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Jan 99 Prog Challenge

Volume Number: 15 (1999)
Issue Number: 1
Column Tag: Programmer's Challenge

January 1999 Programmer's Challenge

by Bob Boonstra, Westford, MA

Sphere Packing

This month we're going to help you recover from the clutter that might result from the holiday season. Imagine that your post-holiday household is filled with gifts, all of which have to be put somewhere. Imagine further that those gifts include sports equipment given to your children, or parents, or siblings, or grandchildren, as the case may be. And finally, imagine that the sports equipment includes a collection of balls of various sizes - basketballs, baseballs, soccer balls, beach balls, etc. (OK, if I've stretched your imagination to the breaking point, think of some other reason you might have a large collection of spherical objects.) We've got to find somewhere to store all of those balls, and space is at a premium. Fortunately, we also have a very large collection of boxes of various sizes, so many, in fact, that you can count on finding a box of the exact size that you might need. In keeping with our desire for a few less difficult problems, your Challenge is to pack the balls into the smallest box possible, so that we can store them efficiently.

The prototype for the code you should write is:

#if defined(__cplusplus)
#if defined (__cplusplus)
extern "C" {
#endif

typedef struct Position {
  double coordinate[3];     /* coordinate[0]==X position, [1]==Y, [2]==Z */
} Position;

void PackSpheres(
    long numSpheres,        /* input: number of spheres to pack */
    double radius[],        /* input: radius of each of numSpheres spheres */
    Position location[]     /* output: location of center of each sphere */
);

#if defined (__cplusplus)
}
#endif

Your PackSpheres routine will be given the number of balls (numSpheres) to be packed away, along with the radius of each of those spheres. The task is simple. Arrange the collection of balls into a rectangular parallelepiped ("box") such that no ball intersects any other ball (i.e., the distance between the centers of any two balls is greater than or equal to the sum of their radii). PackSpheres returns back the coordinates of the center of each ball in the location parameter. Your objective is to minimize the volume of the box that contains all the balls, where the extent of the box in each dimension (X, Y, and Z) is determined by the maximum and minimum coordinates of the balls, considering both the location of the center of the ball and its radius.

While you must ensure that the balls do not intersect, you need not ensure that the balls touch. In our storage room, boxes of balls can contain balls that levitate in the open space between other balls.

The winner will be the solution that minimizes the volume of the box containing all the balls, plus a penalty of 1% of additional storage volume for each millisecond of execution time.

This will be a native PowerPC Challenge, using the latest CodeWarrior environment. Solutions may be coded in C, C++, or Pascal.

Three Months Ago Winner

Congratulations to Pat Brown (Staunton, VA) for submitting the winning solution to the October Hearts Challenge. Pat's solution beat the second-place entry submitted by Tom Saxton and "dummy" entries that rounded out a tournament of four players. Pat's solution was both the faster of the two and the more successful at avoiding point cards, capturing approximately one third fewer points than Tom's solution.

Pat's strategy was fairly simple. His passing strategy is to pass the three highest cards in his hand. By not including a low heart in the pass, this strategy can aid a shoot attempt by an opponent, as well as being dangerous if it passes the queen of spades to the left. When leading, the playing strategy is to force out the queen of spades as quickly as possible, unless of course he has the queen. While he does not attempt to "shoot the moon", he is watchful for attempts by other players to shoot, and holds on to high cards until any potential shoot is spoiled. Otherwise, Pat tries to play the highest legal card that is lower than the current trick leader.

Tom submitted two solutions, a simple one (used in the tournament at Tom's request), and a more sophisticated (but less successful) one. The simple solution also tries to avoid taking tricks and does not attempt to shoot. It is a little more clever in selecting the pass, in that it tries to create a void if possible. It does not keep track of who might be attempting to shoot, and therefore does not attempt to stop them. Tom's second player keeps track of who is void in what suits and tries to shoot when it has a strong hand. However, it isn't quite perfected, and does much worse in a tournament than the first player.

I've included a Point Comparison chart that helps explain the performance of the two players. The vertical bars indicate the number of hands in which each player captured the number of points shown along the horizontal axis. You can see that Pat's solution was slightly more successful at capturing fewer than 4 points in a hand, very successful at avoiding being stuck with the queen of spaces, and extremely effective at capturing fewer than 20 points in a hand. The line graphs show the cumulative effect of the respective strategies on the score.

The table below summarizes the scoring for Pat and Tom's Hearts entries. The teams played a total of 24 matches, consisting of over 25000 hands of 13 tricks each. The Total Points column in the table lists the number of hearts captured during all of those tricks, plus 13 points for each Queen of Spades, and -26 points for each shoot. The table shows the number of tricks "won" by each player, and the number of times each successfully "shot the moon". You can see that Pat's winning solution did not attempt to shoot, and was very successful at avoiding being stuck with all of the point cards. Although not shown in the table, the less-than-intelligent "dummy" players "shot the moon" more often than either Pat or Tom. This was a consequence of their simplistic "strategy" for not taking points, which led them to hold on to high cards longer than a more sophisticated player would have done. Also shown in the table are the execution time of each solution in milliseconds, the total score, including the penalty of one point per millisecond of execution time, and the code and data sizes. As usual, the number in parentheses after the entrant's name is the total number of Challenge points earned in all Challenges prior to this one.

Name Total Points Tricks Won Shoots Time (msec) Score Code Size Data Size
Pat Brown 94775 59703 1 833 95608 3152 398
Tom Saxton (49) 157105 80902 67 1230 158335 2548 72

Top Contestants

Listed here are the Top Contestants for the Programmer's Challenge, including everyone who has accumulated 20 or more points during the past two years. The numbers below include points awarded over the 24 most recent contests, including points earned by this month's entrants.

  1. Munter, Ernst 204
  2. Saxton, Tom 59
  3. Boring, Randy 56
  4. Mallett, Jeff 50
  5. Rieken, Willeke 47
  6. Cooper, Greg 44
  7. Maurer, Sebastian 40
  8. Heithcock, JG 37
  9. Murphy, ACC 34
  10. Nicolle, Ludovic 34
  11. Lewis, Peter 31
  12. Hart, Alan 21
  13. Antoniewicz, Andy 20
  14. Brown, Pat 20
  15. Day, Mark 20
  16. Higgins, Charles 20
  17. Hostetter, Mat 20
  18. Studer, Thomas 20

There are three ways to earn points: (1) scoring in the top 5 of any Challenge, (2) being the first person to find a bug in a published winning solution or, (3) being the first person to suggest a Challenge that I use. The points you can win are:

1st place20 points
2nd place10 points
3rd place7 points
4th place4 points
5th place2 points
finding bug2 points
suggesting Challenge2 points

Here is Pat's winning Hearts solution:

MyHearts.c
Copyright © 1998 Pat Brown

#include "Hearts.h"

/* ***************************************************
 * Hearts.c
 *
 * Author: Pat Brown
 *
 * Trivia: there are 5.36447377655x10^28 different ways that a
 * deck can be dealed out for a game of Hearts.
 */

#define gMAX        52
#define gMIN        1

// Just the relative rankings, 1..52.
// Can be referenced easily using spot and suit value.
/*
        2C,2D,2S,3C,3D,3S,4C,4D,4S,5C,5D,5S,6C,6D,6S,2H,3H,4H,
        5H,6H,7C,7D,7S,8C,8D,8S,9C,9D,9S,7H,8H,9H,10C,10D,10S,
        JC,JD,JS,QC,QD,KC,KD,AC,AD,10H,JH,QH,KS,AS,KH,AH,QS
*/
static const int gCardValue[5][14] =
{
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},    // NoSuit
    {0, 3, 6, 9,12,15,22,25,28,35,38,52,48,49},    // Spade
    {0,16,17,18,19,29,30,31,32,45,46,47,50,51},    // Heart
    {0, 2, 5, 8,11,14,21,24,27,34,37,40,42,44},    // Diamond
    {0, 1, 4, 7,10,13,20,23,26,33,36,39,41,43}     // Club
};

inline int getCardValue(theSuit, theSpot)
        { return gCardValue[theSuit][theSpot]; }

inline UInt16 NEXTSEAT(UInt16 theSeat)
        { return (theSeat+1)%4; }


/************
  Prototypes
*************/
inline static SInt16 findThisCard(const Card theCards[13],
        const Suit theSuit, const Spot theSpot);
static UInt16 findHighestLimitCard(const Card theCards[13],
        const int uLimit);
static UInt16 findLowestLimitCard(const Card theCards[13],
        const int lLimit);
static UInt16 findHighestIndexLimitCard(const Card theCards[13],
        const UInt16 valid[13], const int numValid, const int uLimit);
static UInt16 findLowestIndexLimitCard(const Card theCards[13],
        const UInt16 valid[13], const int numValid, const int lLimit);
static int findValidCards(const Card theCards[13],
        const Suit theSuit, UInt16 validCards[13]);

inline UInt16        findHighestCard(const Card theCards[13])
    { return findHighestLimitCard(theCards,gMAX); }
inline UInt16        findLowestCard(const Card theCards[13])
    { return findLowestLimitCard(theCards,gMIN); }
inline UInt16        findHighestIndexCard(const Card theCards[13],
        const UInt16 valid[13], const int numValid)
    { return findHighestIndexLimitCard(theCards,valid,numValid,gMAX); }
inline UInt16        findLowestIndexCard(const Card theCards[13],
        const UInt16 valid[13], const int numValid)
    { 
        return findLowestIndexLimitCard(theCards,valid,numValid,gMIN); 
    }

/******************
  Global variables
*******************/
static UInt16     mySeat;
// hasPoints is a bitfield of which players have
// taken points in this hand
static int            hasPoints;
// another bitfield of what suits I'm cutting
static int            cuttingSuit;
static int            tryToSpoil;
/******************************************************
runningTotal keeps track of "points" for each player
in a hand. These aren't real points, but a key to
watch for someone trying to pull a sweep.
If someone gets more than six hearts, or the queen of
spades and three hearts, they may be trying to sweep
(unless someone else has points).
*******************************************************/
static int            runningTotal[4];
static Boolean    blackLadyInHand;
static Boolean    blackLadyPlayed;
static Boolean    heartsBroken;

/********************
  Required functions
*********************/

InitTournament
pascal void InitTournament(const UInt16 numPlayers,
                const UInt16 gameEndingScore)
{
    return;
}

InitGame
pascal void InitGame(const UInt32 playerID[4],
                const UInt16 yourSeat)
{
    mySeat = yourSeat;
}

SelectPass
pascal void SelectPass(const Card dealtHand[13],
         const Pass passDirection, UInt16 passedCards[3])
{
    int    i, top, newtop;

// Init globals at the start of a hand.
    blackLadyPlayed = heartsBroken = 
            tryToSpoil = hasPoints = cuttingSuit = 
            runningTotal[0]=runningTotal[1]=runningTotal[2]=runningTotal[3]
            = 0;

    if (passDirection != kNoPass)
    {
        top = gMAX;
        for (i=0; i<3; i++) // get the three highest cards
        {
            newtop = passedCards[i] = 
                    findHighestLimitCard(dealtHand, top);
            top = getCardValue(dealtHand[newtop].suit, 
                                    dealtHand[newtop].spot)-1;
        }
    }
}

PlayTrick
pascal void PlayTrick(const UInt16 trickNumber,
                 const UInt16 trickLeader, const Card yourHand[13],
                 const Card cardsPlayed[4], UInt16 *yourPlay)
{
    UInt16     validCards[13], myCard;
    int            num, i;
    Suit         leadingSuit;
    Spot         whatsTaking;
    UInt16     whosTaking;
    Boolean    pointsTaking;

    if (trickNumber == 0)
    {
    // see if I've been passed the Queen of Spades
        blackLadyInHand = 
                    (findThisCard(yourHand, kSpade, kQueen) >= 0);
        if (trickLeader == mySeat)
        {
            *yourPlay = findThisCard(yourHand, kClub, k2);
            return;
        }
        else
            goto NOTLEADING;
    }
    
    if (trickLeader == mySeat)
    {
        // try to force the Queen of Spades (unless I have it)
        if (!blackLadyPlayed && !blackLadyInHand)
        {
            if (
                (num = findValidCards(yourHand, kSpade, validCards)) != 0)
            {
            myCard = findLowestIndexCard(yourHand, validCards, num);
                // don't play higher than the Queen
                if (yourHand[myCard].spot < kKing)
                {
                    *yourPlay = myCard;
                    return;
                }
            }
        } // (!blackLadyPlayed && !blackLadyInHand)
        num = findValidCards(yourHand, kNoSuit, validCards);
        *yourPlay = findLowestIndexCard(yourHand, validCards, num);
        return;
    } // if (trickLeader == mySeat)

NOTLEADING:    
    leadingSuit = cardsPlayed[trickLeader].suit;
    num=0;
    // this is faster than scanning yourHand every time
    if ((cuttingSuit & (1 << leadingSuit)))
        goto CUTTING;
    if (
        (num = findValidCards(yourHand, leadingSuit, validCards))==1)
    {
    // only one card we can play
        *yourPlay = validCards[0];
        return;
    }
    if (num == 0)
    {
        cuttingSuit |= 1 << leadingSuit;
        goto CUTTING;
    }
    if (num == 0)
    {
CUTTING:
    // we're cutting this suit
        if (trickNumber == 0)
        {
        // Can't play points on the first trick.
        // 51 keeps us from playing the Queen of Spades.
            num = findValidCards(yourHand, kNoSuit, validCards);
            *yourPlay = 
        findHighestIndexLimitCard(yourHand, validCards, num, 51);
            return;
        }
        if (!tryToSpoil)
            *yourPlay = findHighestCard(yourHand);
        else // Save the high cards to spoil a sweep.
            *yourPlay = findLowestCard(yourHand);
        return;
    } // if (num == 0)
    
    // See who's winning this trick so far.
    i = trickLeader;
    pointsTaking = leadingSuit == kHeart;
    whatsTaking = kNoSpot;
    while (i != mySeat)
    {
        if (    (cardsPlayed[i].suit == kSpade) && 
                    (cardsPlayed[i].spot == kQueen))
            pointsTaking = true;
        if (cardsPlayed[i].suit == leadingSuit)
        {
            if (cardsPlayed[i].spot > whatsTaking)
            {
                whatsTaking = cardsPlayed[i].spot;
                whosTaking = i;
            }
        }
        else // (cardsPlayed[i].suit != leadingSuit)
        {
                pointsTaking |= (cardsPlayed[i].suit == kHeart);
        } // if (cardsPlayed[i].suit == leadingSuit) else
        i = NEXTSEAT(i);
    } // while (i != mySeat)

    if ((leadingSuit == kSpade) && blackLadyInHand)
    {
        myCard = findThisCard(yourHand, kSpade, kQueen);
        if (whatsTaking > kQueen) // dump it on King or Ace
        {
            *yourPlay = myCard;
            return;
        }
        else // don't play the Queen of Spades
        {
            for (i=0;i<num;i++)
            {
                if (validCards[i] == myCard)
                {
                    while (++i < num)
                        validCards[i-1] = validCards[i];
                    num-;
                }
            } // for (i=0;i<num;i++)
        } // if (whatsTaking > kQueen) else
    } // if ((leadingSuit == kSpade) && blackLadyInHand)
            
    if (trickLeader == NEXTSEAT(i)) // playing last
    {
        if (!pointsTaking)
        {
            if (tryToSpoil) // don't waste the high cards
                *yourPlay = 
                    findLowestIndexCard(yourHand, validCards, num);
            else
                *yourPlay = 
                    findHighestIndexCard(yourHand, validCards, num);
            return;
        }
        else
        {
            if (tryToSpoil == (1 << whosTaking))
            {
        myCard = findHighestIndexCard(yourHand, validCards, num); 
              if (yourHand[myCard].spot < whatsTaking) // we can't take this trick
              myCard = findLowestIndexCard(yourHand, validCards, num);
                *yourPlay = myCard;
                return;
            }
            else // someone else is spoiling the sweep
            {
                *yourPlay = 
                findHighestIndexLimitCard(yourHand, validCards, num, 
                                    getCardValue(leadingSuit, whatsTaking));
                return;
            }
        } // if (!pointsTaking) else
    } // if (trickLeader == NEXTSEAT(i))
    
    if (tryToSpoil)
    {
        myCard = findHighestIndexCard(yourHand, validCards, num);
    if (yourHand[myCard].spot < whatsTaking) // we can't take this trick
        myCard = findLowestIndexCard(yourHand, validCards, num);
        *yourPlay = myCard;
        return;
    }
    
    // Standard behaviour
    // Play the highest card under the current highest card.
    *yourPlay = findHighestIndexLimitCard(yourHand, validCards, 
                            num, getCardValue(leadingSuit, whatsTaking));
    return;
}

TrickResults
pascal void TrickResults(const Card lastTrick[4],
                const UInt16 trickWinner)
{
// Keep track on who has what points so we can watch for a sweep.
    int    i;
    int    points = 0;
    int    whoWon;

    for (i=0; i<4; i++)
    {
        switch (lastTrick[i].suit)
        {
            case kSpade:
                if (lastTrick[i].spot == kQueen)
                {
                // not 13, we trigger a sweep when "points" hit 7
                    points += 4;
                    blackLadyPlayed = true;
                    blackLadyInHand = false;
                }
                break;
            case kHeart:
                points++;
                heartsBroken = true;
                break;
        }
    } // for (i=0; i<4; i++)
    if (points == 0)
        return;
    points = runningTotal[trickWinner] += points;
    whoWon = 1 << trickWinner;
    hasPoints |= whoWon;
    if (tryToSpoil)
    {
        if (whoWon != tryToSpoil)
            tryToSpoil = 0;
    }
    else // (!tryToSpoil)
    {
        if (trickWinner != mySeat)
            tryToSpoil = ((hasPoints == whoWon) && (points > 6)) 
? whoWon : 0;
    }
}

HandResults
pascal void HandResults(const SInt16 pointsThisHand[4],
                const SInt32 cumPoints[4])
{
    return;
}

/**************
  My functions
***************/

findThisCard
/**************************************
Return the index of a particular card,
or -1 if it's not there.
***************************************/
inline static SInt16 findThisCard(const Card theCards[13],
                const Suit theSuit, const Spot theSpot)
{
    SInt16    c = -1, i = 13;
    
    while ((c<0) && i-)
    {
        if (    (theCards[i].spot == theSpot) && 
                    (theCards[i].suit == theSuit))
                c = i;
    }
    return c;
}

findHighestLimitCard
/*****************************************************
These next few functions find cards based on a limit.
(it's an inclusive limit)
If there are no cards within the limit, then call
the opposite function.
******************************************************/
static UInt16 findHighestLimitCard(const Card theCards[13],
                const int uLimit)
{
    int         i = 13;
    int         points, theValue = 0;
    SInt16    theCard = -1;
    
    while (i-)
    {
        points = getCardValue(theCards[i].suit, theCards[i].spot);
        if ((points > theValue) && (points <= uLimit))
        {
            theCard = i;
            if (uLimit == (theValue = points))
                return theCard;
        }
    }
    if (theCard < 0)
        theCard = findLowestLimitCard(theCards, uLimit);
    return theCard;
}

findLowestLimitCard
static UInt16 findLowestLimitCard(const Card theCards[13],
                const int lLimit)
{
    int         i = 13;
    int         points, theValue = 99;
    SInt16    theCard = -1;
    
    while (i-)
    {
        points = getCardValue(theCards[i].suit, theCards[i].spot);
        if ((points < theValue) && (points >= lLimit))
        {
            theCard = i;
            if (lLimit == (theValue = points))
                return theCard;
        }
    }
    if (theCard < 0)
        theCard = findHighestLimitCard(theCards, lLimit);
    return theCard;
}

findHighestIndexLimitCard
/***************************************************
Index functions use an array of valid card indexes.
************ INFINITE RECURSION WARNING ************
 Do not call these functions with numValid == 0!!!
****************************************************/
static UInt16 findHighestIndexLimitCard(const Card theCards[13],
                const UInt16 valid[13], const int numValid, 
                const int uLimit)
{
    int         i = numValid;
    int         points, theValue = 0;
    SInt16    theCard = -1;
    
    while (i-)
    {
        points = getCardValue(theCards[valid[i]].suit, 
                              theCards[valid[i]].spot);
        if ((points > theValue) && (points <= uLimit))
        {
            theCard = valid[i];
            if (uLimit == (theValue = points))
                return theCard;
        }
    }
    if (theCard < 0)
    theCard = findLowestIndexLimitCard(theCards, valid, numValid, 
                                                 uLimit);
    return theCard;
}

findLowestIndexLimitCard
static UInt16 findLowestIndexLimitCard(const Card theCards[13],
                const UInt16 valid[13], const int numValid, 
                const int lLimit)
{
    int         i = numValid;
    int         points, theValue = 99;
    SInt16    theCard = -1;
    
    while (i-)
    {
        points = getCardValue(theCards[valid[i]].suit, 
                                                    theCards[valid[i]].spot);
        if ((points < theValue) && (points >= lLimit))
        {
            theCard = valid[i];
            if (lLimit == (theValue = points))
                return theCard;
        }
    }
    if (theCard < 0)
theCard = findHighestIndexLimitCard(theCards, valid, numValid, 
                                                   lLimit);
    return theCard;
}

findValidCards
/*********************************************************
Fill an array with indexes to cards of a particular suit.
Returns the number of valid cards (the size of the array)
Passing kNoSuit will fill the list depending on whether
hearts can be played now.
**********************************************************/
static int findValidCards(const Card theCards[13],
                const Suit theSuit, UInt16 validCards[13])
{
    UInt16    i;
    int         num = 0;
    
    if (theSuit == kNoSuit)
    {
        if (heartsBroken)
        {
            for (i=0; i<13; i++)
                if (theCards[i].suit != kNoSuit) validCards[num++] = i;
        }
        else // (!heartsBroken)
        {
            for (i=0; i<13; i++)
            {
                if (    (theCards[i].suit != kHeart) && 
                            (theCards[i].suit != kNoSuit))
                    validCards[num++] = i;
            }
            if (num == 0) // Nothing but hearts left to play.
            {
                for (i=0; i<13; i++)
            if (theCards[i].suit != kNoSuit) validCards[num++] = i;
            }
        } // if (heartsBroken) else
    }
    else // (theSuit != kNoSuit)
    {
        for (i=0; i<13; i++)
        {
            if (theCards[i].suit == theSuit)
                validCards[num++] = i;
        }
    }
    return num;
}

 

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I really like rymdkapsel. Not just because I'm a sucker for games that are cleverly simple or highly stylisitc, but because it's fun and challenging. Actually it's extremely challenging, which is why I was excited to learn that it's getting a couple... | Read more »
Check out the anticipated Angel Stone in...
Fincon has finally revealed Angel Stone in action in the first ever official gameplay trailer for the anticipated hack and slasher. Angel Stone is set in a post-apocalyptic world in which humanity is in danger of being wiped out by the demonic... | Read more »
Moleskine Timepage is an All-New Calenda...
Moleskine Timepage is a bit of a departure for the notebook manufacturer (since it has little to do with notebooks), but it certainly carries their simple and elegant style quite well. [Read more] | Read more »
Jog on Over and Check Out the New Runtas...
Runtastic has put out a fair number of apps to help you sleep, track excercise, and train various parts of your body. Now it's time for your legs to have their own time in the spotlight with Runtastic Leg Trainer. [Read more] | Read more »
It's Lights Out in the Upcoming Pla...
Ember’s Journey is a stark puzzle platformer with a twist: the entire game is played in darkness. The only light you can see by is the one emanating from your own character. [Read more] | Read more »
MooVee - Your Movies Guru (Entertainmen...
MooVee - Your Movies Guru 1.0 Device: iOS iPhone Category: Entertainment Price: $1.99, Version: 1.0 (iTunes) Description: MooVee helps you effortlessly manage your movies, on your iPhone. | Read more »
Geometry Wars 3: Dimensions (Games)
Geometry Wars 3: Dimensions 1.0.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0.0 (iTunes) Description: Enjoy the next chapter in the award-winning Geometry Wars franchise and enjoy stunning, console-quality... | Read more »
CHAOS RINGS Ⅲ (Games)
CHAOS RINGS Ⅲ 1.0.0 Device: iOS Universal Category: Games Price: $19.99, Version: 1.0.0 (iTunes) Description: The newest addition to the popular smartphone RPG series is finally here! ・CHAOS RINGS Overview | Read more »
The Popular Insight Series of Travel Gui...
Getting around in a country when you can't understand the primary language can be tough. Fortunately there are several options available to help wold travellers with the important stuff like giving directions to a cab driver or asking where the... | Read more »

Price Scanner via MacPrices.net

Top Markets Saturation To Slow Global Smartph...
According to a new mobile phone forecast from the International Data Corporation (IDC) Worldwide Quarterly Mobile Phone Tracker, smartphone shipments are expected to grow 11.3% in 2015 — down from 27... Read more
Apple refurbished 2014 13-inch Retina MacBook...
The Apple Store has Apple Certified Refurbished 2014 13″ Retina MacBook Pros available for up to $400 off original MSRP, starting at $979. An Apple one-year warranty is included with each model, and... Read more
What Would the ideal Apple Productivity Platf...
For the past four years I’ve kept a foot in both the Mac and iPad camps respectively. my daily computing hours divided about 50/50 between the two devices with remarkable consistency. However, there’... Read more
PageMeUp 1.2.1 Ten Dollar Page Layout Applica...
Paris, France-based Softobe, an OS X software development company, has announced that their PageMeUp v. 1.2.1, is available on the Mac App Store for $9.99. The license can be installed on up to 5... Read more
Eight New Products For USB Type-C Application...
Fresco Logic, specialists in advanced connectivity technologies and ICs, has introduced two new product families targeting the Type-C connector recently introduced across a number of consumer... Read more
Scripps National Spelling Bee Launches Buzzwo...
Scripps National Spelling Bee fans can monitor the action at the 2015 Spelling Bee with the new Buzzworthy app for iOS, Android and Windows mobile devices. The free Buzzworthy app provides friendly... Read more
13-inch 2.5GHz MacBook Pro on sale for $120 o...
B&H Photo has the 13″ 2.5GHz MacBook Pro on sale for $979 including free shipping plus NY sales tax only. Their price is $120 off MSRP, and it’s the lowest price for this model (except for Apple’... Read more
27-inch 3.3GHz 5K iMac on sale for $1899, $10...
B&H Photo has the new 27″ 3.3GHz 5K iMac on sale for $1899.99 including free shipping plus NY tax only. Their price is $100 off MSRP. Read more
Save up to $50 on iPad Air 2, NY tax only, fr...
B&H Photo has iPad Air 2s on sale for up to $50 off MSRP including free shipping plus NY sales tax only: - 16GB iPad Air 2 WiFi: $469 $30 off - 64GB iPad Air 2 WiFi: $549.99 $50 off - 128GB iPad... Read more
Updated Mac Price Trackers
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: - 15″ MacBook Pros - 13″ MacBook... Read more

Jobs Board

*Apple* Retail - Multiple Positions (US) - A...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
Program Manager, *Apple* Community Support...
**Job Summary** Apple Support Communities ( discussions. apple .com) helps customers get the most from their Apple products and services by providing access to Read more
Senior Data Scientist, *Apple* Retail - Onl...
**Job Summary** Apple Retail - Online sells Apple products to customers around the world. In addition to selling Apple products with unique services such as iPad Read more
*Apple* Solutions Consultant - Retail Sales...
**Job Summary** As an Apple Solutions Consultant (ASC) you are the link between our customers and our products. Your role is to drive the Apple business in a retail Read more
*Apple* Watch SW Application Project Manager...
**Job Summary** The Apple Watch software team is looking for an Application Engineering Project Manager to work on new projects for Apple . The successful candidate Read more
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