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

Civilization VI 1.2.4 - Next iteration o...
Sid Meier’s Civilization VI is the next entry in the popular Civilization franchise. Originally created by legendary game designer Sid Meier, Civilization is a strategy game in which you attempt to... Read more
Skype 8.52.0.138 - Voice-over-internet p...
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
Bookends 13.2.6 - Reference management a...
Bookends is a full-featured bibliography/reference and information-management system for students and professionals. Bookends uses the cloud to sync reference libraries on all the Macs you use.... Read more
BusyContacts 1.4.0 - Fast, efficient con...
BusyContacts is a contact manager for OS X that makes creating, finding, and managing contacts faster and more efficient. It brings to contact management the same power, flexibility, and sharing... Read more
Chromium 77.0.3865.75 - Fast and stable...
Chromium is an open-source browser project that aims to build a safer, faster, and more stable way for all Internet users to experience the web. Version 77.0.3865.75: A list of changes is available... Read more
DiskCatalogMaker 7.5.5 - Catalog your di...
DiskCatalogMaker is a simple disk management tool which catalogs disks. Simple, light-weight, and fast Finder-like intuitive look and feel Super-fast search algorithm Can compress catalog data for... Read more
Alfred 4.0.4 - Quick launcher for apps a...
Alfred is an award-winning productivity application for OS X. Alfred saves you time when you search for files online or on your Mac. Be more productive with hotkeys, keywords, and file actions at... Read more
A Better Finder Rename 10.45 - File, pho...
A Better Finder Rename is the most complete renaming solution available on the market today. That's why, since 1996, tens of thousands of hobbyists, professionals and businesses depend on A Better... Read more
iFinance 4.5.11 - Comprehensively manage...
iFinance allows you to keep track of your income and spending -- from your lunchbreak coffee to your new car -- in the most convenient and fastest way. Clearly arranged transaction lists of all your... Read more
OmniGraffle Pro 7.11.3 - Create diagrams...
OmniGraffle Pro helps you draw beautiful diagrams, family trees, flow charts, org charts, layouts, and (mathematically speaking) any other directed or non-directed graphs. We've had people use... Read more

Latest Forum Discussions

See All

Five Nights at Freddy's AR: Special...
Five Nights at Freddy's AR: Special Delivery is a terrifying new nightmare from developer Illumix. Last week, FNAF fans were sent into a frenzy by a short teaser for what we now know to be Special Delivery. Those in the comments were quick to... | Read more »
Rush Rally 3's new live events are...
Last week, Rush Rally 3 got updated with live events, and it’s one of the best things to happen to racing games on mobile. Prior to this update, the game already had multiplayer, but live events are more convenient in the sense that it’s somewhat... | Read more »
Why your free-to-play racer sucks
It’s been this way for a while now, but playing Hot Wheels Infinite Loop really highlights a big issue with free-to-play mobile racing games: They suck. It doesn’t matter if you’re trying going for realism, cart racing, or arcade nonsense, they’re... | Read more »
Steam Link Spotlight - The Banner Saga 3
Steam Link Spotlight is a new feature where we take a look at PC games that play exceptionally well using the Steam Link app. Our last entry talked about Terry Cavanaugh’s incredible Dicey Dungeons. Read about how it’s a great mobile experience... | Read more »
PSA: GRIS has some issues
You may or may not have seen that Devolver Digital just released GRIS on the App Store, but we wanted to do a quick public service announcement to say that you might not want to hop on buying it just yet. The puzzle platformer has come to small... | Read more »
Explore the world around you in new matc...
Got a hankering for a fresh-feeling Match-3 puzzle game that offers a unique twist? You might find exactly what you’re looking for with What a Wonderful World, a new spin on the classic mobile genre which merges entertaining puzzles with global... | Read more »
Combo Quest (Games)
Combo Quest 1.0 Device: iOS Universal Category: Games Price: $.99, Version: 1.0 (iTunes) Description: Combo Quest is an epic, time tap role-playing adventure. In this unique masterpiece, you are a knight on a heroic quest to retrieve... | Read more »
Hero Emblems (Games)
Hero Emblems 1.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0 (iTunes) Description: ** 25% OFF for a limited time to celebrate the release ** ** Note for iPhone 6 user: If it doesn't run fullscreen on your device... | Read more »
Puzzle Blitz (Games)
Puzzle Blitz 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: Puzzle Blitz is a frantic puzzle solving race against the clock! Solve as many puzzles as you can, before time runs out! You have... | Read more »
Sky Patrol (Games)
Sky Patrol 1.0.1 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0.1 (iTunes) Description: 'Strategic Twist On The Classic Shooter Genre' - Indie Game Mag... | Read more »

Price Scanner via MacPrices.net

Save $150-$250 on 10.2″ WiFi + Cellular iPads...
Verizon is offering $150-$250 discounts on Apple’s new 10.2″ WiFi + Cellular iPad with service. Buy the iPad itself and save $150. Save $250 on the purchase of an iPad along with an iPhone. The fine... Read more
Apple continues to offer 13″ 2.3GHz Dual-Core...
Apple has Certified Refurbished 2017 13″ 2.3GHz Dual-Core non-Touch Bar MacBook Pros available starting at $1019. An standard Apple one-year warranty is included with each model, outer cases are new... Read more
Apple restocks 2018 MacBook Airs, Certified R...
Apple has restocked Certified Refurbished 2018 13″ MacBook Airs starting at only $849. Each MacBook features a new outer case, comes with a standard Apple one-year warranty, and is shipped free. The... Read more
Sunday Sale! 2019 27″ 5K 6-Core iMacs for $20...
B&H Photo has the new 2019 27″ 5K 6-Core iMacs on stock today and on sale for up to $250 off Apple’s MSRP. Overnight shipping is free to many locations in the US. These are the same iMacs sold by... Read more
Weekend Sale! 2019 13″ MacBook Airs for $200...
Amazon has new 2019 13″ MacBook Airs on sale for $200 off Apple’s MSRP, with prices starting at $899, each including free shipping. Be sure to select Amazon as the seller during checkout, rather than... Read more
2019 15″ MacBook Pros now on sale for $350-$4...
B&H Photo has Apple’s 2019 15″ 6-Core and 8-Core MacBook Pros on sale today for $350-$400 off MSRP, starting at $2049, with free overnight shipping available to many addresses in the US: – 2019... Read more
Buy one Apple Watch Series 5 at Verizon, get...
Buy one Apple Watch Series 5 at Verizon, and get a second Watch for 50% off. Plus save $10 on your first month of service. The fine print: “Buy Apple Watch, get another up to 50% off on us. Plus $10... Read more
Sprint offers 64GB iPhone 11 for free to new...
Sprint will include the 64GB iPhone 11 for free for new customers with an eligible trade-in in of the iPhone 7 or newer through September 19, 2019. The fine print: “iPhone 11 64GB $0/mo. iPhone 11... Read more
Verizon offers new iPhone 11 models for up to...
Verizon is offering Apple’s new iPhone 11 models for $500 off MSRP to new customers with an eligible trade-in (see list below). Discount is applied via monthly bill credits over 24 months. Verizon is... Read more
AT&T offers free $300 reward card + free...
AT&T Wireless will include a second free 64GB iPhone 11 with the purchase of one eligible iPhone at full price. They will also include a free $300 rewards card. The fine print: “Buy an elig.... Read more

Jobs Board

Student Employment (Blue *Apple* Cafe) Spri...
Student Employment (Blue Apple Cafe) Spring 2019 Penn State University Campus/Location: Penn State Brandywine Campus City: Media, PA Date Announced: 12/20/2018 Date Read more
Best Buy *Apple* Computing Master - Best Bu...
**732359BR** **Job Title:** Best Buy Apple Computing Master **Job Category:** Store Associates **Location Number:** 000171-Winchester Road-Store **Job Description:** Read more
*Apple* Mobile Master - Best Buy (United Sta...
**732324BR** **Job Title:** Apple Mobile Master **Job Category:** Store Associates **Location Number:** 000013-Fargo-Store **Job Description:** **What does a Best Read more
Best Buy *Apple* Computing Master - Best Bu...
**732455BR** **Job Title:** Best Buy Apple Computing Master **Job Category:** Sales **Location Number:** 000449-Auburn Hills-Store **Job Description:** **What does a Read more
*Apple* Mobility Pro - Best Buy (United Stat...
**732490BR** **Job Title:** Apple Mobility Pro **Job Category:** Store Associates **Location Number:** 000449-Auburn Hills-Store **Job Description:** At Best Buy, Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.