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Feb 96 Challenge
Volume Number:12
Issue Number:2
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.

Intersecting Rectangles

The Challenge this month is to write a routine that will accept a list of rectangles and calculate a result based on the intersections of those rectangles. Specifically, your code will return a list of non-overlapping rectangles that contain all points enclosed by an odd (or even) number of the input rectangles. The prototype for the code you should write is:

void RectangleIntersections(
 const Rect inputRects[], /* list if input rectangles */
 const long numRectsIn,   /* number of inputRects */
 Rect outputRects[], /* preallocated storage for output */
 long *numRectsOut,/* number of outputRects returned */
 const Boolean oddParity  /* see text for explanation */
);

The parameter oddParity indicates whether you are to return rectangles containing points enclosed by an odd number of the numRectsIn inputRects rectangles (oddParity==true) or by an even (nonzero) number of rectangles (oddParity==false). Sufficient storage for the output will be preallocated for you and pointed to by outputRects.

As an example, if you were given these inputRects:

 {0,10,20,30}, {5,15,20,30}

and oddParity were true, you might return the following list of outputRects:

 {0,10,5,15}, {0,15,5,30}, {5,10,15,20}

It would also be correct to return a result that combined the first of these rectangles with either of the other two. If oddParity were false, you would return the following list for the example input:

 {5,15,20,30}

The outputRects must be non-empty and non-overlapping. In the example, it would be incorrect to return the following for the odd parity case:

 {0,10,5,30} {0,10,20,15}

The outputRects you generate must also be maximal, in the sense that each edge of each of the outputRects should pass through a vertex of one of the inputRects. That is, for example, I don’t want you to return a 1¥1 rectangle representing each point enclosed in the desired number of inputRects. Before returning, set *numRectsOut to indicate the number of outputRects you generated.

If you need auxiliary storage, you may allocate any reasonable amount within your code using toolbox routines or malloc, but you must deallocate that storage before returning. (No memory leaks! - I’ll be calling your code many times.)

This native PowerPC Challenge will be scored using the latest Metrowerks compiler, with the winner determined by execution time. If you have any questions, or would like some test data for your code, please send me e-mail at one of the Programmer’s Challenge addresses, or directly to bob_boonstra@mactech.com. Test data will also be sent to the Programmer’s Challenge mailing list, which you can join by sending a message to autoshare@mactech.com with the SUBJECT line “sub challenge YourName”, substituting your real name for YourName.

Two Months Ago Winner

Eight of the 13 solutions submitted for the Find Again And Again Challenge worked correctly. Congratulations to Gustav Larsson (Mountain View, CA) for submitting an entry that was significantly faster than the others. The problem was to write a text search engine optimized to operate repeatedly on the same block of text. A variety of optimization techniques were represented in the solutions, a couple of which are highlighted in the table of results below. Several people optimized for the case where the same word was repeatedly searched for. Some of my tests included this case, and those results are in the columns headed “repeat.” The “random” columns shows results for tests that searched for random occurrences of random words. Each of the tests were run under conditions where only 64KB of auxiliary storage was available, and where much more memory was available. These conditions were weighted 20% and 80% respectively in calculating the total time, since the problem statement promised that ample memory would usually be provided. You can see that Gustav’s solution performed reasonably well when memory was scarce, and very well when memory was plentiful.

Gustav’s solution hashes as many words of the input text as possible in the initialization routine. He uses the Boyer-Moore-Horspool algorithm to find words in any text that was not parsed during initialization. Other features of the approach are described in the well-commented code.

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

64K Memory >>64K Memory code

Name repeat random repeat random time size

Gustav Larsson (67) 1814 3773 62 111 1255 3584

Tom Saxton 46 16400 197 459 3814 2000

Xan Gregg (81) 27 2907 1316 2835 3907 1664

Kevin Cutts (46) 1760 3234 1760 2809 4654 1600

Joseph Ku 8856 14570 121 509 5189 1584

David Cary 60 22665 499 1000 5745 2124

Eric Lengyel (40) 34 10221 29 4697 5831 1188

Ernst Munter (110) 2036 2053 2287 4603 6330 2976

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 88 13. Vineyard, Jeremy 42

4. Larsson, Gustav 87 14. Lengyel, Eric 40

5. Karsh, Bill 80 15. Darrah, Dave 31

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

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

8. Cutts, Kevin 50 18. Lee, Johnny 22

9. Goebel, James 49 19. Noll, Robert 22

10. Nepsund, Ronald 47

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 Gustav’s winning solution:

Find Again and Again

Copyright © 1995 Gustav Larsson

Constants & Types
#define ALPHABET_SIZE 256
#define ALLOC_SIZE(n) ((n+3) & -4L) /* next multiple of 4 */
#define HASH_BUCKETS 1024           /* must be power of 2 */
#define HASH_MASK (HASH_BUCKETS - 1)
#define NO_NULL_CHAR 'A'
#define NULL 0

typedef unsigned char  uchar;
typedef unsigned short ushort;
typedef unsigned long  ulong;

typedef struct Word Word;
typedef struct Occurrence Occurrence;
typedef struct Private Private;

/* 
  A block of occurrence positions.  We pack in as many occurrences as possible into 
  a single block, from 3 to 6 depending on textLength.

  The first entry in the block is always used.  The remaining entries are in use if they 
  are not zero.  These facts are used several places to simplify the code.
*/
struct Occurrence {
  Occurrence *next;
  union {
    ushort pos2[6];   /* 2 bytes/occurrence */
    struct {
      ushort lo[4];
      uchar  hi[4];
    } pos3;           /* 3 bytes/occurrence */
    long pos4[3];     /* 4 bytes/occurrence */
  } p;
};

/*
  There is one Word struct for each distinct word.  The word’s length is stored in the 
  top eight bits of the hash value.  There’s no need to store the characters in the word 
  since we can just look at the first occurrence (first entry in Word.first).
*/
struct Word {
  Word        *next;
  ulong       hash;
  Occurrence  *last;
  Occurrence  first;
};

/*
  The structure of our private storage.  The hashCodes[] array serves two purposes: it 
  distinguishes alphanumeric from non-alphanumeric characters, and it provides a 
  non-zero hash code for each alphanumeric character.  The endParsedText field will 
  be -1 if there was enough private memory to parse all the text.  Otherwise, it points to 
  the start of the unparsed text.  nullChar is used by the BMH_Search() function when 
  we must search unparsed text for an occurrence.
*/
struct Private {
  ulong hashCodes [ ALPHABET_SIZE ];
  Word  *hashTable [ HASH_BUCKETS ];
  long  endParsedText;  /* start of parsed text */
  long  posBytes;       /* POS_x_BYTES, below */
  char  nullChar;       /* char not appearing in the text */
  long  heap;           /* start of private heap  */
};

Macros
/*
  These macros simplify access to the occurrence positions stored in an Occurrence 
  struct.  Posbytes is a macro argument that is usually set to private->posBytes.  
  However, you can also use a constant for posbytes, which lets the compiler choose 
  the right case at compile time, producing smaller and faster code.
*/
#define POS_2_BYTES 1   /* word position fits in 2 bytes */
#define POS_3_BYTES 0   /* fits in 3 bytes; usual case */
#define POS_4_BYTES 2   /* fits in 4 bytes */

#define GET_POS(pos,occur,index,posbytes)           \
  {                                                 \
    if ( (posbytes) == POS_3_BYTES )                \
      pos = ((long)(occur)->p.pos3.hi[index] << 16) \
          + (occur)->p.pos3.lo[index];              \
    else if ( (posbytes) == POS_2_BYTES )           \
      pos = (occur)->p.pos2[index];                 \
    else                                            \
      pos = (occur)->p.pos4[index];                 \
  }

#define SET_POS(pos,occur,index,posbytes)       \
  {                                             \
    if ( (posbytes) == POS_3_BYTES )            \
    {                                           \
      (occur)->p.pos3.hi[index] = (pos) >> 16;  \
      (occur)->p.pos3.lo[index] = (pos);        \
    }                                           \
    else if ( (posbytes) == POS_2_BYTES )       \
      (occur)->p.pos2[index] = pos;             \
    else                                        \
      (occur)->p.pos4[index] = pos;             \
  }

InitFind
void InitFind (
  char *textToSearch,
  long textLength,
  void *privateStorage,
  long storageSize
)
{
  Private *private = privateStorage;

  private->endParsedText =
    InitFindBody(
        (uchar *)textToSearch,
        textLength,
        privateStorage,
        (uchar *)privateStorage + storageSize
    );

  if ( private->endParsedText != -1 )
    private->nullChar =
      PickNullChar(
            private,
            (uchar *)textToSearch + private->endParsedText,
            (uchar *)textToSearch + textLength );
  else
    private->nullChar = NO_NULL_CHAR;
}

InitFindBody
/*
  This function does most of the work for InitFind().  The arguments have been recast 
  into a more useful form; uchar and ulong are used a lot so that we don’t have to 
  worry about the sign, especially when indexing private->hashCodes[].

  The return value is the character position when the unparsed text begins (if we run 
  out of private storage), or -1 if all the text was parsed.
*/
static long InitFindBody (
  uchar   *textToSearch,
  long    textLength,
  Private *private,
  uchar   *endPrivateStorage
)
{
  uchar       *alloc, *textPos, *textEnd, *wordStart;
  long        wordLength;
  ulong       hash, code;
  Word        *word;
  Occurrence  *occur;

/*
  Init table of hash codes.  The remaining entries are guaranteed to be initialized to 
  zero.  The hash codes were chosen so that any two codes differ by at least five bits.
  */
  {
    ulong *table = private->hashCodes;  /* reduces typing */

    table['0'] = 0xFFC0;  table['5'] = 0xF492;
    table['1'] = 0xFE07;  table['6'] = 0xF31E;
    table['2'] = 0xF98B;  table['7'] = 0xF2D9;
    table['3'] = 0xF84C;  table['8'] = 0xCF96;
    table['4'] = 0xF555;  table['9'] = 0xCE51;

    table['A'] = 0xC9DD;  table['N'] = 0xA245;
    table['B'] = 0xC81A;  table['O'] = 0x9F0A;
    table['C'] = 0xC503;  table['P'] = 0x9ECD;
    table['D'] = 0xC4C4;  table['Q'] = 0x9941;
    table['E'] = 0xC348;  table['R'] = 0x9886;
    table['F'] = 0xC28F;  table['S'] = 0x959F;
    table['G'] = 0xAF5C;  table['T'] = 0x9458;
    table['H'] = 0xAE9B;  table['U'] = 0x93D4;
    table['I'] = 0xA917;  table['V'] = 0x9213;
    table['J'] = 0xA8D0;  table['W'] = 0x6DD3;
    table['K'] = 0xA5C9;  table['X'] = 0x6C14;
    table['L'] = 0xA40E;  table['Y'] = 0x6B98;
    table['M'] = 0xA382;  table['Z'] = 0x6A5F;

    table['a'] = 0x6746;  table['n'] = 0x3C88;
    table['b'] = 0x6681;  table['o'] = 0x3B04;
    table['c'] = 0x610D;  table['p'] = 0x3AC3;
    table['d'] = 0x60CA;  table['q'] = 0x37DA;
    table['e'] = 0x5D85;  table['r'] = 0x361D;
    table['f'] = 0x5C42;  table['s'] = 0x3191;
    table['g'] = 0x5BCE;  table['t'] = 0x3056;
    table['h'] = 0x5A09;  table['u'] = 0x0D19;
    table['i'] = 0x5710;  table['v'] = 0x0CDE;
    table['j'] = 0x56D7;  table['w'] = 0x0B52;
    table['k'] = 0x515B;  table['x'] = 0x0A95;
    table['l'] = 0x509C;  table['y'] = 0x078C;
    table['m'] = 0x3D4F;  table['z'] = 0x064B;
  }

  /*  Determine the number of bytes needed to store each occurrence position. */
  if ( textLength <= 0x10000L )
    private->posBytes = POS_2_BYTES;
  else if ( textLength <= 0x1000000L )
    private->posBytes = POS_3_BYTES;
  else
    private->posBytes = POS_4_BYTES;

  /* Set up variables to handle allocation of private storage. */
  alloc = (uchar *)&private->heap;

  /* Parse the text */
  textPos = textToSearch;
  textEnd = textPos + textLength;

  while ( textPos != textEnd )
  {
    /* Search for start of word */
    while ( private->hashCodes[*textPos] == 0 )
    {
      textPos++;
      if ( textPos == textEnd )
        return -1;  /* parse all text */
    }
    wordStart = textPos;

    /* Search for end of word; generate hash value too */
    hash = 0;
    while ( textPos != textEnd &&
            (code = private->hashCodes[ *textPos ]) != 0 )
    {
      hash = (hash << 1) ^ code;
      textPos++;
    }
    wordLength = textPos - wordStart;
    hash = (hash & 0xFFFFFF) | (wordLength << 24);

    /*
      Record the occurrence.  First we see if a Word struct exists for this word and 
      whether we need to allocate a new Occurrence struct.
    */
    word = LookupWord(
                private,
                (char *)textToSearch,
                (char *)wordStart,
                wordLength,
                hash );
    if ( word )
    {
      long allocateNewBlock, blockSize, i, pos;

      /*
        This word has occurred before, so it already has a Word struct.  See if there’s 
        room in the last Occurrence block for another entry.  Remember that entry #0 in 
        the Occurrence block is always in use, so we can start checking at entry #1 for a 
        non-zero entry.
      */
      occur = word->last;
      allocateNewBlock = TRUE;
      switch ( private->posBytes )
      {
        case POS_2_BYTES:  blockSize = 6; break;
        case POS_3_BYTES:  blockSize = 4; break;
        case POS_4_BYTES:  blockSize = 3; break;
      }

      for ( i = 1; i < blockSize; i++ )
      {
        GET_POS( pos, occur, i, private->posBytes )
        if ( pos == 0 )
        {
          SET_POS( wordStart - textToSearch, occur, i,
                   private->posBytes )
          allocateNewBlock = FALSE;
          break;
        }
      }

      if ( allocateNewBlock )
      {
        /* Block is full.  Allocate new Occurrence block */
        occur = (Occurrence *) alloc;
        alloc += ALLOC_SIZE( sizeof(Occurrence) );
        if ( alloc >= endPrivateStorage )
          return wordStart-textToSearch; /* out of memory */

        /* Init the new struct and link it to the end of the occurence list. */
        SET_POS( wordStart - textToSearch, occur, 0,
                 private->posBytes )
        word->last->next = occur;
        word->last = occur;
      }
    }
    else
    {
      long i;

/* This is a new word.  Allocate a new Word struct, which contains an Occurrence 
    struct too.  */
      word = (Word *) alloc;
      alloc += ALLOC_SIZE( sizeof(Word) );
      if ( alloc >= endPrivateStorage )
        return wordStart-textToSearch ;  /* out of memory */

      /*  Link it to the start of the Word list, coming off the hash table. */
      word->next = private->hashTable[ hash & HASH_MASK ];
      private->hashTable[ hash & HASH_MASK ] = word;

      /* Init the Word struct */
      word->hash = hash;
      word->last = &word->first;

      /* Init the Occurrence struct */
      SET_POS( wordStart - textToSearch, &word->first, 0,
               private->posBytes )
    }
  }

  /* Finished parsing text */
  return -1;
}

FindWordOccurrence
long FindWordOccurrence (
  char *wordToFind,
  long wordLength,
  long occurrenceToFind,
  char *textToSearch,
  long textLength,
  void *privateStorage,
  long storageSize
)
{
  Private *private = privateStorage;
  Word  *word;
  ulong hash;

  /* Make occurenceToFind zero-based */
  occurrenceToFind--;

  /* Generate hash value for word to find */
  hash = 0;
  {
    long remain = wordLength;
    uchar *p = (uchar *) wordToFind;
    while ( remain > 0 )
    {
      hash = (hash << 1) ^ private->hashCodes[*p++];
      remain--;
    }
    hash = (hash & 0xFFFFFF) | (wordLength << 24);
  }

  /* Look for word/occurrence in hash table */
  word = LookupWord( private, textToSearch, wordToFind,
                     wordLength, hash );
  if ( word )
  {
    Occurrence *occur = &word->first;
    long blockSize, pos, i;

    /* Word exists in hash table, so go down the occurrence list.  */
    switch ( private->posBytes )
    {
      case POS_2_BYTES: blockSize = 6;  break;
      case POS_3_BYTES: blockSize = 4;  break;
      case POS_4_BYTES: blockSize = 3;  break;
    }

    while ( occur && occurrenceToFind >= blockSize )
    {
      occurrenceToFind -= blockSize;
      occur = occur->next;
    }

    if ( occur )
    {
      GET_POS( pos, occur, occurrenceToFind,
               private->posBytes )
      if ( occurrenceToFind == 0 || pos != 0 )
        return pos;
      occurrenceToFind -= blockSize;
    }

    occur = word->last;
    for ( i = 0; i < blockSize; i++ )
    {
      GET_POS( pos, occur, i, private->posBytes )
      if ( pos == 0 )
        occurrenceToFind++;
    }
  }

  /* Not in parsed text, so check the unparsed text */
  if ( private->endParsedText != -1 )
  {
    char *p;
    if ( wordLength > 3 )
      p = BMH_Search(
              private->hashCodes,
              wordToFind,
              wordLength,
              occurrenceToFind,
              textToSearch + private->endParsedText,
              textToSearch + textLength,
              private->nullChar );
    else
      p = SimpleSearch(
              private->hashCodes,
              wordToFind,
              wordLength,
              occurrenceToFind,
              textToSearch + private->endParsedText,
              textToSearch + textLength );
    if (p)
      return (p - textToSearch);
  }

  /* Not found */
  return -1;
}

LookupWord 
/* Look up a word in the hash table */
static Word *LookupWord (
  Private *private,
  char    *textToSearch,
  char    *wordText,
  long    wordLength,
  ulong   hash
)
{
  Word *word = private->hashTable[ hash & HASH_MASK ];
  while ( word )
  {
    if ( word->hash == hash )
    {
      char *w1, *w2;
      long pos, remain = wordLength;

      /*
        The hash values match, so compare characters to make sure it’s the right word.  
        We already know the word length is correct since the length is contained
        in the upper eight bits of the hash value.
      */
      GET_POS( pos, &word->first, 0, private->posBytes )
      w1 = textToSearch + pos;
      w2 = wordText;
      while ( remain-- > 0 && *w1++ == *w2++ )
        ;
      if ( remain == -1 )
        return word;
    }
    word = word->next;
  }
  return NULL;
}

PickNullChar 
/*
  Find a character that doesn’t appear anywhere in the unparsed text.  BMH_Search() is 
  faster if such a character can be found.
*/
static char PickNullChar (
  Private *private,
  uchar   *textStart,
  uchar   *textEnd
)
{
  long i;
  uchar *p, occurs[ ALPHABET_SIZE ];

  for ( i = 0; i < ALPHABET_SIZE; i++ )
    occurs[i] = FALSE;

  for ( p = textStart; p < textEnd; p++ )
    occurs[*p] = TRUE;

  for ( i = 0; i < ALPHABET_SIZE; i++ )
    if ( occurs[i] == FALSE && private->hashCodes[i] == 0 )
      return i;

  return NO_NULL_CHAR;
}

BMH_Search
/*
  Search the unparsed text using the Boyer-Moore-Horspool algorithm.  Ideally a null 
  character is supplied (one that appears in neither the search string nor the text being 
  searched).  This allows the inner loop to be faster.
*/
static char *BMH_Search (
  ulong *hashCodes,       /* private->hashCodes     */
  char  *wordToFind,
  long  wordLength,
  long  occurrenceToFind, /* 0 is first occurrence  */
  char  *textStart,       /* start of unparsed text */
  char  *textEnd,         /* end of unparsed text   */
  char  nullChar          /* private->nullChar      */
)
{
  long  i;
  char  *text, *wordEnd;
  char  word[256];
  long  offset[ ALPHABET_SIZE ];

  /*
    Copy the search string to a private buffer, where
    the first character is the null character.
  */
  word[0] = nullChar;
  for ( i = 0; i < wordLength; i++ )
    word[i+1] = wordToFind[i];

  /* Set up the offset[] lookup table */
  for ( i = 0; i < ALPHABET_SIZE; i++ )
    offset[i] = wordLength;

  for ( i = 1; i < wordLength; i++ )
    offset[ word[i] ] = wordLength - i;

  /* Let the search begin... */
  wordEnd = word + wordLength;
  text = textStart + wordLength - 1;

  if ( nullChar == NO_NULL_CHAR )
  {
    /* No null character, so use a slower inner loop */
    while ( text < textEnd )
    {
      long i;
      char *p, *q;
      for ( i = wordLength, p = wordEnd, q = text;
            i > 0 && *p == *q;
            i--, p--, q-- )
        ;
/*If i == 0, we have found the search string.  Now we make sure that it is delimited.*/
      if ( i == 0 && hashCodes[*q] == 0 &&
           (text+1 == textEnd || hashCodes[text[1]] == 0) )
      {
        if ( occurrenceToFind == 0 )
          return q+1;
        occurrenceToFind--;
      }

      text += offset[*text];
    }
  }
  else
  {
    /* There is a null character (usual case), 
        so we can use a faster and simpler inner loop. */
    while ( text < textEnd )
    {
      char *p, *q;
      for ( p = wordEnd, q = text; *p == *q; p--, q-- )
        ;
      if ( p == word && hashCodes[*q] == 0 &&
           (text+1 == textEnd || hashCodes[text[1]] == 0) )
      {
        if ( occurrenceToFind == 0 )
          return q+1;
        occurrenceToFind--;
      }
      text += offset[*text];
    }
  }
  return NULL;
}

SimpleSearch
/*
  Search the unparsed text using a simple search algorithm.  Note that wordLength 
  must be 1, 2, or 3.  This algorithm runs faster than BMH_Search() for small search 
  strings.
*/
static char *SimpleSearch(
  ulong *hashCodes,       /* private->hashCodes      */
  char  *wordToFind,
  long  wordLength,       /* 1..3                    */
  long  occurrenceToFind, /* 0 is 1st occurrence     */
  char  *textStart,       /* start of unparsed text  */
  char  *textEnd          /* end of all text         */
)
{
  char *text, first;

  first = wordToFind[0];
  text = textStart;

  if ( wordLength == 1 )
  {
    while ( text < textEnd )
    {
      while ( text < textEnd && *text != first )
        text++;
      if ( hashCodes[*(text-1)] == 0 &&
           hashCodes[text[wordLength]] == 0 )
      {
        if ( occurrenceToFind == 0 )
          return text;
        occurrenceToFind--;
      }
    text++;
    }
  }
  else if ( wordLength == 2 )
  {
    while ( text < textEnd )
    {
      while ( text < textEnd && *text != first )
        text++;
      if ( text[1] == wordToFind[1] &&
           hashCodes[*(text-1)] == 0 &&
           hashCodes[text[wordLength]] == 0 )
      {
        if ( occurrenceToFind == 0 )
          return text;
        occurrenceToFind--;
      }
    text++;
    }
  }
  else /* wordLength == 3 */
  {
    while ( text < textEnd )
    {
      while ( text < textEnd && *text != first )
        text++;
      if ( text[1] == wordToFind[1] &&
           text[2] == wordToFind[2] &&
           hashCodes[*(text-1)] == 0 &&
           hashCodes[text[wordLength]] == 0 )
      {
        if ( occurrenceToFind == 0 )
          return text;
        occurrenceToFind--;
      }
    text++;
    }
  }
  return NULL;
}

 

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Six fantastic ways to spend National Vid...
As if anyone needed an excuse to play games today, I am about to give you one: it is National Video Games Day. A day for us to play games, like we no doubt do every day. Let’s not look a gift horse in the mouth. Instead, feast your eyes on this... | Read more »
Old School RuneScape players turn out in...
The sheer leap in technological advancements in our lifetime has been mind-blowing. We went from Commodore 64s to VR glasses in what feels like a heartbeat, but more importantly, the internet. It can be a dark mess, but it also brought hundreds of... | Read more »
Today's Best Mobile Game Discounts...
Every day, we pick out a curated list of the best mobile discounts on the App Store and post them here. This list won't be comprehensive, but it every game on it is recommended. Feel free to check out the coverage we did on them in the links below... | Read more »
Nintendo and The Pokémon Company's...
Unless you have been living under a rock, you know that Nintendo has been locked in an epic battle with Pocketpair, creator of the obvious Pokémon rip-off Palworld. Nintendo often resorts to legal retaliation at the drop of a hat, but it seems this... | Read more »
Apple exclusive mobile games don’t make...
If you are a gamer on phones, no doubt you have been as distressed as I am on one huge sticking point: exclusivity. For years, Xbox and PlayStation have done battle, and before this was the Sega Genesis and the Nintendo NES. On console, it makes... | Read more »
Regionally exclusive events make no sens...
Last week, over on our sister site AppSpy, I babbled excitedly about the Pokémon GO Safari Days event. You can get nine Eevees with an explorer hat per day. Or, can you? Specifically, you, reader. Do you have the time or funds to possibly fly for... | Read more »
As Jon Bellamy defends his choice to can...
Back in March, Jagex announced the appointment of a new CEO, Jon Bellamy. Mr Bellamy then decided to almost immediately paint a huge target on his back by cancelling the Runescapes Pride event. This led to widespread condemnation about his perceived... | Read more »
Marvel Contest of Champions adds two mor...
When I saw the latest two Marvel Contest of Champions characters, I scoffed. Mr Knight and Silver Samurai, thought I, they are running out of good choices. Then I realised no, I was being far too cynical. This is one of the things that games do best... | Read more »
Grass is green, and water is wet: Pokémo...
It must be a day that ends in Y, because Pokémon Trading Card Game Pocket has kicked off its Zoroark Drop Event. Here you can get a promo version of another card, and look forward to the next Wonder Pick Event and the next Mass Outbreak that will be... | Read more »
Enter the Gungeon review
It took me a minute to get around to reviewing this game for a couple of very good reasons. The first is that Enter the Gungeon's style of roguelike bullet-hell action is teetering on the edge of being straight-up malicious, which made getting... | Read more »

Price Scanner via MacPrices.net

Take $150 off every Apple 11-inch M3 iPad Air
Amazon is offering a $150 discount on 11-inch M3 WiFi iPad Airs right now. Shipping is free: – 11″ 128GB M3 WiFi iPad Air: $449, $150 off – 11″ 256GB M3 WiFi iPad Air: $549, $150 off – 11″ 512GB M3... Read more
Apple iPad minis back on sale for $100 off MS...
Amazon is offering $100 discounts (up to 20% off) on Apple’s newest 2024 WiFi iPad minis, each with free shipping. These are the lowest prices available for new minis among the Apple retailers we... Read more
Apple’s 16-inch M4 Max MacBook Pros are on sa...
Amazon has 16-inch M4 Max MacBook Pros (Silver and Black colors) on sale for up to $410 off Apple’s MSRP right now. Shipping is free. Be sure to select Amazon as the seller, rather than a third-party... Read more
Red Pocket Mobile is offering a $150 rebate o...
Red Pocket Mobile has new Apple iPhone 17’s on sale for $150 off MSRP when you switch and open up a new line of service. Red Pocket Mobile is a nationwide MVNO using all the major wireless carrier... Read more
Switch to Verizon, and get any iPhone 16 for...
With yesterday’s introduction of the new iPhone 17 models, Verizon responded by running “on us” promos across much of the iPhone 16 lineup: iPhone 16 and 16 Plus show as $0/mo for 36 months with bill... Read more
Here is a summary of the new features in Appl...
Apple’s September 2025 event introduced major updates across its most popular product lines, focusing on health, performance, and design breakthroughs. The AirPods Pro 3 now feature best-in-class... Read more
Apple’s Smartphone Lineup Could Use A Touch o...
COMMENTARY – Whatever happened to the old adage, “less is more”? Apple’s smartphone lineup. — which is due for its annual refresh either this month or next (possibly at an Apple Event on September 9... Read more
Take $50 off every 11th-generation A16 WiFi i...
Amazon has Apple’s 11th-generation A16 WiFi iPads in stock on sale for $50 off MSRP right now. Shipping is free: – 11″ 11th-generation 128GB WiFi iPads: $299 $50 off MSRP – 11″ 11th-generation 256GB... Read more
Sunday Sale: 14-inch M4 MacBook Pros for up t...
Don’t pay full price! Amazon has Apple’s 14-inch M4 MacBook Pros (Silver and Black colors) on sale for up to $220 off MSRP right now. Shipping is free. Be sure to select Amazon as the seller, rather... Read more
Mac mini with M4 Pro CPU back on sale for $12...
B&H Photo has Apple’s Mac mini with the M4 Pro CPU back on sale for $1259, $140 off MSRP. B&H offers free 1-2 day shipping to most US addresses: – Mac mini M4 Pro CPU (24GB/512GB): $1259, $... Read more

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