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Jan 96 Challenge
Volume Number:12
Issue Number:1
Column Tag:Programmer’s Challenge

Programmer’s Challenge

By Bob Boonstra, Westford, Massachusetts

Note: Source code files accompanying article are located on MacTech CD-ROM or source code disks.

Sliding Tiles

You have all probably seen small versions of the puzzle that is the basis for this month’s Challenge: a 4-by-4 grid of interlocking tiles, with one empty tile among the 16 cells allowing the puzzle to be scrambled by sliding adjacent cells into the empty location. This month the Challenge is to write code that will unscramble a larger version of the Sliding Tiles puzzle.

The prototype for the code you should write is:

typedef Boolean  /*legalMove*/ (*MoveProc)(
                     /* Callback procedure to move tile at                 */
  long tileToMoveRow,/*   these coordinates into the location              */
  long tileToMoveCol /*   of adjacent empty tile                      */
);
  
void SolveTiles(
  long *tiles,      /* pointer to array of tiles where            */
  long numRows,     /*   tile (row,col) is at                  */
  long numCols,     /*   *(tiles + row*numCols + col)             */
  MoveProc MakeMove /* Callback procedure to move a tile                      */
);

You will be given a pointer tiles into an array of tile values, the number of rows and columns in the puzzle (numRows and numCols, respectively), and the address of a callback procedure MakeMove used to tell my test code about the moves you make to solve the puzzle. The tiles array will be initialized with the values 0..numRows*numCols-1, in an order scrambled by the calling routine. The value 0 represents the empty tile.

Your code should make a sequence of calls to MakeMove and return when the puzzle is solved. Each MakeMove call exchanges the empty tile with the indicated adjacent tile. The puzzle is solved when you have moved each tile into its proper location: moving the tile with value i into location tiles[i] (i.e., row=i/numCols and col=i%numCols).

The callback routine will be something like the code provided below:

static long gNumRows,gNumCols;    /* initialized by test code */
static long gEmptyRow,gEmptyCol;  /* initialized by test code */
static long *gTiles;              /* initialized by test code */

#define TileValue(tiles,row,col) *(tiles+(row)*gNumCols+(col))
#define OutOfRange(val,num)  (((val)<0) || ((val)>=(num)))
  
static Boolean MakeMove(long tileToMoveRow,long tileToMoveCol) 
{
  long diff;
  if (OutOfRange(tileToMoveRow,gNumRows)) return false;
  if (OutOfRange(tileToMoveCol,gNumCols)) return false;
  if (tileToMoveRow == gEmptyRow) {
    diff = tileToMoveCol - gEmptyCol;
  } else if (tileToMoveCol == gEmptyCol) {
    diff = tileToMoveRow - gEmptyRow;
  } else {
    return false;
  }
  if ((diff != -1) && (diff != 1)) return false;
  TileValue(gTiles,gEmptyRow,gEmptyCol) = 
    TileValue(gTiles,tileToMoveRow,tileToMoveCol);
  gEmptyRow = tileToMoveRow;
  gEmptyCol = tileToMoveCol;
  TileValue(gTiles,gEmptyRow,gEmptyCol) = 0;
}

As an example, given the initial conditions:

         long tiles[] = {1,4,0,3,5,2};
         SolveTiles(tiles,2,3,MakeMove);

you could generate the following moves:

         MakeMove(1,2);
         MakeMove(1,1);
         MakeMove(0,1);
         MakeMove(0,0);

to transform the puzzle like this:

        1 4 0  ==>  1 4 2  ==>  1 4 2  ==>  1 0 2  ==>  0 1 2
        3 5 2       3 5 0       3 0 5       3 4 5       3 4 5

It turns out that half of the possible permutations of the values 0..numRows*numCols-1 are “illegal” in that they cannot be reached from the “solved” state. The calling routine will provide a legal starting state - you don’t have to worry about the puzzle being unsolvable.

The number of moves you make to solve the puzzle is not an explicit criterion in determining the winner, but the winner will be determined by total execution time, including the time used by the callback routine, as we did in the Master MindReader challenge a few months back. Note that you are not permitted to optimize the callback routine - its purpose is to provide a fixed time penalty for each move your solution routine makes.

This will be a native PowerPC Challenge, scored using the Symantec 8.0.3 compiler. Good luck. Email me with any questions, or - better yet - join the Programmer’s Challenge Mailing List

Mailing List Reminder

Many Challenge readers have already joined the Programmer’s Challenge Mailing List announced last month. The list is being used to distribute the latest Challenge, provide answers to questions about the current Challenge, and discuss suggestions for future Challenges. The Challenge problem is posted to the list sometime between the 20th and the 25th of the month.

To subscribe to the list, send a message to autoshare@mactech.com with the SUBJECT line “sub challenge YourName”, substituting your real name for YourName. To unsubscribe from the list, send a message to autoshare@mactech.com with the SUBJECT line “unsub challenge”.

Two Months Ago Winner

Congratulations to Eric Lengyel (Blacksburg, VA) for submitting the fastest entry to the EnclosingBounds Challenge. The problem was to find the smallest rectangle enclosing all of the non-white pixels in a PixMap. Eight of the 13 entries submitted worked correctly, but Eric’s solution was significantly faster than the others. This is Eric’s second victory in three months, following his first-place finish in the September Reversible Scrambling Algorithm Challenge.

The winning solution uses a clever technique to minimize the number of comparisons required to find the enclosing rectangle. Rather than test each pixel to determine if it is non-white, Eric logically ORs the values for all pixels in a row (for the indexed color cases), taking advantage of the fact that white is always represented by a zero value. A single comparison then determines whether that row contains only white pixels. Working separately from the top and bottom of the selection rectangle identifies the top and bottom rows of the enclosing rectangle. A similar technique applied to columns finds the left and right boundaries of the rectangle. For the direct (32-bit) color case, the approach is similar, except that pixel values in a row or column are logically ANDed, taking advantage of the fact that white is represented by the value 0x00FFFFFF.

Here are the times and code sizes for each of the correct entries. Numbers in parentheses after a person’s name indicate that person’s cumulative point total for all previous Challenges, not including this one.

Name time time time test code data
1-bit 8-bit 32-bit time size size

Eric Lengyel (20) 13 66 272 340 1608 320

Ernst Munter (100) 22 96 326 427 2980 32

Miguel Cruz Picao 34 110 476 593 3328 44

John Sweeney 75 145 502 659 4416 624

Bill Karsh (78) 54 135 517 662 1600 8

Tom Saxton 146 170 560 758 1044 132

Chris Rudolph 514 289 973 1354 1420 8

P.L. 6197 4672 5384 11181 656 24

The times listed above were all achieved using the Metrowerks CodeWarrior 7 compiler. Running the winning entry with code generated by the Symantec and MrC compilers (with all speed optimizations enabled in each case) gave some interesting results, with the MrC code executing in 2/3 to 3/4 of the time required by the others:

Compiler (version) time time time
1-bit 8-bit 32-bit

MrC / MPW (1.0f2) 10 52 183

Metrowerks C (1.3.2) 13 66 272

Symantec (8.0.3) 17 75 292

An investigation of the generated code provides some insight into these numbers. CodeWarrior generates the following code for one of the inner loops in the winning solution:

         for (i = 0; i < numWholeWords; i++)
00000064: 7D274B78  mr       r7,r9
00000068: 38A00000  li       r5,0
0000006C: 48000014  b        *+20     ; $00000080
         {
            accumulator |= *(long *) k;
            k += 4;
         }
00000070: 80070000  lwz      r0,0(r7)
00000074: 38A50001  addi     r5,r5,1
00000078: 7C630378  or       r3,r3,r0
0000007C: 38E70004  addi     r7,r7,4
00000080: 7C052000  cmpw     r5,r4
00000084: 4180FFEC  blt      *-20     ; $00000070

By comparison, MrC generates the following longer, but faster code:

         for (i = 0; i < numWholeWords; i++)
00F8 006C     48000018   b         $+0x0018      ; 0x00000084
00FC 0070   X 4E800020   blr
0100 0074     31290001   addic     r9,r9,1
0104 0078     7D4A3814   addc      r10,r10,r7
0108 007C   X 7C093000   cmpw      r9,r6
010C 0080   X 4080FFF0   bge       $-0x0010      ; 0x00000070
0110 0084   X 40990028   ble       cr6,$+0x0028  ; 0x000000AC
0114 0088   X 7D0903A6   mtctr     r8            ; CTR = 9
0118 008C   X 2C080001   cmpwi     r8,1
011C 0090   X 4181000C   bgt       $+0x000C      ; 0x0000009C
0120 0094   X 38600001   li        r3,1
0124 0098   X 7C6903A6   mtctr     r3            ; CTR = 9
0128 009C   X 318AFFFC   subic     r12,r10,4
         {
            accumulator |= *(long *) k;
            k += 4;
         }
012C 00A0     846C0004   lwzu      r3,0x0004(r12)
0130 00A4     7C6B5B78   or        r11,r3,r11
0134 00A8   X 4200FFF8   bdnz      $-0x0008      ; 0x000000A0

Notice that the inner loop is 6 instructions in the CodeWarrior version but only 3 instructions in the MrC code. The key to the difference is the use of the mtctr, lwzu, and bdnz instructions. The mtctr instruction loads the special purpose CTR register, which the bdnz instruction decrements and tests, branching when CTR is nonzero (similar to what the DBRA instruction does on 68K machines). The bdnz instruction replaces 3 instructions generated by CodeWarrior. The lwzu instruction loads a value from memory, but also stores the effective address back into the register used for the indirect memory access, replacing 2 CodeWarrior instructions. Reading disassembled compiler-optimized PowerPC code takes a little practice, but it can provide some insight into what the compiler is doing to you (or for you). Those interested in learning more are referred to the many PowerPC articles in past issues of MacTech, including a two part series by Bill Karsh in August and September of 1994.

Top Contestants of All Time

Here are the Top Contestants for the Programmer’s Challenges to date, including everyone who has accumulated more than 20 points. The numbers below include points awarded for this month’s entrants.

Rank Name Points Rank Name Points

1. [Name deleted] 176 11. Mallett, Jeff 44

2. Munter, Ernst 110 12. Kasparian, Raffi 42

3. Gregg, Xan 81 13. Vineyard, Jeremy 42

4. Karsh, Bill 80 14. Lengyel, Eric 40

5. Larsson, Gustav 67 15. Darrah, Dave 31

6. Stenger, Allen 65 16. Landry, Larry 29

7. Riha, Stepan 51 17. Elwertowski, Tom 24

8. Goebel, James 49 18. Lee, Johnny 22

9. Nepsund, Ronald 47 19. Noll, Robert 22

10. Cutts, Kevin 46

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 5th place 2 points

2nd place 10 points finding bug 2 points

3rd place 7 points suggesting Challenge 2 points

4th place 4 points

Here is Eric’s winning solution:

EnclosingBounds

Copyright © 1995 Eric Lengyel

/*
  This algorithm is based on the following idea.  Assuming that we are going to have to
  check many rows or columns which don’t contain any non-white pixels, it is faster to 
  combine all of the pixels in a row or column and look at the end result than it is to 
  check each pixel individually.  This is done by ORing entire rows or columns 
  together for 1-bit and 8-bit deep pixel maps and ANDing entire rows or columns 
  together for 32-bit deep pixel maps.  The two different methods are necessary 
  because for 1-bit and 8-bit pixel maps, white is represented by zeros and for 32-bit 
  pixel maps, white is represented by ones.

  The mask tables below are used with 1-bit and 8-bit deep pixel maps.  They are 
  needed when the left or right side of the selection rectangle is not word aligned.
*/

long LeftMask1[32] =
   {0xFFFFFFFF, 0x7FFFFFFF, 0x3FFFFFFF, 0x1FFFFFFF,
    0x0FFFFFFF, 0x07FFFFFF, 0x03FFFFFF, 0x01FFFFFF,
    0x00FFFFFF, 0x007FFFFF, 0x003FFFFF, 0x001FFFFF,
    0x000FFFFF, 0x0007FFFF, 0x0003FFFF, 0x0001FFFF,
    0x0000FFFF, 0x00007FFF, 0x00003FFF, 0x00001FFF,
    0x00000FFF, 0x000007FF, 0x000003FF, 0x000001FF,
    0x000000FF, 0x0000007F, 0x0000003F, 0x0000001F,
    0x0000000F, 0x00000007, 0x00000003, 0x00000001};

long RightMask1[32] =
   {0x80000000, 0xC0000000, 0xE0000000, 0xF0000000,
    0xF8000000, 0xFC000000, 0xFE000000, 0xFF000000,
    0xFF800000, 0xFFC00000, 0xFFE00000, 0xFFF00000,
    0xFFF80000, 0xFFFC0000, 0xFFFE0000, 0xFFFF0000,
    0xFFFF8000, 0xFFFFC000, 0xFFFFE000, 0xFFFFF000,
    0xFFFFF800, 0xFFFFFC00, 0xFFFFFE00, 0xFFFFFF00,
    0xFFFFFF80, 0xFFFFFFC0, 0xFFFFFFE0, 0xFFFFFFF0,
    0xFFFFFFF8, 0xFFFFFFFC, 0xFFFFFFFE, 0xFFFFFFFF};

long LeftMask8[4] =
   {0xFFFFFFFF, 0x00FFFFFF, 0x0000FFFF, 0x000000FF};

long RightMask8[4] =
   {0xFF000000, 0xFFFF0000, 0xFFFFFF00, 0xFFFFFFFF};

long DirectWhite = 0x00FFFFFF;  // Value of white pixel
                                // in 32-bit map.

EnclosingBounds
void EnclosingBounds(PixMapHandle pm,
   Rect selection, Rect *enclosingRect)
{
   PixMapPtr   map;
   long        pixelSize, rowBytes, accumulator,
               leftMask, rightMask, baseAddr,
               leftSide, rightSide, topSide, bottomSide,
               numWholeWords, needLeftMask, needRightMask,
               i, j, k, l, m;

   map = *pm;

/*  Compute position of selection rectangle relative to upper-left corner of pixel map. */

   leftSide = selection.left - map->bounds.left;
   rightSide = selection.right - map->bounds.left;
   topSide = selection.top - map->bounds.top;
   bottomSide = selection.bottom - map->bounds.top;

/*  Check validity of selection rectangle.  */

   if ((rightSide <= leftSide) || (bottomSide <= topSide))
   {
      enclosingRect->left = enclosingRect->right =
         enclosingRect->top = enclosingRect->bottom = 0;
      return;
   }

/*  Determine characteristics of pixel map.  */

   rowBytes = map->rowBytes;
   if (rowBytes >= 0) pixelSize = 1;  // BitMap
   else pixelSize = map->pixelSize;   // PixelMap
   rowBytes &= 0x3FFF;                // Strip flags
   baseAddr = (long) map->baseAddr;

/*  Handle 1-bit and 8-bit deep pixel maps with same chunk
  of code.  32-bit deep pixel map handled separately.  */

   if (pixelSize != 32)
   {

/*  Move baseAddr over to the first column of the selection rectangle, still keeping it 
  word aligned.  Then determine what masks are needed for leftmost and rightmost 
  words in the selection and how many whole words there are in between.  */

      if (pixelSize == 1)
      {
         baseAddr += (leftSide >> 5) << 2;
         leftMask = LeftMask1[leftSide & 0x1F];
         rightMask = RightMask1[(rightSide - 1) & 0x1F];
         numWholeWords = (rightSide >> 5) -
            ((leftSide + 31) >> 5);
      }
      else
      {
         baseAddr += leftSide & 0xFFFC;
         leftMask = LeftMask8[leftSide & 3];
         rightMask = RightMask8[(rightSide - 1) & 3];
         numWholeWords = (rightSide >> 2) -
            ((leftSide + 3) >> 2);
      }

/*  Set flags indicating what masks are in use.  If the left and right boundaries of the 
  selection fall within the same word, then take the intersection of the left and right 
  masks and only consider one column of words.  */

      needLeftMask = (leftMask + 1 != 0);
      needRightMask = (rightMask + 1 != 0);
      if (numWholeWords < 0)
      {
         leftMask &= rightMask;
         needRightMask = 0;
      }

/*  Find first row with a non-white pixel by ORing the
  whole row together and checking for a non-zero result.  */

      j = topSide;
      accumulator = 0;
      m = baseAddr + j * rowBytes;  // Top-left corner
      do
      {
         k = m;
         if (needLeftMask)
         {
            accumulator |= (*(long *) k) & leftMask;
            k += 4;
         }
         for (i = 0; i < numWholeWords; i++)
         {
            accumulator |= *(long *) k;
            k += 4;
         }
         if (needRightMask)
         {
            accumulator |= (*(long *) k) & rightMask;
         }
         if (accumulator != 0) break;
         m += rowBytes;
      } while (++j < bottomSide);
      if (j == bottomSide)    // Whole selection is white
      {
         enclosingRect->left = enclosingRect->right =
            enclosingRect->top = enclosingRect->bottom = 0;
         return;
      }
                topSide = j;

/*  Find last row with a non-white pixel.  */

      j = bottomSide - 1;
      accumulator = 0;
      m = baseAddr + j * rowBytes;  // Bottom-left corner
      do
      {
         k = m;
         if (needLeftMask)
         {
            accumulator |= (*(long *) k) & leftMask;
            k += 4;
         }
         for (i = 0; i < numWholeWords; i++)
         {
            accumulator |= *(long *) k;
            k += 4;
         }
         if (needRightMask)
         {
            accumulator |= (*(long *) k) & rightMask;
         }
         if (accumulator != 0) break;
         m -= rowBytes;
      } while (--j >= topSide);
      bottomSide = j + 1;

/*  Find leftmost column containing a non-white pixel.  */

      accumulator = 0;
      m = baseAddr + topSide * rowBytes;
      l = 0;
      if (needLeftMask)
      {
         k = m;
         j = topSide;
         do
         {
            accumulator |= (*(long *) k) & leftMask;
            k += rowBytes;
         } while (++j < bottomSide);
         if (accumulator != 0) goto leftFound;
         l += 4;
      }
      for (i = 0; i < numWholeWords; i++)
      {
         k = m + l;
         j = topSide;
         do
         {
            accumulator |= *(long *) k;
            k += rowBytes;
         } while (++j < bottomSide);
         if (accumulator != 0) goto leftFound;
         l += 4;
      }
      if (needRightMask)
      {
         k = m + l;
         j = topSide;
         do
         {
            accumulator |= (*(long *) k) & rightMask;
            k += rowBytes;
         } while (++j < bottomSide);
      }

/*  When we get to here, we have narrowed down the left-most non-white to the 
  word.  The value in the accumulator will tell us the exact column of the pixel.  We 
  then move baseAddr over to the last column of the selection rectangle (word 
  aligned).  */

leftFound:
      if (pixelSize == 1)
      {
         leftSide = (leftSide & 0xFFFFFFE0) + (l << 3);
         while (accumulator >= 0)
         {
            leftSide++;
            accumulator <<= 1;
         }
         baseAddr = (long) map->baseAddr +
            (((rightSide - 1) >> 5) << 2);
      }
      else
      {
         leftSide = (leftSide & 0xFFFFFFFC) + l;
         while ((accumulator & 0xFF000000) == 0)
         {
            leftSide++;
            accumulator <<= 8;
         }
         baseAddr = (long) map->baseAddr +
            ((rightSide - 1) & 0xFFFC);
      }

/*  Find rightmost column containing a non-white pixel.  */

      accumulator = 0;
      m = baseAddr + topSide * rowBytes;
      l = 0;
      if (needRightMask)
      {
         k = m;
         j = topSide;
         do
         {
            accumulator |= (*(long *) k) & rightMask;
            k += rowBytes;
         } while (++j < bottomSide);
         if (accumulator != 0) goto rightFound;
         l += 4;
      }
      for (i = 0; i < numWholeWords; i++)
      {
         k = m - l;
         j = topSide;
         do
         {
            accumulator |= *(long *) k;
            k += rowBytes;
         } while (++j < bottomSide);
         if (accumulator != 0) goto rightFound;
         l += 4;
      }
      if (needLeftMask)
      {
         k = m - l;
         j = topSide;
         do
         {
            accumulator |= (*(long *) k) & leftMask;
            k += rowBytes;
         } while (++j < bottomSide);
      }
rightFound:
      if (pixelSize == 1)
      {
         rightSide = ((rightSide + 31) & 0xFFFFFFE0) - (l << 3);
         while ((accumulator & 1) == 0)
         {
            rightSide--;
            accumulator >>= 1;
         }
      }
      else
      {
         rightSide = ((rightSide + 3) & 0xFFFFFFFC) - l;
         while ((accumulator & 0x000000FF) == 0)
         {
            rightSide--;
            accumulator >>= 8;
         }
      }
   }

/*  Now for the code which handles 32-bit deep pixel maps.  For direct pixels white is 
  ones, unlike indexed pixels where white is zeros.  We will use the same technique, 
  but we will have to AND the rows and columns together.  We don’t have to worry 
  about left and right masks - in 32-bit deep pixel maps every pixel is word aligned.  */

   else
   {
      baseAddr += leftSide << 2;
      numWholeWords = rightSide - leftSide;

/*  Find first row.  */

      j = topSide;
      accumulator = DirectWhite;
      m = baseAddr + j * rowBytes;
      do
      {
         k = m;
         i = 0;
         do
         {
            accumulator &= *(long *) k;
            k += 4;
         } while (++i < numWholeWords);
         if (accumulator != DirectWhite) break;
         m += rowBytes;
      } while (++j < bottomSide);
      if (j == bottomSide)       // All white pixels
      {
         enclosingRect->left = enclosingRect->right =
            enclosingRect->top = enclosingRect->bottom = 0;
         return;
      }
      topSide = j;

/*  Find last row.  */

      j = bottomSide - 1;
      accumulator = DirectWhite;
      m = baseAddr + j * rowBytes;
      do
      {
         k = m;
         i = 0;
         do
         {
            accumulator &= *(long *) k;
            k += 4;
         } while (++i < numWholeWords);
         if (accumulator != DirectWhite) break;
         m -= rowBytes;
      } while (--j >= topSide);
      bottomSide = j + 1;

/*  Find leftmost column.  */

      accumulator = DirectWhite;
      m = baseAddr + topSide * rowBytes;
      l = 0;
      i = 0;
      do
      {
         k = m + l;
         j = topSide;
         do
         {
            accumulator &= *(long *) k;
            k += rowBytes;
         } while (++j < bottomSide);
         if (accumulator != DirectWhite) break;
         l += 4;
      } while (++i < numWholeWords);
      leftSide += l >> 2;

/*  Find rightmost column.  */

      baseAddr = (long) map->baseAddr +
         (rightSide << 2) - 4;
      accumulator = DirectWhite;
      m = baseAddr + topSide * rowBytes;
      l = 0;
      i = 0;
      do
      {
         k = m - l;
         j = topSide;
         do
         {
            accumulator &= *(long *) k;
            k += rowBytes;
         } while (++j < bottomSide);
         if (accumulator != DirectWhite) break;
         l += 4;
      } while (++i < numWholeWords);
      rightSide -= l >> 2;
   }

/*  Return enclosing rectangle in the pixel map’s local coordinates.  */

   enclosingRect->left = leftSide + map->bounds.left;
   enclosingRect->right = rightSide + map->bounds.left;
   enclosingRect->top = topSide + map->bounds.top;
   enclosingRect->bottom = bottomSide + map->bounds.top;
}

 

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Realistic Sims are very fun experiences and give gamers an excellent chance to experience other walks of life, and Gamabilis has released its hyper-real farm management game Roots of Tomorrow. Whilst the more arcade-type games like Stardew Valley... | Read more »
Best iPhone Game Updates: ‘Streets of Ra...
Hello everyone, and welcome to the week! It’s time once again for our look back at the noteworthy updates of the last seven days. We’ve got a nice mix of Apple Arcade, free-to-play, and even a proper paid game. We don’t see those often! So yes, a... | Read more »
The House of Da Vinci 3 launches on Andr...
Following its earlier release on iOS this year, The House of Da Vinci 3 has also officially launched on Android devices. Blue Brain Games' 3D puzzle adventure boasts an average rating of 4.9/5 and will give players the much-awaited conclusion to... | Read more »
‘Oxenfree: Netflix Edition’ Is Out Now o...
Over the weekend, Netflix and Nightschool Studio announced and released Oxenfree: Netflix Edition (Free) worldwide on iOS and Android. This new version of Oxenfree: Netflix Edition is a separate release, and the prior version that I own, is no... | Read more »
‘Genshin Impact’ Version 3.1 Update Pre-...
Genshin Impact (Free) version 3.1 ‘King Deshret and the Three Magi’ goes live in a few days across iOS, Android, PC, PS5, and PS4. As with prior updates, pre-installation for the upcate has just gone live a few days before release. | Read more »
We’re Digging ‘Shovel Knight Dig’ – The...
We spend the bulk of this week’s podcast talking about the new iPhone 14. Specifically, the iPhone 14 Pro Max which both Eli and myself picked up. The consensus seems to be: They’re great! They’re iPhones! We do lay down our hot takes on all the new... | Read more »
TouchArcade Game of the Week: ‘Loose Noz...
There aren’t a lot of stories like that of the development of Loose Nozzles, and of those games that do have an interesting development story, even fewer are actually decent games to play. Loose Nozzles nails both, though. The way it was created is... | Read more »
SwitchArcade Round-Up: ‘Shovel Knight Di...
Hello gentle readers, and welcome to the SwitchArcade Round-Up for September 23rd, 2022. In today’s article, we’ve got the rest of this week’s releases to look at. There are actually a few big games today, including the hot-hot-hot Shovel Knight Dig... | Read more »

Price Scanner via MacPrices.net

13-inch Apple MacBook Airs with M2 processors...
Amazon has 13″ MacBook Airs with M2 CPUs in stock today and on sale for $1099. Shipping is free. Their prices are $100 off Apple’s MSRP, and they are the lowest prices available for M2-powered Macs... Read more
AR Glasses That Work With Apple’s Hardware? T...
NEWS – Lenovo has created quite the spectacle(s) with its latest product. “Apple Glass” — the purported name of Apple’s forthcoming AR glasses — is not expected to be released until 2025 (at the... Read more
New today at Apple: 13-inch M2 MacBook Pros f...
Apple 13″ MacBook Pros with M2 CPUs in stock and available today starting at $1169, Certified Refurbished, and ranging up to $150 off original MSRP. These are the cheapest 13″ M2 MacBook Pros for... Read more
Sunday Sale: 13″ Apple M1 MacBook Air availab...
Amazon has Space Gray Apple 13″ M1 MacBook Airs on sale for $690.95 for an extremely limited time. Other models are on sale for $849. Their price for the Space Gray model is the cheapest we’ve ever... Read more
Use our exclusive Apple Price Trackers to fin...
Our Apple award-winning price trackers are the best place to look for the lowest prices and latest sales on all the latest Apple gear this season. Scan our price trackers for the latest information... Read more
New promo at Verizon: Get Apple Watch Series...
Purchase a new iPhone 14 at Verizon, and get an Apple Watch Series 8 for as low as $5 per month. $120 in promo credits for the Watch are spread over a 36 month term, reducing the price of the Watch... Read more
Visible drops prices on Apple iPhone 13 model...
Verizon’s low-cost wireless cell service, Visible has dropped prices on iPhone 13 models to new low prices starting at $599: – iPhone 13 Pro Max: starting at $980 + free $200 gift card – iPhone 13... Read more
Back in stock! 14″ MacBook Pros with Apple M1...
Amazon has restocked 14″ MacBook Pros M1 Pro CPUs for $400 off MSRP, starting at only $1599. Shipping is free. Be sure to make your purchase from Amazon rather than a third-party seller. Their prices... Read more
This is the final week to take advantage of A...
Apple’s Back to School promotion for 2022 ends on September 26, 2022. As part of this promotion, Apple will include a free $150 Apple Gift Card with the purchase of any MacBook Air, MacBook Pro, or... Read more
Mac Studio with M1 Max CPU back in stock toda...
Apple has the base standard-configuration Mac Studio available again in their Certified Refurbished section for $1799, and it’s in stock today. Each Mac Studio comes with Apple’s one-year warranty,... Read more

Jobs Board

Physician Assistant, Primary Care, *Apple*...
Physician Assistant, Primary Care, Apple Valley (1.07FTE) + Job ID: 65766 + Department: AV Primary Care + City: Apple Valley, MN + Location: HP - Apple Read more
Operations Manager - Mac/ *Apple* Engineerin...
…Responsible for the day-to-day activities relating to the engineering of Apple Macs in a complex, multi-platform environment. Demonstrates strong leadership, Read more
Lead Developer - *Apple* tvOS - Rumble (Uni...
…earnings, and positive sentiment About the role: We are looking for a Lead Apple tvOS Developer to join our application engineering team to expand our video centric Read more
Systems Administrator - *Apple* Devices / J...
…Administration **Duties and Responsibilities** + Configure and maintain the client's Apple Device Management (ADM) solution. The current solution is JAMF supporting Read more
Sr Product Manager, *Apple* TV Platforms -...
…an experienced senior product manager to drive the strategy and requirements for our Apple TV devices, acting as the champion and owner of the holistic experience in Read more
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