TweetFollow Us on Twitter

Oct 92 Challenge
Volume Number:8
Issue Number:6
Column Tag: Programmers' Challenge

Programmers' Challenge

By Mike Scanlin, MacTutor Regular Contributing Author

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

Programming Challenge of the Month - NAME NO ONE MAN

This month’s challenge involves palindromes -- things that read the same backward and forward (like the letters in “name no one man” or “a toyota”). The goal is to write a routine that finds the nth palindrome greater than a given baseNumber (when it’s displayed as a base 10 integer without leading zeros). Our numeric palindromes will only consist of digits from 0 to 9 and will not be larger than 9 digits long (return -1 if the palindrome requested is larger than 999,999,999). The prototype is:

long FindNthPalindrome(baseNumber, n)
 long baseNumber;
 short  n;

Example:

Input:  baseNumber = 107
 n = 3

Output:

 function result = 131

Remember, speed is more important than size. This is a fairly simple programming challenge -- but how fast can you make it?

Congratulations

To Aaron Zick (San Francisco, CA) for winning the very first MacTutor Programming Challenge (rubber banded pegs). Among the submitted solutions yielding correct results, his was the fastest and the second smallest. He will be receiving a cool t-shirt as soon as they are available.

The key to writing a fast routine was knowing that you don’t have to use trig functions to calculate the area of a convex polygon. As William Karsh (Manteno, IL) explained in his well commented solution, the area of a “simply connected, piecewise differentiable” region can be computed as follows: For each segment going around the perimeter, bounded by points p1 to p2, calculate p1.h * (p2.v - p1.v) - p1.v * (p2.h - p1.h). The area is the sum of all of these pieces (you may need to multiply by -1 for orientation). Sorry, William, you had the right idea but your code was twice as large and 5% slower than the winning solution.

Jim Walker (Columbia, SC) deserves mention for the smallest code (half the size of the winning solution) and for reminding us that you can calculate the area of a triangle by using the following macro (which might come in handy in one of your own applications, so keep it in mind): AREA(x, y, z) = ((z.h-y.h) * (y.v-x.v) - (z.v-y.v) * (y.h-x.h)) (the sign will be negative if going from x to y to z involves a left turn). Unfortunately Jim’s easy-to-read and elegant routine was 5% to 25% slower than Aaron’s.

Here’s Aaron’s winning solution to the August Challenge (some comments have been removed for space reasons. Aaron’s complete source is on the source code disk):

/* Max holes per side of the peg board. */
#define HOLES 13
 
void GetPerimeter( Point thePegs[], short 
 numPegs, Point outerPegs[], short 
 sideLast[] );
void GetEdgePegs( Point outerPegs[], short 
 test, short last, Point edgePegs[], 
 short *numEdgePegs );
void CheckEdgePegs( Point edgePegs[], short 
 *numEdgePegs, Point newPeg, short first);
void IntegrateArea( Point edgePegs[], short 
 numEdgePegs, Fixed *area ); 
 
/*****************************************/
/* BandedPegs takes an array of points 
 * representing pegs on a pegboard and 
 * returns an array of points representing 
 * the pegs that would be touched by a 
 * rubber band surrounding as many pegs as  
 * possible. It also returns the area thus               surrounded. 
*/
void BandedPegs( short numPegs, Point thePegs[],
 short *numEdgePegs, Point edgePegs[], Fixed *area )
{
    Point   outerPegs[4*(HOLES-1)+1];
    short   sideLast[4], first, last, i;
 
    if( numPegs > 3 ) {
    
        GetPerimeter( thePegs, numPegs, outerPegs, sideLast );
        
 /* Initialize some variables and march around
  * the sides of the board. */
        *numEdgePegs = first = i = 0;
        do {
 /* If there's at least one new peg along the
  * column tops (bottoms), see which ones contact
  * the rubber band. */
            last = sideLast[i++];
            if( first < last ) {
                GetEdgePegs( outerPegs, first, last, edgePegs,
                 numEdgePegs );
                first = last;
            }
 /* Count all pegs from the last (first) column
  * as edge pegs. */
            last = sideLast[i++];
            while( first < last )
                edgePegs[(*numEdgePegs)++] = outerPegs[first++];
        } while( i < 4 ); /* Repeat for four sides. */
    }
    else { 
      /* With 3 or fewer pegs, all will touch the rubber band. */
        *numEdgePegs = numPegs;
        for( i = 0; i < numPegs; i++ ) edgePegs[i] = thePegs[i];
        if( numPegs < 3 ) {
        /* With less than 3 pegs, area must be 0. */
            *area = 0;
            return;
        }
    }
    
    IntegrateArea( edgePegs, *numEdgePegs, area );
    
 /* If there are more than 3 pegs, and they are all
  * in a straight line (indicated by a zero area),
  * the above algorithm will have counted the interior
  * points twice.  The following will remove the
  * redundant set of interior points.  Note that
  * it's also okay for 3 pegs, but no fewer. */
    if( *area == 0 )
      *numEdgePegs = (*numEdgePegs + 3)/2;
}
 
/*******************************************************/
/* This function finds the pegs which roughly
 * define the four sides of the rubber band. */
 
void GetPerimeter( Point thePegs[], short numPegs,
 Point outerPegs[], short sideLast[] )
{
    short   colmin[HOLES], colmax[HOLES],
            rowmin[HOLES], rowmax[HOLES],
            col, row, col1, col2, n;
 
    for( n = 0; n < HOLES; n++  ) {
        colmin[n] = rowmin[n] = HOLES;
        colmax[n] = rowmax[n] = -1;
    }
 /* Check each peg to see if it sets a new extreme
 * in any row or column. */
    for( n = 0; n < numPegs; n++ ) {
        row = thePegs[n].v;
        col = thePegs[n].h;
        if( col < colmin[row] ) colmin[row] = col;
        if( col > colmax[row] ) colmax[row] = col;
        if( row < rowmin[col] ) rowmin[col] = row;
        if( row > rowmax[col] ) rowmax[col] = row;
    }
 /* Collect the pegs at the tops of each column. */
    n = -1;
    for( col = 0; col < HOLES; col++ ) {
        if( (row = rowmin[col]) < HOLES ) {
            outerPegs[++n].v = row;
            outerPegs[n].h = col;
        }
    }
    sideLast[0] = n;
    col1 = outerPegs[0].h;
    col2 = outerPegs[n].h;
 /* Collect all but the top peg of the last column,
  * from top to bottom. */
    for( row = rowmin[col2] + 1; row <= rowmax[col2]; row++ ) {
        if( colmax[row] == col2 ) {
            outerPegs[++n].v = row;
            outerPegs[n].h = col2;
        }
    }
    sideLast[1] = n;
 /* From last to first, collect the pegs at the
  * bottoms of all but the last column. */
    for( col = col2 - 1; col >= col1; col-- ) {
        if( (row = rowmax[col]) >= 0 ) {
            outerPegs[++n].v = row;
            outerPegs[n].h = col;
        }
    }
    sideLast[2] = n;
 /* Collect all but the bottom peg of the first column,
  * from bottom to top. */
    for( row = rowmax[col1] - 1; row >= rowmin[col1]; row-- ) {
        if( colmin[row] == col1 ) {
            outerPegs[++n].v = row;
            outerPegs[n].h = col1;
        }
    }
    sideLast[3] = n;
}
 
/*******************************************************/
/* This function finds the pegs which would push
 * a rubber band to the left of a line between a
 * given starting point and a given ending point.
 * It counts the starting point (but not the
 * ending point) as such a peg. */
 
void GetEdgePegs( Point outerPegs[], short test, short last,
                  Point edgePegs[], short *numEdgePegs )
{
    Point   testPeg, backPeg, nextPeg;
    short   convex, first;
 
    first = *numEdgePegs;

    backPeg = edgePegs[(*numEdgePegs)++] = outerPegs[test];
    nextPeg = outerPegs[last];
 /* Loop through the array of outerPegs from the
  * one after the starting point to the one just
  * before the ending point. */
    while( ++test < last ) {
        testPeg = outerPegs[test];
 /* See if the path connecting backPeg, testPeg,
  * and nextPeg is convex, straight, or concave. */
        if( (convex = (nextPeg.v-backPeg.v)*(testPeg.h-backPeg.h)
 -(testPeg.v-backPeg.v)*(nextPeg.h-backPeg.h)) >= 0 ) {
 /* If convex or straight, count the test
  * peg as an edge peg. */
            edgePegs[(*numEdgePegs)++] = backPeg = testPeg;
 /* If convex, the rubber band's path will change,
  * so we need to check previous edge pegs to see
  * if they are still edge pegs. */
            if( convex > 0 )
              CheckEdgePegs( edgePegs, numEdgePegs, testPeg, first );
        }
    }
}
 
/*******************************************************/

/* If a peg just added to the list of edge pegs
 * has extended the rubber band, this routine will
 * search backward through the list, throwing out pegs
 * that are no longer contacted, until it finds one
 * that still is. */
 
void CheckEdgePegs( Point edgePegs[], short *numEdgePegs,
                    Point newPeg, short first )
{
    Point   testPeg, backPeg;
    short   test;
 
    test = *numEdgePegs - 1;
 /* Loop backward through the list of edge pegs,
  * starting with the one before that just added,
  * stopping before the first that can't be removed. */
    while( --test > first ) {
        testPeg = edgePegs[test];
        backPeg = edgePegs[test-1];
 /* If the path between newPeg, testPeg,
  * and backPeg is concave, remove the peg. */
        if( (newPeg.v-backPeg.v)*(testPeg.h-backPeg.h)
 -(testPeg.v-backPeg.v)*(newPeg.h-backPeg.h) < 0 )
            edgePegs[test] = edgePegs[--(*numEdgePegs)];
        else
        return;
    }
}
 
/*******************************************************/
 
/* This function integrates the area enclosed
 * by a rubber band. */
 
void IntegrateArea( Point edgePegs[],
 short numEdgePegs, Fixed *area ) 
{
    Point   thePeg, lastPeg;
    long    integral = 0;
    short   i;
 /* Starting and ending with the last peg,
  * integrate double the area under the closed path. */
    lastPeg = edgePegs[numEdgePegs-1];
    for( i = 0; i < numEdgePegs; i++ ) {
        thePeg = edgePegs[i];
        integral += (thePeg.h + lastPeg.h)*(thePeg.v - lastPeg.v);
        lastPeg = thePeg;
    }
 /* Correct a negative integral if the path was
  * counterclockwise. */
    if( integral < 0 ) integral = -integral;
 /* By shifting, simultaneously halve the integral
  * and convert it to a fixed. */
    *area = (Fixed)( integral << 15 );
}

 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Microsoft Office 2016 15.25 - Popular pr...
Microsoft Office 2016 - Unmistakably Office, designed for Mac. The new versions of Word, Excel, PowerPoint, Outlook and OneNote provide the best of both worlds for Mac users - the familiar Office... Read more
FileZilla 3.21.0 - Fast and reliable FTP...
FileZilla (ported from Windows) is a fast and reliable FTP client and server with lots of useful features and an intuitive interface. Version 3.21.0: Fixed Vulnerabilities Fixed a string format... Read more
Fantastical 2.2.5 - Create calendar even...
Fantastical 2 is the Mac calendar you'll actually enjoy using. Creating an event with Fantastical is quick, easy, and fun: Open Fantastical with a single click or keystroke Type in your event... Read more
The Hit List 1.1.26 - Advanced reminder...
The Hit List manages the daily chaos of your modern life. It's easy to learn - it's as easy as making lists. And it's powerful enough to let you plan, then forget, then act when the time is right.... Read more
Typinator 6.10 - Speedy and reliable tex...
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
EtreCheck 3.0.2 - For troubleshooting yo...
EtreCheck is an app that displays the important details of your system configuration and allow you to copy that information to the Clipboard. It is meant to be used with Apple Support Communities to... Read more
FileZilla 3.21.0 - Fast and reliable FTP...
FileZilla (ported from Windows) is a fast and reliable FTP client and server with lots of useful features and an intuitive interface. Version 3.21.0: Fixed Vulnerabilities Fixed a string format... Read more
EtreCheck 3.0.2 - For troubleshooting yo...
EtreCheck is an app that displays the important details of your system configuration and allow you to copy that information to the Clipboard. It is meant to be used with Apple Support Communities to... Read more
Microsoft Office 2016 15.25 - Popular pr...
Microsoft Office 2016 - Unmistakably Office, designed for Mac. The new versions of Word, Excel, PowerPoint, Outlook and OneNote provide the best of both worlds for Mac users - the familiar Office... Read more
Typinator 6.10 - Speedy and reliable tex...
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

Bowmasters tips, tricks and hints
At least for this writer, archery was one of the more pleasant surprises of the 2016 Rio Olympics. As opposed to target shooting with guns, which was dreadfully boring, watching people shoot arrows at targets was pretty darn cool. [Read more] | Read more »
Best apps for watching live TV
The Olympics have come and gone, leaving nearly everyone in a temporary state of "What the heck am I going to watch on TV right now?" Besides old reruns of Golden Girls, but that goes without saying. [Read more] | Read more »
What is Flip Diving, and why has it take...
Move over Pokemon GO. There's a new king in town, and it's "the world's #1 cliff diving game." [Read more] | Read more »
5 places where Pokemon GO is still numbe...
In the U.S., the bloom is off the Pokemon Go rose ever so slightly. It's still doing great, sitting atop the top grossing chart as it has for some time, but it's no longer among the top 10 free apps in downloads, possibly because darn near... | Read more »
Madden NFL Mobile: How defense has chang...
Saying that defense is not a priority in Madden NFL Mobile is a bit of an understatement. In asynchronous head-to-head play, you don't take control of your defenders at all, as the AI manages them while your opponent plays offense. When it's your... | Read more »
Feed Hawk (News)
Feed Hawk 1.0.1 Device: iOS Universal Category: News Price: $2.99, Version: 1.0.1 (iTunes) Description: Feed Hawk makes it easy to subscribe to the RSS feed of the website you are visiting. From within Safari, simply open a share... | Read more »
Reigns character guide: Who's who i...
Know your foes. Keep your friends close, but your enemies closer. And there are probably some other cliches that would apply to your perilous spot on the throne in Reigns as well. [Read more] | Read more »
Match 3 puzzler Small Lime is now availa...
Set to hit Android and IOS on the 17th August, Small Lime is the newest match 3 mobile game, and hopes to throw something a little different into the mix. If you love match 3 puzzles, but are tired of the same old ideas being re-hashed again and... | Read more »
Deus Ex GO tips, tricks, and hints
When Square Enix Montreal first hit us with Hitman GO,it was seen as a clever board game twist on a property that you wouldn't normally think would fit that kind of format. Lara Croft GOexpanded things even further while keeping some of the same... | Read more »
Leap of Fate (Games)
Leap of Fate 1.0 Device: iOS Universal Category: Games Price: $3.99, Version: 1.0 (iTunes) Description: *** Minimum hardware: iPad 4, iPad mini 2, iPhone 5s. *** | Read more »

Price Scanner via MacPrices.net

Typinator 6.10 comes with 50 improvements – G...
Ergonis Software today announced release of Typinator 6.10, a new version of their text expander utility for macOS. Typinator 6.10 comes with 50 improvements, including new features, compatibility... Read more
Taxi Sim 2016 Puts Users Behind the Wheel in...
Ovilex Soft today announces Taxi Sim 2016, an update to their ultra-realistic 3D driving simulator app for iOS and Android devices — literally a global event what with the company’s nearly 450,000... Read more
11-inch 1.6GHz/128GB MacBook Air on sale for...
Amazon has the current-generation 11″ 1.6GHz/128GB MacBook Air (sku MJVM2LL/A) on sale for $788 for a limited time. Their price is $111 off MSRP, and it’s the lowest price available for this model. Read more
Apple refurbished Mac minis available for up...
Apple has Certified Refurbished Mac minis available starting at $419. Apple’s one-year warranty is included with each mini, and shipping is free: - 1.4GHz Mac mini: $419 $80 off MSRP - 2.6GHz Mac... Read more
Apple refurbished 13-inch Retina MacBook Pros...
Apple has Certified Refurbished 13″ Retina MacBook Pros available for up to $270 off the cost of new models. An Apple one-year warranty is included with each model, and shipping is free: - 13″ 2.7GHz... Read more
12-inch 32GB and 128GB WiFi iPad Pros on sale...
B&H Photo has 12″ 32GB & 128GB WiFi Apple iPad Pros on sale for up to $70 off MSRP, each including free shipping. B&H charges sales tax in NY only: - 12″ Space Gray 32GB WiFi iPad Pro: $... Read more
Apple refurbished 11-inch MacBook Airs availa...
Apple has Certified Refurbished 11″ MacBook Airs (the latest models), available for up to $170 off the cost of new models. An Apple one-year warranty is included with each MacBook, and shipping is... Read more
WaterField Launches Kickstarter for Intrepid...
San Francisco based WaterField Design have announced their first Kickstarter campaign for the one-of-a-kind Intrepid iPhone Travel Wallet. The all-new design includes iPhone play-through capability... Read more
Five of Top 10 Worldwide Mobile Phone Vendors...
Global sales of smartphones to end users totaled 344 million units in the second quarter of 2016, a 4.3 percent increase over the same period in 2015, according to Gartner, Inc. Overall sales of... Read more
DriveSavers Offers $300 Off Data Recovery Ser...
DriveSavers, with more than 30 years of experience recovering photos, videos, contact lists, financial records and other important data that may have been kept on devices damaged or even destroyed by... Read more

Jobs Board

*Apple* Retail - Multiple Positions Germanto...
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* Professional Learning Specialist - A...
# Apple Professional Learning Specialist Job Number: 51234379 Portland, Maine, Maine, United States Posted: Aug. 18, 2016 Weekly Hours: 40.00 **Job Summary** The Read more
Lead *Apple* Solutions Consultant - Apple (...
# Lead Apple Solutions Consultant Job Number: 51218465 Richmond, VA, Virginia, United States Posted: Aug. 18, 2016 Weekly Hours: 40.00 **Job Summary** The Lead ASC Read more
*Apple* Solutions Consultant - Apple (United...
# Apple Solutions Consultant Job Number: 51218534 Pleasant Hill, California, United States Posted: Aug. 18, 2016 Weekly Hours: 40.00 **Job Summary** As an Apple Read more
*Apple* Retail - Multiple Positions Chestnut...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.