%Copyright 2006, Adarsh Krishnamurthy (me.berkeley.edu/~adarsh) and Athulan Vijayaraghavan (me.berkeley.edu/~athulan)

clc; clear all;
%recursive backtracker - 3d
tic
%size of the maze - only square
n = 5;

n_cells = n*n;

%listing all the cells with a uid in an array
ctr = 1;
for i = 1:n
    for j = 1:n
        cells_face_1(ctr, :) = [1 i j i-1 j-1 n i-1 j n i j n i j-1 n];
        
        cells_face_2(ctr, :) = [2 i j i-1 0 j-1 i-1 0 j i 0 j i 0 j-1];
        
        cells_face_3(ctr, :) = [3 i j i-1 n-j+1 0 i-1 n-j 0 i n-j 0 i n-j+1 0];
        
        cells_face_4(ctr, :) = [4 i j i-1 n n-j+1 i-1 n n-j i n n-j i n n-j+1];
        
        cells_face_5(ctr, :) = [5 i j 0 j-1 i-1 0 j-1 i 0 j i 0 j i-1];
        
        cells_face_6(ctr, :) = [6 i j n j-1 n-i+1 n j-1 n-i n j n-i n j n-i+1];
        
        ctr = ctr + 1;
    end
end
cells = [cells_face_1; cells_face_2; cells_face_3; cells_face_4; cells_face_5; cells_face_6];

%listing all the edges in an array
edges = [];
k = 1;
for i = 1:n
    for j = 1:n+1
        edges_face1(k, :) = [i-1 j-1 0 i j-1 0];
        edges_face1(k+1, :) = [j-1 i-1 0 j-1 i 0];
        
        edges_face2(k, :) = [i-1 j-1 n i j-1 n];
        edges_face2(k+1, :) = [j-1 i-1 n j-1 i n];
                
        edges_face3(k, :) = [0 i-1 j-1 0 i j-1];
        edges_face3(k+1, :) = [0 j-1 i-1 0 j-1 i];
                
        edges_face4(k, :) = [n i-1 j-1 n i j-1];
        edges_face4(k+1, :) = [n j-1 i-1 n j-1 i];
                
        edges_face5(k, :) = [i-1 0 j-1 i 0 j-1];
        edges_face5(k+1, :) = [j-1 0 i-1 j-1 0 i];
                
        edges_face6(k, :) = [i-1 n j-1 i n j-1];
        edges_face6(k+1, :) = [j-1 n i-1 j-1 n i];
        
        k = k + 2;
    end
end
edges = [edges_face1; edges_face2; edges_face3; edges_face4; edges_face5; edges_face6];
edges = unique(edges, 'rows');


%initialize the cell stack
stack = [];

%choose a random cell to begin with
r = ceil(length(cells)*(rand));
stack(1, :) = cells(r, 1:3);
visited = [];

ctr = 1;

while length(stack)>0
    ctr;
     current_cell = stack(end, :); %set the current cell
     visited(end+1, :) = current_cell; %add current cell to the stack
     current_neighbors = neighbors3d(current_cell, n); %find the neighbors
     current_neighbors = setdiff(current_neighbors, visited, 'rows'); %remove those visited
    
    if size(current_neighbors, 1)==0
        stack(end, :) = [];
    elseif size(current_neighbors, 1)>0     
        r = ceil(size(current_neighbors, 1)*(rand));
        chosen_neighbor = current_neighbors(r, :);
        stack(end+1, :) = chosen_neighbor;
    end
    
    ctr = ctr + 1;
end
ctr


for j = 1:length(visited)-1
    j
    %pull up first cell
    [p i r] = intersect(cells(:, 1:3), visited(j, :) ,'rows');
    pts_1 = [cells(i,4) cells(i,5) cells(i,6); cells(i,7) cells(i,8) cells(i,9); cells(i,10) cells(i,11) cells(i,12); cells(i,13) cells(i,14) cells(i,15)];
    
    [p i r] = intersect(cells(:, 1:3), visited(j+1, :) ,'rows');
    pts_2 = [cells(i,4) cells(i,5) cells(i,6); cells(i,7) cells(i,8) cells(i,9); cells(i,10) cells(i,11) cells(i,12); cells(i,13) cells(i,14) cells(i,15)];
    
    common_edge = intersect(pts_1, pts_2, 'rows');
    common_edgeA = [common_edge(1, :) common_edge(2, :)];
    common_edgeB = [common_edge(2, :) common_edge(1, :)];
    
    for k = 1:length(edges)
        if edges(k, :) == common_edgeA
            edges(k, :) = [0 0 0 0 0 0];
        end
        if edges(k, :) == common_edgeB
            edges(k, :) = [0 0 0 0 0 0];
        end
    end    
end
figure(2);

figure(2); axis square; hold on;
for i = 1:length(edges)
    x = [edges(i, 1) edges(i, 4)];
    y = [edges(i, 2) edges(i, 5)];
    z = [edges(i, 3) edges(i, 6)];
    plot3(x, y, z);
    h = plot3(x, y, z);
    set(h, 'LineWidth', 4);

end
    fill3([0 0 n n], [0 n n 0], [0 0 0 0], 'y');
    fill3([0 0 n n], [0 n n 0], [n n n n], 'y');
    fill3([0 0 n n], [0 0 0 0], [0 n n 0], 'y');
    fill3([0 0 n n], [n n n n], [0 n n 0], 'y');
    fill3([0 0 0 0], [0 0 n n], [0 n n 0], 'y');
    fill3([n n n n], [0 0 n n], [0 n n 0], 'y');    


%show_maze(n, edges);

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