Programmers’ Challenge

By Mike Scanlin, MacTech Magazine Regular Contributing Author

MAGIC ADDITIONS

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.

TWO MONTHS AGO WINNER

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!).

TRAVELLING SALESMAN NOTE

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)
 charPnt++;
 //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;
 else
 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;
 else
 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).