Paste: playoffmatrix

% unplayo
% complete unplay for ayo
% along with payoff matrices for each possibility
% by Rex Ford
% James Madison University

% Collecting information


function unplayo

% calculates the number of stones obtained
% by making a certain choice on a board
    function [score,board] = advantage(board,choice)
        number_there=board(choice);
        board(choice)=0;
        pos=choice;
        for x=1:number_there
            pos=mod(pos,length(board))+1;
            if(pos==choice)
                pos=mod(pos,length(board))+1;
            end
            board(pos)=board(pos)+1;
        end
        % now, we must steal!
        score=0;
        while((board(pos)==2 || board(pos)==3) && ~same_side(board,choice,pos))
            score=score+board(pos);
            board(pos)=0;
            pos=pos-1;
            if(pos==0)
                pos=length(board);
            end
        end
    end

% calculates the payoff matrix
% for a given board
    function pom(board)
        n=length(board)/2;
        fprintf('[\n');
        for b=1:n
             [p,board2]=advantage(board,b);
           for k=1:n
               q=advantage(board2,k+n);
              fprintf('(%i,%i) ',p,q); 
           end
           fprintf('\n');
        end
        fprintf(']\n');
    end

    function skip=find_skip(state)
        % finding the number we are skipping
        skip=1;
        while(state(skip)~=0 && skip<3)
            skip=skip+1;
        end
    end
    function [fin_state,choice] = unplay_wrapping(state,start_pos,wraps)
        pos=start_pos;
        collection=0;
        % finding the lowest value that isn't the skip bin
        skip=find_skip(state);
        while(state(pos)>0 || wraps>0)
            if(pos==skip && wraps>0)
                wraps=wraps-1;
                if(pos>1)
                    pos=pos-1;
                else
                    pos=length(state);
                end
            elseif(pos~=skip)
                state(pos)=state(pos)-1;
                collection=collection+1;
                if(pos>1)
                    pos=pos-1;
                else
                    pos=length(state);
                end
            end
        end
        state(pos)=collection;
        fin_state=state;
        choice=pos;
    end


    function [fin_states,choices] = unplay(state,start_pos)
        fin_states=zeros(1,length(state));
        choices=zeros(1,1);
        skip=find_skip(state);
        % start 'lowest' on a non-zero
        lowest=1;
        while(state(lowest)==0)
            lowest=lowest+1;
        end
        %set 'lowest' to the index of the min
        for q=1:length(state)
            if(state(q)~=0 && state(q) < state(lowest) && q~=skip)
                lowest=q;
            end
        end
        for wraps=0:state(lowest)
            [fin_states(wraps+1,:),choices(wraps+1,1)] = unplay_wrapping(state,start_pos,wraps);
        end
    end

% tells if a position is on 'my' side
    function is_it = my_side(state,x)
        is_it=same_side(state,1,x);
    end

% are these two positions on the same side?
    function is_it =same_side(state,x,y)
        is_it=false;
        n=length(state)/2;
        if(x>n && y>n)
            is_it=true;
        end
        if(x<=n && y<=n)
            is_it=true;
        end
    end

    function even=is_even(state)
        even=true;
       for x=1:length(state)-1
            even=even && (state(x)==state(x+1));
       end
    end


    function [good_answers,good_choices]=filter_results(answers,choices,state)
        x=1;
        [the_length,the_width]=size(answers);
        while(x<=the_length)
            the_min = min(answers(x,:));
            the_right_min = min(answers(x,floor(the_width/2)+1:the_width));
            test_board=answers(x,:);
            [s,test_result]=advantage(test_board,choices(x,:));
            if(the_min<0 ||(the_right_min>0 && is_even(answers(x,:))==false ) || choices(x)>the_width/2 || isequal(test_result,state)==false)
                answers(x,:)=[];
                choices(x,:)=[];
                x=x-1;
                [the_length,the_width]=size(answers);
            end
            x=x+1;
        end
        good_answers=answers;
        good_choices=choices;
    end

    function amount=zero_length(state,x)
        k=0;
        while(x-k>length(state)/2 && state(x-k)==0)
            k=k+1;
        end
        amount=k;
    end

    function the_array=to_bin_array(x,width)
        bin=dec2bin(x);
        [bin_length,bin_width]=size(bin);
        the_array=zeros(1,width);
        for idx=1:bin_width
            the_array(idx)=bin(bin_width-idx+1)-48;
        end
    end

%% Here is the beginning of the actual program:

bins=input('how many bins? ');
while(mod(bins,2)~=0)
    bins=input('you must enter an even number. ');
end
state=zeros(1,bins);
for i=1:bins
    fprintf('bin %i: ',i);
    state(i)=input('how many? ');
end
state

% Here is the meat:
answers=zeros(1,length(state));
choices=zeros(1,1);
original_state=state;
for j=length(state):-1:1
    if(state(j)==0 && same_side(state,1,j)==false)
        num_zeros=zero_length(state,j);
        % for every combination of 2's and 3's in this 
        % strand of zeros that is num_zeros long
        for b=0:2^(num_zeros)-1
            my_array=to_bin_array(b,num_zeros);
            my_array=my_array+ones(size(my_array))*2;
            state(j-num_zeros+1:j)=my_array(1,1:num_zeros);
            [new_answers,new_choices]=unplay(state,j);
            answers=[answers;new_answers];
            choices=[choices;new_choices];
            state=original_state;
        end
    elseif(state(j)~=0)
        [new_answers,new_choices]=unplay(state,j);
        answers=[answers;new_answers];
        choices=[choices;new_choices];
        state=original_state;
    end
end

answers(1,:)=[];
choices(1,:)=[];
[answers,choices]=filter_results(answers,choices,state);

% at this point, answers contains all of the possible previous states
% and choices contains all of the correlating bins sown

for t=1:size(answers)
    fprintf('state %i :',t);
    answers(t,:)
    choice=choices(t)
    pom(answers(t,:));
end

end