TweetFollow Us on Twitter

Towers
Volume Number:2
Issue Number:1
Column Tag:Threaded Code

Animated Hanoi Towers in NEON

By Jörg Langowski, EMBL, c/o I.L.L., Grenoble Cedex, France, MacTutor Editorial Board

Lately, we have had a number of requests for a column on NEON. Since no neon articles have been forth coming, I have been asked to temporarily switch from my usual Forth ramblings to NEON. Since NEON is so close to Forth, we have decided to show a NEON example this month for a change. In light of this, we will re-name this column "Threaded Code" to cover all the Forth like object oriented languages that are Forth derivatives on the Mac.

The principles of object oriented programming have already been explained in several earlier columns (see LISP V1#6, NEON V1#8), so I am not going to dwell on that here. Rather, we are going to look at the famous Towers of Hanoi algorithm from an object-oriented point of view, gaining some on-hands experience with an example that - I feel - is particularly appropriate for this approach.

Let's recall: The 'towers' are three stacks of disks (Fig. 1). The leftmost one is filled with n disks stacked on top of one another in order of decreasing size, the other two are initially empty. The objective is to move the disks from the leftmost to the rightmost position, one by one, in such a way that a larger disk is never put on top of a smaller one. This works if one uses the middle position as a 'scratchpad' (try it out with pieces of paper), even though this is a rather tiresome procedure, if performed manually.

Fig. 1: Initial and final positions of Towers of Hanoi.

This is, of course, where Mac comes in; and the algorithm to solve the puzzle is very short if written recursively. In pseudo-Pascal it would look like this (see also John Bogan's Modula-2 column in V1#6):

procedure hanoi (n, start, inter, finish:integer);
    begin
     if n<>0 then 
 begin
 hanoi (n-1, start, finish, inter);
 move (n, start, finish);
 hanoi (n-1, inter, start, finish)
 end
    end;

where n is the number of disks, and start, inter and finish denote the starting, scratch and final positions for the disks. move is a procedure that (somehow) moves the disk from one stack to another.

OK, so if we set up a stack of disks, provide three towers to put them on to, and execute this procedure, we should be able to watch how Macintosh solves the Towers problem.

There are two things to notice: First, the definition is obviously recursive, second, we have to be careful how to represent our data.

Recursive definitions - NEON and MacForth

A very simple recursive procedure is the definition of the factorial of an integer number, which is given at the very beginning of the program example (listing 1). This definition works in NEON; you may refer to a word within the definition of the word itself (By the way, even if you weren't allowed to do it that way, you could resort to the forward declaration).

MacForth, however, sets the smudge bit in the vocabulary while compiling a new definition; therefore the word being defined is not known to the system at compile time and cannot be referred to by itself. You have probably seen the effect of the smudge bit already; when the compiler exits a declaration due to an error, words will show the first letter of the latest definition changed (in fact, it has the 8th bit set). One can easily circumvent this restriction by writing

: factorial   [ smudge ] 
   dup if dup 1- factorial * else drop 1 then ;
smudge

i.e., executing smudge during the compilation of factorial and resetting it afterwards. This will give a working definition, within the limit that is given by the 32-bit maximum integer size of the Macintosh.

Representation of disks and towers as NEON objects

Since we are, in fact, simulating material objects, moving them around and also displaying the result of our simulation on the screen, the Towers of Hanoi problem seems to be idealy suited for an object oriented language like NEON. We could define 'disks' as objects that can be drawn, put on top of other objects, called 'towers' and moved between them. The towers will automatically keep track of how many disks are on them, the disks will 'know' what tower they are on and how to 'draw themselves'.

The Three Towers

There is one predefined class in NEON, ordered-col, that represents a list of variable size. Elements of that list are 4-byte entities. A tower in our example will be an ordered-col of specified maximum size. In addition, it will have a certain position on the screen, which can be accessed by the methods getX: and getY: and a draw: method that draws the tower at its position in the current grafPort. That's all we need as a 'stacking device' for the disks. Everything else is taken care of by the disks themselves, as you will see soon.

The instance variables needed for every object of class tower are: rects that correspond to the base and the post, and ints that contain the x and y position of the center of the base.

Now we could start our simulation by creating three tower objects, e.g.

 tower babylon
 tower london
 tower pisa

Except for the fact that this looks cute, there is really no advantage in having named objects here. Just to make the point, and as an example how objects can be made to refer to other objects, we set up the three towers as a 3-element 4-byte array towers. This gives the additional advantage that we can refer to them by index. The array is initialized by the word make.towers, which shows how one can create 'nameless' objects on the heap with the heap> prefix (in my review copy of NEON, this information is hidden somewhere in the pages of Part III Chapter 1; I am confident that a revised manual will have this in the glossary).

xcenter ycenter ndisks heap> tower will leave on the stack the address of a new object of class tower created on the heap. The tower contains ndisks disks, and its base is centered at (xcenter,ycenter).

ndisks make.towers creates three of these gizmos equally spaced near the bottom of the screen, each of them having space for disks, but no disks on them yet. Their addresses are put into the array towers.

draw.towers will draw the towers, but not the disks. In this definition you see how one makes use of late binding; we want to send a draw: message to an object which is exactly known only at execution time (since towers could contain any kind of address). Therefore, if we want to draw the i-th tower, we have to write draw: [ i at: towers ] . (The same is true in immediate execution mode: draw: addr will abort with an error message, while draw: [ addr ] will do the correct thing, if addr is the address of a 'drawable' object. )

After you're finished with the example, you might want to dispose of them by calling dispose.towers. The same should be done to the disks; try writing a definition that will do the job.

Moving around the disks

The disk objects are more complicated than the towers. They have to be initialized and drawn; they will come in different sizes; and they will move around, sitting on one of the three stacks at any given time.

Since the disks won't shrink or grow, their size is known at initialization time and will be passed as a parameter to classinit:. This method also needs to know which tower the disk is on at the beginning (we pass the address of the tower object and put it into the instance variable which). The newly created disk it then put on top of the tower which it is associated with.

The draw: method is not quite general for disks, but very specialized for Hanoi disks: it makes use of the fact that a disk is only drawn right after it has been put on top of a stack. Since the size of that stack is known (by executing size: [ get: which ] ), the position of the topmost disk is exactly determined. Therefore, draw: calculates first the coordinates of the center of the disk and saves them in instance variables for later use, then does the necessary Quickdraw calls. If one wanted to do other things with the disks, e.g. drawing them at different places, one might want to factor out the code that calculates the coordinates.

undraw: removes the disk from its position (but not from the list which is being kept in the tower), and redraws the little black rectangle, the part of the post that had been overwritten previously. Here again, you see that a special assumption about the behavior of the disk is made: namely, that it does not cover anything but a certain part of the tower post.

dest move: finally will move a disk from wherever it was to the tower dest, undrawing and redrawing as necessary.

Object Interdependence

You see the line that we draw between general and specialized behavior of objects. The fact that a disk is displayed as a pattern-filled rectangle that takes up a certain amount of space on the screen is a behavior that would be general to any 'disk-like' object (unless we choose to rotate it as well). Association to another object, the tower, would also be something that could be implemented into an idealized 'general' disk. But the fact that this other object has a certain shape and that the disk can only be put onto it in a certain manner is extra information which the disk 'knows' about and which is used within the code that defines some of its methods.

To make the objects even more independent, 'MacDraw-like', would require a much more sophisticated interface between towers and disks than given here. One would then rather start by defining a subclass of window which has e.g. an ordered-col of objects associated to it, and which would be updated each time one of the objects is moved. I felt this would have created too much overhead to the program example. But you can see that MacDraw is not very far away, just go ahead and create that window, a set of objects and their appropriate behavior, and there you go... send us the code when you're done, we'll publish it.

Main routine

The main routine simply creates a Hanoi puzzle of ndisks disks and draws the initial position. ndisks i j k hanoi will move those disks ( or less, if you set ndisks differently) according to the rules of the game from tower i via j to k. Try

10 main
10 0 1 2 hanoi

or, to create a 'forbidden' pattern

10 main
5 0 1 2 hanoi
5 0 2 1 hanoi
5 1 0 2 hanoi

Have fun! Determined FORTH programmers might try to rewrite this example into MacForth or some other Forth. The Hanoi routine itself is simple. Doing the data representation in the same way should look rather more complicated...

Change of address

We have moved in the meantime. Please address all questions, remarks, suggestions, etc. regarding this column to:

Jörg Langowski

EMBL, c/o I.L.L., 156X

F-38042 Grenoble Cedex

France

Listing 1: Towers of Hanoi code
( © 110285 MacTutor by JL )
: factorial   dup if dup 1- factorial * else drop 1 then ;

:class tower <super ordered-col
        rect base
        rect column
        int xcenter
        int ycenter

    :M classinit: ( xcenter ycenter -- )
            put: ycenter put: xcenter 
            get: xcenter 70 -  get: ycenter 16 - 
            get: xcenter 70 +  get: ycenter   put: base
            get: xcenter 4 -   get: ycenter 
 limit: self 10 * 50 +  -
            get: xcenter 4 +   get: ycenter 16 - 
 put: column 
    ;M

    :M draw:  0 syspat dup fill: base fill: column ;M
    :M getX:   get: xcenter ;M
    :M getY:   get: ycenter ;M

;class

:class disk  <super object
        int size
        var which
        rect image
        int xc  int yc
    :M classinit: ( which size -- )   
                    put: size  put: which 
                    addr: self  add: [ get: which ] ;M
    :M draw: 
            getX: [ get: which ] put: xc 
            getY: [ get: which ] 
                 12 - size: [ get: which ] 10 * - put: yc
            get: xc get: size -  get: yc 4-   
            get: xc get: size +  get: yc 4+  put: image
            3 syspat fill: image  draw: image 
    ;M

    :M undraw: 19 syspat fill: image
            get: xc 4- get: yc 4- 
            get: xc 4+ get: yc 4+  put: image
            0 syspat fill: image
    ;M

    :M move: { dest -- }
            undraw: self
            addr: self add: [ dest ]
            size: [ get: which ] 1-  
            remove: [ get: which ]
            dest put: which   draw: self
    ;M
;class
3 array towers
: make.towers { ndisks -- }
   3 0 do 
      i 150 * 100 +  280 ndisks  heap> tower  
      i to: towers  loop ;

: draw.towers
   3 0 do draw: [ i at: towers ] loop ;

: dispose.towers   3 0 do  i dispose: towers loop ;

: hanoi { n start inter finish -- }
   n if   n 1-  start finish inter hanoi
          finish at: towers  
               move: [ last: [ start at: towers ] ]   
          n 1-   inter start finish hanoi
     then
;
: main  { ndisks -- }
    ndisks make.towers  cls draw.towers
    ndisks 0 do 
       0 at: towers 6 ndisks i - 4* + heap> disk drop 
                       draw: [ last: [ 0 at: towers ] ] loop
;
 
AAPL
$567.34
Apple Inc.
+42.59
MSFT
$39.37
Microsoft Corpora
-0.32
GOOG
$527.22
Google Inc.
+0.28

MacTech Search:
Community Search:

Software Updates via MacUpdate

Cyberduck 4.4.4 - FTP and SFTP browser....
Cyberduck is a robust FTP/FTP-TLS/SFTP browser for the Mac whose lack of visual clutter and cleverly intuitive features make it easy to use. Support for external editors and system technologies such... Read more
TechTool Pro 7.0.3 - Hard drive and syst...
TechTool Pro is now 7, and this is the most advanced version of the acclaimed Macintosh troubleshooting utility created in its 20-year history. Micromat has redeveloped TechTool Pro 7 to be fully 64... Read more
MacFamilyTree 7.1.6 - Create and explore...
MacFamilyTree gives genealogy a facelift: it's modern, interactive, incredibly fast, and easy to use. We're convinced that generations of chroniclers would have loved to trade in their genealogy... Read more
EtreCheck 1.9.9 - For troubleshooting yo...
EtreCheck is a simple little app to display the important details of your system configuration and allow you to copy that information to the Clipboard. It is meant to be used with Apple Support... Read more
TeamViewer 9.0.28116 - Establish remote...
TeamViewer gives you remote control of any computer or Mac over the Internet within seconds, or can be used for online meetings. Find out why more than 200 million users trust TeamViewer! Free for... Read more
Viber 4.1.0 - Send messages and make cal...
Viber lets you send free messages and make free calls to other Viber users, on any device and network, in any country! Viber syncs your contacts, messages and call history with your mobile device,... Read more
Apple iOS 7.1.1 - The latest version of...
The latest version of iOS can be downloaded through iTunes. Apple iOS 7 brings an all-new design and all-new features. Simplicity Simplicity is often equated with minimalism. Yet true simplicity is... Read more
1Password 4.3 - Powerful password manage...
1Password is a password manager that uniquely brings you both security and convenience. It is the only program that provides anti-phishing protection and goes beyond password management by adding Web... Read more
Lens Blur 1.3.0 - True out-of-focus boke...
Let Lens Blur transform your existing photo into true SLR-quality out-of-focus bokeh effect! Everyone needs a gorgeous personalized background for a social profile, blog, Web/UI design, presentation... Read more
VMware Fusion 6.0.3 - Run Windows apps a...
VMware Fusion allows you to create a Virtual Machine on your Mac and run Windows (including Windows 8.1) and Windows software on your Mac. Run your favorite Windows applications alongside Mac... Read more

Latest Forum Discussions

See All

Yomi Review
Yomi Review By Rob Thomas on April 24th, 2014 Our Rating: :: C-C-C-COMBO BREAKERiPad Only App - Designed for the iPad Round One – Fight! No quarters required for this iOS adaptation of a tabletop adaptation of the arcade fighting... | Read more »
Injustice: Gods Among Us Updated with Ne...
Injustice: Gods Among Us Updated with New Characters, Leaderboards, Gear, and Online Multiplayer Posted by Rob Rich on April 24th, 2014 [ | Read more »
Spin It Review
Spin It Review By Jordan Minor on April 24th, 2014 Our Rating: :: SPIN ME RIGHT ROUNDUniversal App - Designed for iPhone and iPad Spin It has a fine puzzle game model, but its execution lacks energy.   | Read more »
Productivity App NoteSuite is Having its...
Productivity App NoteSuite is Having its Biggest Sale Ever, Just for One Week Posted by Rob Rich on April 24th, 2014 [ permalink ] | Read more »
Wayward Souls Review
Wayward Souls Review By Carter Dotson on April 24th, 2014 Our Rating: :: CARRY ON, WAYWARD SONUniversal App - Designed for iPhone and iPad Wayward Souls is a roguelike-inspired action-RPG that sets a high bar for other games to... | Read more »
The Sandbox Gets Update, Receives New Ca...
The Sandbox Gets Update, Receives New Campaign and New Elements Posted by Tre Lawrence on April 24th, 2014 [ permalink ] Universal App - Designed for iPhone and iPad | Read more »
Football Management Simulator One For El...
Football Management Simulator One For Eleven Released Worldwide Today for iOS Posted by Simon Reed on April 24th, 2014 [ permalink ] Free-To-Play football management title One For E | Read more »
Leo’s Fortune Review
Leo’s Fortune Review By Jordan Minor on April 24th, 2014 Our Rating: :: FORTUNATE SONUniversal App - Designed for iPhone and iPad Leo’s Fortune delivers a platforming experience as creative and refined as any console game.   | Read more »
Suited Up (Games)
Suited Up 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: Suited Up is a difficult, one-touch platformer that requires players to visualize each jump. The controls in Suited Up are simple,... | Read more »
MyTP One Mountain - Ski, Freeski and Sno...
MyTP One Mountain - Ski, Freeski and Snowboard 1.0.0 Device: iOS Universal Category: Games Price: $.99, Version: 1.0.0 (iTunes) Description: As real snow is melting away in the snow parks around the northern hemisphere, it's now time... | Read more »

Price Scanner via MacPrices.net

16GB 1st generation iPad mini available for $...
Radio Shack has a select number of refurbished 1st generation 16GB WiFi iPad minis available for $199.99 on their online store. Choose free shipping or free ship-to-store. We expect these to sell out... Read more
13-inch 2.5GHz MacBook Pro on sale for $100 o...
B&H Photo has the 13″ 2.5GHz MacBook Pro on sale for $1099 including free shipping plus NY sales tax only. Their price is $100 off MSRP. Read more
iPad Sales “Lull” A Reality Correction Of Unm...
I have lots of time for Jean-Louis Gassée, the former Apple Computer executive (1981 to 1990) who succeeded Steve Jobs as head of Macintosh development when the latter was dismissed in 1985. Mr.... Read more
Apple Makes OS X Betas Available To All – Wit...
Apple’s OS X Beta Seed Program, which lets you install the latest pre-release builds, try it out, and submit your feedback, is now open to anyone who wants to sign on rather than to developers and... Read more
Apple Releases iOS 7.1.1 Update
The latest iOS 7.1.1 update contains improvements, bug fixes and security updates, including: • Further improvements to Touch ID fingerprint recognition • Fixes a bug that could impact keyboard... Read more
Logitech Announces Thinner, Lighter, More Fle...
Logitech has announced an update to its Ultrathin for iPad Air, iPad mini and iPad mini with Retina display, improving the flexibility and design of its award-winning predecessor with an even thinner... Read more
Logitech Introduces Hinge, Big Bang and Turna...
Logitech has announced expansion of its tablet product line with three new cases – the Logitech Hinge, the Logitech Big Bang and the Logitech Turnaround – each for the iPad Air, iPad mini and iPad... Read more
WaterField’s Rough Rider Leather Messenger Ba...
WaterField Designs have announced the new 15-inch size of their popular Rough Rider leather messenger bag, a vintage-looking bag that combines Old West charm and ruggedness with distinctly modern... Read more
New Mac Pro on sale, save $100 on the 4-Core...
J&R has the new 4-Core Mac Pro in stock today and on sale for $2899 including free shipping plus NY sales tax only. Their price is $100 off MSRP, and it’s the lowest price available for this... Read more
Apple refurbished iMacs available for up to $...
The Apple Store has Apple Certified Refurbished 2013 iMacs available for up to $300 off the cost of new models. Apple’s one-year warranty is standard, and shipping is free. - 27″ 3.4GHz iMac – $1699... Read more

Jobs Board

*Apple* Solutions Consultant (ASC) - Apple (...
**Job Summary** The ASC is an Apple employee who serves as an Apple brand ambassador and influencer in a Reseller's store. The ASC's role is to grow Apple Read more
*Apple* Solutions Consultant (ASC) - Apple (...
**Job Summary** The ASC is an Apple employee who serves as an Apple brand ambassador and influencer in a Reseller's store. The ASC's role is to grow Apple Read more
Position Opening at *Apple* - Apple (United...
…customers purchase our products, you're the one who helps them get more out of their new Apple technology. Your day in the Apple Store is filled with a range of Read more
*Apple* Solutions Consultant (ASC) - Apple (...
**Job Summary** The ASC is an Apple employee who serves as an Apple brand ambassador and influencer in a Reseller's store. The ASC's role is to grow Apple Read more
*Apple* Inc. Research Data Specialist - Appl...
…of Worldwide Market Research & Intelligence. The team is responsible for conducting Apple branded consumer market research. It is also responsible for analyzing data Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.