USING MATLAB For the game 2048, develop code (MATLAB) to move the tiles in eithe
ID: 3865653 • Letter: U
Question
USING MATLAB
For the game 2048, develop code (MATLAB) to move the tiles in either the up, down, left, or right direction.
Given the location of the tiles, calculate how the tiles and score will change for each move.
Create the following two functions (MATLAB):
•MoveLeftRight
–Summary: Given the board as a 4x4 matrix, determine the new board after moving left or right
–Inputs: board (4x4 matrix), current score (numeric value), left (boolean value)
–Outputs: new board (4x4 matrix), new score (numeric value)
–Example to move left: [newBoard,newScore] = MoveLeftRight(board,score,true);
–Example to move right: [newBoard,newScore] = MoveLeftRight(board,score,false);
•MoveUpDown
–Summary: Given the board as a 4x4 matrix, determine how the new board after moving up or down
–Inputs: board (4x4 matrix), current score (numeric value), up (boolean value)
–Outputs: new board (4x4 matrix), new score (numeric value)
–Example to move up: [newBoard,newScore] = MoveUpDown(board,score,true);
–Example to move down: [newBoard,newScore] = MoveUpDown(board,score,false);
Explanation / Answer
function npuzzle(cmd)
% npuzzle % Start Main N-Puzzle Interface
% npuzzle('fifteen') % Start new 15-Puzzle w/o Main Interface
% Developed by Per-Anders Ekstrm, 2003-2007 Facilia AB.
if ~nargin
npuzzle('init')
return;
end
if ~(ischar(cmd)||isscalar(cmd))
return;
end
switch cmd
%------------------------------------------------------------------
case 'init'
% MAIN FIGURE
scrsz = get(0,'ScreenSize');
hFigure = figure( ...
'Name','N-Puzzle', ...
'Menubar','none',...
'NumberTitle','off', ...
'KeyPressFcn','npuzzle(double(get(gcbf,''Currentcharacter'')))', ...
'Units','pixels', ...
'Tag','npuzzle', ...
'Position',[(scrsz(3)-510)/2 (scrsz(4)-500)/2 510 500], ...
'Color',[.95 .95 .95], ...
'Colormap',[1 1 1;.93 .97 .93;1 1 .6;.6 .8 1;.6 1 .6;1 .6 .6], ...
'Visible','on');
% MENU
FileMenu = uimenu(hFigure,'Label','File');
uimenu(FileMenu,'Label','New Game','Accelerator','N','Callback','npuzzle(''NewGame'')');
NewBoard = uimenu(FileMenu,'Label','New Board');
uimenu(NewBoard,'Label','3 (2x2)','Callback','npuzzle(''three'')');
uimenu(NewBoard,'Label','8 (3x3)','Callback','npuzzle(''eight'')');
uimenu(NewBoard,'Label','15 (4x4)','Callback','npuzzle(''fifteen'')');
uimenu(NewBoard,'Label','24 (5x5)','Callback','npuzzle(''twentyfour'')');
uimenu(NewBoard,'Label','35 (6x6)','Callback','npuzzle(''thirtyfive'')');
uimenu(NewBoard,'Label','48 (7x7)','Callback','npuzzle(''fourtyeight'')');
uimenu(NewBoard,'Label','Custom ...','Separator','on','Callback','npuzzle(''CustomBoard'')');
uimenu(FileMenu,'Label','Import Game ...','Callback','npuzzle(''ImportGame'')');
uimenu(FileMenu,'Label','Solve Game','Separator','on','Callback','npuzzle(''Solve'')');
uimenu(FileMenu,'Label','Exit','Accelerator','Q','Separator','on','Callback','delete(gcf)');
EditMenu = uimenu(hFigure,'Label','Edit');
uimenu(EditMenu,'Label','Undo','Accelerator','Z','Callback','npuzzle(''Undo'')','Tag','Undo');
uimenu(EditMenu,'Label','Redo','Accelerator','R','Callback','npuzzle(''Redo'')','Tag','Redo');
HelpMenu = uimenu(hFigure,'Label','Help');
uimenu(HelpMenu,'Label','Help','Accelerator','H','Callback','helpwin npuzzle');
uimenu(HelpMenu,'Label','Simulate History','Callback','npuzzle(''SimulateHistory'')','Separator','on');
uimenu(HelpMenu,'Label','About','Callback','npuzzle(''About'')','Separator','on');
% MATRIX AXES
axes( ...
'Parent',hFigure, ...
'Units','normalized', ...
'Clipping','on', ...
'Position',[0.02 0.02 0.96 0.96]);
axis('square')
% Start a new board with N=16
startgame(16)
%------------------------------------------------------------------
case 'Surface'
ud = get(gca,'UserData');
set(gcf,'Name',[num2str(ud.N-1) '-Puzzle'])
EdgeColor = [.6 .6 .6];
FaceColor = [1 1 1];
FontSize = .5/ud.n;
HoleColor = [.3 .3 .3];
delete(findobj(gca,'Tag','Surface'))
delete(findobj(gca,'Tag','Hole'))
arrayfun(@(x)delete(findobj(gca,'Tag',num2str(x))),1:1000)
% MATRIX SURFACE
CData = zeros(ud.n+1,ud.n+1);
surface( ...
zeros(size(CData)),CData, ...
'Parent',gca, ...
'ButtonDownFcn','npuzzle(''ButtonDown'');', ...
'EdgeColor',EdgeColor, ...
'FaceColor',FaceColor, ...
'LineWidth',1,...
'Tag','Surface')
axis off
hold on
% TEXT FIELDS
arrayfun(@(x)text( ...
'Position',[mod(x-1,ud.n)+1 ud.n+1-ceil(x/ud.n)]+.5, ...
'String','', ...
'FontUnits','normalized', ...
'FontSize',FontSize, ...
'Tag',num2str(x), ...
'ButtonDownFcn','npuzzle(''ButtonDown'');', ...
'HorizontalAlignment','center'), ...
1:ud.N)
% EMPTY FIELD
fill(1,1,HoleColor, ...
'ButtonDownFcn','npuzzle(''ButtonDown'');', ...
'Tag','Hole')
%------------------------------------------------------------------
case 'three'
startgame(4)
%------------------------------------------------------------------
case 'eight'
startgame(9)
%------------------------------------------------------------------
case 'fifteen'
startgame(16)
%------------------------------------------------------------------
case 'twentyfour'
startgame(25)
%------------------------------------------------------------------
case 'thirtyfive'
startgame(36)
%------------------------------------------------------------------
case 'fourtyeight'
startgame(49)
%------------------------------------------------------------------
case 'CustomBoard'
prompt = {'Input Size of Board (N):'};
name = 'Custom Board Size';
options.Resize = 'on';
answer = inputdlg(prompt,name,1,{'15'},options);
if ~isempty(answer)
N = str2double(answer{1})+1;
n = round(sqrt(N));
if n^2==N
startgame(N)
else
errordlg('Input Size (N) Not Accepted','Custom Board Size')
end
end
%------------------------------------------------------------------
case 'NewGame'
ud = get(gca,'UserData');
board = shuffleboard(1:ud.N,10000); % Shuffle the board
ud.board = board;
ud.boardhistory = ud.board;
ud.histpos = 1;
ud.starttime = clock;
ud.endtime = [];
set(gca,'UserData',ud);
set(findobj(gcf,'Tag','Undo'),'Enable','off')
set(findobj(gcf,'Tag','Redo'),'Enable','off')
drawboard()
drawpos()
%------------------------------------------------------------------
case 'ImportGame'
prompt = {'Input Game as a Vector or a Matrix:'};
name = 'Import Game';
options.Resize = 'on';
answer = inputdlg(prompt,name,1,{''},options);
if ~isempty(answer)&&~isempty(answer{1})
board = str2num(answer{1})';
board = board(:)';
N = length(board);
n = round(sqrt(N));
if ~isempty(board)&&n^2==N&&~ismember(0,ismember(1:N,board))
ud = get(gca,'UserData');
ud.board = board;
ud.N = N;
ud.n = n;
ud.currpos = 1;
ud.boardhistory = ud.board;
ud.histpos = 1;
ud.starttime = clock;
ud.endtime = [];
set(gca,'UserData',ud);
set(findobj(gcf,'Tag','Undo'),'Enable','off')
set(findobj(gcf,'Tag','Redo'),'Enable','off')
npuzzle('Surface')
drawboard()
drawpos()
else
errordlg('Input Game Not Accepted','Import Game')
end
end
%------------------------------------------------------------------
case 'SimulateHistory'
set(gcf,'Color',[.7 0 0],'Pointer','watch','CloseRequestFcn','','KeyPressFcn','')
ud = get(gca,'UserData');
for i=1:ud.histpos
hole = find(ud.boardhistory(i,:)==ud.N);
x = mod(hole-1,ud.n)+1;
y = ud.n+1-ceil(hole/ud.n);
delete(findobj(gca,'tag','currpos'))
plot(x+[0 .995 .995 0 0]+0.005,y+[0 0 .995 .995 0],'r', ...
'LineWidth',2, ...
'Tag','currpos')
pause(.2)
arrayfun(@(x)set(findobj(gca,'tag',num2str(x)), ...
'String',num2str(ud.boardhistory(i,x))), ...
1:ud.N)
set(findobj(gca,'tag','Hole'), ...
'XData',x+[0 .99 .99 0 0]+0.005,...
'YData',y+[0 0 .99 .99 0]+0.005)
pause(.3)
end
set(gcf,'Color',[.95 .95 .95],'Pointer','arrow','CloseRequestFcn','closereq','KeyPressFcn','npuzzle(double(get(gcbf,''Currentcharacter'')))')
drawpos()
%------------------------------------------------------------------
case 'Solve'
ud = get(gca,'UserData');
if sum(ud.board(:)'==1:ud.N)~=ud.N % if not solved
set(gcf,'Color',[.7 0 0],'Pointer','watch','CloseRequestFcn','','KeyPressFcn','')
pause(.2)
boardhistory = solve(ud.board);
ud.boardhistory = [ud.boardhistory(1:ud.histpos,:);boardhistory];
ud.board = 1:ud.N;
set(gca,'UserData',ud);
set(findobj(gcf,'Tag','Redo'),'Enable','off')
set(findobj(gcf,'Tag','Undo'),'Enable','on')
ud = get(gca,'UserData');
for i=ud.histpos:size(ud.boardhistory,1)
hole = find(ud.boardhistory(i,:)==ud.N);
x = mod(hole-1,ud.n)+1;
y = ud.n+1-ceil(hole/ud.n);
delete(findobj(gca,'tag','currpos'))
plot(x+[0 .995 .995 0 0]+0.005,y+[0 0 .995 .995 0],'r', ...
'LineWidth',2, ...
'Tag','currpos')
pause(.01)
arrayfun(@(x)set(findobj(gca,'tag',num2str(x)), ...
'String',num2str(ud.boardhistory(i,x))), ...
1:ud.N)
set(findobj(gca,'tag','Hole'), ...
'XData',x+[0 .99 .99 0 0]+0.005,...
'YData',y+[0 0 .99 .99 0]+0.005)
pause(.03)
end
ud.histpos = size(ud.boardhistory,1);
set(gca,'UserData',ud);
pause(.2)
set(gcf,'Color',[.95 .95 .95],'Pointer','arrow','CloseRequestFcn','closereq','KeyPressFcn','npuzzle(double(get(gcbf,''Currentcharacter'')))')
drawpos()
end
%------------------------------------------------------------------
case 'Undo'
ud = get(gca,'UserData');
if ud.histpos>1
ud.histpos = ud.histpos-1;
ud.board = ud.boardhistory(ud.histpos,:);
set(gca,'UserData',ud);
drawboard()
set(findobj(gcf,'Tag','Redo'),'Enable','on')
end
if ud.histpos<=1
set(findobj(gcf,'Tag','Undo'),'Enable','off')
end
%------------------------------------------------------------------
case 'Redo'
ud = get(gca,'UserData');
if ud.histpos<size(ud.boardhistory,1)
ud.histpos = ud.histpos+1;
ud.board = ud.boardhistory(ud.histpos,:);
set(gca,'UserData',ud);
drawboard()
set(findobj(gcf,'Tag','Undo'),'Enable','on')
end
if size(ud.boardhistory,1)<=ud.histpos
set(findobj(gcf,'Tag','Redo'),'Enable','off')
end
%------------------------------------------------------------------
case 'ButtonDown' % MouseClick
ud = get(gca,'UserData');
n = sqrt(ud.N);
pos = get(gca,'CurrentPoint');
ud.currpos = sub2ind([n n],floor(pos(1,1)),ud.n+1-floor(pos(1,2)));
set(gca,'UserData',ud);
drawpos()
% If not left-click, treat as space
if ~strcmpi('normal',get(gcf,'SelectionType'))
npuzzle(32)
end
%------------------------------------------------------------------
case 28 % left
ud = get(gca,'UserData');
if ud.currpos~=1
ud.currpos = ud.currpos-1;
set(gca,'UserData',ud);
drawpos()
end
%------------------------------------------------------------------
case 29 % right
ud = get(gca,'UserData');
if ud.currpos~=ud.N
ud.currpos = ud.currpos+1;
set(gca,'UserData',ud);
drawpos()
end
%------------------------------------------------------------------
case 30 % up
ud = get(gca,'UserData');
if ud.currpos>ud.n
ud.currpos = ud.currpos-ud.n;
set(gca,'UserData',ud);
drawpos()
end
%------------------------------------------------------------------
case 31 % down
ud = get(gca,'UserData');
if ud.currpos<=ud.N-ud.n
ud.currpos = ud.currpos+ud.n;
set(gca,'UserData',ud);
drawpos()
end
%------------------------------------------------------------------
case 32 % space
ud = get(gca,'UserData');
n = sqrt(ud.N);
hole = find(ud.board==ud.N);
bx = mod(hole-1,n)+1;
by = ud.n+1-ceil(hole/n);
cx = mod(ud.currpos-1,n)+1;
cy = ud.n+1-ceil(ud.currpos/n);
if (bx==cx&&abs(by-cy)==1)||(by==cy&&abs(bx-cx)==1)
ud.board(hole) = ud.board(ud.currpos);
ud.board(ud.currpos) = ud.N;
ud.histpos = ud.histpos+1;
ud.boardhistory(ud.histpos,:) = ud.board;
if size(ud.boardhistory,1)>ud.histpos
ud.boardhistory(ud.histpos+1:end,:) = [];
end
set(findobj(gcf,'Tag','Redo'),'Enable','off')
set(findobj(gcf,'Tag','Undo'),'Enable','on')
ud.currpos = hole;
set(gca,'UserData',ud);
drawboard()
drawpos()
if isempty(ud.endtime)
checksolution()
end
end
%------------------------------------------------------------------
case 'About'
ico = ones(13)*3; % create simple icon matrix
ico(:,1:4:13) = 1;
ico(1:4:13,:) = 1;
ico(10:12,10:12) = 2;
map = [0 0 0;.5 .5 .6;1 1 1];
msgbox(sprintf([...
'Graphical User Interface for playing the N-Puzzle. '...
'Developed by Per-Anders Ekstrm, 2003-2007 Facilia AB '...
'E-mail: peranders.ekstrom@facilia.se']),...
'About N-Puzzle','custom',ico,map)
end
end
%% FUNCTION: DRAWBOARD
function drawboard()
ud = get(gca,'UserData');
arrayfun(@(x)set(findobj(gca,'tag',num2str(x)), ...
'String',num2str(ud.board(x))), ...
1:ud.N)
hole = find(ud.board==ud.N);
x = mod(hole-1,ud.n)+1;
y = ud.n+1-ceil(hole/ud.n);
set(findobj(gca,'Tag','Hole'), ...
'XData',x+[0 .99 .99 0 0]+0.005,...
'YData',y+[0 0 .99 .99 0]+0.005)
end
%% FUNCTION: DRAWPOS
function drawpos()
ud = get(gca,'UserData');
delete(findobj(gca,'tag','currpos'))
x = mod(ud.currpos-1,ud.n)+1;
y = ud.n+1-ceil(ud.currpos/ud.n);
plot(x+[0 .995 .995 0 0]+0.005,y+[0 0 .995 .995 0],'r', ...
'LineWidth',2, ...
'Tag','currpos')
end
%% FUNCTION: SHUFFLEBOARD
function board = shuffleboard(board,times)
N = length(board);
n = sqrt(N);
hole = find(board==N);
for i=1:times
move = [1 -1 n -n];
x = mod(hole-1,n)+1;
y = ceil(hole/n);
switch x
case 1
move(2) = 1;
case n
move(1) = -1;
end
switch y
case 1
move(4) = n;
case n
move(3) = -n;
end
newhole = hole + move(ceil(rand*4));
board(hole) = board(newhole);
hole = newhole;
end
board(newhole) = N;
end
%% FUNCTION: CHECKSOLUTION
function checksolution()
ud = get(gca,'UserData');
if ~ismember(0,ud.board==1:ud.N)
ud.endtime = clock;
set(gca,'UserData',ud);
ico = ones(13)*3; % create simple icon matrix
ico(:,1:4:13) = 1;
ico(1:4:13,:) = 1;
ico(10:12,10:12) = 2;
map = [0 0 0;.5 .5 .6;1 1 1];
msgbox(sprintf([...
'CONGRATULATIONS! '...
'Start time: %s '...
'End time: %s '...
'Elapsed time: %d seconds '...
'Number of moves: %d'],...
datestr(ud.starttime,13),...
datestr(ud.endtime,13),...
round(etime(ud.endtime,ud.starttime)),...
ud.histpos),...
'Finished N-Puzzle','custom',ico,map)
end
end
%% FUNCTION: STARTGAME
function startgame(N)
ud = get(gca,'UserData');
ud.N = N;
ud.n = sqrt(N);
ud.currpos = 1;
set(gca,'UserData',ud);
npuzzle('Surface')
npuzzle('NewGame')
end
%% FUNCTION: SOLVE
function solution = solve(board)
board = board(:)';
solution = [];
N = length(board);
n = sqrt(N);
tilePos = @(tile,board)find(board==tile);
holePos = @(board)tilePos(N,board);
column = @(pos)mod(pos-1,n)+1;
row = @(pos)ceil(pos/n);
%% PHASE 1
% 1. Find the next tile you want to place in position in the top row.
% 2. If it is not the last tile of the row, it is fairly easy to place
% correctly, simply keep the following points in mind:
% 1. Never disturb any previously placed pieces.
% 2. To move the tile in a certain direction, move the other tiles
% around until the space is next to your tile on the side you want
% to move it to. Then you can move the tile.
% 3. If the last tile is not already in position, bring it to the position
% directly below its correct spot, with the space directly below that.
% Then move tiles in the following directions:
% Down, down, right, up, left, up, right, down, down, left, up.
% This should place the piece in position.
% Note it does temporarily disturb the previously placed tile.
for cr=1:n-2 % for all rows except last two rows
for cc=1:n-1 % for all columns except last column
currentTile = cc+(cr-1)*n;
% if tile not at correct position
if tilePos(currentTile,board)~=currentTile %
% if current tile is at bottom row, move it up one step
if row(tilePos(currentTile,board)) == n
% move hole to position above it
moveHoleToRowColumn(n-1,column(tilePos(currentTile,board)))
% pop the position up one step by moving hole down
moveHole('down')
end
% move hole to bottom or side of current tile
while row(holePos(board))<n && row(holePos(board))<row(tilePos(currentTile,board))
moveHole('down');
end
if tilePos(currentTile,board)==currentTile
continue
end
% if current tile is not at correct column
while column(tilePos(currentTile,board)) ~= cc
% move hole to bottom or under tile
while row(holePos(board))<n && row(holePos(board))<=row(tilePos(currentTile,board))
moveHole('down');
end
if tilePos(currentTile,board)==currentTile
continue
end
% move hole to left/right of current tile
if column(tilePos(currentTile,board)) <= cc
while column(holePos(board))<column(tilePos(currentTile,board))+1
moveHole('right');
end
while column(holePos(board))>column(tilePos(currentTile,board))+1
moveHole('left');
end
elseif column(tilePos(currentTile,board)) > cc
while column(holePos(board))>column(tilePos(currentTile,board))-1
moveHole('left');
end
while column(holePos(board))<column(tilePos(currentTile,board))-1
moveHole('right');
end
end
% move hole up to same row of current tile
if row(holePos(board)) > row(tilePos(currentTile,board))
while row(holePos(board)) > row(tilePos(currentTile,board))
moveHole('up');
end
end
if column(holePos(board)) > column(tilePos(currentTile,board))
moveHole('left');
else
moveHole('right');
end
end
% now tile is supposed to be at correct column
% if current tile is not at correct row
while row(tilePos(currentTile,board)) ~= cr
moveHoleToRowColumn(row(tilePos(currentTile,board))+1,column(tilePos(currentTile,board))+1)
moveHole('up','up','left','down')
end
end
end
currentTile = cr*n;
% if tile not at correct position
if tilePos(currentTile,board)~=currentTile
% if current tile is at bottom row
if row(tilePos(currentTile,board)) == n
% move hole to position above it
moveHoleToRowColumn(n-1,column(tilePos(currentTile,board)))
% pop the position up one step
moveHole('down')
end
% move hole to bottom or side of current tile
if row(holePos(board))~=n && row(holePos(board))<=row(tilePos(currentTile,board))
while row(holePos(board))<n && row(holePos(board))<row(tilePos(currentTile,board))
moveHole('down');
end
end
if tilePos(currentTile,board)==currentTile
continue
end
% if current tile is not at correct column
while column(tilePos(currentTile,board)) ~= n
% move hole to bottom or under tile
while row(holePos(board))<n && row(holePos(board))<=row(tilePos(currentTile,board))
moveHole('down');
end
if tilePos(currentTile,board)==currentTile
continue
end
% move hole to left/right of current tile
if column(tilePos(currentTile,board)) <= cc
while column(holePos(board))<column(tilePos(currentTile,board))+1
moveHole('right');
end
while column(holePos(board))>column(tilePos(currentTile,board))+1
moveHole('left');
end
elseif column(tilePos(currentTile,board)) > cc
while column(holePos(board))>column(tilePos(currentTile,board))-1
moveHole('left');
end
while column(holePos(board))<column(tilePos(currentTile,board))-1
moveHole('right');
end
end
% move hole up to same row of current tile
while row(holePos(board)) > row(tilePos(currentTile,board))
moveHole('up');
end
if column(holePos(board)) > column(tilePos(currentTile,board))
moveHole('left');
else
moveHole('right');
end
end
% move last tile to under its position
while row(tilePos(currentTile,board)) > cr+1
moveHoleToRowColumn(row(tilePos(currentTile,board))+1,n-1)
moveHole('up','up','right','down')
end
% move hole to underneath it
moveHoleToRowColumn(cr+2,n)
moveHole('up','up','left','down','right','down','left','up','up','right','down')
end
end
%% PHASE 2
% 1. Use the technique in phase 1 to solve each row in turn, until there
% are only two rows left.
% 2. Rotate the puzzle a quarter turn to the right. The left column of the
% two rows becomes the top row now.
% 3. Use the technique in phase 1 to solve each row in turn, until there
% are only two rows left. This means there is only a 2x2 square left to
% solve.
% 4. Move the pieces in the remaining 2x2 square around until one piece is
% positioned correctly, and the space is in the correct spot. The other
% two tiles should automatically be correctly positioned as well.
% 5. If there are two tiles that need to be swapped, then this cannot be
% done unless two other tiles are swapped as well. If there are two
% identical tiles somewhere in the puzzle, then you will have to swap
% them and solve the rest again.
% turn the board
for cc=1:n-2 % for all columns except last two columns
cr = n; % last row
currentTile = cc+(cr-1)*n;
% if tile not at correct position
if tilePos(currentTile,board)~=currentTile %
% if tile is not at last row, make it
if row(tilePos(currentTile,board)) ~= n
moveHoleToRowColumn(n,column(tilePos(currentTile,board)))
moveHole('up')
end
while column(tilePos(currentTile,board)) ~= cc
moveHoleToRowColumn(n-1,column(tilePos(currentTile,board)))
moveHole('left','down','right')
end
end
currentTile = cc+(cr-2)*n;
% if tile not at correct position
if tilePos(currentTile,board)~=currentTile
% move hole toright if it might disturb other pieces
if column(holePos(board))==cc
moveHole('right');
end
if tilePos(currentTile,board)==currentTile
continue
end
% tile is not at row n-1, make it
if row(tilePos(currentTile,board)) ~= n-1
moveHoleToRowColumn(n-1,column(tilePos(currentTile,board)))
moveHole('down')
end
% move last tile to under its position
while column(tilePos(currentTile,board)) ~= cc+1
moveHoleToRowColumn(n,column(tilePos(currentTile,board)))
moveHole('left','up','right')
end
% move hole to right side of it
moveHoleToRowColumn(n,cc+2);moveHole('up')
moveHole('left','left','down','right','up','right','down','left','left','up','right')
end
end
% Last 2x2 square
count = 0;
while holePos(board)~=n*n || tilePos((n-1)*n,board)~=(n-1)*n
if row(holePos(board))==n
if column(holePos(board))==n
moveHole('up')
else
moveHole('right')
end
else
if column(holePos(board))==n
moveHole('left')
else
moveHole('down')
end
end
count = count+1;
if count>10 % unsolvable
break
end
end
function swap(x,y)
xp = (board==x);
yp = (board==y);
board(xp) = y;
board(yp) = x;
end
function moveHole(varargin)
hp = find(board==N);
for ii=1:nargin
switch varargin{ii}
case 'left'
hp = hp-1;
case 'right'
hp = hp+1;
case 'up'
hp = hp-n;
case 'down'
hp = hp+n;
end
swap(N,board(hp))
solution = [solution;board];
end
end
function moveHoleToRowColumn(x,y)
while row(holePos(board)) < x
moveHole('down')
end
while row(holePos(board)) > x
moveHole('up')
end
while column(holePos(board)) < y
moveHole('right')
end
while column(holePos(board)) > y
moveHole('left')
end
end
end
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