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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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How to navigate the terrain in Sky Charm...
Sky Charms is a whimsical match-'em up adventure that uses creative level design to really ramp up the difficulty. [Read more] | Read more »
Victorious Knight (Games)
Victorious Knight 1.3 Device: iOS Universal Category: Games Price: $1.99, Version: 1.3 (iTunes) Description: New challenges awaits you! Experience fresh RPG experience with a unique combat mechanic, packed with high quality 3D... | Read more »
Agent Gumball - Roguelike Spy Game (Gam...
Agent Gumball - Roguelike Spy Game 1.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0 (iTunes) Description: Someone’s been spying on Gumball. What the what?! Two can play at that game! GO UNDERCOVERSneak past enemy... | Read more »
Runaway Toad (Games)
Runaway Toad 1.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0 (iTunes) Description: It ain’t easy bein’ green! Tap, hold, and swipe to help Toad hop to safety in this gorgeous new action game from the creators of... | Read more »
PsyCard (Games)
PsyCard 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: From the makers och Card City Nights, Progress To 100 and Ittle Dew PSYCARD is a minesweeper-like game set in a cozy cyberpunk... | Read more »
Sago Mini Robot Party (Education)
Sago Mini Robot Party 1.0 Device: iOS Universal Category: Education Price: $2.99, Version: 1.0 (iTunes) Description: -- Children's Technology Review Editor's Choice -- | Read more »
How to get a high score in every level o...
Sky Charms is an adorable match three puzzler that provides a decent challenge thanks to its creative level design. It regularly presents something new, forcing you to think on your feet. [Read more] | Read more »

Price Scanner via MacPrices.net

Apple restocks Certified Refurbished Mac mini...
Apple has restocked Certified Refurbished 2014 Mac minis, with models available starting at $419. Apple’s one-year warranty is included with each mini, and shipping is free: - 1.4GHz Mac mini: $419 $... Read more
15-inch 2.2GHz Retina MacBook Pro on sale for...
Amazon.com has the 15″ 2.2GHz Retina MacBook Pro on sale for $1699.99 including free shipping. Their price is $300 off MSRP, and it’s the lowest price available for this model from any reseller (and... Read more
Apple Beats Microsoft at Own Game; Amazon Pri...
First quarter seasonality combined with an overall disinterested customer base led to an annual decline of 14.7% in worldwide tablet shipments during the first quarter of 2016 (1Q16). Worldwide... Read more
Tablets Had Worst Quarter Since 2012, says St...
The global tablet market began 2016 just as 2015 left off, down. Tablet shipments fell 10% to 46.5 million units during the Q1 2016, according to the new “Preliminary Global Tablet Shipments and... Read more
Clearance 13-inch MacBook Airs, Apple refurbi...
Apple recently dropped prices on certified refurbished 2015 13″ MacBook Airs with 4GB of RAM with models now available starting at $759. An Apple one-year warranty is included with each MacBook, and... Read more
Clearance 12-inch Retina MacBooks, Apple refu...
Apple has dropped prices on Certified Refurbished 2015 12″ Retina MacBooks with models now available starting at $929. Apple will include a standard one-year warranty with each MacBook, and shipping... Read more
Aleratec Releases Mac Software Upgrade for 1...
California based Aleratec Inc., designer, developer and manufacturer of Portable Device Management (PDM) charge/sync products for mobile devices and professional-grade duplicators for hard disk... Read more
Sale! Amazon offers 27-inch iMac, 13-inch 2.9...
Amazon has the 27″ 3.2GHz 5K iMac and the 13″ 3.9GHz Retina MacBook Pro on sale for $300 off MSRP, each including free shipping, for a limited time: - 27″ 3.2GHz/1TB HD 5K iMac (model MK462LL/A): $... 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
13-inch 2.7GHz/128GB Retina MacBook Pro on sa...
Take $200 off MSRP on the price of a new 13″ 2.7GHz/128GB Retina MacBook Pro (model MF839LL/A) at Amazon. Shipping is free: - 13″ 2.7GHz/128GB Retina MacBook Pro: $1099.99 $200 off MSRP Act now if... Read more

Jobs Board

Automotive Sales Consultant - Apple Ford Linc...
…you. The best candidates are smart, technologically savvy and are customer focused. Apple Ford Lincoln Apple Valley is different, because: $30,000 annual salary 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
*Apple* Solutions Consultant - Apple (United...
# Apple Solutions Consultant Job Number: 48260200 Phoenix, Arizona, United States Posted: Apr. 22, 2016 Weekly Hours: 40.00 **Job Summary** As an Apple Solutions Read more
Restaurant Manager (Neighborhood Captain) - A...
…in every aspect of daily operation. WHY YOU'LL LIKE IT: You'll be the Big Apple . You'll solve problems. You'll get to show your ability to handle the stress and Read more
Simply Mac *Apple* Specialist- Service Repa...
Simply Mac is the largest premier retailer of Apple products in the nation. In order to support our growing customer base, we are currently looking for a driven Read more
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