Tic Tac Toe Simulator - Searching a 3-D matrix for cases where 2-dimensions are identical

I wrote a Monte Carlo code that randomly generates completed games of Tic-Tac-Toe in a 3x3 "A" matrix. Each game is stored in a 3x3xN "Games" matrix, where N is the number of games being simulated.

My question is the following: once I have a 3x3xN "Games" matrix of Tic-Tac-Toe games, how can I search the "Games" matrix to determine which games are identical? My goal for this code is to determine the number of unique, non-identical games of Tic-Tac-Toe.

Below I have is the code for generating a number of random games:

    %Number of games per simulation
    N = 1E6;
    Games = zeros(3,3,N);
    Unique = zeros(3,3,N+1);
    ticker = 1;

    for i = 1:N;
        A = zeros(3,3);
        flag = 0;
        turn = 1;
        while flag == 0;
            %Player 1 goes first, Player 2 goes next, switch
            if turn == 1;
                n = 1;
            else if turn ==0;
                    n = 2;
                end
            end

            %Check to see if board is full BEFORE player makes move
            Full = all(A(:) > 0);
            if Full == 1
                break
            end

            %Turn repeats until a marker is placed or board is full
            flag_2 = 0;
            while flag_2 == 0;

                %Checks if board is full
                Full = all(A(:) > 0);
                if Full == 1
                    break
                end

                %Pick a coordinate
                x = randi(3);
                y = randi(3);

                %Player Places Marker unless board is full
                if A(x,y) == 0;
                    A(x,y) = n;
                    flag_2 = 1;
                end
            end

            %Checks for win conditions (8 possible)
            flag_winner = 0;
            %Check rows
            if A(1,1) == A(1,2) && A(1,1) == A(1,3) && A(1,1) ~= 0; %Row1
                flag_winner = 1;
            elseif A(2,1) == A(2,2) && A(2,1) == A(2,3) && A(2,1) ~= 0; %Row2
                flag_winner = 2;
            elseif A(3,1) == A(3,2) && A(3,1) == A(3,3) && A(3,1) ~= 0; %Row3
                flag_winner = 3;
                %Check columns
            elseif A(1,1) == A(2,1) && A(1,1) == A(3,1) && A(1,1) ~= 0; %Col1
                flag_winner = 4;
            elseif A(1,2) == A(2,2) && A(1,2) == A(3,2) && A(1,2) ~= 0; %Col2
                flag_winner = 5;
            elseif A(1,3) == A(2,3) && A(1,3) == A(3,3) && A(1,3) ~= 0; %Col3
                flag_winner = 6;
                %Check Diagonals
            elseif A(1,1) == A(2,2) && A(1,1) == A(3,3) && A(1,1) ~= 0; %UpD
                flag_winner = 7;
            elseif A(3,1) == A(2,2) && A(3,1) == A(1,3) && A(3,1) ~= 0; %DownD
                flag_winner = 8;
            end

            %End game if there is a winner
            if flag_winner ~= 0;
                winner = n;
                break
            end

            %Change Player's Turn
            turn = 1 - turn;
        end

        %Stores game
        Games(:,:,i) = A(:,:);
    end

Below is the search method I am currently using; it is placed after the game generation code and runs through the games after all games have been made and stored in the "Games" matrix.

    %Compare games to see which games are identical
    %Counter variable s(i)
    for  i = 1:N
        s(i) = 0;
        Test = Games(:,:,i);
        for j = i+1:N
            if Test == Games(:,:,j);
                s(i) = s(i) + 1;
                break
            end
        end
    end

    %How many similar games?
    Similar = nnz(s);

    %How many unique games?
    Unique(q) = N - Similar

Any assistance would be greatly appreciated!

Answer 1

[Rik]

If you merge the first two dimensions, you should be able to use the unique function with the 'row' option.

A2=squeeze([A(1,:,:) A(2,:,:) A(3,:,:)]);

[William Murray]

I used your method and it yielded the same results as the search method I implemented. That said, using these functions were significantly faster than the method I was doing. I can't think of any errors with either search method, but having another method available to validate my own results makes me more confident with my program. Thanks for the help!

I am attaching the code I used for reference, this is placed outside the main loop:

    %Matlab Forum Solution
    Games2 = squeeze([Games(1,:,:) Games(2,:,:) Games(3,:,:)]);
    Games2 = transpose(Games2);

    %Check for unique values
    [Rows,ia,ic] = unique(Games2(:,1:9),'rows');
    Size_games = size(Rows);
    Number_games(q) = Size_games(1)