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

Hopper Disassembler 4.3.2- - Binary disa...
Hopper Disassembler is a binary disassembler, decompiler, and debugger for 32- and 64-bit executables. It will let you disassemble any binary you want, and provide you all the information about its... Read more
GraphicConverter 10.5.1 - $39.95
GraphicConverter is an all-purpose image-editing program that can import 200 different graphic-based formats, edit the image, and export it to any of 80 available file formats. The high-end editing... Read more
Delicious Library 3.7 - Import, browse a...
Delicious Library allows you to import, browse, and share all your books, movies, music, and video games with Delicious Library. Run your very own library from your home or office using our... Read more
Adobe Animate CC 2017 18.0.0.107 - Anima...
Animate CC 2018 is available as part of Adobe Creative Cloud for as little as $19.99/month (or $9.99/month if you're a previous Flash Professional customer). Animate CC 2018 (was Flash CC) lets you... Read more
Adobe After Effects CC 2018 15.0 - Creat...
After Effects CC 2018 is available as part of Adobe Creative Cloud for as little as $19.99/month (or $9.99/month if you're a previous After Effects customer). The new, more connected After Effects CC... Read more
Adobe Premiere Pro CC 2018 12.0.0 - Digi...
Premiere Pro CC 2018 is available as part of Adobe Creative Cloud for as little as $19.99/month (or $9.99/month if you're a previous Premiere Pro customer). Adobe Premiere Pro CC 2018 lets you edit... Read more
Alarm Clock Pro 10.3 - $19.95
Alarm Clock Pro isn't just an ordinary alarm clock. Use it to wake you up in the morning, send and compose e-mails, remind you of appointments, randomize the iTunes selection, control an internet... Read more
Adobe Lightroom 20170919-1412-ccb76bd] -...
Adobe Lightroom is available as part of Adobe Creative Cloud for as little as $9.99/month bundled with Photoshop CC as part of the photography package. Lightroom 6 is also available for purchase as a... Read more
Adobe Illustrator CC 2018 22.0.0 - Profe...
Illustrator CC 2018 is available as part of Adobe Creative Cloud for as little as $19.99/month (or $9.99/month if you're a previous Illustrator customer). Adobe Illustrator CC 2018 is the industry... Read more
Hopper Disassembler 4.3.0- - Binary disa...
Hopper Disassembler is a binary disassembler, decompiler, and debugger for 32- and 64-bit executables. It will let you disassemble any binary you want, and provide you all the information about its... Read more

ICEY (Games)
ICEY 1.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0 (iTunes) Description: ICEY is a 2D side-scrolling action game. As you follow the narrator's omnipresent voice, you will see through ICEY's eyes and learn the... | Read more »
The best new games we played this week -...
We've made it, folks. Another weekend is upon us. It's time to sit back and relax with the best new releases of the week. Puzzles, strategy RPGs, and arcade games abound this week. There's a lot of quality stuff to unpack this week, so let's hop... | Read more »
Wheels of Aurelia (Games)
Wheels of Aurelia 1.0.1 Device: iOS Universal Category: Games Price: $3.99, Version: 1.0.1 (iTunes) Description: | Read more »
Halcyon 6: Starbase Commander guide - ti...
Halcyon 6 is a well-loved indie RPG with stellar tactical combat and some pretty good writing, too. It's now landed on the App Store, so mobile fans, if you're itching for a good intergalactic adventure, here's your game. Being a strategy RPG, the... | Read more »
Game of Thrones: Conquest guide - how to...
Fans of base building games might be excited to know that yet another entry in the genre has materialized - Game of Thrones: Conquest. Yes, you can now join the many kingdoms of the famed book series, or create your own, as you try to conquer... | Read more »
Halcyon 6: Starbase Commander (Games)
Halcyon 6: Starbase Commander 1.4.2.0 Device: iOS Universal Category: Games Price: $6.99, Version: 1.4.2.0 (iTunes) Description: An epic space strategy RPG with base building, deep tactical combat, crew management, alien diplomacy,... | Read more »
Legacy of Discord celebrates its 1 year...
It’s been a thrilling first year for fans of Legacy of Discord, the stunning PvP dungeon-crawling ARPG from YOOZOO Games, and now it’s time to celebrate the game’s first anniversary. The developers are amping up the festivities with some exciting... | Read more »
3 reasons to play Thunder Armada - the n...
The bygone days of the Battleship board game might have past, but naval combat simulators still find an audience on mobile. Thunder Armada is Chinese developer Chyogames latest entry into the genre, drawing inspiration from the explosive exchanges... | Read more »
Experience a full 3D fantasy MMORPG, as...
Those hoping to sink their teeth into a meaty hack and slash RPG that encourages you to fight with others might want to check out EZFun’s new Eternity Guardians. Available to download for iOS and Android, Eternity Guardians is an MMORPG that lets... | Read more »
Warhammer Quest 2 (Games)
Warhammer Quest 2 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: Dungeon adventures in the Warhammer World are back! | Read more »

Price Scanner via MacPrices.net

Save $100 on 13″ MacBook Airs, prices start a...
Adorama has 2017 13″ MacBook Airs on sale today for $100 off MSRP including free shipping. Adorama charges NY & NJ sales tax only: – 13″ 1.8GHz/128GB MacBook Air (MQD32LL/A): $899, $100 off MSRP... Read more
1.4GHz Mac mini available for $399, $100 off...
TigerDirect has the 1.4GHz Mac mini on sale today for $399 including free shipping. Their price is $100 off MSRP, and it’s the lowest price available for this model. Although currently out of stock,... Read more
21″ 2.3GHz iMac on sale for $999, save $100
MacMall has the 21″ 2.3GHz iMac (MMQA2LL/A) on sale today for $999 including free shipping. Their price is $100 off MSRP, and it’s the lowest price available for this model. Read more
12″ iPad Pros on sale for $50 off MSRP, no ta...
Adorama has 12″ iPad Pros on sale today for $50 off MSRP. Shipping is free, and Adorama charges sales tax in NY & NJ only: – 12″ 64GB iPad Pro: $749, save $50 – 12″ 256GB iPad Pro: $899, save $50... Read more
9″ iPads on sale for $30 off, starting at $29...
MacMall has 9″ iPads on sale for $30 off including free shipping: – 9″ 32GB iPad: $299 – 9″ 128GB iPad: $399 Read more
Apple restocks full line of refurbished 13″ M...
Apple has restocked a full line of Apple Certified Refurbished 2017 13″ MacBook Pros for $200-$300 off MSRP. A standard Apple one-year warranty is included with each MacBook, and shipping is free.... Read more
13″ 3.1GHz/256GB MacBook Pro on sale for $167...
Amazon has the 2017 13″ 3.1GHz/256GB Space Gray MacBook Pro on sale today for $121 off MSRP including free shipping: – 13″ 3.1GHz/256GB Space Gray MacBook Pro (MPXV2LL/A): $1678 $121 off MSRP Keep an... Read more
13″ MacBook Pros on sale for up to $120 off M...
B&H Photo has 2017 13″ MacBook Pros in stock today and on sale for up to $120 off MSRP, each including free shipping plus NY & NJ sales tax only: – 13-inch 2.3GHz/128GB Space Gray MacBook... Read more
15″ MacBook Pros on sale for up to $200 off M...
B&H Photo has 15″ MacBook Pros on sale for up to $200 off MSRP. Shipping is free, and B&H charges sales tax in NY & NJ only: – 15″ 2.8GHz MacBook Pro Space Gray (MPTR2LL/A): $2249, $150... Read more
Roundup of Apple Certified Refurbished iMacs,...
Apple has a full line of Certified Refurbished 2017 21″ and 27″ iMacs available starting at $1019 and ranging up to $350 off original MSRP. Apple’s one-year warranty is standard, and shipping is free... Read more

Jobs Board

Engineering Manager, *Apple* Retail Enginee...
# Engineering Manager, Apple Retail Engineering Job Number: 58139948 Santa Clara Valley, California, United States Posted: 20-Oct-2017 Weekly Hours: 40.00 **Job Read more
*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
Commerce Engineer, *Apple* Media Products -...
Commerce Engineer, Apple Media Products (New York City) Job Number: 113028813New York City, New York, United StatesPosted: Sep. 20, 2017Weekly Hours: 40.00 Job Read more
US- *Apple* Store Leader Program - Apple (Un...
US- Apple Store Leader Program Job Number: VariousUnited StatesPosted: Oct. 19, 2017Retail Store Job Summary Learn and grow as you explore the art of leadership at Read more
Product Manager - *Apple* Pay on the *Appl...
Job Summary Apple is looking for a talented product manager to drive the expansion of Apple Pay on the Apple Online Store. This position includes a unique Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.