TweetFollow Us on Twitter

Jan 93 Challenge
Volume Number:9
Issue Number:1
Column Tag:Challenge

Programmers' Challenge

By Mike Scanlin, MacTech Magazine Regular Contributing Author

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

Challenge of the Month: Travelling Salesman

Recent discussions with friends about fuel efficiency reminded me of a problem I once had in a linear algebra class: A travelling salesman needs to visit a set of cities. He can go from any city to any other city and must visit each city exactly once. The question is, what is the optimal order of visitation that minimizes total distance travelled?

The prototype of the function you write is:

void OptimalPath(numCities,
 startCityIndex, citiesPtr,
 optimalPathPtr)
unsigned short numCities;
unsigned short  startCityIndex;
Point *citiesPtr;
Point *optimalPathPtr;
Example:

Input:

 numCities = 6
 startCityIndex = 2
 *citiesPtr = {1,4}, {2,2}, {2,1}, {5,7}, {4,6}, {2,6}

Output:

 *optimalPathPtr = {2,1}, {2,2}, {1,4}, {2,6}, {4,6}, {5,7}

numCities is a 1-based count of the number of cities to be visited (between 3 and 20, inclusive); startCityIndex is a zero-based index of the city in which the salesman starts ((2,1) in this example); citiesPtr is a pointer to an array of city locations (x and y locations are positive integers from 0 to 32767; each entry in the array is unique - no duplicate cities); optimalPathPtr points to an array (allocated by the caller) that OptimalPath fills in with the coordinates of the cities that the salesman should visit, in the order he should visit them (the first entry will always be citiesPtr[startCityIndex]).

October Challenge winner!

The winner of the October “Name no one man” palindrome challenge is Stepan Riha (location unknown). His superb solution is overflowing with neat optimization tricks, starting from a good understanding of the problem at hand (right algorithm) and continuing on to efficient implementation details like precomputed multiplication tables (right code). This is a perfect example of what we’re looking for here in the Programmer’s Challenge column. Nice job, Stepan!

Credit is also given to three people who submitted solutions that were relatively close to Stepan’s winning time and code size: Leonid Braginsky (22% slower; Brighton, MA), Allen Stenger (37% slower; Gardena, CA) and Eric Slosser (40% slower; Berkeley, CA).

To those people who submitted solutions that use a precomputed lookup table containing every palindrome from 0 to 999,999,999 I have three words: Get a life. I can hear the moaning from here, “That’s not fair! He said the primary criteria was speed!” Well, that’s true, it is. However, there comes a point in programming when you have to sacrifice speed for reasonable code size and/or memory usage. It is my personal opinion that taking 30K+ to do what Stepan does in 426 bytes is not the right approach.

I have received several requests for statistics regarding the Programmer’s Challenge. Readers want to know how many entries I get, what test data I use, what the winning time and code size is, etc. I can and will satisfy some of those requests. Unfortunately, I can’t publish my test bench program or test data because of space constraints. But I can tell you that I generally test with several hand calculated values to verify that functions are returning correct results. Then I call each function several thousand times with random (same random seed for everyone; it’s fair) as well as average case inputs. I test edge cases but I don’t dwell on these. I’m not trying to trick people (a couple of people asked me about negative palindromes since I used long instead of unsigned long in my baseNumber parameter-it was an oversight on my part, not a trick); I’m just looking for good, fast code that handles a wide range of inputs.

Having said that, here are some numbers that I can share with you: The “pegs” challenge received 9 entries, “spell CAT” received 21 entries and “palindromes” received 22 entries. Of the 22 entries for palindromes, one gave bogus results, one gave a divide-by-zero error and three others took way too long (or were caught in some kind of infinite loop) so I stopped timing them. Of the remaining entries, the slowest one was 4.3 times slower than the winner and the largest one that didn’t use a huge lookup table was 2.8 times larger than the winner.

Name No one man

/* 1 */
/* FindNthPalindrome by Stepan Riha
 *
 * This algorithm works with the following
 * fact in mind: An N-digit string can form
 * 9 * 10^((N-1)/2) palindromes:
 *
 * Odd N: Even N:
 * 1st  100..000..001100..0000..001
 * 2nd  100..010..001100..0110..001
 * 3rd  100..020..001100..0220..001
 * 100.......001 100........001
 * 10th 100..090..001100..0990..001
 * 11th 100..101..001100..1001..001
 * 12th 100..111..001100..1111..001
 * ............. ..............
 * last-1 999..989..999   999..9889..999
 * last 999..999..999999..9999..999
 *
 * Speedups are achieved bye replacing x*10
 * with (x<<1 + x<<3) and by doing conversions
 * requireing x/10 and x%10 on my own
 * approximating 1/10 with 3/32. Also, I use
 * a lookup table for powers of 10, etc.
 */
 
/* Precomputed values:
 palins10 is an array of 9*10^((n-1)/2)
 multpow10is a multiplication table of
 10^n (last row is all 10^9
 because of integer overflow)
*/
 
static long palins10[] = {
 9L, 9L, 90L, 90L, 900L, 900L, 9000L,
 9000L, 90000L, 90000L, 900000L
};

static long multpow10[100] = {
 0L, 1L, 2L, 3L, 4L,
 5L, 6L, 7L, 8L, 9L,
 0L, 10L, 20L, 30L, 40L,
 50L, 60L, 70L, 80L, 90L,
 0L, 100L, 200L, 300L, 400L,
 500L, 600L, 700L, 800L, 900L,
 0L, 1000L, 2000L, 3000L, 4000L,
 5000L, 6000L, 7000L, 8000L, 9000L,
 0L, 10000L, 20000L, 30000L, 40000L,
 50000L, 60000L, 70000L, 80000L, 90000L,
 0L, 100000L, 200000L, 300000L, 400000L,
 500000L, 600000L, 700000L, 800000L,
 900000L,
 0L, 1000000L, 2000000L, 3000000L, 4000000L,
 5000000L, 6000000L, 7000000L, 8000000L,
 9000000L,
 0L, 10000000L, 20000000L, 30000000L,
 40000000L, 50000000L, 60000000L, 70000000L,
 80000000L, 90000000L,
 0L, 100000000L, 200000000L, 300000000L,
 400000000L, 500000000L, 600000000L,
 700000000L, 800000000L, 900000000L,
 0L, 1000000000L, 1000000000L, 1000000000L,
 1000000000L, 1000000000L, 1000000000L,
 1000000000L, 1000000000L, 1000000000L
};

/* (x * 10) */
#define Times10(x) ((x<<1) + (x<<3)) 
/* x *= 10 */
#define MultBy10(x) x += x + (x<<3)
/* (x * 3 / 32) */
#define ApproxDiv10(x) ((x>>4)+(x>>5))
/* (x/2) */
#define Half(x) ((x)>>1)
 
long FindNthPalindrome(long baseNumber, short n);

long FindNthPalindrome(register long base, short n)
{
 register long num, dig, mult10, remain,
 *lop, *hip, *multpow;
 long   buffer[16];
 
 if (base >= 1000000000L)
 /* to big to start with */
 return -1L;
 
 if (!(num = n))
 /* 0th palindrome doesn't exist */
 return base;
 
 /* palindrome =
  *     n-th palindrome > baseNumber */
 
 /* Find dig = (number of digits in
  * baseNumber) - 1
  * Find how many dig-digit palindromes
  * are smaller than the baseNumber
  */
 
 if (base < 10) { /* baseNumber <= 9 */
 dig = 0;
 /* all 1-digit strings are
  * palindromes (duh!)
  */
 num += base - 1; 
 }
 else { /* baseNumber is >= 10 */
 /* Convert baseNumber to string.
  * This is faster than using /1
  * and %10
  */
 lop = buffer; dig = -1;
 while (base) {
 remain = base; base = 0;
 goto division1;
 while (mult10) {
 base += mult10;
 remain -= Times10(mult10);
 division1:
 mult10 = ApproxDiv10(remain);
 }
 if (remain >= 10) {
 base++; remain -= 10;
 }
 *lop++ = remain; dig++;
 }
 /* Find how many dig-digit palindromes
  * are smaller than this string
  * Start searching from the middle
  */
 hip = (lop = buffer) + Half(dig+1);
 lop += (base = Half(dig));
 multpow = multpow10;
 for(; base >= 0 && *lop==*hip;
   hip++, lop--, multpow += 10, base--)
 num += multpow[*hip];
 if (base >= 0) {
 if (*hip > *lop)
 num--;
 for(; base >= 0;
   hip++, multpow += 10, base--)
 num += multpow[*hip];
 }
 /* adjust for no leading zero */
 num -= multpow[-9]; 
 } /* if (baseNumber < 10) */
 
 /* palindrome =
  *num-th palindrome > 10^dig */
 
 /* Find how many digits the palindrome
  * will have
  */
 hip = (lop = palins10) + dig;
 while (num >= 0)
 num -= *hip++;
 num += *(--hip);
 dig = hip - lop;
 if (dig >= 9)
 /* i.e. baseNumber > 999999999
  * (dig is always <= 10) */
 return -1L;
 
 /* palindrome =
  *num-th dig-digit palindrome */
 
 /* Find the num-th dig-digit paindrome.
  * Calculate final palindrome string. This
  * is faster than using /10 and %10
  * Use lop and hip to point in the correct
  * row in the multiplication table
  * Start filling digits from the middle of
  * the string
  */
 base = Half(dig+1);
 hip = (lop = multpow10) + Times10(base);
 base = Half(dig);
 lop += Times10(base);
 base = 0L;
 while (num) {
 remain = num; num = 0;
 goto division2;
 while (mult10) {
 num += mult10;
 remain -= Times10(mult10);
 division2:
 mult10 = ApproxDiv10(remain);
 }
 if (remain >= 10) {
 num++; remain -= 10;
 }
 base += lop[remain];
 if (lop < hip)
 /* don't count middle digit twice */
 base += hip[remain];
 lop -= 10; hip += 10;
 }
 /* adjust for no leading zero */  
 lop = multpow10 + 1; 
 base += *lop;
 if (dig) {
 MultBy10(dig);
 base += lop[dig];
 }

 return base;
}

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 “I won the MacTech Magazine Programming Challenge” T-shirt (not to be found in stores).{1}

In order to make fair comparisons between solutions, all solutions must be in ANSI compatible C. 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 15th 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 e-mail. 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.

{1} The prize is subject to change in the event of production problems.

 
AAPL
$118.93
Apple Inc.
-0.07
MSFT
$47.81
Microsoft Corpora
+0.06
GOOG
$541.83
Google Inc.
+1.46

MacTech Search:
Community Search:

Software Updates via MacUpdate

Adobe Photoshop Elements 13.0 - Consumer...
Adobe Photoshop Elements 12--the #1 selling consumer photo editing software--helps you edit pictures with powerful, easy-to-use options and share them via print, the web, Facebook, and more.Version... Read more
Skype 7.2.0.412 - Voice-over-internet ph...
Skype allows you to talk to friends, family and co-workers across the Internet without the inconvenience of long distance telephone charges. Using peer-to-peer data transmission technology, Skype... Read more
HoudahSpot 3.9.6 - Advanced file search...
HoudahSpot is a powerful file search tool built upon MacOS X Spotlight. Spotlight unleashed Create detailed queries to locate the exact file you need Narrow down searches. Zero in on files Save... Read more
RapidWeaver 6.0.3 - 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
iPhoto Library Manager 4.1.10 - Manage m...
iPhoto Library Manager lets you organize your photos into multiple iPhoto libraries. Separate your high school and college photos from your latest summer vacation pictures. Or keep some photo... Read more
iExplorer 3.5.1.9 - View and transfer al...
iExplorer is an iPhone browser for Mac lets you view the files on your iOS device. By using a drag and drop interface, you can quickly copy files and folders between your Mac and your iPhone or... Read more
MacUpdate Desktop 6.0.3 - Discover and i...
MacUpdate Desktop 6 brings seamless 1-click installs and version updates to your Mac. With a free MacUpdate account and MacUpdate Desktop 6, Mac users can now install almost any Mac app on macupdate.... Read more
SteerMouse 4.2.2 - Powerful third-party...
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
iMazing 1.1 - Complete iOS device manage...
iMazing (was DiskAid) is the ultimate iOS device manager with capabilities far beyond what iTunes offers. With iMazing and your iOS device (iPhone, iPad, or iPod), you can: Copy music to and from... Read more
PopChar X 7.0 - Floating window shows av...
PopChar X helps you get the most out of your font collection. With its crystal-clear interface, PopChar X provides a frustration-free way to access any font's special characters. Expanded... Read more

Latest Forum Discussions

See All

Mystery Case Files: Dire Grove, Sacred G...
Mystery Case Files: Dire Grove, Sacred Grove HD Review By Jennifer Allen on November 28th, 2014 Our Rating: iPad Only App - Designed for the iPad A decent new installment for the popular Mystery Case Files series.   | Read more »
Castaway Paradise – Tips, Tricks, and St...
Ahoy there, castaways: Were you curious about our own thoughts regarding this pristine shipwreck? Check out our Castaway Paradise review! Castaway Paradise is out for iOS, finally giving mobile gamers the opportunity to enjoy the idyllic lifestyle... | Read more »
Castaway Paradise VIP Subs are on Sale f...
Castaway Paradise VIP Subs are on Sale for a Limited Time, and a Special Holiday Update is Coming Soon Posted by Rob Rich on November 28th, 2014 [ | Read more »
Primitive Review
Primitive Review By Jordan Minor on November 28th, 2014 Our Rating: :: FOLK ARTUniversal App - Designed for iPhone and iPad True to its name, Primitive is about as straightforward as runners get.   | Read more »
7 tips to get ahead of the competition i...
7 tips to get ahead of the competition in Dynasty of Dungeons Posted by Simon Reed on November 28th, 2014 [ permalink ] Playcrab has launched their action-packed new dungeon crawler, Dynasty of Dungeons, today. | Read more »
Master of Tea Kung Fu Review
Master of Tea Kung Fu Review By Jordan Minor on November 28th, 2014 Our Rating: :: ONE DROP RULESUniversal App - Designed for iPhone and iPad Master of Tea Kung Fu is a creative and complex caffeinated brawler.   | Read more »
Monster Strike Review
Monster Strike Review By Campbell Bird on November 28th, 2014 Our Rating: :: BILLIARD STRATEGYUniversal App - Designed for iPhone and iPad Collect monsters and battle by flinging them across the battlefield in this strangely... | Read more »
Proun+ Review
Proun+ Review By Jennifer Allen on November 28th, 2014 Our Rating: :: TWITCHY RACINGUniversal App - Designed for iPhone and iPad Twitchy racing aplenty in Proun+, an enjoyably tricky title.   | Read more »
Lucha Amigos (Games)
Lucha Amigos 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: Forget Ninja Turtles, and meet Wrestlers Turtles! Crazier, Spicier and…Bouncier! Sling carapaces of 7 Luchadores to knock all... | Read more »
Record of Agarest War Zero (Games)
Record of Agarest War Zero 1.0 Device: iOS Universal Category: Games Price: $7.99, Version: 1.0 (iTunes) Description: HyperDevbox Holiday Turkey Black Friday Special Pricing! To celebrate the opening of the holiday season HyperDevbox... | Read more »

Price Scanner via MacPrices.net

Up To 75% Off Infovole Text Apps Over Black F...
Infovole’s entire range of apps, including the Textkraft family of word processors for iPads and iPhones, is being offered at 50-75% off over the Black Friday and Cyber Monday weekend. The five-day... Read more
Black Friday: Up to $60 off Mac minis, NY tax...
 B&H Photo has new 2014 Mac minis on sale for up to $60 off MSRP as part of their Black Friday sale. Shipping is free, and B&H charges NY sales tax only: - 1.4GHz Mac mini: $449.99 $50 off... Read more
Black Friday: 27-inch 5K iMac for $2299, save...
 B&H Photo continues to offer Black Friday sale prices on the 27″ 3.5GHz 5K iMac, in stock today and on sale for $2299 including free shipping plus NY sales tax only. Their price is $200 off MSRP... Read more
Karalux Announces 24K Gold-Plated iPhone 6
Karalux, a Vietnam-based jewellery firm, has launched a unique 24 karat gold-plated iPhone 6 version with gold-cast monolithic dragon on its back panel. The real 24 karat gold plated enclosure doesn’... Read more
Black Friday: 13-inch 2.6GHz Retina MacBook P...
 B&H Photo has lowered their price for the 13″ 2.6GHz/128GB Retina MacBook Pro to $1159 for Black Friday. That’s $140 off MSRP, and it’s the lowest price for this model (except for Apple’s $1099... Read more
View all the Black Friday sales on our Mac Pr...
We’ve updated our Mac Price Trackers with the latest information on prices, bundles, and availability on systems from Apple’s authorized internet/catalog resellers. View Black Friday sale prices at a... Read more
Black Friday: 11-inch MacBook Air for $779, s...
 Best Buy has lowered their price for the 2014 11″ 1.4GHz/128GB MacBook Air to $779.99 for Black Friday. That’s $120 off MSRP. Choose free shipping or free local store pickup (if available). Sale... Read more
Apple Store Black Friday sale for 2014: $100...
BLACK FRIDAY The Apple Store has posted their Black Friday deals for 2014. Receive a $100 PRODUCT(RED) branded iTunes gift card with the purchase of select Macs, $50 with iPads, and $25 with iPods,... Read more
Black Friday: 15% off iTunes Gift Cards
Staples is offering 15% off $50 and $100 iTunes Gift Cards on their online store as part of their Black Friday sale. Click here for more information. Shipping is free. Best Buy is offering $100... Read more
BEVL Releases Dock Tailored for iPhone 6 and...
Seattle based BEVL has released their first product: an iPhone dock that is divergent in build quality, rock-solid function and visual simplicity to complement the iPhone. BEVL is now accepting... 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
Senior Event Manager, *Apple* Retail Market...
…This senior level position is responsible for leading and imagining the Apple Retail Team's global event strategy. Delivering an overarching brand story; in-store, Read more
*Apple* Retail - Multiple Positions (US) - A...
Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, you're also the 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* 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
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.