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

Dash 3.4.0 - Instant search and offline...
Dash is an API documentation browser and code snippet manager. Dash helps you store snippets of code, as well as instantly search and browse documentation for almost any API you might use (for a full... Read more
RapidWeaver 7.1.7 - Create template-base...
RapidWeaver is a next-generation Web design application to help you easily create professional-looking Web sites in minutes. No knowledge of complex code is required, RapidWeaver will take care of... Read more
Printopia 2.1.22 - Share Mac printers wi...
Run Printopia on your Mac to share its printers to any capable iPhone, iPad or iPod Touch. Printopia will also add virtual printers, allowing you to save print-outs to your Mac and send to apps.... Read more
SteerMouse 5.0 - Powerful third-party mo...
SteerMouse is an advanced driver for USB and Bluetooth mice. It also supports Apple Mighty Mouse very well. SteerMouse can assign various functions to buttons that Apple's software does not allow,... Read more
Arq 5.5.1 - Online backup to Google Driv...
Arq is super-easy online backup for Mac and Windows computers. Back up to your own cloud account (Amazon Cloud Drive, Google Drive, Dropbox, OneDrive, Google Cloud Storage, any S3-compatible server... Read more
Slack 2.3.0 - Collaborative communicatio...
Slack is a collaborative communication app that simplifies real-time messaging, archiving, and search for modern working teams. Version 2.3.0: Note: Now requires OS X 10.8 or later New The app... Read more
Cocktail 10.1 - General maintenance and...
Cocktail is a general purpose utility for macOS that lets you clean, repair and optimize your Mac. It is a powerful digital toolset that helps hundreds of thousands of Mac users around the world get... Read more
Firefox 49.0.2 - Fast, safe Web browser.
Firefox offers a fast, safe Web browsing experience. Browse quickly, securely, and effortlessly. With its industry-leading features, Firefox is the choice of Web development professionals and casual... Read more
Art Text 3.1 - $49.99
Art Text is graphic design software to create stunning illustrations, such as badges, flyers, logos, social headers and icons, text mockups, website graphics and buttons, picture captions, word art,... Read more
AirRadar 3.1.9 - $9.95
With AirRadar, scanning for wireless networks is now easier and more personalized! It allows you to scan for open networks and tag them as favourites or filter them out. View detailed network... Read more

Latest Forum Discussions

See All

Oh...Sir! The Insult Simulator (Games)
Oh...Sir! The Insult Simulator 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: | Read more »
WitchSpring2 (Games)
WitchSpring2 1.27 Device: iOS Universal Category: Games Price: $3.99, Version: 1.27 (iTunes) Description: This is the story of Luna, the Moonlight Witch as she sets out into the world. This is a sequel to Witch Spring. Witch Spring 2... | Read more »
4 popular apps getting a Halloween makeo...
'Tis the season for all things spooky. So much, so, in fact, that even apps are getting into the spirt of things, dressing up in costume and spreading jack o' lanterns all about the place. These updates bring frightening new character skins, scary... | Read more »
Pokémon GO celebrates Halloween with can...
The folks behind Pokémon GO have some exciting things planned for their Halloween celebration, the first in-game event since it launched back in July. Starting October 26 and ending on November 1, trainers will be running into large numbers of... | Read more »
Best Fiends Forever Guide: How to collec...
The fiendship in Seriously's hit Best Fiends has been upgraded this time around in Best Fiends Forever. It’s a fast-paced clicker with lots of color and style--kind of reminiscent of a ‘90s animal mascot game like Crash Bandicoot. The game... | Read more »
5 apps for the budding mixologist
Creating your own cocktails is something of an art form, requiring a knack for unique tastes and devising interesting combinations. It's easy to get started right in your own kitchen, though, even if you're a complete beginner. Try using one of... | Read more »
5 mobile strategy games to try when you...
Strategy enthusiasts everywhere are celebrating the release of Civilization VI this week, and so far everyone seems pretty satisfied with the first full release in the series since 2010. The series has always been about ultra-addictive gameplay... | Read more »
Popclaire talk to us about why The Virus...
Humanity has succumbed to a virus that’s spread throughout the world. Now the dead have risen with a hunger for human flesh, and all that remain are a few survivors. One of those survivors has just called you for help. That’s the plot in POPCLAIRE’... | Read more »
Oceans & Empires preview build sets...
Hugely ambitious sea battler Oceans & Empires is available to play in preview form now on Google Play - but download it quickly, as it’s setting sail away in just a few days. [Read more] | Read more »
Rusty Lake: Roots (Games)
Rusty Lake: Roots 1.1.4 Device: iOS Universal Category: Games Price: $2.99, Version: 1.1.4 (iTunes) Description: James Vanderboom's life drastically changes when he plants a special seed in the garden of the house he has inherited.... | Read more »

Price Scanner via

Apple refurbished 2015 13-inch MacBook Airs a...
Apple has Certified Refurbished 2015 13″ MacBook Airs available starting at $759. An Apple one-year warranty is included with each MacBook, and shipping is free: - 2015 13″ 1.6GHz/4GB/128GB MacBook... Read more
64GB Apple TV on sale for $159, save $40
Best Buy has the 64GB Apple TV on sale for $40 off MSRP on their online store. Choose free shipping or free local store pickup (if available). Sale price for online orders only, in-store price may... Read more
EyeQue Introduces iOS And Android Based Advan...
Affordable vision technologies developers EyeQue have announced what they claim to be the world’s most advanced intelligent vision solution, pitched as enabling anyone, anywhere to easily and... Read more
Smartwatch Market Tanks, Declining 51.6% in 2...
The worldwide smartwatch market experienced a round of growing pains in the third quarter of 2016 (3Q16), resulting in a year-over-year decline in shipment volumes. According to data from the... Read more
CAZE announces Ultra Thin Glass Screen Protec...
Hong Kong based CAZE has announced its first ultra thin glass screen protector, the Glazz Pro for iPhone 7/7 Plus. Glazz Pro is made from chemically reinforced glass with an anti-fingerprint... Read more
11-inch MacBook Airs on sale for up to $120 o...
Newegg has 11″ MacBook Airs on sale for up to $120 off MSRP. Shipping is free: - 11″ 1.6GHz/128GB MacBook Air: $799.99 $100 off MSRP - 11″ 1.6GHz/256GB MacBook Air: $979 $120 off MSRP Read more
Up to $300 off Macs, $20 off iPads with Apple...
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
Apple’s Thursday “Hello Again” Event A Largel...
KGI Securities analyst Ming-Chi Kuo, who has a strong record of Apple hardware prediction accuracy, forecasts in a new note to investors released late last week that a long-overdue redo of the... Read more
12-inch Retina MacBooks on sale for $100 off...
Amazon has 2016 12″ Apple Retina MacBooks on sale for $100 off MSRP. Shipping is free: - 12″ 1.1GHz Silver Retina MacBook: $1199.99 $100 off MSRP - 12″ 1.1GHz Gold Retina MacBook: $1199.99 $100 off... Read more
Save up to $600 with Apple refurbished Mac Pr...
Apple has Certified Refurbished Mac Pros available for up to $600 off the cost of new models. An Apple one-year warranty is included with each Mac Pro, and shipping is free. The following... Read more

Jobs Board

*Apple* Retail - Multiple Positions - Apple,...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
*Apple* Solutions Consultant - Apple (United...
# Apple Solutions Consultant Job Number: 52812872 Houston, Texas, United States Posted: Oct. 18, 2016 Weekly Hours: 40.00 **Job Summary** As an Apple Solutions Read more
Lead *Apple* Solutions Consultant - Apple (...
# Lead Apple Solutions Consultant Job Number: 52812906 Houston, Texas, United States Posted: Oct. 18, 2016 Weekly Hours: 40.00 **Job Summary** The Lead ASC is an Read more
*Apple* Retail - Multiple Positions- Towson,...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
Software Engineering Intern: Integration / QA...
Job Summary Apple is currently seeking enthusiastic interns who can work full-time for a minimum of 12-weeks between Fall 2015 and Summer 2016. Our software Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.