TweetFollow Us on Twitter

May 93 Challenge
Volume Number:9
Issue Number:5
Column Tag:Programmers’ Challenge

Programmers’ Challenge

By Mike Scanlin, MacTech Magazine Regular Contributing Author

Note: Source code files accompanying article are located on MacTech CD-ROM or source code disks.


Thanks to WarrenPM (America Online) for suggesting this month’s Challenge: Find all of the correct addition problems of the form: 123 + 456 = 789 using each of the digits 1 through 9 once each in every solution. For example: 124 + 659 = 783 is true, uses only the digits 1 through 9 and uses each only once.

The prototype of the function you write is:

unsigned short CountMagicAdditions();

You’re not required to produce the actual equations as output, only the correct number of them. Note: This does not mean you should write a separate function that precomputes the answer and then submit a solution that consists of return (kNumMagicAdditions);. Also note that “124 + 659 = 783” and “659 + 124 = 783” are the same thing and only count as 1 magic addition.

Warren says that he wrote a version in AppleSoft BASIC years ago that did lots of string manipulation and took two days to run on his Apple ][. Hopefully your solution in C on my Quadra 700 will run somewhat faster. If you’re really motivated, you could make CountMagicAdditions take a parameter n which would range in value from 3 to 9 and would represent the number of digits used by each equation (and the values of the digits are from 1 to n). For instance: “1 + 2 = 3” is the only solution when n = 3. This more general purpose routine is not required to win the Challenge, though.


This month we have our first repeat winner of the Programmer’s Challenge. Congratulations to Ronald Nepsund (Northridge, CA) for winning the “Count Unique Words” challenge (Ronald previously won the Travelling Salesman challenge). Close behind, with similar algorithms but slightly different implementations are David Biolsi (Ithaca, NY) and Richard Parker (Irvine, CA).

Here’s a summary of the entries that didn’t crash. The bytes column is the code size, test 1 is the ticks to complete a 17K input file yielding 796 unique words; and test 2 is the ticks to complete a 40K input file yielding 817 unique words (each test was run 20 times and the ticks represent the total time for all instances of each of the two tests):

Name bytes test 1 test 2

Ronald Nepsund 660 63 127

David Biolsi 636 86 146

Richard Parker 386 96 168

Bob Boonstra 856 107 212

JohnnyL 782 124 247

Stepan Riha 418 157 248

Mark Nilsen 588 137 264

Dave Darrah 266 6180 16240

Thank you to all the people who responded to my request for feedback on this column. I will implement as many of your good ideas as I can. The basic feeling was that the challenges are about the right difficulty level as they are but that once in a while a really hard or really easy one might be nice. The vote on Mac-only vs. platform-independent Challenges is split 50/50.

Several people complained about not having enough time to work on the challenge. Neil is working on a way to make the new challenges available electronically before the issue that contains them arrives in your mail box. [Check the online services for more information. See page two for info on which services we support. - Ed.] Hopefully that will help. The other option is to separate the challenge from the solution by three months instead of two. If the electronic option doesn’t help then we may go that route.

I received my second complaint that I don’t provide enough info in the challenge specification to adequately solve it. For instance, in the Count Unique Words challenge one person wondered if he was allowed to overwrite the input buffer or not. Well, I don’t think I’m capable of predicting all such questions up front but I will make more of an effort to eliminate confusion. Also, in the event that I give a less than clear specification, you can always e-mail me at one of the Challenge addresses for clarification (which is probably better than making a really gross wrong assumption and having your entry disqualified).

One question raised by two people that relates to the specification issue is the ANSI compatibility issue and whether or not you’re allowed to make toolbox calls. I had assumed that since this was a Mac magazine people would feel free to call NewPtr instead of malloc (as many who have submitted solutions have done). I guess that was a bad assumption. So, the rules now state that you may make toolbox calls if you want to. There will probably be a Challenge some day that is Mac-specific and requires toolbox interaction but you’re certainly not required to use the toolbox if arriving at the solution doesn’t necessitate it (do whatever is fastest!).


Thanks to Stepan Riha (Austin, TX) for pointing out a further optimization in the Travelling Salesman winning solution. Since you’re not really concerned with the actual distance between points but only the relative distance between points, you don’t need to use square root at all; you can just compare the squares of the distances instead (which is faster). As Stepan says, “A careful analysis of a problem can often improve performance better than careful optimization. Combination of the two gives you truly great code!”

Here’s Ronald’s Count Unique Words winning solution:

 * Unique word count by Ronald M. Nepsund
 * The original text is uppercased with all non
 * alphabetic characters turned to zero. The list of
 * unique words works as follows: The word is used to
 * to index into a 1024 entry hash table. The hash
 * table contains pointers to the beginning of a linked
 * list of word entries. Each word entry holds the
 * length of the word and a pointer to the first
 * occurance of the word in the original text. The
 * linked list is ordered first by the length of the
 * words and secondly alphabetically

#define kHashMask0x003FF
#define kHashSize0x00400

typedef struct tNode{
 short  length;
 Ptr    wordPtr;
 struct tNode    *nextNode;
} WordTableRec, *WordTablePtr;

/* compare two strings */
short stringCmp(register short length,
 register char *pnt1,
 register char *pnt2)
 while (-length > 0 && *pnt1==*pnt2) {
 pnt1++; pnt2++;
 return *pnt1-*pnt2;

unsigned short
CountUniqueWords(Ptr textPtr,
 unsigned short byteCount)
 Ptr    endPnt,wordStartPtr;
 register char   *charPnt;
 register long   hash;
 long   count;
 register short  wordLength;
 unsigned short  totalWords = 0;
 short  i,cmp;
 WordTablePtr    *hashTable;
 WordTablePtr    wordTable;
 register WordTablePtr  linkPtr;
 WordTablePtr    last,wordTableEntry;
 char   charTypeTable[256];
 long   *zeroTblPtr;
 //total possable number of words = 16556
 //assuming a maximum size buffer of text
 //I will use a hash table size of 1024
 count = 4L * kHashSize;
 //array of (NULL)Ptr’s
 hashTable = (WordTablePtr *) NewPtrClear(count);
 if (hashTable == 0L)
 while (TRUE)
 SysBeep(10); //not enough memory
 count = 16556L * sizeof(WordTableRec);
 wordTable = (WordTablePtr) NewPtr(count);
 if (wordTable == 0L)
 while (TRUE)
 SysBeep(10); //not enough memory
 //zero out the ‘charTypeTable’
 zeroTblPtr = (long *) &charTypeTable;
 for (i=0; i<64; i++)
 *zeroTblPtr++ = 0;

 //init lookup table used for uppercasing and 
 //identifying non letter characters
 for (i=0;i<26; i++)
 charTypeTable[i+(Byte) ‘A’] =
 charTypeTable[i+(Byte) ‘a’] =
   (char) (i+((Byte) ‘A’));
 totalWords = 0;
 charPnt = textPtr;
 endPnt = textPtr + byteCount;
 while (charPnt < endPnt) {
 //skip spaces
 while (charPnt < endPnt &&
   charTypeTable[*charPnt] == 0)
 //pointer to begining of new word
 wordStartPtr = charPnt;  
 hash = 0;
 if (endPnt-charPnt > 255) {
 //at least 255 characters left
 //advance to the end of the word
 //we can assume that a word is <=255 characters long
 //uppercasing the text
 //and doing a hash function
 while (*charPnt = charTypeTable[*charPnt])
 hash = (hash << 4)  + *charPnt++ - 
 ‘A’ + (hash >> 10);
 else {
 while (charPnt < endPnt &&
   (*charPnt = charTypeTable[*charPnt]))
 hash = (hash << 4) + *charPnt++ - ‘A’ + (hash >> 10);
 wordLength = charPnt-wordStartPtr;

 hash &= kHashMask;
 linkPtr = (WordTablePtr) hashTable[hash];
 last = NULL;
 if (linkPtr==NULL) {
 //this hash entry has not been used yet
 wordTableEntry = &wordTable[totalWords++];
 hashTable[hash] = wordTableEntry;
 wordTableEntry->length   = wordLength;
 wordTableEntry->wordPtr  = wordStartPtr;
 wordTableEntry->nextNode = 0;
 else {
 //the entries are ordered by word length
 //find the first entry that is as long or longer
 while (linkPtr != NULL && linkPtr->length < wordLength)
 last = linkPtr;
 linkPtr = linkPtr->nextNode;
 if (linkPtr == NULL) {
 //no other entries as long as this one
 wordTableEntry = &wordTable[totalWords++];
 if (last == NULL)
 hashTable[hash] = wordTableEntry;
 last->nextNode = wordTableEntry;
 wordTableEntry->length = wordLength;
 wordTableEntry->wordPtr= wordStartPtr;
 wordTableEntry->nextNode= NULL;
 else if (linkPtr->length > wordLength) {
 //insert betean ‘last’ and ‘linkPtr’
 wordTableEntry = &wordTable[totalWords++];
 if (last == NULL) {
 wordTableEntry->nextNode = hashTable[hash];
 hashTable[hash] = wordTableEntry;
 else {
 wordTableEntry->nextNode = last->nextNode;
 last->nextNode = wordTableEntry;
 wordTableEntry->length = wordLength;
 wordTableEntry->wordPtr= wordStartPtr;
 else {
 //check entries with same word lengths
 while (linkPtr != NULL &&
   linkPtr->length == wordLength &&
   (cmp = stringCmp(wordLength, wordStartPtr,
   linkPtr->wordPtr)) <0) {
 last = linkPtr;
 linkPtr = linkPtr->nextNode;
 if (linkPtr == NULL) {
 //end of list and no match
 wordTableEntry = &wordTable[totalWords++];
 if (last == NULL)
 hashTable[hash] = wordTableEntry;
 last->nextNode = wordTableEntry;
 wordTableEntry->length = wordLength;
 wordTableEntry->wordPtr= wordStartPtr;
 wordTableEntry->nextNode= 0;
 else if (linkPtr->length > wordLength || cmp>0)   
 //insert word entry here
 wordTableEntry = &wordTable[totalWords++];
 if (last == NULL) { //hash table to point here
 wordTableEntry->nextNode = hashTable[hash];
 hashTable[hash] = wordTableEntry;
 else {
 wordTableEntry->nextNode= last->nextNode;
 last->nextNode = wordTableEntry;
 wordTableEntry->length  = wordLength;
 wordTableEntry->wordPtr = wordStartPtr;
 DisposePtr((Ptr) hashTable);
 DisposePtr((Ptr) wordTable);
 return totalWords;

The Rules

Here’s how it works: Each month there will be a different programming challenge presented here. First, you must write some code that solves the challenge. Second, you must optimize your code (a lot). Then, submit your solution to MacTech Magazine (formerly MacTutor). A winner will be chosen based on code correctness, speed, size and elegance (in that order of importance) as well as the postmark of the answer. In the event of multiple equally desirable solutions, one winner will be chosen at random (with honorable mention, but no prize, given to the runners up). The prize for the best solution each month is $50 and a limited edition “The Winner! MacTech Magazine Programming Challenge” T-shirt (not to be found in stores).

In order to make fair comparisons between solutions, all solutions must be in ANSI compatible C (i.e., don’t use Think’s Object extensions). However, you may call any routine in the Macintosh toolbox you want (i.e., it doesn’t matter if you use NewPtr instead of malloc). All entries will be tested with the FPU and 68020 flags turned off in THINK C. When timing routines, the latest version of THINK C will be used (with ANSI Settings plus “Honor ‘register’ first” and “Use Global Optimizer” turned on) so beware if you optimize for a different C compiler.

The solution and winners for this month’s Programmers’ Challenge will be published in the issue two months later. All submissions must be received by the 10th day of the month printed on the front of this issue.

All solutions should be marked “Attn: Programmers’ Challenge Solution” and sent to Xplain Corporation (the publishers of MacTech Magazine) via “snail mail” or preferably, e-mail - AppleLink: MT.PROGCHAL, Internet:, and CompuServe: 71552,174. If you send via snail mail, please include a disk with the solution and all related files (including contact information). See page 2 for information on “How to Contact Xplain Corporation.”

MacTech Magazine reserves the right to publish any solution entered in the Programming Challenge of the Month and all entries are the property of MacTech Magazine upon submission. The submission falls under all the same conventions of an article submission.


Community Search:
MacTech Search:

Software Updates via MacUpdate

Markly 1.5.3 - Create measurement and de...
Markly is a measurement and design-spec plugin/extension for Photoshop and Sketch. It is made for modern Web designers and app front-end developers. You can add specification marks simply by clicking... Read more
Suitcase Fusion 6 17.3.0 - Font manageme...
Suitcase Fusion 6 is the creative professional's font manager. Every professional font manager should deliver the basics: spectacular previews, powerful search tools, and efficient font organization... Read more
Nisus Writer Pro 2.1.2 - Multilingual wo...
Nisus Writer Pro is a powerful multilingual word processor, similar to its entry level products, but brings new features such as table of contents, indexing, bookmarks, widow and orphan control,... Read more
calibre 2.40.0 - Complete e-book library...
Calibre is a complete e-book library manager. Organize your collection, convert your books to multiple formats, and sync with all of your devices. Let Calibre be your multi-tasking digital librarian... Read more
Vivaldi - An advanced browser...
Vivaldi is a browser for our friends. In 1994, two programmers started working on a web browser. Our idea was to make a really fast browser, capable of running on limited hardware, keeping in mind... Read more
OmniPlan 3.0 - Robust project management...
With OmniPlan, you can create logical, manageable project plans with Gantt charts, schedules, summaries, milestones, and critical paths. Break down the tasks needed to make your project a success,... Read more
Yummy FTP 1.11 - FTP/SFTP/FTPS client fo...
Yummy FTP is an FTP + SFTP + FTPS file transfer client which focuses on speed, reliability and productivity. Whether you need to transfer a few files or a few thousand, schedule automatic backups, or... Read more
Tweetbot 2.1 - Popular Twitter client. (...
Tweetbot is a full-featured OS X Twitter client with a lot of personality. Whether it's the meticulously-crafted interface, sounds and animation, or features like multiple timelines and column views... Read more
MacPilot 8.0 - Enable over 1,200 hidden...
MacPilot gives you the power of UNIX and the simplicity of Macintosh, which means a phenomenal amount of untapped power in your hands! Use MacPilot to unlock over 1,200 features, and access them all... Read more
Typinator 6.7 - Speedy and reliable text...
Typinator turbo-charges your typing productivity. Type a little. Typinator does the rest. We've all faced projects that require repetitive typing tasks. With Typinator, you can store commonly used... Read more

Balloony Land offers a fresh twist on th...
Balloony Land by Palringo offers a fresh twist on the match three genre and is out now on iOS and Android. First-off, you'll be popping balloons instead of crushing candy and the balloons will float up and fill the empty spaces instead of dropping... | Read more »
Graphic - vector illustration and design...
Graphic - vector illustration and design 1.0 Device: iOS iPhone Category: Productivity Price: $2.99, Version: 1.0 (iTunes) Description: Autodesk Graphic is a powerful full-featured vector drawing and illustration application right in... | Read more »
Sago Mini Babies (Education)
Sago Mini Babies 1.0 Device: iOS Universal Category: Education Price: $2.99, Version: 1.0 (iTunes) Description: Introducing the Sago Mini babies. Boys and girls love caring for these adorable characters. Feed Robin her favorite mush... | Read more »
PAUSE - Relaxation at your fingertip (H...
PAUSE - Relaxation at your fingertip 1.1 Device: iOS iPhone Category: Healthcare & Fitness Price: $1.99, Version: 1.1 (iTunes) Description: | Read more »
Super Sharp (Games)
Super Sharp 1.1 Device: iOS Universal Category: Games Price: $1.99, Version: 1.1 (iTunes) Description: Your finger has never been so sharp! Cut with skill to complete the 120 ingenious physics levels of Super Sharp and become a cut... | Read more »
Assembly - Graphic design for everyone...
Assembly - Graphic design for everyone 1.0 Device: iOS Universal Category: Photography Price: $2.99, Version: 1.0 (iTunes) Description: Assembly is the easiest most powerful design tool on the App Store. Create anything you can... | Read more »
Dub Dash (Games)
Dub Dash 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: ARE YOU READY FOR THE ULTIMATE CHALLENGE? UNIQUE SYMBIOSIS OF MUSIC AND GRAPHICS | Read more »
Leave Me Alone (Games)
Leave Me Alone 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: 33% off launch sale!!! Somewhere between the 1980s and 1990s there exists a world that never was. A world of skatepunks,... | Read more »
YAMGUN (Games)
YAMGUN 1.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0 (iTunes) Description: The invasion has begun! Protect the walls of the citadel against waves of enemies! But watch out, you will soon run out of ammo...... | Read more »
Chesh (Games)
Chesh 1.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0 (iTunes) Description: It’s like chess, only not at all. ***40% off for a limited time to celebrate our launch!*** Chesh is a game of skill, strategy, luck,... | Read more »

Price Scanner via

TP-LINK Next-Gen Routers Support a Large Numb...
TP-LINK, specialists in consumer and business networking products, have announced the availability of Archer C2600, the company’s next-generation router featuring wireless AC, multi-user MIMO, and 4-... Read more
Apple’s Education discount saves up to $300 o...
Purchase a new Mac or iPad using Apple’s Education Store and take up to $300 off MSRP. All teachers, students, and staff of any educational institution qualify for the discount. Shipping is free, and... Read more
Save up to $350 with Apple refurbished iMacs
Apple has Certified Refurbished iMacs available for up to $350 off the cost of new models. Apple’s one-year warranty is standard, and shipping is free: - 27″ 3.5GHz 5K iMac – $1949 $350 off MSRP - 27... Read more
Mac Pros on sale for up to $300 off MSRP
B&H Photo has Mac Pros on sale for up to $300 off MSRP. Shipping is free, and B&H charges sales tax in NY only: - 3.7GHz 4-core Mac Pro: $2818.99, $181 off MSRP - 3.5GHz 6-core Mac Pro: $3699... Read more
5K iMacs on sale for up to $150 off MSRP, fre...
B&H Photo has the 27″ 3.3GHz 5K iMac on sale for $1899.99 including free shipping plus NY tax only. Their price is $100 off MSRP. They have the 27″ 3.5GHz 5K iMac on sale for $2149, $150 off MSRP... Read more
Twelve South Redesigns BookArc For Today’s Sm...
Twelve South has announced a redesigned version of their very first product, BookArc for MacBook. Tailored specifically for the newest generation of MacBooks, BookArc holds the new, smaller Apple... Read more
Phone 6s Tips & Tricks – Tips Book For iP...
Poole, United Kingdom based Tap Guides Ltd. has announced the release and immediate availability of iPhone 6s Tips & Tricks, an in-depth eBook available in the iBookstore that’s priced just $2.99... Read more
Apple refurbished 2014 13-inch Retina MacBook...
Apple has Certified Refurbished 2014 13″ Retina MacBook Pros available for up to $400 off original MSRP, starting at $979. An Apple one-year warranty is included with each model, and shipping is free... Read more
13-inch 2.5GHz MacBook Pro on sale for $994,...
Best Buy has the 13″ 2.5GHz MacBook Pro available for $994.99 on their online store. Choose free shipping or free instant local store pickup (if available). Their price is $105 off MSRP. Price valid... Read more
Is The iPad Pro Really A Serious Laptop Repla...
Probably not, at least for productive professionals and other power users. Steve Jobs declared that we’d entered the “post-PC Era” with the advent of the original iPad in 2010, a phrase we don’t hear... Read more

Jobs Board

*Apple* Desktop Analyst - KDS Staffing (Unit...
…work with some of the brightest engineers. Job Description Title: Apple Desktop AnalystPosition Type: Full-time PermanentLocation: White Plains, NYHot Points:Depth of Read more
*Apple* Retail Online, Customer Experience R...
**Job Summary** Apple Retail's Online Store sells Apple products to customers around the world. In addition to selling Apple products with unique services such Read more
Frameworks Engineer, *Apple* Watch - Apple...
**Job Summary** Join the team that is shaping the future of software development for Apple Watch! As a software engineer on the Apple Watch Frameworks team you will Read more
Senior Manager, Global Direct Marketing *App...
**Job Summary** Apple Retail is looking for an experienced Direct Marketing Leader to join its Marketing team. This position will take a leadership role in creating Read more
*Apple* Online Store Expansion - Apple (Unit...
**Job Summary** The Online Apple Store is seeking a person to lead its expansion into new countries. Based in Cupertino, CA, this person will develop and maintain an Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.