing parenthesis is where most of the work is done. % It sets |V| to the value of placing a piece in the cell % $(|Q|,|J|)$, zero if the move does not flip any of the opponent's % pieces, or if the cell is outside the board. After performing % that calculation, if |V| is zero, the move was not valid, % and we query the user again. % \begin{verbatim} % ~q{?{Row and column? e.g. E6*}\read.to\EX\D\meaning\E ;} % ~\D#1->#2#3#4;{Q`#2@Q-`@J`#3@J-`0)(V?{Invalid move #2#3.}q]} % \end{verbatim} % % So\ldots{} how do we compute the \enquote{value} of a move? % It is automatically invalid if |j| does not return $0$: % either the cell is occupied, or it is outside the board. % Then for each of the $8$ directions around the cell, % we count the number of pieces that are flipped in that % direction. The direction is stored as two counters, % |S| and |K|, each $\pm 1$ or $0$. We call |,| a first % time to test whether flipping should happen in that direction, % and, if it is (as indicated by the global value of |Z|), % call it again to actually flip. The call to |,| must happen % within a group, because it directly changes the row and column % numbers |Q| and |J|, following which cell is being queried. % \begin{verbatim} % ~){V0 (jS1z1z0z.S0z1z.S.z1z0z.]} % ~z#1{{K#1Z1{Y1,}(Z,]}} % \end{verbatim} % % The macro |,| is recursive. At each step, move $(|Q|,|J|)$ % in the direction $(|S|,|K|)$. Then, if that cell (|j|) % contains a piece belonging to the other player (|T|), % do some stuff |(Y!^P!;2]O| and repeat. What is it that % we do? Well, if the condition |Y| is met (I don't remember % how that works), we set the current cell to belong to the % player, globally, and change the score difference by $2$ % (see |;|), also globally. Then, we compute with |O| the value % corresponding to the cell that we might be flipping (see |O|). % % Otherwise (|/|), if the cell (|j|) contains a piece from the % current player (|P|), it means we have reached the end of a % run of the form \meta{initial cell} \meta{opponent's pieces} % \meta{own piece}, hence the \meta{opponent's pieces} should % count as flipped if we place our piece in the \meta{initial % cell}. Until there, all changes to |V| were local, returning % to the old value at the end of the group that |,| is contained % in. Since the run in that direction was successful, we escape % the value of |V| from the group with |\global V=V|. Under % some conditions, we set the boolean |Z| to true, globally (|!Z0|), % which triggers a second call to |,| with different setting, % and actually flips the opponent's pieces. % \begin{verbatim} % ~,{@QS@JK[j=T(Y!^P!;2]O,/[j=P!VV(I(Y/!Z0]]]]} % \end{verbatim} % % I moved those |O| and |"| guys a little bit in this explanation, % but not in the original implemenation, because it is hard % to sync. We assign weights to each of the $64$ cells: % \begin{center} % \halign{&\hfil#\hfil\cr % 9 & 1 & 6 & 6 & 6 & 6 & 1 & 9 \cr % 1 & 1 & 2 & 2 & 2 & 2 & 1 & 9 \cr % 6 & 2 & 4 & 4 & 4 & 4 & 2 & 6 \cr % 6 & 2 & 4 & 4 & 4 & 4 & 2 & 6 \cr % 6 & 2 & 4 & 4 & 4 & 4 & 2 & 6 \cr % 6 & 2 & 4 & 4 & 4 & 4 & 2 & 6 \cr % 1 & 1 & 2 & 2 & 2 & 2 & 1 & 9 \cr % 9 & 1 & 6 & 6 & 6 & 6 & 1 & 9 \cr} % \end{center} % All weights are positive, so that every move which flips a piece % ends up with a positive overall value. The AI would be better if % the places next to corners had a negative weight, but I would have % too much code to rewrite for that to work. We really have three % types of rows and three types of columns. Converting from |Q| % or |J| is done by |"|, then we assemble the two as a number % in the range $[0,8]$, and use another \cs{ifcase} construction % to produce the weights. % \begin{verbatim} % ~O{Z"Q\multiplyZ3@Z"J@V(Z9|1|6|1|1|2|6|2|4] } % ~"#1{(#1|0|1|2|2|2|2|1|0]} % \end{verbatim} % % The counter |R| keeps track of the score difference, % and is updated with |;2| (when flipping a piece) or |;1| (when % adding a piece). The counter |R| should be \cs{advance}d (|@|) % by a positive amount when the current player |P| is player |0|, % and a negative amount for player |-|. % \begin{verbatim} % ~;{@R(P|-]} % \end{verbatim} % % After printing the board, we go through every cell and find the % one with the highest value. The macro \cs{A}, does one row, hence % |\:\A| does all the rows. Store the argument as the row number |Q|, % then loop over columns. After setting the column number |J| to % its argument, \cs{C} calls |)|, which as explained above computes % the value of placing a piece there, throws away that case if it flips % nothing, otherwise also counts the weight of the current cell. Then % update the best value |W| and the best row |U| and column |L| if % the new |V| is larger than |W|. % \begin{verbatim} % ~\A#1{Q#1:\C} % ~\C#1{J#1)[0WWVUQLJ]]} % \end{verbatim} % % We won't need |~| as \cs{def} anymore, so we reuse it as the main command. % \begin{itemize} % \item First exchange the players: set |P| equal to |T|, but first expand % the value of |P| after |T| to set that as well. % \item Secondly, open an alignment, with a repeating preamble adding a space % at its end. Then message a new-line (we should be using |?| rather than % |M| here, I think) to keep a clean output. Afterwards, print the top line % with |'|, the eight lines of the bulk with |_|, and the bottom line, % which happens to end with |?{*}*|, \emph{i.e.}, ends with \cs{cr}: % we can thus close the alignment, and cause \TeX{} to output the page. % \item After printing, it is time to check whether there is a move or not. % We don't want to flip pieces at this stage, hence set the boolean |I| % to false ($1$). And we reset the best value to $0$, unless it was % already $0$ (which means that the previous player had no available % move), in which case we set it to $-1$. Then loop over rows, finding % the best value (see \cs{A}). Reset the boolean |I| to be true. % \item If a move was found in the previous step ($|W|>0$), either % use it if the player is the AI, or query the user. The various % booleans are set up in such a way as to do the flipping, so % calling |)| does it. Then also put a player's piece in the current % cell |^|, and increase the score difference by $1$. % \item Finally, if neither player could move, declare the game ended, % give the score, and \cs{end} the run. Otherwise, repeat. % \end{itemize} % Of course, after defining |~|, we call it. Let's play! % \begin{verbatim} % ~~{ % PXTXTNP % \halign{&## *M{*}'_1A_2B_3C_4D_5E_6F_7G_8H'}\vfil\break % I1 W(W./0] :\AI0 % [0R-/0] wins by N[0>R-]R].} % X\end % ] % ~ % } % ~ % \end{verbatim} % % \end{document}