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Jul 98 Prog Challenge

Volume Number: 14 (1998)
Issue Number: 7
Column Tag: Programmer's Challenge

Jul 97 Programmer's Challenge

by Bob Boonstra, Westford, MA

Going Up?

Welcome to the Programmer's Challenge Skyscraper. Your Challenge this month is to assume control of our skyscraper's elevators and efficiently move a dedicated crew of simulated employees up and down the building.

The prototype for the code you should write is:

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

#define kMaxFloors 500
#define kMaxElevators 100
#define kElevatorCapacity 16

typedef enum {         /* commanded action for elevator car */
  kGoingUp=1,          /* send car up one floor */
  kGoingDown,          /* send car down one floor */
  kStoppedGoingUp,     /* stop car at an intermediate floor, car going up */
  kStoppedGoingDown,   /* stop car at an intermediate floor, car going down */
  kStoppedIdle         /* stop car, car in idle state */
} CarAction;

typedef struct CarState {
  long atFloor;        /* current location of car */
  long goingToFloor[kMaxFloors];
    /* goingToFloor[i] is the number of passengers in the car is going to floor [i] */
 } CarState;

typedef Boolean (*AdvanceTimeProc) (
                      /* return value of TRUE means Elevator should exit */
  CarAction action[kMaxElevators],  /* direction you move each elevator */
  CarState newState[kMaxElevators],  /* returns new state of each elevator */
  Boolean stopsAtFloor[kMaxFloors],
     /* stopsAtFloor[i]==TRUE means elevator stops at floor i */
  Boolean callGoingUp[kMaxFloors], 
     /* callGoingUp[i]==TRUE means a passenger on floor i wants to go up */
  Boolean callGoingDown[kMaxFloors]
     /* callGoingDown[i]==TRUE means a passenger on floor i wants to go down */
);

void Elevator(
  long numFloors,     /* number of floors in our building, < kMaxFloors */
  long numElevators,  /* number of elevators in our building, <
                         kMaxElevators */
  AdvanceTimeProc AdvanceTime  /* callback to get new state */
);
#if defined(__cplusplus)
}
#endif

Your Elevator routine will be called with the number of floors (numFloors) in our simulated skyscraper, the number of elevators (numElevators) at your command, and a callback routine (AdvanceTime). You should repeatedly call AdvanceTime, commanding an action and a set of constraints (stopsAtFloor) for each elevator car and receiving back the newState of each car. AdvanceTime will also provide an indicator of whether any prospective passengers on floor i have called an elevator to take them higher (callGoingUp[i]) or lower (callGoingDown[i]).

The newState returned by AdvanceTime provides the location of each car and the number of occupants. atFloor is the floor at which the car is now located. Our elevator passengers are extraordinarily cooperative -- on entering, they all indicate their destination by pressing the button corresponding to their floor, whether or not that floor has already been selected, allowing AdvanceTime to give you an accurate count of the passengers going to floor i (goingToFloor[i]). Our passengers are also extraordinarily swift --they exit and enter in such an orderly fashion that the passenger exchange takes place in one time step.

Each call to AdvanceTime will move all the elevators one floor in the direction you indicate. If you stop the car by setting action to kStoppedGoingUp, kStoppedGoingDown, or kStoppedIdle, passengers headed for the current floor will exit and new passengers, up to kElevatorCapacity, will enter. Almost always, passengers headed to higher (or lower) floors will only enter elevators that are kStoppedGoingUp (kStoppedGoingDown) or kStoppedIdle, but occasionally someone will be confused and enter an elevator headed in the wrong direction.

You are free to run your elevators anyway you see fit, except that a car declared to be kGoingUp (or kGoingDown) needs to continue going up (or down) until all passengers headed in that direction have exited. You can designate elevators to be express elevators by setting stopsAtFloor[i] to be FALSE for floors where this elevator does not stop. Passengers will only enter cars that will stop at their intended destination. You can change the stopsAtFloor values at any time, but you need to be careful not to strand passengers -- you can command the car to stop at any time, but the door will only open at floor i if stopsAtFloor[i] is TRUE.

The objective of this Challenge is to deliver passengers to their destinations as expeditiously as possible. You incur a cost of one point for each passenger for each time step from the time s/he presses the call button until the time s/he exits the elevator. You also incur one point for each 10 milliseconds of execution time, including the time spent by AdvanceTime. Stranding a passenger inside an elevator or not responding to an elevator call button results in disqualification of your solution. The solution that incurs the fewest points wins the Challenge. There are no storage constraints for this Challenge, except that it must execute on my 96MB 8500/200.

The Challenge will simulate a normal workday in our simulated skyscraper. People arrive at the beginning of the day either by entering the parking garage at floor 0 or by walking into the main entrance at floor 1. They work in approximately equal numbers on floors 2 through numFloors-1. During the day, they move about the building as necessary. Somewhere in the middle of the day, most of them take a lunch break, either at the cafeteria on floor 2 or by leaving the building. Nearly everyone leaves the building at the end of the day. However, as advanced as our elevators are, they don't have a clock, so you'll have to establish your strategy without knowing the time of day.

This will be a native PowerPC Challenge, using the latest CodeWarrior environment. Solutions may be coded in C, C++, or Pascal. Ernst Munter wins two Challenge points for suggesting this problem, way back in November, 1996.

Three Months Ago Winner

Congratulations to Sebastian Maurer for submitting the winning entry to the April Mancala Challenge. Sebastian won a round-robin tournament whose object was to efficiently capture the most stones in a variant of the ancient game of Mancala. In our variant of the game, the number of bowls ranged from 8 to 32, instead of the traditional 14, and players were allowed to move in either the clockwise or counter-clockwise directions. Congratulations also to JG Heithcock, whose solution actually captured more stones than Sebastian's did, but used better than 50% more execution time to do so. Both of the top solutions used an alpha-beta minmax technique to identify the best move, but Sebastian's heuristic for pruning the tree, combined with the time penalty of one stone per 100ms of execution time, gave him the higher overall score. Sebastian gained a little extra efficiency by partitioning his code into two parallel versions, one for playing first and another for playing second.

Twelve people submitted Mancala solutions, and eleven of those solutions participated in the tournament. (One solution occasionally made illegal moves, so it was eliminated to avoid unevenly affecting the scores of the other players.) The tournament consisted of seven test cases, with board sizes of 8, 12, 16, 20, 24, 28, and 32 bowls. Each solution played against each other solution twice in each test case, once playing first, and once playing second. The top solutions all used some variant of the minmax algorithm, while the lower ranking solutions used simpler heuristics, like always favoring moves that dropped the last stone into their mancala.

The table below lists the results of the tournament, with the solutions ranked in order of total points earned. It lists total execution time for the tournament, the total number of stones captured, the solution rank if execution time had been ignored, total points earned, as well as code size, data size, and programming language used. As usual, the number in parentheses after the entrant's name is the total number of Challenge points earned in all Challenges to date prior to this one.

NameTime (secs)Cum StonesRank (stones)Cum PointsCode SizeData SizeLang
Sebastian Maurer (10)54.1614764214222.403488136C
JG Heithcock85.3714897114043.26178448C++
Ken Krugler97.4514627313652.464288308C++
Randy Boring (73)59.9014055413456.028048824C
Eric Kenninga21.1013399513187.9914584894C++
Willeke Rieken (47)3.6311667611630.7440888C++
Simon Jensen-Fellows0.3311512711508.6833646147C, Res
Dennis Jones (10)2.7610383910355.412556125C++
Eric Hangstefer (9)0.05102521010251.543724124C
Ernst Munter (362)104.7611178810130.42791613C++
Josh Cooley0.279446119443.29222864C
K. H.0.00Errors120.003772104C++

Top Contestants

Here are the Top Contestants for the Programmer's Challenge, including everyone who has accumulated more than 10 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 210 points
  2. Boring, Randy 70 points
  3. Cooper, Greg 61 points
  4. Mallett, Jeff 50 points
  5. Rieken, Willeke 47 points
  6. Nicolle, Ludovic 34 points
  7. Lewis, Peter 31 points
  8. Maurer, Sebastian 30 points
  9. Gregg, Xan 24 points
  10. Murphy, ACC 24 points
  11. Hart, Alan 21 points
  12. Antoniewicz, Andy 20 points
  13. Day, Mark 20 points
  14. Higgins, Charles 20 points
  15. Hostetter, Mat 20 points
  16. Studer, Thomas 20 points

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 place 20 points
2nd place 10 points
3rd place 7 points
4th place 4 points
5th place 2 points
finding bug 2 points
suggesting Challenge 2 points

Here is Sebastian's winning solution to the Mancala Challenge:

Mancala.C
Copyright 1998, Sebastian M. Maurer

#include <stdio.h>
#include "Mancala.h"

enum { kDefault, kPlayAgain, kGameOver };
typedef long StateOfGame;

// There are two versions of almost every routine
// so we don't have to decide at run time
// which side to play on. It speeds things up a
// little bit
// AlphaBeta1 and AlphaBeta2 are the recursive searchers
// for each of the two players. They return the value of
// best move (returned in *chosenBowl, *chosenDirection).
// For a description of Minimax and Alphabeta searches,
// see Peter Norvig's
// "Paradigms of Artificial Intelligence Programming"

#define kMaxSignedLong    0x7FFFFFFF

Prototypes
long AlphaBeta1(
  long depth,
  long board[],
  long *boardStorage,
  const long boardSize,
  long *chosenBowl,
  long *chosenDirection,
  long lowerBound,
  /* any big negative number to enter recursion */
  long upperBound      
  /* any big positive number to enter recursion */
);

long AlphaBeta2(
  long depth,
  long board[],
  long *boardStorage,
  const long boardSize,
  long *chosenBowl,
  long *chosenDirection,
  long lowerBound,
  long upperBound
);

// DropStones -- play the move
// Return true if we get to play again

Boolean DropStones1(
  long board[],
  const long boardSize,
  long bowlPlayed,
  long directionPlayed
);

Boolean DropStones2(
  long board[],
  const long boardSize,
  long bowlPlayed,
  long directionPlayed
);

// SideEmpty returns true if the side is empty
// (and the game is over)

Boolean FirstSideEmpty(
  long board[],
  const long halfBoardSize
);

Boolean SecondSideEmpty(
  long board[],
  const long boardSize
);
// Moves all the remaining stones
// to the appropriate Mancala

void RemainingToMancala(
  long board[],
  const long boardSize,
  const Boolean playerOne
);

// DoMove Drops the stones, checks if the game
// is over (if so, cleans up the board), and
// returns kGameOver, kPlayAgain, or kDefault
StateOfGame DoMove1(
  long board[],
  const long boardSize,
  long bowlPlayed,
  long directionPlayed
);

StateOfGame DoMove2(
  long board[],
  const long boardSize,
  long bowlPlayed,
  long directionPlayed
);

// Called only once from
// within Mancala
Boolean ClaimingVictory(
  long board[],
  const long boardSize,
  const Boolean playerOne
);

Mancala
Boolean Mancala(        /* return true if claiming victory */
  long board[]          /* on entry, board[i] is number of stones in bowl i */
                      /* on exit, board reflects the results of your move */
  const long boardSize,  /* number of bowls in the board, including mancalas */
  void *privStorage,    /* pointer to 1MB of storage for your use */
  const Boolean newGame,  /* true for your first move of a game */
  const Boolean playerOne,  /* true when you are the first player */
  long *bowlPlayed,        /* return the number of the bowl you played from */
  long *directionPlayed    /* return 1 if you played counter-clockwise, */
                        /* return -1 if you played clockwise */
)
{
#pragma unused(newGame)
  // Q&D way to decide how far to search
  // so that we don't lose too much time
  long depth;
  switch (boardSize)
  {
    case 8: depth = 10; break;
    case 10: depth = 8; break;
    case 12:
    case 14: depth = 6; break;
    case 16: 
    case 18: depth = 5; break;
    case 20: 
    case 22: 
    case 24: 
    case 26: depth = 4; break;
    case 28: 
    case 30: 
    case 32: depth = 3; break;
    default: depth = 1; break;
  }

  // Start recursion and play move
  if (playerOne) {
    AlphaBeta1(depth, board, (long*)privStorage,
      boardSize, bowlPlayed, directionPlayed,
      -kMaxSignedLong, kMaxSignedLong);
    DropStones1(board, boardSize,
      *bowlPlayed, *directionPlayed);
  }
  else
  {
    AlphaBeta2(depth, board, (long*)privStorage,
      boardSize, bowlPlayed, directionPlayed,
      -kMaxSignedLong, kMaxSignedLong);
    DropStones2(board, boardSize,
      *bowlPlayed, *directionPlayed);
  }
  
  // Correct to proper convention
  *directionPlayed = - (*directionPlayed);
  return ClaimingVictory(board, boardSize, playerOne);
}

AlphaBeta1
long AlphaBeta1(
  long depth,
  long board[],
  long *boardStorage,
  const long boardSize,
  long *chosenBowl,
  long *chosenDirection,
  long lowerBound,
  long upperBound
)
{
  long myMancala, hisMancala, firstBowl, halfBoardSize;
  long bowl, dir, value, bestBowl, bestDir;
  long *workingBoard;
  
  halfBoardSize = boardSize / 2;
  workingBoard = boardStorage + depth * boardSize;
  myMancala = 0;
  hisMancala = halfBoardSize;
  firstBowl = 1;
  
  for (bowl = firstBowl; bowl < hisMancala; bowl++)
    if (board[bowl] > 0)
    {
      StateOfGame result;
      long i;

      dir = -1;

      // The following trick speeds the whole program
      // up by about 1 percent... take it or leave it
      for (i = 0; i < halfBoardSize; i++)
        ((double*)workingBoard)[i] =
          ((double*)board)[i];
        
      result = DoMove1(workingBoard, boardSize,
                bowl, dir);
      if ((depth == 0) || (result == kGameOver))
        value = workingBoard[myMancala] -
              workingBoard[hisMancala];
      else
      {
        if (result == kPlayAgain)
          value = AlphaBeta1(
                depth - 1, workingBoard,
                boardStorage, boardSize,
                chosenBowl, chosenDirection,
                lowerBound, upperBound);
        else
          value = - AlphaBeta2(
                depth - 1, workingBoard,
                boardStorage, boardSize,
                chosenBowl, chosenDirection,
                - upperBound, - lowerBound);
      }

      if (value > lowerBound)
      {
        bestBowl = bowl;
        bestDir = dir;
        lowerBound = value;
        
        if (lowerBound >= upperBound)
          break;
      }

      dir = 1;

      for (i = 0; i < halfBoardSize; i++)
        ((double*)workingBoard)[i] =
          ((double*)board)[i];
        
      result = DoMove1(workingBoard, boardSize, bowl, dir);
      if ((depth == 0) || (result == kGameOver))
        value = workingBoard[myMancala] -                   workingBoard[hisMancala];
      else
      {
        if (result == kPlayAgain)
          value = AlphaBeta1(
                depth - 1, workingBoard,
                boardStorage, boardSize,
                chosenBowl, chosenDirection,
                lowerBound, upperBound);
        else
          value = - AlphaBeta2(
                depth - 1, workingBoard,
                boardStorage, boardSize,
                chosenBowl, chosenDirection,
                - upperBound, - lowerBound);
      }

      if (value > lowerBound)
      {
        bestBowl = bowl;
        bestDir = dir;
        lowerBound = value;
        
        if (lowerBound >= upperBound)
          break;
      }
      
    }
  
  *chosenBowl = bestBowl;
  *chosenDirection = bestDir;
  return lowerBound;
}

AlphaBeta2
long AlphaBeta2(
  long depth,
  long board[],
  long *boardStorage,
  const long boardSize,
  long *chosenBowl,
  long *chosenDirection,
  long lowerBound,
  long upperBound
)
{
  long myMancala, hisMancala, firstBowl, halfBoardSize;
  long bowl, dir, value, bestBowl, bestDir;
  long *workingBoard;
  
  halfBoardSize = boardSize / 2;

  workingBoard = boardStorage + depth * boardSize;
  myMancala = halfBoardSize;
  hisMancala = 0;
  firstBowl = myMancala + 1;
  for (bowl = firstBowl; bowl < boardSize; bowl++)
    if (board[bowl] > 0)
    {
      long i, result;

      dir = -1;

      for (i = 0; i < halfBoardSize; i++)
        ((double*)workingBoard)[i] =
          ((double*)board)[i];
      
      result = DoMove2(workingBoard, boardSize,
                bowl, dir);
    if ((depth == 0) || (result == kGameOver))
        value = workingBoard[myMancala] -
              workingBoard[hisMancala];
      else
      {
        if (result == kPlayAgain)
          value = AlphaBeta2(
                depth - 1, workingBoard,
                boardStorage, boardSize,
                chosenBowl, chosenDirection,
                lowerBound, upperBound);
        else
          value = - AlphaBeta1(
                depth - 1, workingBoard,
                boardStorage, boardSize,
                chosenBowl, chosenDirection,
                - upperBound, - lowerBound);
      }
      if (value > lowerBound)
      {
        bestBowl = bowl;
        bestDir = dir;
        lowerBound = value;
        if (lowerBound >= upperBound)
          break;
      }
      
      dir = 1;
      
      for (i = 0; i < halfBoardSize; i++)
        ((double*)workingBoard)[i] =
          ((double*)board)[i];

      result = DoMove2(workingBoard, boardSize,
                bowl, dir);
      if ((depth == 0) || (result == kGameOver))
        value = workingBoard[myMancala] -
              workingBoard[hisMancala];
      else
      {
        if (result == kPlayAgain)
          value = AlphaBeta2(
                depth - 1, workingBoard,
                boardStorage, boardSize,
                chosenBowl, chosenDirection,
                lowerBound, upperBound);
        else
          value = - AlphaBeta1(
                depth - 1, workingBoard,
                boardStorage, boardSize,
                chosenBowl, chosenDirection,
                - upperBound, - lowerBound);
      }

      if (value > lowerBound)
      {
        bestBowl = bowl;
        bestDir = dir;
        lowerBound = value;
        if (lowerBound >= upperBound)
          break;
      }

    }
  
  *chosenBowl = bestBowl;
  *chosenDirection = bestDir;
  return lowerBound;
}

DropStones1
/***
Boolean DropStones()
Drops stones, return true if we get to play again
***/

inline Boolean DropStones1(
  long board[],
  const long boardSize,
  long bowlPlayed,
  long directionPlayed
)
{
  long myMancala, hisMancala, firstBowl, lastBowl;
  long stonesInHand, nextBowl;

  myMancala = 0;
  hisMancala = boardSize / 2;
  firstBowl = 1;
  lastBowl = hisMancala - 1;

  stonesInHand = board[bowlPlayed];
  board[bowlPlayed] = 0;
  nextBowl = bowlPlayed;
  /* Drop stones */
  while (stonesInHand > 0) {
    nextBowl += directionPlayed;
    
    if (nextBowl == hisMancala)
      nextBowl += directionPlayed;
    else
    {
      if (nextBowl < 0)
        nextBowl = boardSize - 1;
      else
        if (nextBowl == boardSize)
          nextBowl = 0;
    }
    board[nextBowl] += 1;
    stonesInHand -= 1;
  }
  
  /* Perform capture */
  if ((board[nextBowl] == 1) &&
    (nextBowl >= firstBowl) &&
    (nextBowl <= lastBowl))
  {
    board[nextBowl] = 0;
    board[myMancala] += 
      (1 + board[boardSize - nextBowl]);
    board[boardSize - nextBowl] = 0;
  }
  
  /* Return true if get to play again */
  return (nextBowl == myMancala);
}

DropStones2
inline Boolean DropStones2(
  long board[],
  const long boardSize,
  long bowlPlayed,
  long directionPlayed
)
{
  long myMancala, firstBowl, lastBowl;
  long stonesInHand, nextBowl;

  myMancala = boardSize / 2;
  firstBowl = myMancala + 1;
  lastBowl = boardSize - 1;

  stonesInHand = board[bowlPlayed];
  board[bowlPlayed] = 0;
  nextBowl = bowlPlayed;
  /* Drop stones */
  while (stonesInHand > 0) {
    nextBowl += directionPlayed;
    
    if (nextBowl <= 0)
      nextBowl = boardSize - 1;
    else
      if (nextBowl == boardSize)
        nextBowl = 1;
    board[nextBowl] += 1;
    stonesInHand -= 1;
  }
  
  /* Perform capture */
  if ((board[nextBowl] == 1) &&
    (nextBowl >= firstBowl) &&
    (nextBowl <= lastBowl))
  {
    board[nextBowl] = 0;
    board[myMancala] +=
      (1 + board[boardSize - nextBowl]);
    board[boardSize - nextBowl] = 0;
  }
  
  /* Return true if get to play again */
  return (nextBowl == myMancala);
}

FirstSideEmpty
/*
Boolean FirstSideEmpty()
Checks to see if first side has no stones left in it
*/
inline Boolean FirstSideEmpty(
  long board[],
  const long halfBoardSize
) 
{
  long bowl;
  for(bowl = halfBoardSize - 1; bowl > 0; bowl--)
    if (board[bowl] != 0)
      return false;
  return true;
}


SecondSideEmpty
/*
Boolean SecondSideEmpty()
Checks to see if first side has no stones left in it
*/
inline Boolean SecondSideEmpty(
  long board[],
  const long boardSize
) 
{
  long bowl;
  long halfBoardSize = boardSize / 2;
  for(bowl = boardSize - 1; bowl > halfBoardSize; bowl--)
    if (board[bowl] != 0)
      return false;
  return true;
}

RemainingToMancala
/*
void RemainingToMancala()
Moves remaining stones on specified side into Mancala
*/
inline void RemainingToMancala(
  long board[],
  const long boardSize,
  const Boolean playerOne
)
{
  long mancala, firstBowl, lastBowl, bowl;

  if (playerOne) {
    mancala = 0;
    firstBowl = 1;
    lastBowl = boardSize / 2 - 1;
  } else {
    mancala = boardSize / 2;
    firstBowl = boardSize / 2 + 1;
    lastBowl = boardSize - 1;
  }  
  
  for(bowl = firstBowl; bowl <= lastBowl; bowl++)
  {
    board[mancala] += board[bowl];
    board[bowl] = 0;
  }
}


DoMove1
/***
StateOfGame DoMove()
Drops the specified stones and cleans up the board 
if the game is over.
***/

inline StateOfGame DoMove1(
  long board[],
  const long boardSize,
  long bowlPlayed,
  long directionPlayed
)
{
  Boolean getToPlayAgain;

  getToPlayAgain = DropStones1(board, boardSize,
            bowlPlayed, directionPlayed);

  if (FirstSideEmpty(board, boardSize / 2)) {
    RemainingToMancala(board, boardSize, false);
    return kGameOver;
  }
  
  if (SecondSideEmpty(board, boardSize)) {
    RemainingToMancala(board, boardSize, true);
    return kGameOver;
  }
  
  if (getToPlayAgain)
    return kPlayAgain;
  else
    return kDefault;
}

DoMove2
inline StateOfGame DoMove2(
  long board[],
  const long boardSize,
  long bowlPlayed,
  long directionPlayed
)
{
  Boolean getToPlayAgain;
  
  getToPlayAgain = DropStones2(board, boardSize,
            bowlPlayed, directionPlayed);

  if (FirstSideEmpty(board, boardSize / 2)) {
    RemainingToMancala(board, boardSize, false);
    return kGameOver;
  }
  
  if (SecondSideEmpty(board, boardSize)) {
    RemainingToMancala(board, boardSize, true);
    return kGameOver;
  }
  
  if (getToPlayAgain)
    return kPlayAgain;
  else
    return kDefault;
}

ClaimingVictory
/* Boolean ClaimingVictory()
  Only called before returning from Mancala
  Does not clean up the board
*/
Boolean ClaimingVictory(
  long board[],
  const long boardSize,
  const Boolean playerOne
)
{
  long bowl;
  long sum = 0;
  long halfBoardSize = boardSize / 2;
  
  if (FirstSideEmpty(board, halfBoardSize))
  {
    for (bowl = halfBoardSize + 1;
        bowl < boardSize; bowl++)
      sum += board[bowl];
    if (playerOne)
      return board[0] > (sum + board[halfBoardSize]);
    else
      return board[0] < (sum + board[halfBoardSize]);
  }
  if (SecondSideEmpty(board, boardSize))
  {
    for (bowl = 1; bowl < halfBoardSize; bowl++)
      sum += board[bowl];
    if (playerOne)
      return (board[0] + sum) > board[halfBoardSize];
    else
      return (board[0] + sum) < board[halfBoardSize];
  }
  return false;
}
 

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Tennis Club Story 1.03 Device: iOS Universal Category: Games Price: $4.99, Version: 1.03 (iTunes) Description: Aim for the ace position of tennis club prestige in this simulation! Your leadership decides if players make it to the big... | Read more »
Juggernaut Wars guide - How to use skill...
Juggernaut Warsis a brand new auto-RPG on iOS and Android that challenges you to build a team of heroes, send them out into various different missions to defeat waves of heroes, and level them up to increase their power. The actual combat itself... | Read more »
Check out the new Pirate Attack update i...
Love pirates and board games? Well, you'll love the new Pirate Attack themed update that just launched in Game of Dice. It adds a bunch of new content themed around pirates, like an all new event map based on a pirate ship which revamps the toll... | Read more »
Splash Cars guide - How to paint the tow...
Splash Cars is an arcade driving game that feels like a hybrid between Dawn of the Plow and Splatoon. In it, you'll need to drive a car around to repaint areas of a town that have lost all of their color. Check out these tips to help you perform... | Read more »
The best video player on mobile
We all know the stock video player on iOS is not particularly convenient, primarily because it asks us to hook a device up to iTunes to sync video in a world that has things like Netflix. [Read more] | Read more »
Four apps to help improve your Super Bow...
Super Bowl Sunday is upon us, and whether you’re a Panthers or a Broncos fan you’re no doubt gearing up for it. [Read more] | Read more »
LooperSonic (Music)
LooperSonic 1.0 Device: iOS Universal Category: Music Price: $4.99, Version: 1.0 (iTunes) Description: LooperSonic is a multi-track audio looper and recorder that will take your loops to the next level. Use it like a loop pedal to... | Read more »
Space Grunts guide - How to survive
Space Grunts is a fast-paced roguelike from popular iOS developer, Orange Pixel. While it taps into many of the typical roguelike sensibilities, you might still find yourself caught out by a few things. We delved further to find you some helpful... | Read more »

Price Scanner via MacPrices.net

What iPad Pro Still Needs To Make It Truly Pr...
I love my iPad Air 2. So much that I’m grudgingly willing to put up with its compromises and limitations as a production tool in order to take advantage of its virtues. However, since a computer for... Read more
21-inch 3.1GHz 4K on sale for $1399, $100 off...
B&H Photo has the 21″ 3.1GHz 4K iMac on sale $1399 for a limited time. Shipping is free, and B&H charges NY sales tax only. Their price is $100 off MSRP: - 21″ 3.1GHz 4K iMac (MK452LL/A): $... Read more
Apple price trackers, updated continuously
Scan our Apple Price Trackers for the latest information on sales, bundles, and availability on systems from Apple’s authorized internet/catalog resellers. We update the trackers continuously: - 15″... Read more
Save up to $240 with Apple Certified Refurbis...
Apple is now offering Certified Refurbished 12″ Retina MacBooks for up to $240 off the cost of new models. Apple will include a standard one-year warranty with each MacBook, and shipping is free. The... 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
Apple refurbished Time Capsules available for...
Apple has certified refurbished Time Capsules available for $120 off MSRP. Apple’s one-year warranty is included with each Time Capsule, and shipping is free: - 2TB Time Capsule: $179, $120 off - 3TB... Read more
13-inch 2.5GHz MacBook Pro (refurbished) avai...
Apple has Certified Refurbished 13″ 2.5GHz MacBook Pros available for $829, or $270 off the cost of new models. Apple’s one-year warranty is standard, and shipping is free: - 13″ 2.5GHz MacBook Pros... Read more
Apple refurbished 15-inch Retina MacBook Pros...
Apple has Certified Refurbished 2015 15″ Retina MacBook Pros available for up to $380 off the cost of new models. An Apple one-year warranty is included with each model, and shipping is free: - 15″ 2... Read more
New Liquid Crystal Technology Prevents Automo...
Researchers at the University of Central Florida have developed three new liquid crystal mixtures which will allow automobile displays to operate at unprecedented high and low temperatures In... Read more
BookBook For iPad Pro Coming Soon
The iPad Pro is a device unlike any other, and with Apple Pencil, it’s the ideal portable sketchpad: all that’s missing is the modern easel and portfolio to go. TwelveSouth’s BookBook for iPad Pro... Read more

Jobs Board

Lead Engineer - *Apple* OSX & Hardware...
Lead Engineer - Apple OSX & Hardware **Job ID:** 3125919 **Full/Part\-Time:** Full\-time **Regular/Temporary:** Regular **Listed:** 2016\-02\-10 **Location:** Cary, Read more
*Apple* System Analyst - ATOS IT Services...
Apple System AnalystReference no.198783CountryUSARegionUS - CALIFORNIACityUS - CALIFORNIA - BURBANKPosition TypeProfessionalJob AreaIT SupportJob TypeFull 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* 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
*Apple* Subject Matter Expert - Experis (Uni...
This position is for an Apple Subject Matter Expert to assist in developing the architecture, support and services for integration of Apple devices into the domain. Read more
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