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
;
 

Community Search:
MacTech Search:

Software Updates via MacUpdate

iFFmpeg 6.4.0 - Convert multimedia files...
iFFmpeg is a comprehensive media tool to convert movie, audio and media files between formats. The FFmpeg command line instructions can be very hard to master/understand, so iFFmpeg does all the hard... Read more
Thunderbird 52.2.0 - Email client from M...
As of July 2012, Thunderbird has transitioned to a new governance model, with new features being developed by the broader free software and open source community, and security fixes and improvements... Read more
Airfoil 5.6.1 - Send audio from any app...
Airfoil allows you to send any audio to AirPort Express units, Apple TVs, and even other Macs and PCs, all in sync! It's your audio - everywhere. With Airfoil you can take audio from any... Read more
Apple Remote Desktop Client 3.9.3 - Clie...
Apple Remote Desktop Client is the best way to manage the Mac computers on your network. Distribute software, provide real-time online help to end users, create detailed software and hardware reports... Read more
jAlbum Pro 14.0 - Organize your digital...
jAlbum Pro has all the features you love in jAlbum, but comes with a commercial license. You can create gorgeous custom photo galleries for the Web without writing a line of code! Beginner-friendly... Read more
jAlbum 14.0 - Create custom photo galler...
With jAlbum, you can create gorgeous custom photo galleries for the Web without writing a line of code! Beginner-friendly, with pro results - Simply drag and drop photos into groups, choose a design... Read more
Vitamin-R 2.48 - Personal productivity t...
Vitamin-R creates the optimal conditions for your brain to work at its best by structuring your work into short bursts of distraction-free, highly focused activity alternating with opportunities for... Read more
Beamer 3.3 - Stream any movie file from...
Beamer streams to your Apple TV.... Plays any movie file - Just like the popular desktop movie players, Beamer accepts all common formats, codecs and resolutions. AVI, MKV, MOV, MP4, WMV, FLV. To... Read more
Shredo 1.2.2 - $9.99
Shredo is a beautiful, functional file-shredding and privacy scan utility. It permanently shreds files, folders, and external volumes' contents to keep information secure and impossible for anyone to... Read more
Final Draft 10.0.3 - Industry-leading sc...
Final Draft allows you to use your creative energy to focus on the content; let Final Draft take care of the style. Final Draft is the number-one selling application specifically designed for writing... Read more

Latest Forum Discussions

See All

The House of da Vinci (Games)
The House of da Vinci 1.0.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0.0 (iTunes) Description: Enter The House of Da Vinci, a new must-try 3D puzzle adventure game. Solve mechanical puzzles, discover hidden... | Read more »
Solve the disappearance of history’s gre...
Blue Brain Games invites you to indulge in an immersive hands-on 3D puzzle adventure in similar vein to The Room series, with its debut release The House of Da Vinci. Set during the historic period of the Italian Renaissance (when Leonardo himself... | Read more »
Age of Rivals (Games)
Age of Rivals 3.3 Device: iOS Universal Category: Games Price: $.99, Version: 3.3 (iTunes) Description: Deep civilization-building strategy in a fast-paced card game! | Read more »
Panthera Frontier (Games)
Panthera Frontier 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: | Read more »
Angry Birds Evolution beginner's gu...
Angry Birds changes things up a fair bit in its latest iteration, Angry Birds Evolution. The familiar sling-shot physics mechanics are still there, but the game now features team-based gameplay, RPG elements, and a new top-down view. With all of... | Read more »
Sega Forever is for the retro game fans
Sega is launching a new retro games service titled Sega Forever, in a move that's sure to delight games enthusiasts with a bit of nostalgia. Sega's releasing five classic games for free. The titles include Sonic the Hedgehog, Phantasy Star II,... | Read more »
The Little Acre (Games)
The Little Acre 1.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0 (iTunes) Description: | Read more »
Lovely adventure game 'The Little A...
The Little Acre makes its way from PC to iOS today and it's a real charmer. It's a lovely little adventure game set in 1950's Ireland, gorgeously animated in a style slightly reminiscent of old Disney films. The game won a lot of praise for its... | Read more »
Futurama: Worlds of Tomorrow officially...
Futurama: Worlds of Tomorrow arrives next Thursday, and it features . . . Stephen Hawking? Turns out a few of your favorite science super stars, including Bill Nye, Neil DeGrasse Tyson, and George Takei will be making an appearance alongside the... | Read more »
MU Origin’s new update offers exciting c...
MU Origin is kicking off the summer with style. Its latest update is a real doozy, offering up plenty of fresh content. New challenges, some extra help for newcomers, and new costumes are just a few of the things you will find in the new patch. | Read more »

Price Scanner via MacPrices.net

Clearance 2016 MacBook Pros available for up...
B&H Photo has clearance 2016 13″ and 15″ MacBook Pros in stock today and on sale for up to $400 off original MSRP. Shipping is free, and B&H charges NY & NJ sales tax only: - 15″ 2.7GHz... Read more
Apple Ranks 9th In comScore Top 50 U.S. Digit...
comScore, Inc. has released its monthly ranking of U.S. online activity at the top digital media properties for May 2017 based on data from comScore Media Metrix Multi-Platform. * Entity has... Read more
10.5-inch iPad Pros available for up to $20 o...
B&H Photo has the new 2017 10.5″ iPad Pros available for up to $20 off MSRP including free shipping plus NY & NJ sales tax only: - 64GB iPad Pro WiFi: $649 - 256GB iPad Pro WiFi: $749 - 512GB... Read more
Three Off-The-Beaten-Track iOS Apps That Dese...
One of the great things about using iPads and iPhones is the vast selection of apps available for most anything you want or need to do. The three outlined in this article have been in my core app... Read more
Apple No. 1 Spot In Gartner Top 100 Vendors i...
Gartner, Inc. has unveiled the top global 100 vendors in IT in 2016 based on their revenue across IT (excluding communication services) and component market segments. In the Gartner Global Top 100:... Read more
Clearance iMacs available for up to $300 off...
B&H Photo has clearance 21″ and 27″ Apple iMacs available starting at $949, each including free shipping plus NY & NJ sales tax only: - 27″ 3.3GHz iMac 5K: $1999 $300 off original MSRP - 27″... Read more
1.4GHz Mac mini, refurbished, available for $...
The Apple Store has Apple Certified Refurbished 1.4GHz Mac minis available for $419. Apple’s one-year warranty is included, and shipping is free. Their price is $80 off MSRP, and it’s the lowest... Read more
Free Mixoo iOS Photo Editing App Gets Major U...
Button Software Technology has announced Mixoo 3.0, an important feature update to the company’s photo editor for iOS devices. Mixoo offers amazing ways to edit as well as decorate personal photo... Read more
FNable 2.0 Function Key Enabling Software Get...
Briksoftware has released FNable 2.0 With Touch Bar Support, a major new version of the function key enabling software now compatible with Touch Bar keyboards. FNable’s simplicity that allows users... Read more
Clearance 2016 12-inch Retina MacBooks, Apple...
Apple recently dropped prices on Certified Refurbished 2016 12″ Retina MacBooks, with models now available starting at $1019. Apple will include a standard one-year warranty with each MacBook, and... Read more

Jobs Board

Security Data Analyst - *Apple* Information...
…data sources need to be collected to allow Information Security to better protect Apple employees and customers from a wide range of threats.Act as the subject matter Read more
Lead *Apple* Solutions Consultant - Apple I...
…integrity, and trust.Success Metrics/Key Performance Indicators:Quantitative* Year over Year growth in Apple Product and Beyond the Box sales in the assigned Point of Read more
*Apple* Solutions Consultant till v%u00E5r...
…ethics, integrity, and trust.Success Metrics/Key Performance Indicators:QuantitativeYear over Year growth in Apple Product and Beyond the Box sales in the assigned Point Read more
Sr. Software Engineer, *Apple* Retail - App...
Apple Retail is looking for a Software Engineer…You'll work on projects that touch all aspects of Apple Retail Point-of-Sale system, and will leverage your strong Read more
*Apple* Solutions Consultant (Asc) - PT - Cu...
…important role that the ASC serves is that of providing an excellent Apple Customer Experience. Responsibilities include:* Promoting Apple products and solutions Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.