TweetFollow Us on Twitter

Mar 98 Challenge

Volume Number: 14 (1998)
Issue Number: 3
Column Tag: Programmer's Challenge

Programmer's Challenge

by Bob Boonstra, Westford, MA

Help Peter Get Home

Last summer, while he was on his way back to Perth from MacHack, Peter Lewis suggested a challenge based on airline schedules. His idea was to select the quickest route from an origin to a destination, given a schedule of flights between pairs of cities. This month's Challenge is based on Peter's suggestion, but embellished to capture the "probabilistic" nature of airline travel these days.

Your job is to write a routine FindQuickestRoute that will route Peter from his departureAirport to his arrivalAirport in as few simulated flight hours as possible. Peter's trip begins on startDay at startTime. He has a list of airports to which he can fly, and an airlineSchedule of flights between pairs of those airports. The airlineSchedule consists of a flightNumber that will take him from a fromAirport to a toAirport, nominally departing at a scheduledDepartureTime, and nominally taking nominalFlightDuration seconds to get there. The scheduledDepartureTime is expressed in the local time zone of the fromAirport, which is provided as a timeOffset from Universal Time associated with each of the airports. Some of the flights in the airlineSchedule operate only on particular days, described in the operatingDays associated with each flightNumber.

Each of the airports has a minConnectTime, which is the minimum amount of time following one's arrival at the airport before one can catch a connecting flight. This applies to the initial flight, which must be scheduled to leave at least minConnectTime after the startTime of Peter's adventure. Each subsequent connecting leg must also be scheduled to leave at least minConnectTime after the actual arrival time of the preceding leg.

Sounds simple enough so far, right? Except that airplanes seldom depart or arrive on time. So we have introduced a little randomness in our simulated airline operations. The actual departure time of each flight is modeled as a random variable with an exponential distribution, governed by the parameter lambdaDeparture. The duration of each flight is also modeled as an exponential distribution, governed by lambdaDuration. When you decide to take a flight, the callback routine myGetFlightTime will roll the exponential dice for you and return the number of minutes the flight actually took, measured from the scheduledDepartureTime, taking into account the departure delay and the duration delay. A few facts for those whose probability theory is a little rusty: an exponential distribution with parameter t has a probability density function of t*exp(-tx), an expected value of (1/t), and a variance of 1/t2.

The prototype for the code you should write is:

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

typedef char FlightNum[8],AirportName[64];

typedef enum {
 Sunday=0, Monday, Tuesday, Wednesday, Thursday, Friday, 
 Saturday} DayOfWeek;

typedef struct MyTime {
 long hour;   /* 0-23, 0==midnight */
 long min;    /* 0-59 */
} MyTime;

typedef struct {
 AirportName name;     /* airport name */
 MyTime timeOffset;    /* local time offset relative to Universal Time */
                       /* 0 == Greenwich, {-5,0}==Eastern Time, etc. */
 MyTime minConnectTime;/* minimum time to make a connection at this airport */
} Airport;

typedef struct {
 FlightNum flightNumber;
 AirportName fromAirport;
 AirportName toAirport;
 MyTime scheduledDepartureTime;  /* local departure time from fromAirport */
 MyTime nominalFlightDuration;   /* nominal flight duration */
 float lambdaDeparture;          /* parameter for actual flight departure
                                    (mins) */
 float lambdaDuration;           /* parameter for actual flight duration
                                    (mins) */
 Boolean operatingDays[7];       /* if operatingDays[d], flight valid on 
                                    day d */
} Flight;

typedef long (*GetFlightTime) (
      /* returns actual flight duration from scheduledDepartureTime in minutes */
 FlightNum flightNumber          /* flight number taken */
);

long FindQuickestRoute(          /* return travel time in seconds */
 AirportName departureAirport,   /* origin airport */
 AirportName arrivalAirport,     /* destination airport */
 DayOfWeek startDay,             /* day the adventure begins (local time) */
 MyTime startTime,               /* time the adventure begins (local time) */
 Airport airports[],             /* places to fly from/to */
 long numAirports,               /* number of entries in airports[] */
 Flight airlineSchedule[],       /* flights to choose from */
 long numFlights,                /* number of entries in airlineSchedule[] */
 GetFlightTime myGetFlightTime   /* callback that provides actual flight
                                    duration */
);

#if defined(__cplusplus)
}
#endif

My test code will keep track of the flights you choose in the myGetFlightTime routine. It will ensure that operatingDays and minConnectTime constraints are met, that the fromAirport for travel leg n+1 is the same as the toAirport for travel leg n, etc. Violations of these constraints will result in a 24 hour simulated time penalty.

Test cases will include several trials for each departure/arrival pair to average out randomness. The winner will be the solution that routes Peter to his destinations in the least amount of time, where time is calculated as cumulative simulated travel time plus a penalty of 1 simulated hour for every second of execution time required by your FindQuickestRoute solution.

This will be a native PowerPC Challenge, using the latest CodeWarrior environment. Solutions may be coded in C, C++, or Pascal. Thanks to Peter Lewis for inspiring this Challenge -- he wins two Challenge points for the suggestion.

Three Months Ago Winner

If the number of entries to the December Challenge is any indication, many Programmer's Challenge readers are also avid crossword puzzle-ists. Congratulations to Mat Hostetter (location unknown) for submitting the fastest of 14 entries Clueless Crosswords Challenge. The problem was to solve (or actually, to generate) a crossword puzzle given the pattern of open and blocked cells, along with a dictionary of words from which to choose. The dictionary contained up to ten extra words for each word in the crossword puzzle solution, making multiple solutions were possible.

The evaluation is based on the time required to solve each of five crossword puzzles three times, each time with the dictionary sorted differently. I used each puzzle three times because a number of contestants reported that execution time varied significantly depending on the sort order of the dictionary, a fact that was borne out in my tests. Some of the entries took two orders of magnitude more time to solve a puzzle for one sort order than for the same puzzle with a different sort order. The winning entry exhibited significantly less variability, ranging from a 4% difference for one crossword puzzle to a 63% difference for another puzzle.

Like many of the entries submitted, Mat's solution has a recursive component. To accommodate recursion, I gave each entry 512K of stack space.

The key to efficient solution of this Challenge was propagating the constraints imposed by puzzle squares where an "across" word intersected a "down" word. The style of crossword puzzle provided in the test code and used to evaluate this Challenge contained many blocks of cells that were 4x4 or larger, resulting in many such intersections. Mat uses a set of filter_for_length_N routines to efficiently propagate constraints imposed by the intersections. When reading the modestly commented code, pay particular attention to the create_placements routine used to identify possible word locations, and to the tighten_constraints routine used to eliminate conflicting word placements.

Five of the entries had not solved one or more test cases after ten minutes or more, exceeding my ability to wait for an answer. In these cases, a test time of 10 minutes was assessed.

The table below lists the total execution time in seconds for the fifteen test cases, code size, data size, and programming language for each entry. 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. The entries marked with an asterisk are those which did not complete one or more test cases in the 10 minutes mentioned above.

Name                    Time   Code      Data  Language
Mat Hostetter           0.37  14196       200  C
Brad Smith              1.36   7532     61835  C
Tom Saxton (12)         1.42   4132         8  C
Jens Martin Bengaard    9.76   4108     16628  C++
Xan Gregg (114)        23.73   4536    224584  C
Randy Boring (73)      74.56   4260     35158  C
Ernst Munter (310)    107.81   5824     16460  C++
Sebastian Maurer (10) 389.23   3968       112  C++
Rainer Brockerhoff    606.03   4609    165577  C
(*) ACC Murphy (34)  2400.29   6528  10212602  Pascal
(*) Mike Miller      2433.70  10052       428  C++
(*) Eric Kenninga    5599.22   6076       188  C++
(*) Steve Wozniac    5925.92   2836        64  C
(*) H.L.             9000.00   6780      1732  C++

Top 20 Contestants

Here are the Top Contestants for the Programmer's Challenge, including everyone who has accumulated more than 10 points during that the past two years. The numbers below include points awarded over the 24 most recent contests, including points earned by this month's entrants.

Rank  Name                Points
 1.   Munter, Ernst          200  
 2.   Boring, Randy           73
 3.   Cooper, Greg            61
 4.   Lewis, Peter            61
 5.   Mallett, Jeff           50
 6.   Nicolle, Ludovic        48
 7.   Murphy, ACC             34
 8.   Gregg, Xan              28
 9.   Antoniewicz, Andy       24
10.   Day, Mark               20
11.   Higgins, Charles        20
12.   Hostetter, Mat          20
13.   Studer, Thomas          20
14.   Gundrum, Eric           15
15.   Hart, Alan              14
16.   O'Connor, Turlough      14
17.   Picao, Miguel Cruz      14

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 Mat's winning solution:

Crossword.c
© 1997 Mat Hostetter

#define kMaxSize 32
typedef char Puzzle[kMaxSize][kMaxSize];  /* referenced as [x][y] */

void Crossword(
 Puzzle thePuzzle,    /* return solved puzzle here */
 char *dictionary[],  /* array of words to choose from */
 long puzzleSize,    /* number of rows/cols in puzzle */
 long dictSize        /* number of words in dictionary */
);

/* Program begins here */

#include <ctype.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/* Must be at least 32 bits, and ideally exactly 32 bits. */
typedef long letter_mask_t;

typedef struct {
 const char *original_word;
 unsigned char letter[1]; /* variable-sized array of values [1, 26]. */
} move_t;

/* Non-portable hack to compute size of above struct given how many
 * letters it has. It rounds up to sizeof(void *) to guarantee
 * alignment constraints are met. */
#define MOVE_SIZE(n)                  \
 (((sizeof(void *) + (n) + (sizeof(void *) - 1))    \
  / sizeof(void *))                  \
  * sizeof(void *))

#define NEXT_MOVE(m, n) ((move_t *) ((char *) (m) + (n)))

typedef enum {
 CYCLENESS_UNKNOWN,
 IN_CYCLE,
 NOT_IN_CYCLE
} cycleness_t;

typedef struct _placement_t {
 /* number of entries in `move' array. */
 long num_moves;

 /* If this == current_mark, this placement_t is "marked". We use
  * this for things like recursive searches. */
 unsigned long mark;

 /* Number of letters in each entry of the `move' array. */
 unsigned short letters_per_move;
 
 /* Byte size of each element in the `move' array. */
 unsigned short move_size;

 /* Where does this start? */
 unsigned short start_x, start_y;

 /* Direction this heads. */
 unsigned short dx, dy;

 /* Is this partition part of a cyclic dependency? */
 cycleness_t in_cycle;

 /* Totally done with this placement? */
 char done;

 /* Field temporarily used during recursion. */
 long depth;

 /* 1D index into the board where each letter is placed. */
 unsigned long where[kMaxSize]; 
 
 /* Other placements that intersect this one. */
 struct _placement_t *neighbor[kMaxSize + 1]; 
        /* NULL-terminated. */

 /* array of variable-size objects! Don't dereference this array normally. */
 move_t *move;
} placement_t;

/* No -1 so we can save room for NULL at the end. */
#define PLACEMENT_SIZE(n) \
    (sizeof(placement_t) + (n) * sizeof(move_t *))

filter_for_length_1
static void
filter_for_length_1(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(1));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(1));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   m = NEXT_MOVE(m, MOVE_SIZE(1));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
}

filter_for_length_2
static void
filter_for_length_2(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(2));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(2));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   m = NEXT_MOVE(m, MOVE_SIZE(2));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
}

filter_for_length_3
static void
filter_for_length_3(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(3));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(3));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   m = NEXT_MOVE(m, MOVE_SIZE(3));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
}

filter_for_length_4
static void
filter_for_length_4(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 const letter_mask_t global_mask_3 = 
      letters_allowed[p->where[3]];
 letter_mask_t allowed_by_us_3 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(4));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))
    || !(global_mask_3 & (1 << m->letter[3]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(4));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   allowed_by_us_3 |= 1 << m->letter[3];
   m = NEXT_MOVE(m, MOVE_SIZE(4));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
 allowed_by_us[3] = allowed_by_us_3;
}

filter_for_length_5
static void
filter_for_length_5(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 const letter_mask_t global_mask_3 = 
      letters_allowed[p->where[3]];
 letter_mask_t allowed_by_us_3 = 0;
 const letter_mask_t global_mask_4 = 
      letters_allowed[p->where[4]];
 letter_mask_t allowed_by_us_4 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(5));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))
    || !(global_mask_3 & (1 << m->letter[3]))
    || !(global_mask_4 & (1 << m->letter[4]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   void *copy2 = ((void **)last)[2];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   ((void **)m)[2] = copy2;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(5));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   allowed_by_us_3 |= 1 << m->letter[3];
   allowed_by_us_4 |= 1 << m->letter[4];
   m = NEXT_MOVE(m, MOVE_SIZE(5));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
 allowed_by_us[3] = allowed_by_us_3;
 allowed_by_us[4] = allowed_by_us_4;
}

filter_for_length_6
static void
filter_for_length_6(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 const letter_mask_t global_mask_3 = 
      letters_allowed[p->where[3]];
 letter_mask_t allowed_by_us_3 = 0;
 const letter_mask_t global_mask_4 = 
      letters_allowed[p->where[4]];
 letter_mask_t allowed_by_us_4 = 0;
 const letter_mask_t global_mask_5 = 
      letters_allowed[p->where[5]];
 letter_mask_t allowed_by_us_5 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(6));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))
    || !(global_mask_3 & (1 << m->letter[3]))
    || !(global_mask_4 & (1 << m->letter[4]))
    || !(global_mask_5 & (1 << m->letter[5]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   void *copy2 = ((void **)last)[2];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   ((void **)m)[2] = copy2;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(6));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   allowed_by_us_3 |= 1 << m->letter[3];
   allowed_by_us_4 |= 1 << m->letter[4];
   allowed_by_us_5 |= 1 << m->letter[5];
   m = NEXT_MOVE(m, MOVE_SIZE(6));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
 allowed_by_us[3] = allowed_by_us_3;
 allowed_by_us[4] = allowed_by_us_4;
 allowed_by_us[5] = allowed_by_us_5;
}

filter_for_length_7
static void
filter_for_length_7(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 const letter_mask_t global_mask_3 = 
      letters_allowed[p->where[3]];
 letter_mask_t allowed_by_us_3 = 0;
 const letter_mask_t global_mask_4 = 
      letters_allowed[p->where[4]];
 letter_mask_t allowed_by_us_4 = 0;
 const letter_mask_t global_mask_5 = 
      letters_allowed[p->where[5]];
 letter_mask_t allowed_by_us_5 = 0;
 const letter_mask_t global_mask_6 = 
      letters_allowed[p->where[6]];
 letter_mask_t allowed_by_us_6 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(7));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))
    || !(global_mask_3 & (1 << m->letter[3]))
    || !(global_mask_4 & (1 << m->letter[4]))
    || !(global_mask_5 & (1 << m->letter[5]))
    || !(global_mask_6 & (1 << m->letter[6]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   void *copy2 = ((void **)last)[2];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   ((void **)m)[2] = copy2;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(7));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   allowed_by_us_3 |= 1 << m->letter[3];
   allowed_by_us_4 |= 1 << m->letter[4];
   allowed_by_us_5 |= 1 << m->letter[5];
   allowed_by_us_6 |= 1 << m->letter[6];
   m = NEXT_MOVE(m, MOVE_SIZE(7));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
 allowed_by_us[3] = allowed_by_us_3;
 allowed_by_us[4] = allowed_by_us_4;
 allowed_by_us[5] = allowed_by_us_5;
 allowed_by_us[6] = allowed_by_us_6;
}

filter_for_length_8
static void
filter_for_length_8(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 const letter_mask_t global_mask_3 = 
      letters_allowed[p->where[3]];
 letter_mask_t allowed_by_us_3 = 0;
 const letter_mask_t global_mask_4 = 
      letters_allowed[p->where[4]];
 letter_mask_t allowed_by_us_4 = 0;
 const letter_mask_t global_mask_5 = 
      letters_allowed[p->where[5]];
 letter_mask_t allowed_by_us_5 = 0;
 const letter_mask_t global_mask_6 = 
      letters_allowed[p->where[6]];
 letter_mask_t allowed_by_us_6 = 0;
 const letter_mask_t global_mask_7 = 
      letters_allowed[p->where[7]];
 letter_mask_t allowed_by_us_7 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(8));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))
    || !(global_mask_3 & (1 << m->letter[3]))
    || !(global_mask_4 & (1 << m->letter[4]))
    || !(global_mask_5 & (1 << m->letter[5]))
    || !(global_mask_6 & (1 << m->letter[6]))
    || !(global_mask_7 & (1 << m->letter[7]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   void *copy2 = ((void **)last)[2];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   ((void **)m)[2] = copy2;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(8));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   allowed_by_us_3 |= 1 << m->letter[3];
   allowed_by_us_4 |= 1 << m->letter[4];
   allowed_by_us_5 |= 1 << m->letter[5];
   allowed_by_us_6 |= 1 << m->letter[6];
   allowed_by_us_7 |= 1 << m->letter[7];
   m = NEXT_MOVE(m, MOVE_SIZE(8));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
 allowed_by_us[3] = allowed_by_us_3;
 allowed_by_us[4] = allowed_by_us_4;
 allowed_by_us[5] = allowed_by_us_5;
 allowed_by_us[6] = allowed_by_us_6;
 allowed_by_us[7] = allowed_by_us_7;
}

filter_for_length_9
static void
filter_for_length_9(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 const letter_mask_t global_mask_3 = 
      letters_allowed[p->where[3]];
 letter_mask_t allowed_by_us_3 = 0;
 const letter_mask_t global_mask_4 = 
      letters_allowed[p->where[4]];
 letter_mask_t allowed_by_us_4 = 0;
 const letter_mask_t global_mask_5 = 
      letters_allowed[p->where[5]];
 letter_mask_t allowed_by_us_5 = 0;
 const letter_mask_t global_mask_6 = 
      letters_allowed[p->where[6]];
 letter_mask_t allowed_by_us_6 = 0;
 const letter_mask_t global_mask_7 = 
      letters_allowed[p->where[7]];
 letter_mask_t allowed_by_us_7 = 0;
 const letter_mask_t global_mask_8 = 
      letters_allowed[p->where[8]];
 letter_mask_t allowed_by_us_8 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(9));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))
    || !(global_mask_3 & (1 << m->letter[3]))
    || !(global_mask_4 & (1 << m->letter[4]))
    || !(global_mask_5 & (1 << m->letter[5]))
    || !(global_mask_6 & (1 << m->letter[6]))
    || !(global_mask_7 & (1 << m->letter[7]))
    || !(global_mask_8 & (1 << m->letter[8]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   void *copy2 = ((void **)last)[2];
   void *copy3 = ((void **)last)[3];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   ((void **)m)[2] = copy2;
   ((void **)m)[3] = copy3;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(9));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   allowed_by_us_3 |= 1 << m->letter[3];
   allowed_by_us_4 |= 1 << m->letter[4];
   allowed_by_us_5 |= 1 << m->letter[5];
   allowed_by_us_6 |= 1 << m->letter[6];
   allowed_by_us_7 |= 1 << m->letter[7];
   allowed_by_us_8 |= 1 << m->letter[8];
   m = NEXT_MOVE(m, MOVE_SIZE(9));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
 allowed_by_us[3] = allowed_by_us_3;
 allowed_by_us[4] = allowed_by_us_4;
 allowed_by_us[5] = allowed_by_us_5;
 allowed_by_us[6] = allowed_by_us_6;
 allowed_by_us[7] = allowed_by_us_7;
 allowed_by_us[8] = allowed_by_us_8;
}

filter_for_length_10
static void
filter_for_length_10(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 const letter_mask_t global_mask_3 = 
      letters_allowed[p->where[3]];
 letter_mask_t allowed_by_us_3 = 0;
 const letter_mask_t global_mask_4 = 
      letters_allowed[p->where[4]];
 letter_mask_t allowed_by_us_4 = 0;
 const letter_mask_t global_mask_5 = 
      letters_allowed[p->where[5]];
 letter_mask_t allowed_by_us_5 = 0;
 const letter_mask_t global_mask_6 = 
      letters_allowed[p->where[6]];
 letter_mask_t allowed_by_us_6 = 0;
 const letter_mask_t global_mask_7 = 
      letters_allowed[p->where[7]];
 letter_mask_t allowed_by_us_7 = 0;
 const letter_mask_t global_mask_8 = 
      letters_allowed[p->where[8]];
 letter_mask_t allowed_by_us_8 = 0;
 const letter_mask_t global_mask_9 = 
      letters_allowed[p->where[9]];
 letter_mask_t allowed_by_us_9 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(10));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))
    || !(global_mask_3 & (1 << m->letter[3]))
    || !(global_mask_4 & (1 << m->letter[4]))
    || !(global_mask_5 & (1 << m->letter[5]))
    || !(global_mask_6 & (1 << m->letter[6]))
    || !(global_mask_7 & (1 << m->letter[7]))
    || !(global_mask_8 & (1 << m->letter[8]))
    || !(global_mask_9 & (1 << m->letter[9]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   void *copy2 = ((void **)last)[2];
   void *copy3 = ((void **)last)[3];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   ((void **)m)[2] = copy2;
   ((void **)m)[3] = copy3;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(10));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   allowed_by_us_3 |= 1 << m->letter[3];
   allowed_by_us_4 |= 1 << m->letter[4];
   allowed_by_us_5 |= 1 << m->letter[5];
   allowed_by_us_6 |= 1 << m->letter[6];
   allowed_by_us_7 |= 1 << m->letter[7];
   allowed_by_us_8 |= 1 << m->letter[8];
   allowed_by_us_9 |= 1 << m->letter[9];
   m = NEXT_MOVE(m, MOVE_SIZE(10));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
 allowed_by_us[3] = allowed_by_us_3;
 allowed_by_us[4] = allowed_by_us_4;
 allowed_by_us[5] = allowed_by_us_5;
 allowed_by_us[6] = allowed_by_us_6;
 allowed_by_us[7] = allowed_by_us_7;
 allowed_by_us[8] = allowed_by_us_8;
 allowed_by_us[9] = allowed_by_us_9;
}


filter_for_length_11
static void
filter_for_length_11(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 const letter_mask_t global_mask_3 = 
      letters_allowed[p->where[3]];
 letter_mask_t allowed_by_us_3 = 0;
 const letter_mask_t global_mask_4 = 
      letters_allowed[p->where[4]];
 letter_mask_t allowed_by_us_4 = 0;
 const letter_mask_t global_mask_5 = 
      letters_allowed[p->where[5]];
 letter_mask_t allowed_by_us_5 = 0;
 const letter_mask_t global_mask_6 = 
      letters_allowed[p->where[6]];
 letter_mask_t allowed_by_us_6 = 0;
 const letter_mask_t global_mask_7 = 
      letters_allowed[p->where[7]];
 letter_mask_t allowed_by_us_7 = 0;
 const letter_mask_t global_mask_8 = 
      letters_allowed[p->where[8]];
 letter_mask_t allowed_by_us_8 = 0;
 const letter_mask_t global_mask_9 = 
      letters_allowed[p->where[9]];
 letter_mask_t allowed_by_us_9 = 0;
 const letter_mask_t global_mask_10 = 
      letters_allowed[p->where[10]];
 letter_mask_t allowed_by_us_10 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(11));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))
    || !(global_mask_3 & (1 << m->letter[3]))
    || !(global_mask_4 & (1 << m->letter[4]))
    || !(global_mask_5 & (1 << m->letter[5]))
    || !(global_mask_6 & (1 << m->letter[6]))
    || !(global_mask_7 & (1 << m->letter[7]))
    || !(global_mask_8 & (1 << m->letter[8]))
    || !(global_mask_9 & (1 << m->letter[9]))
    || !(global_mask_10 & (1 << m->letter[10]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   void *copy2 = ((void **)last)[2];
   void *copy3 = ((void **)last)[3];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   ((void **)m)[2] = copy2;
   ((void **)m)[3] = copy3;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(11));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   allowed_by_us_3 |= 1 << m->letter[3];
   allowed_by_us_4 |= 1 << m->letter[4];
   allowed_by_us_5 |= 1 << m->letter[5];
   allowed_by_us_6 |= 1 << m->letter[6];
   allowed_by_us_7 |= 1 << m->letter[7];
   allowed_by_us_8 |= 1 << m->letter[8];
   allowed_by_us_9 |= 1 << m->letter[9];
   allowed_by_us_10 |= 1 << m->letter[10];
   m = NEXT_MOVE(m, MOVE_SIZE(11));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
 allowed_by_us[3] = allowed_by_us_3;
 allowed_by_us[4] = allowed_by_us_4;
 allowed_by_us[5] = allowed_by_us_5;
 allowed_by_us[6] = allowed_by_us_6;
 allowed_by_us[7] = allowed_by_us_7;
 allowed_by_us[8] = allowed_by_us_8;
 allowed_by_us[9] = allowed_by_us_9;
 allowed_by_us[10] = allowed_by_us_10;
}

filter_for_length_12
static void
filter_for_length_12(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 const letter_mask_t global_mask_3 = 
      letters_allowed[p->where[3]];
 letter_mask_t allowed_by_us_3 = 0;
 const letter_mask_t global_mask_4 = 
      letters_allowed[p->where[4]];
 letter_mask_t allowed_by_us_4 = 0;
 const letter_mask_t global_mask_5 = 
      letters_allowed[p->where[5]];
 letter_mask_t allowed_by_us_5 = 0;
 const letter_mask_t global_mask_6 = 
      letters_allowed[p->where[6]];
 letter_mask_t allowed_by_us_6 = 0;
 const letter_mask_t global_mask_7 = 
      letters_allowed[p->where[7]];
 letter_mask_t allowed_by_us_7 = 0;
 const letter_mask_t global_mask_8 = 
      letters_allowed[p->where[8]];
 letter_mask_t allowed_by_us_8 = 0;
 const letter_mask_t global_mask_9 = 
      letters_allowed[p->where[9]];
 letter_mask_t allowed_by_us_9 = 0;
 const letter_mask_t global_mask_10 = 
      letters_allowed[p->where[10]];
 letter_mask_t allowed_by_us_10 = 0;
 const letter_mask_t global_mask_11 = 
      letters_allowed[p->where[11]];
 letter_mask_t allowed_by_us_11 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(12));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))
    || !(global_mask_3 & (1 << m->letter[3]))
    || !(global_mask_4 & (1 << m->letter[4]))
    || !(global_mask_5 & (1 << m->letter[5]))
    || !(global_mask_6 & (1 << m->letter[6]))
    || !(global_mask_7 & (1 << m->letter[7]))
    || !(global_mask_8 & (1 << m->letter[8]))
    || !(global_mask_9 & (1 << m->letter[9]))
    || !(global_mask_10 & (1 << m->letter[10]))
    || !(global_mask_11 & (1 << m->letter[11]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   void *copy2 = ((void **)last)[2];
   void *copy3 = ((void **)last)[3];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   ((void **)m)[2] = copy2;
   ((void **)m)[3] = copy3;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(12));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   allowed_by_us_3 |= 1 << m->letter[3];
   allowed_by_us_4 |= 1 << m->letter[4];
   allowed_by_us_5 |= 1 << m->letter[5];
   allowed_by_us_6 |= 1 << m->letter[6];
   allowed_by_us_7 |= 1 << m->letter[7];
   allowed_by_us_8 |= 1 << m->letter[8];
   allowed_by_us_9 |= 1 << m->letter[9];
   allowed_by_us_10 |= 1 << m->letter[10];
   allowed_by_us_11 |= 1 << m->letter[11];
   m = NEXT_MOVE(m, MOVE_SIZE(12));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
 allowed_by_us[3] = allowed_by_us_3;
 allowed_by_us[4] = allowed_by_us_4;
 allowed_by_us[5] = allowed_by_us_5;
 allowed_by_us[6] = allowed_by_us_6;
 allowed_by_us[7] = allowed_by_us_7;
 allowed_by_us[8] = allowed_by_us_8;
 allowed_by_us[9] = allowed_by_us_9;
 allowed_by_us[10] = allowed_by_us_10;
 allowed_by_us[11] = allowed_by_us_11;
}

filter_for_length_13
static void
filter_for_length_13(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 const letter_mask_t global_mask_3 = 
      letters_allowed[p->where[3]];
 letter_mask_t allowed_by_us_3 = 0;
 const letter_mask_t global_mask_4 = 
      letters_allowed[p->where[4]];
 letter_mask_t allowed_by_us_4 = 0;
 const letter_mask_t global_mask_5 = 
      letters_allowed[p->where[5]];
 letter_mask_t allowed_by_us_5 = 0;
 const letter_mask_t global_mask_6 = 
      letters_allowed[p->where[6]];
 letter_mask_t allowed_by_us_6 = 0;
 const letter_mask_t global_mask_7 = 
      letters_allowed[p->where[7]];
 letter_mask_t allowed_by_us_7 = 0;
 const letter_mask_t global_mask_8 = 
      letters_allowed[p->where[8]];
 letter_mask_t allowed_by_us_8 = 0;
 const letter_mask_t global_mask_9 = 
      letters_allowed[p->where[9]];
 letter_mask_t allowed_by_us_9 = 0;
 const letter_mask_t global_mask_10 = 
      letters_allowed[p->where[10]];
 letter_mask_t allowed_by_us_10 = 0;
 const letter_mask_t global_mask_11 = 
      letters_allowed[p->where[11]];
 letter_mask_t allowed_by_us_11 = 0;
 const letter_mask_t global_mask_12 = 
      letters_allowed[p->where[12]];
 letter_mask_t allowed_by_us_12 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(13));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))
    || !(global_mask_3 & (1 << m->letter[3]))
    || !(global_mask_4 & (1 << m->letter[4]))
    || !(global_mask_5 & (1 << m->letter[5]))
    || !(global_mask_6 & (1 << m->letter[6]))
    || !(global_mask_7 & (1 << m->letter[7]))
    || !(global_mask_8 & (1 << m->letter[8]))
    || !(global_mask_9 & (1 << m->letter[9]))
    || !(global_mask_10 & (1 << m->letter[10]))
    || !(global_mask_11 & (1 << m->letter[11]))
    || !(global_mask_12 & (1 << m->letter[12]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   void *copy2 = ((void **)last)[2];
   void *copy3 = ((void **)last)[3];
   void *copy4 = ((void **)last)[4];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   ((void **)m)[2] = copy2;
   ((void **)m)[3] = copy3;
   ((void **)m)[4] = copy4;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(13));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   allowed_by_us_3 |= 1 << m->letter[3];
   allowed_by_us_4 |= 1 << m->letter[4];
   allowed_by_us_5 |= 1 << m->letter[5];
   allowed_by_us_6 |= 1 << m->letter[6];
   allowed_by_us_7 |= 1 << m->letter[7];
   allowed_by_us_8 |= 1 << m->letter[8];
   allowed_by_us_9 |= 1 << m->letter[9];
   allowed_by_us_10 |= 1 << m->letter[10];
   allowed_by_us_11 |= 1 << m->letter[11];
   allowed_by_us_12 |= 1 << m->letter[12];
   m = NEXT_MOVE(m, MOVE_SIZE(13));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
 allowed_by_us[3] = allowed_by_us_3;
 allowed_by_us[4] = allowed_by_us_4;
 allowed_by_us[5] = allowed_by_us_5;
 allowed_by_us[6] = allowed_by_us_6;
 allowed_by_us[7] = allowed_by_us_7;
 allowed_by_us[8] = allowed_by_us_8;
 allowed_by_us[9] = allowed_by_us_9;
 allowed_by_us[10] = allowed_by_us_10;
 allowed_by_us[11] = allowed_by_us_11;
 allowed_by_us[12] = allowed_by_us_12;
}

filter_for_length_14
static void
filter_for_length_14(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 const letter_mask_t global_mask_3 = 
      letters_allowed[p->where[3]];
 letter_mask_t allowed_by_us_3 = 0;
 const letter_mask_t global_mask_4 = 
      letters_allowed[p->where[4]];
 letter_mask_t allowed_by_us_4 = 0;
 const letter_mask_t global_mask_5 = 
      letters_allowed[p->where[5]];
 letter_mask_t allowed_by_us_5 = 0;
 const letter_mask_t global_mask_6 = 
      letters_allowed[p->where[6]];
 letter_mask_t allowed_by_us_6 = 0;
 const letter_mask_t global_mask_7 = 
      letters_allowed[p->where[7]];
 letter_mask_t allowed_by_us_7 = 0;
 const letter_mask_t global_mask_8 = 
      letters_allowed[p->where[8]];
 letter_mask_t allowed_by_us_8 = 0;
 const letter_mask_t global_mask_9 = 
      letters_allowed[p->where[9]];
 letter_mask_t allowed_by_us_9 = 0;
 const letter_mask_t global_mask_10 = 
      letters_allowed[p->where[10]];
 letter_mask_t allowed_by_us_10 = 0;
 const letter_mask_t global_mask_11 = 
      letters_allowed[p->where[11]];
 letter_mask_t allowed_by_us_11 = 0;
 const letter_mask_t global_mask_12 = 
      letters_allowed[p->where[12]];
 letter_mask_t allowed_by_us_12 = 0;
 const letter_mask_t global_mask_13 = 
      letters_allowed[p->where[13]];
 letter_mask_t allowed_by_us_13 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(14));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))
    || !(global_mask_3 & (1 << m->letter[3]))
    || !(global_mask_4 & (1 << m->letter[4]))
    || !(global_mask_5 & (1 << m->letter[5]))
    || !(global_mask_6 & (1 << m->letter[6]))
    || !(global_mask_7 & (1 << m->letter[7]))
    || !(global_mask_8 & (1 << m->letter[8]))
    || !(global_mask_9 & (1 << m->letter[9]))
    || !(global_mask_10 & (1 << m->letter[10]))
    || !(global_mask_11 & (1 << m->letter[11]))
    || !(global_mask_12 & (1 << m->letter[12]))
    || !(global_mask_13 & (1 << m->letter[13]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   void *copy2 = ((void **)last)[2];
   void *copy3 = ((void **)last)[3];
   void *copy4 = ((void **)last)[4];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   ((void **)m)[2] = copy2;
   ((void **)m)[3] = copy3;
   ((void **)m)[4] = copy4;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(14));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   allowed_by_us_3 |= 1 << m->letter[3];
   allowed_by_us_4 |= 1 << m->letter[4];
   allowed_by_us_5 |= 1 << m->letter[5];
   allowed_by_us_6 |= 1 << m->letter[6];
   allowed_by_us_7 |= 1 << m->letter[7];
   allowed_by_us_8 |= 1 << m->letter[8];
   allowed_by_us_9 |= 1 << m->letter[9];
   allowed_by_us_10 |= 1 << m->letter[10];
   allowed_by_us_11 |= 1 << m->letter[11];
   allowed_by_us_12 |= 1 << m->letter[12];
   allowed_by_us_13 |= 1 << m->letter[13];
   m = NEXT_MOVE(m, MOVE_SIZE(14));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
 allowed_by_us[3] = allowed_by_us_3;
 allowed_by_us[4] = allowed_by_us_4;
 allowed_by_us[5] = allowed_by_us_5;
 allowed_by_us[6] = allowed_by_us_6;
 allowed_by_us[7] = allowed_by_us_7;
 allowed_by_us[8] = allowed_by_us_8;
 allowed_by_us[9] = allowed_by_us_9;
 allowed_by_us[10] = allowed_by_us_10;
 allowed_by_us[11] = allowed_by_us_11;
 allowed_by_us[12] = allowed_by_us_12;
 allowed_by_us[13] = allowed_by_us_13;
}

filter_for_length_15
static void
filter_for_length_15(placement_t *p, 
      letter_mask_t *letters_allowed,
      letter_mask_t *allowed_by_us)
{
 move_t *m, *last;
 const letter_mask_t global_mask_0 = 
      letters_allowed[p->where[0]];
 letter_mask_t allowed_by_us_0 = 0;
 const letter_mask_t global_mask_1 = 
      letters_allowed[p->where[1]];
 letter_mask_t allowed_by_us_1 = 0;
 const letter_mask_t global_mask_2 = 
      letters_allowed[p->where[2]];
 letter_mask_t allowed_by_us_2 = 0;
 const letter_mask_t global_mask_3 = 
      letters_allowed[p->where[3]];
 letter_mask_t allowed_by_us_3 = 0;
 const letter_mask_t global_mask_4 = 
      letters_allowed[p->where[4]];
 letter_mask_t allowed_by_us_4 = 0;
 const letter_mask_t global_mask_5 = 
      letters_allowed[p->where[5]];
 letter_mask_t allowed_by_us_5 = 0;
 const letter_mask_t global_mask_6 = 
      letters_allowed[p->where[6]];
 letter_mask_t allowed_by_us_6 = 0;
 const letter_mask_t global_mask_7 = 
      letters_allowed[p->where[7]];
 letter_mask_t allowed_by_us_7 = 0;
 const letter_mask_t global_mask_8 = 
      letters_allowed[p->where[8]];
 letter_mask_t allowed_by_us_8 = 0;
 const letter_mask_t global_mask_9 = 
      letters_allowed[p->where[9]];
 letter_mask_t allowed_by_us_9 = 0;
 const letter_mask_t global_mask_10 = 
      letters_allowed[p->where[10]];
 letter_mask_t allowed_by_us_10 = 0;
 const letter_mask_t global_mask_11 = 
      letters_allowed[p->where[11]];
 letter_mask_t allowed_by_us_11 = 0;
 const letter_mask_t global_mask_12 = 
      letters_allowed[p->where[12]];
 letter_mask_t allowed_by_us_12 = 0;
 const letter_mask_t global_mask_13 = 
      letters_allowed[p->where[13]];
 letter_mask_t allowed_by_us_13 = 0;
 const letter_mask_t global_mask_14 = 
      letters_allowed[p->where[14]];
 letter_mask_t allowed_by_us_14 = 0;
 last = (move_t *) ((char *) p->move + 
      (p->num_moves - 1) * MOVE_SIZE(15));
 for (m = p->move; m->original_word != NULL; )
 {
  if (  !(global_mask_0 & (1 << m->letter[0]))
    || !(global_mask_1 & (1 << m->letter[1]))
    || !(global_mask_2 & (1 << m->letter[2]))
    || !(global_mask_3 & (1 << m->letter[3]))
    || !(global_mask_4 & (1 << m->letter[4]))
    || !(global_mask_5 & (1 << m->letter[5]))
    || !(global_mask_6 & (1 << m->letter[6]))
    || !(global_mask_7 & (1 << m->letter[7]))
    || !(global_mask_8 & (1 << m->letter[8]))
    || !(global_mask_9 & (1 << m->letter[9]))
    || !(global_mask_10 & (1 << m->letter[10]))
    || !(global_mask_11 & (1 << m->letter[11]))
    || !(global_mask_12 & (1 << m->letter[12]))
    || !(global_mask_13 & (1 << m->letter[13]))
    || !(global_mask_14 & (1 << m->letter[14]))) {
   void *copy0 = ((void **)last)[0];
   void *copy1 = ((void **)last)[1];
   void *copy2 = ((void **)last)[2];
   void *copy3 = ((void **)last)[3];
   void *copy4 = ((void **)last)[4];
   ((void **)m)[0] = copy0;
   ((void **)m)[1] = copy1;
   ((void **)m)[2] = copy2;
   ((void **)m)[3] = copy3;
   ((void **)m)[4] = copy4;
   last->original_word = NULL;
   --p->num_moves;
   last = NEXT_MOVE(last, -MOVE_SIZE(15));
  } else {
   allowed_by_us_0 |= 1 << m->letter[0];
   allowed_by_us_1 |= 1 << m->letter[1];
   allowed_by_us_2 |= 1 << m->letter[2];
   allowed_by_us_3 |= 1 << m->letter[3];
   allowed_by_us_4 |= 1 << m->letter[4];
   allowed_by_us_5 |= 1 << m->letter[5];
   allowed_by_us_6 |= 1 << m->letter[6];
   allowed_by_us_7 |= 1 << m->letter[7];
   allowed_by_us_8 |= 1 << m->letter[8];
   allowed_by_us_9 |= 1 << m->letter[9];
   allowed_by_us_10 |= 1 << m->letter[10];
   allowed_by_us_11 |= 1 << m->letter[11];
   allowed_by_us_12 |= 1 << m->letter[12];
   allowed_by_us_13 |= 1 << m->letter[13];
   allowed_by_us_14 |= 1 << m->letter[14];
   m = NEXT_MOVE(m, MOVE_SIZE(15));
  }
 }
 allowed_by_us[0] = allowed_by_us_0;
 allowed_by_us[1] = allowed_by_us_1;
 allowed_by_us[2] = allowed_by_us_2;
 allowed_by_us[3] = allowed_by_us_3;
 allowed_by_us[4] = allowed_by_us_4;
 allowed_by_us[5] = allowed_by_us_5;
 allowed_by_us[6] = allowed_by_us_6;
 allowed_by_us[7] = allowed_by_us_7;
 allowed_by_us[8] = allowed_by_us_8;
 allowed_by_us[9] = allowed_by_us_9;
 allowed_by_us[10] = allowed_by_us_10;
 allowed_by_us[11] = allowed_by_us_11;
 allowed_by_us[12] = allowed_by_us_12;
 allowed_by_us[13] = allowed_by_us_13;
 allowed_by_us[14] = allowed_by_us_14;
}

typedef filter_func_t
typedef void (*filter_func_t)(placement_t *, 
      letter_mask_t *, letter_mask_t *);
static const filter_func_t filter_func[16] = { 0,
 filter_for_length_1,
 filter_for_length_2,
 filter_for_length_3,
 filter_for_length_4,
 filter_for_length_5,
 filter_for_length_6,
 filter_for_length_7,
 filter_for_length_8,
 filter_for_length_9,
 filter_for_length_10,
 filter_for_length_11,
 filter_for_length_12,
 filter_for_length_13,
 filter_for_length_14,
 filter_for_length_15,
};


/* Assorted constants, in an enum so debugger knows about them. */
enum {
 /* Bit mask indicating all letters. */
 ALL_LETTERS = (1 << 26) - 1,

 /* Bit mask indicating "this square is not an intersection point
  * so ignore it". */
 NOT_INTERSECTION_POINT = 0x7FFFFFFF,

 /* Empty square in the puzzle. */
 EMPTY_SQUARE = 0
};

static unsigned long current_mark = 1;

#define set_placement_mark(p)   ((p)->mark = current_mark)
#define clear_placement_mark(p)  ((p)->mark = current_mark - 1)
#define placement_is_marked(p)  ((p)->mark == current_mark)
#define clear_all_placement_marks() (++current_mark)


count_num_placements
/* Returns the total number of placements in the puzzle. */
static long
count_num_placements(Puzzle puzzle, long puzzle_size)
{
 long x, y, num_placements = 0;

 /* Horizontal placements. */
 for (y = 0; y < puzzle_size; y++)
  for (x = 0; x < puzzle_size - 1; x++)
   if (puzzle[x][y] == EMPTY_SQUARE && 
              puzzle[x + 1][y] == EMPTY_SQUARE)
    {
     ++num_placements;
     for (x++; x < puzzle_size && 
                        puzzle[x][y] == EMPTY_SQUARE; x++)
      ;
    }

 /* Vertical placements. */
 for (x = 0; x < puzzle_size; x++)
  for (y = 0; y < puzzle_size - 1; y++)
   if (puzzle[x][y] == EMPTY_SQUARE && 
              puzzle[x][y + 1] == EMPTY_SQUARE)
    {
     ++num_placements;
     for (y++; y < puzzle_size && 
                        puzzle[x][y] == EMPTY_SQUARE; y++)
      ;
    }

 return num_placements;
}

identify_placements
static placement_t *
identify_placements(Puzzle puzzle, long puzzle_size, 
      long *num_placements_ptr,
      placement_t *square_to_placement[kMaxSize][kMaxSize][2],
      char interesting_length[kMaxSize + 1])
{
 /* Create an empty map from squares to the placements that intersect. */
 long x, y, num_placements;
 placement_t *p, *placement;

 num_placements = count_num_placements(puzzle, puzzle_size);
 p = placement = (placement_t *) calloc(num_placements, 
                                        sizeof p[0]);
 /* Find all horizontal placements. */
 for (y = 0; y < puzzle_size; y++)
  for (x = 0; x < puzzle_size - 1; x++)
   if (puzzle[x][y] == EMPTY_SQUARE && 
              puzzle[x + 1][y] == EMPTY_SQUARE)
    {
     const long start_x = x;
     p->start_x = x;
     p->start_y = y;
     p->dx = 1;
     p->dy = 0;
     for (; x < puzzle_size && 
                        puzzle[x][y] == EMPTY_SQUARE; x++)
      square_to_placement[x][y][0] = p;
     ++p;
     interesting_length[x - start_x] = 1;
    }

 /* Find all vertical placements. */
 for (x = 0; x < puzzle_size; x++)
  for (y = 0; y < puzzle_size - 1; y++)
   if (puzzle[x][y] == EMPTY_SQUARE && 
              puzzle[x][y + 1] == EMPTY_SQUARE)
    {
     const long start_y = y;
     p->start_x = x;
     p->start_y = y;
     p->dx = 0;
     p->dy = 1;
          for (; y < puzzle_size && puzzle[x][y] ==
               EMPTY_SQUARE; 
                        y++)
      square_to_placement[x][y][1] = p;
     ++p;
     interesting_length[y - start_y] = 1;
    }
 /* assert(p == &placement[num_placements]); */

 *num_placements_ptr = num_placements;
 return placement;
}

intersect_placement_with_global_mask
/* Takes the list of moves allowed by a placement and uses that set
 * to tighten what's globally allowed for the squares it intersects.
 * "Marks" any placements whose word lists are changed as a result. */
static void
intersect_placement_with_global_mask(const placement_t *p,
      letter_mask_t *global_mask)
{
 const unsigned long move_size = p->move_size;
 int i;

 for (i = p->letters_per_move - 1; i >= 0; i--)
  {
   move_t *m;
   letter_mask_t mask = 0, g;

   /* Figure out the union of all letters valid for each square. */
   for (m = p->move; m->original_word != NULL; 
                m = NEXT_MOVE(m, move_size))
    mask |= 1 << m->letter[i];

   g = global_mask[p->where[i]];
   if ((g & mask) != g)
    {
     /* Mark this neighbor as being in need of further refinement,
      * since we have just disallowed some of his moves. */
     set_placement_mark(p->neighbor[i]);

     /* Note the new, tighter restriction on this square. */
     global_mask[p->where[i]] = g & mask;
    }
  }
}

create_ascii_to_letter
/* Creates an array mapping ASCII letter values to numbers 0-25. */
static void
create_ascii_to_letter(unsigned char ascii_to_letter[256])
{
 int let;
 memset(ascii_to_letter, 0, 256);
 for (let = 0; let < 26; let++)
  ascii_to_letter['a' + let] = 
          ascii_to_letter['A' + let] = let;
}

partition_words_by_length
static void
partition_words_by_length(char *dictionary[], long dict_size,
      const char interesting_length[kMaxSize + 1],
      const char **words_of_length[kMaxSize + 1],
      long num_words_of_length[kMaxSize + 1],
      void **mem_to_free_on_cleanup)
{
 long num_words_left[kMaxSize + 1], num_useful_words, 
          i, j, w, k;
 const char **r;
 void *raw_words_mem;
 
 /* Figure out how many words there are of each length. */
 for (i = 0; i <= kMaxSize; i++)
  num_words_of_length[i] = 0;
 num_useful_words = 0;
 for (w = 0; w < dict_size; w++)
  {
   size_t len = strlen(dictionary[w]);
   if (len <= kMaxSize && interesting_length[len])
    {
     ++num_words_of_length[len];
     ++num_useful_words;
    }
  }

 /* Allocate room for a pointer vector for each word length.
  * We'll just put all of the pointer vectors together into
  * one big block of memory, separated by a NULL pointer. */
 raw_words_mem = 
      malloc((num_useful_words + kMaxSize + 1) * sizeof r[0]);
 r = (const char **) raw_words_mem;
 for (k = 0; k <= kMaxSize; k++)
  {
   const long num_words_of_this_length = 
            num_words_of_length[k];
   words_of_length[k] = r;
   r[num_words_of_this_length] = NULL;
   r += num_words_of_this_length + 1;
           /* leave room for terminating NULL */
  }

 /* Note the words of each length. */
 memcpy(num_words_left, num_words_of_length, 
        sizeof num_words_left);
 for (j = 0; j < dict_size; j++)
  {
   size_t len = strlen(dictionary[j]);
   if (len <= kMaxSize && interesting_length[len])
    words_of_length[len][--num_words_left[len]] = 
                  dictionary[j];
  }

 /* Report the block of memory to free when done. */
 *mem_to_free_on_cleanup = raw_words_mem;
}

tighten_constraints
static int
tighten_constraints(placement_t *placement, long num_placements,
      letter_mask_t *letters_allowed, int do_acyclic)
{
 placement_t **orig_stack, **stack, *p;
 long n;

 stack = orig_stack = malloc((num_placements + 1) * 
        sizeof orig_stack[0]);
 *stack++ = NULL;

 /* On entry, we've marked every placement that needs to be explored
  * further, so push those on the stack. */
 for (n = num_placements - 1; n >= 0; n--)
  {
   placement_t *t = &placement[n];
   if (placement_is_marked(t))
    *stack++ = t;
  }

 while ((p = *--stack) != NULL)
  {
   letter_mask_t allowed_by_us[kMaxSize];
   long i;
   
   if (p->done || 
              (!do_acyclic && p->in_cycle == NOT_IN_CYCLE))
    continue;

   if (p->letters_per_move < 
                  sizeof filter_func / sizeof filter_func[0])
    (*filter_func[p->letters_per_move])(p, 
                      letters_allowed, allowed_by_us);
   else
    {
     letter_mask_t global_mask[kMaxSize];
     long i, move_size;
     move_t *m, *last;
    
     move_size = p->move_size;
     memset(allowed_by_us, 0, sizeof allowed_by_us);
    
     /* For speed, stash globally allowed letters in linear array. */
     for (i = 0; i < p->letters_per_move; i++)
      global_mask[i] = letters_allowed[p->where[i]];
    
     /* Loop through all words here, discarding illegal words and
      * accruing a new union mask. */
     last = (move_t *) ((char *) p->move + 
                  (p->num_moves - 1) * p->move_size);
     for (m = p->move; m->original_word != NULL; )
      {
       long j;
     
       /* See if word is legal. */
       for (j = p->letters_per_move - 1; j >= 0; j--)
        if (!(global_mask[j] & (1 << m->letter[j])))
         break;
       
       if (j < 0)
        {
         /* It's legal. Note the possible letters and move on. */
        long k;
        for (k = p->letters_per_move - 1; k >= 0; k--)
          allowed_by_us[k] |= 1 << m->letter[k];
         m = NEXT_MOVE(m, move_size);
        }
       else
        {
         /* It's illegal. Delete this move by replacing it with
          * the last move in the list. Profiling shows this is
          * a hotspot, so inline a memcpy using our knowledge
          * about what moves look like. */
         char *from, *to;
         long ctr;
         from = (char *) last;
         to = (char *) m;
         for (ctr = move_size; 
                          (ctr -= sizeof(void *)) >= 0; )
          *(void **)(to + ctr) = 
                                *(void **)(from + ctr);
         
         last->original_word = NULL;
         --p->num_moves;
         last = NEXT_MOVE(last, -move_size);
        }
      }
    }

   if (p->num_moves == 0)
    {
     /* No moves --> no solution. Quit now! */
     free(orig_stack);
     return 0;
    }

   /* Propagate our constraints to the global grid. If we actually
    * change anything, note that we need to recompute the valid
    * words list for whomever intersects the newly tightened square. */
   for (i = p->letters_per_move - 1; i >= 0; i--)
    {
     letter_mask_t g = letters_allowed[p->where[i]];
     if ((g & allowed_by_us[i]) != g)
      {
       placement_t *nbr;
       letters_allowed[p->where[i]] = 
                      g & allowed_by_us[i];
       nbr = p->neighbor[i];
       if (!placement_is_marked(nbr))
        {
         *stack++ = nbr;
         set_placement_mark(nbr);
        }
      }
    }

   clear_placement_mark(p);
  }

 free(orig_stack);
 return 1;
}

place_word
static void
place_word(Puzzle puzzle, int x, int y, int dx, int dy, 
          const char *word)
{
 for (; *word; word++)
  {
   puzzle[x][y] = *word;
   x += dx;
   y += dy;
  }
}

place_move
static void
place_move(Puzzle puzzle, placement_t *p, move_t *m)
{
 place_word(puzzle, p->start_x, p->start_y, 
            p->dx, p->dy, m->original_word);
}

solve_trivial_placements
/* Go ahead and fill in every placement where there's only one choice. */
static void
solve_trivial_placements(Puzzle puzzle, placement_t *placement,
        long num_placements)
{
 long i;

 /* Go ahead and make any move where there's only one choice. */
 for (i = 0; i < num_placements; i++)
  {
   placement_t *p = &placement[i];
   if (p->num_moves == 1)
    {
     place_move(puzzle, p, &p->move[0]);
     free(placement[i].move);
     placement[i].move = NULL;
     p->num_moves = 0;
     p->done = 1;
    }
  }
}

create_placements
static placement_t *
create_placements(Puzzle puzzle, long puzzle_size,
      char *dictionary[], long dict_size,
      letter_mask_t letters_allowed[kMaxSize * kMaxSize],
      long *letters_allowed_size_ptr,
      long *num_placements_ptr)
{
 /* Do we care about words of length n? */
 char interesting_length[kMaxSize + 1];
 long n, num_placements;
 placement_t *placement;
 const char **words_of_length[kMaxSize + 1];
 long num_words_of_length[kMaxSize + 1];
 move_t **hash_table = NULL;
 unsigned long max_hash_table_size = 0;
 void *mem_to_free;

 /* Maps [A-Za-z] to the numbers 1-26, zero for all others. */
 unsigned char ascii_to_letter[256];

 /* Maps intersection squares to unique contiguous numbers.
  * Undefined garbage for non-intersection squares. */
 unsigned long square_to_packed_linear[kMaxSize][kMaxSize];
 unsigned long num_packed_linears = 0;

 /* Gives us the up to two placements that intersect the given square. */
 placement_t *square_to_placement[kMaxSize][kMaxSize][2];

 /* Initialize assorted arrays. */
 memset(square_to_placement, 0, sizeof square_to_placement);
 memset(interesting_length, 0, sizeof interesting_length);

 create_ascii_to_letter(ascii_to_letter);

 /* Create all of the placement structs, etc. */
 placement = identify_placements(puzzle, puzzle_size, 
      &num_placements, square_to_placement, interesting_length);

 /* Figure out all of the words of the various lengths we want. */
 partition_words_by_length(dictionary, dict_size, 
      interesting_length, words_of_length, num_words_of_length,
      &mem_to_free);

 /* Loop through each partition and set up its neighbors and move list,
  * and reflect our move list on the global state. */
 for (n = 0; n < num_placements; n++)
  {
   placement_t *t = &placement[n];
   long num_intersect_squares = 0;
   long x, y, dx, dy, length;
   letter_mask_t mask[kMaxSize];

   /* If anyone marked us as needing further refinement, clear it
    * since we're going to do that refinement now. */
   clear_placement_mark(t);

   dx = t->dx;
   dy = t->dy;

   for (x = t->start_x, y = t->start_y, length = 0;
      x < puzzle_size && y < puzzle_size && 
                      puzzle[x][y] == EMPTY_SQUARE;
      x += dx, y += dy, length++)
    {
     placement_t *p0 = square_to_placement[x][y][0];
     placement_t *nbr;

     /* default to all letters being allowed for this square. */
     mask[length] = NOT_INTERSECTION_POINT;

     if (p0 != NULL && p0 != t)
      nbr = p0;
     else
      {
       placement_t *p1 = square_to_placement[x][y][1];
       if (p1 != NULL && p1 != t)
        nbr = p1;
       else
        nbr = NULL;
      }
     if (nbr != NULL)
      {
       /* If we are the first partition to visit this intersect
        * point (i.e. this neighbor hasn't been processed) then
        * add this square to the global list of interesting
        * squares. */
       if (nbr->letters_per_move != 0)
        mask[length] = 
                  letters_allowed
                  [square_to_packed_linear[x][y]];
       else
        {
          mask[length] = ALL_LETTERS;
         letters_allowed[num_packed_linears] = 
                            ALL_LETTERS;
         square_to_packed_linear[x][y] = 
                            num_packed_linears++;
        }

       /* We intersected some other placement here. This means we
        * care about this square. */
       t->neighbor[num_intersect_squares] = nbr;
       t->where[num_intersect_squares] = 
                      square_to_packed_linear[x][y];
       num_intersect_squares++;
      }
    }

   t->letters_per_move = num_intersect_squares;
   t->move_size = MOVE_SIZE(num_intersect_squares);

   if (t->letters_per_move == 0)
    {
     /* Plug in anything that fits. */
     if (num_words_of_length[length] == 0)
      {
       /* No solution! */
       goto done;
      }
     place_word(puzzle, t->start_x, t->start_y, 
                  t->dx, t->dy, words_of_length[length][0]);
     t->done = 1;
     t->num_moves = 0;
     t->move = NULL;
     continue;
    }

   /* Create all the moves for this placement. */
     t->move = (move_t *) malloc((num_words_of_length[length]+1)
                 * MOVE_SIZE(length));

   {
    const char **w;
    move_t *m = t->move;
    unsigned long hash_table_size;

    hash_table_size = num_words_of_length[length] * 3 + 16;
    if (hash_table_size > max_hash_table_size)
     {
      free(hash_table);
      max_hash_table_size = hash_table_size;
      hash_table = calloc(max_hash_table_size, 
                    sizeof hash_table[0]);
     }
    else
     memset(hash_table, 0, hash_table_size * 
                    sizeof hash_table[0]);

    for (w = words_of_length[length]; *w; w++)
     {
      const char *s = *w;
      unsigned long hash;
      long ix, out;

      hash = 1;
      for (ix = out = 0; s[ix] != '\0'; ix++)
       if (mask[ix] != NOT_INTERSECTION_POINT)
        {
         int letter = 
                    ascii_to_letter[(unsigned char) s[ix]];
         if ((mask[ix] & (1 << letter)) == 0)
          break;
         hash = (hash * 26) + letter;
         m->letter[out++] = letter;
        }

      /* If we made it all the way to the end without failing,
       * then add this word to the list. */
      if (s[ix] == '\0')
       {
        const move_t *test_move;
        long j;

        hash %= hash_table_size;

       while ((test_move = hash_table[hash]) != NULL)
        {
        for (j = t->letters_per_move - 1; j>=0; j--)
          if (test_move->letter[j] != m->letter[j])
            break;
          if (j < 0)
           break;
          if (++hash >= hash_table_size)
           hash -= hash_table_size;
         }
        if (test_move == NULL)
         {
          hash_table[hash] = m;
          m->original_word = *w;
          ++t->num_moves;
          m = NEXT_MOVE(m, t->move_size);
         }
       }
     }

    /* Terminate our list with a NULL pointer. */
    m->original_word = NULL;
   }

   /* Compute global implications of the legal words here. */
   intersect_placement_with_global_mask(t, letters_allowed);
  }

 solve_trivial_placements(puzzle, placement, num_placements);

done:
 /* We don't need this memory any more, so free it. */
 free(hash_table);
 free(mem_to_free);

 /* Recursively propagate around constraints. */
 tighten_constraints(placement, num_placements, 
          letters_allowed, 1);

 *letters_allowed_size_ptr = num_packed_linears;
 *num_placements_ptr = num_placements;
 return placement;
}

partition_aux
/* Recursive helper function for `partition_and_mark_cycles'. */
static long
partition_aux(placement_t *p, placement_t ***partition, 
      placement_t *parent, long depth)
{
 placement_t **nbrs, *nbr;
 long retval = depth;

 /* Add this placement to our partition. */
 set_placement_mark(p);
 p->depth = depth;
 p->in_cycle = NOT_IN_CYCLE;
 if (!p->done)
  {
   **partition = p;
   ++*partition;

   for (nbrs = p->neighbor; (nbr = *nbrs) != NULL; nbrs++)
    {
     long x;
     
     if (nbr == parent)
      continue;
     
     if (placement_is_marked(nbr))
      x = nbr->depth;
     else
      x = partition_aux(nbr, partition, p, depth + 1);
     if (x <= retval)
      {
       p->in_cycle = IN_CYCLE;
       retval = x;
      }
    }
  }

 return (p->in_cycle == IN_CYCLE) ? retval : 10000000;
}

partition_and_mark_cycles
/* Store all non-solved placements reachable from root that are part of
 * some cycle into partition. */
static long
partition_and_mark_cycles(placement_t *root, 
      placement_t **partition)
{
 placement_t **end_partition, **in, **out, *p;

 /* Put everything in the partition into the array, and mark each
  * that's part of a cycle. */
 end_partition = partition;
 clear_all_placement_marks();
 partition_aux(root, &end_partition, NULL, 1);
 *end_partition = NULL;

 /* Remove everything that's not part of a cycle. */
 for (in = out = partition; (p = *in) != 0; in++)
  if (p->in_cycle == IN_CYCLE)
   *out++ = p;
 *out = NULL;

 return out - partition;
}

solve_partition
/* Tries to solve a partition. Returns true on success. */
static int
solve_partition(Puzzle puzzle, placement_t **partition, 
      long partition_size, letter_mask_t *letters_allowed, 
      long letters_allowed_size, placement_t *all_placements, 
      long all_placements_size, placement_t *start)
{
 placement_t *p, *most_popular;
 move_t **backup_move, *m;
 long *backup_num_moves, i;
 letter_mask_t *backup_letters_allowed;
 placement_t **new_partition;
 int success = 0;
 long bla_size;
 long move_size;

 /* Make a backup copy of our letters_allowed array. */
 bla_size = letters_allowed_size * 
          sizeof backup_letters_allowed[0];
 backup_letters_allowed = malloc(bla_size);
 memcpy(backup_letters_allowed, letters_allowed, bla_size);
 
 /* Make backup copies of our move lists. */
 backup_move = malloc(partition_size * sizeof backup_move[0]);
 backup_num_moves = 
      malloc(partition_size * sizeof backup_num_moves[0]);

 /* Allocate room to hold this. */
 new_partition = 
  malloc((all_placements_size + 1) * sizeof new_partition[0]);

 p = most_popular = NULL;
 
 for (i = 0; i < partition_size; i++)
  {
   placement_t *q = partition[i];
   long size;

   backup_num_moves[i] = q->num_moves;
   size = (q->num_moves + 1) * q->move_size;
   backup_move[i] = malloc(size);
   memcpy(backup_move[i], q->move, size);

   if (q == start)
    p = q;
   else if (most_popular == NULL
        || q->letters_per_move > 
                            most_popular->letters_per_move)
    most_popular = q;
  }

 if (p == NULL)
  p = most_popular;

 /* Hypothetically lay down this move. */
 move_size = p->move_size;
 for (m = p->move; m->original_word; 
              m = NEXT_MOVE(m, move_size))
  {
   long r;
   
   /* Actually lay this move down on the board. */
   place_move(puzzle, p, m);

   /* Remember that this placement is "done". */
   p->done = 1;

   /* Tighten grid and update all neighbors who may care. */
   clear_all_placement_marks();
   for (r = p->letters_per_move - 1; r >= 0; r--)
    {
     letter_mask_t g = letters_allowed[p->where[r]];
     letter_mask_t mask = 1 << m->letter[r];
     if (g != mask)
      {
       letters_allowed[p->where[r]] = mask;
       set_placement_mark(p->neighbor[r]);
      }
    }

   /* Propagate constraints and check for contradiction. */
   if (!tighten_constraints(all_placements, 
            all_placements_size, letters_allowed, 0))
    goto failed;
   
   {
    placement_t **nbrs, *nbr;

    /* No contradiction yet, so try our children. */
    for (nbrs = p->neighbor; (nbr = *nbrs) != 0; nbrs++)
    {
     long new_partition_size;
     new_partition_size = 
              partition_and_mark_cycles(nbr, new_partition);
     if (new_partition_size > 0 && 
                !solve_partition(puzzle, new_partition,
                      new_partition_size, letters_allowed, 
                      letters_allowed_size, all_placements, 
                      all_placements_size, nbr))
      goto failed;
    }
   }

   /* Woohoo! We did it! */
   success = 1;
   break;

   /* This didn't work, so restore state. */
  failed:
   p->done = 0;
   for (r = 0; r < partition_size; r++)
    {
     placement_t *q = partition[r];
     q->num_moves = backup_num_moves[r];
     /* FIXME - don't actually need to copy on the last pass...
      * just assign pointer to backup memory and free the bad copy. */
     memcpy(q->move, backup_move[r], 
                        (q->num_moves + 1) * q->move_size);
    }
   memcpy(letters_allowed, backup_letters_allowed,
       letters_allowed_size * sizeof letters_allowed[0]);
  }

 /* Housecleaning. */
 free(new_partition);
 free(backup_letters_allowed);
 for (i = 0; i < partition_size; i++)
  free(backup_move[i]);
 free(backup_num_moves);
 free(backup_move);

 return success;
}


solve_acyclic_aux
static void
solve_acyclic_aux(Puzzle puzzle, placement_t *p,
         letter_mask_t *letters_allowed)
{
 /* Find any legal move and make it. */
 move_t *m;
 long move_size, loop_start;

 if (p->done)
  return;
 
 move_size = p->move_size;
 loop_start = p->letters_per_move - 1;

 for (m = p->move; m->original_word; 
                  m = NEXT_MOVE(m, move_size))
  {
   long k;
   for (k = loop_start; k >= 0; k--)
    if (!(letters_allowed[p->where[k]] & 
                            (1 << m->letter[k])))
     break;
   if (k < 0)
    {
     long j;
     
     /* Make the move. */
     place_move(puzzle, p, m);
     
     /* Tighten up the board for everyone else. */
     for (j = loop_start; j >= 0; j--)
      letters_allowed[p->where[j]] = 1 << m->letter[j];

     p->done = 1;

     /* Flood out to our neighbors and do them too. */
     for (j = loop_start; j >= 0; j--)
      solve_acyclic_aux(puzzle, p->neighbor[j], 
                    letters_allowed);

     /* Stop looking for a word. */
     break;
    }
  }
}

solve_acyclic_stragglers
/* The main algorithm guarantees we solve things that are part of
 * cycles but not those things which are not part of cycles, because
 * they are utterly trivial given the information we've computed.
 * This solves those last acyclic pieces. */
static void
solve_acyclic_stragglers(Puzzle puzzle,
    placement_t *placement, long num_placements,
    letter_mask_t *letters_allowed)
{
 long i;
 for (i = 0; i < num_placements; i++)
  {
   placement_t *p = &placement[i];
   if (!p->done && p->num_moves > 0)
    solve_acyclic_aux(puzzle, p, letters_allowed);
  }
}


Crossword
void Crossword(
 Puzzle thePuzzle,    /* return solved puzzle here */
 char *dictionary[],  /* array of words to choose from */
 long puzzleSize,    /* number of rows/cols in puzzle */
 long dictSize        /* number of words in dictionary */
)
{
 letter_mask_t letters_allowed[kMaxSize * kMaxSize];
 long num_placements, i, letters_allowed_size;
 placement_t *placement, **partition;
 int success = 1;

 /* Create our placement structures. */
 placement = create_placements(thePuzzle, puzzleSize, 
      dictionary, dictSize, letters_allowed, 
      &letters_allowed_size, &num_placements);

 /* Find disjoint portions of the graph and solve them. */
 partition = malloc((num_placements + 1) * sizeof partition[0]);
 for (i = 0; i < num_placements; i++)
  {
   placement_t *p = &placement[i];
   if (p->num_moves > 0 && p->in_cycle == CYCLENESS_UNKNOWN)
    {
     long partition_size = 
                    partition_and_mark_cycles(p, partition);
     if (partition_size > 0)
      success &= solve_partition(thePuzzle, partition, 
                    partition_size, letters_allowed, 
                    letters_allowed_size, placement, 
                    num_placements, NULL);
    }
  }

 if (success)
  {
   /* Recompute all constraints for everyone not yet solved. */
   for (i = 0; i < num_placements; i++)
    set_placement_mark(&placement[i]);
   tighten_constraints(placement, num_placements, 
                letters_allowed, 1);
   
   /* Go through and solve them. */
   solve_acyclic_stragglers(thePuzzle, placement, 
                num_placements, letters_allowed);
  }
 
 /* House cleaning. */
 free(partition);
 for (i = 0; i < num_placements; i++)
  free(placement[i].move);
 free(placement);
}
 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Notion 2.1.9 - A unified workspace for m...
Notion is the unified workspace for modern teams. Features: Integration with Slack Documents Wikis Tasks More guests: invite up to 10 collaborators, friends & family to your pages Page... Read more
Spotify 1.2.0.1165 - Stream music, creat...
Spotify is a streaming music service that gives you on-demand access to millions of songs. Whether you like driving rock, silky R&B, or grandiose classical music, Spotify's massive catalogue puts... Read more
Thunderbird 102.5.1 - Email client from...
As of July 2012, Thunderbird has transitioned to a new governance model, with new features being developed by the broader free software and open source community, and security fixes and improvements... Read more
Pinegrow 7.03 - Mockup and design web pa...
Pinegrow (was Pinegrow Web Designer) is desktop app that lets you mockup and design webpages faster with multi-page editing, CSS and LESS styling, and smart components for Bootstrap, Foundation,... Read more
Adobe After Effects 2022 23.1 - Create p...
The new, more connected Adobe After Effects can make the impossible possible. Get powerful new features like a Live 3D Pipeline that brings CINEMA 4D scenes in as layers - without intermediate... Read more
SteerMouse 5.6.7 - Powerful third-party...
SteerMouse is an advanced driver for USB and Bluetooth mice. SteerMouse can assign various functions to buttons that Apple's software does not allow, including double-clicks, modifier clicks,... Read more
Wireshark 4.0.2 - Network protocol analy...
Wireshark is one of the world's foremost network protocol analyzers, and is the standard in many parts of the industry. It is the continuation of a project that started in 1998. Hundreds of... Read more
Adobe Premiere Pro 2022 23.1 - Digital v...
Adobe Premiere Pro is available as part of Adobe Creative Cloud for as little as $54.99/month. The price on display is a price for annual by-monthly plan for Adobe Premiere Pro only. Adobe Premiere... Read more
1Password 8.9.10 - Powerful password man...
1Password is a password manager that uniquely brings you both security and convenience. It is the only program that provides anti-phishing protection and goes beyond password management by adding Web... Read more
FotoMagico 6.3 - Powerful slideshow crea...
FotoMagico lets you create professional slideshows from your photos and music with just a few, simple mouse clicks. It sports a very clean and intuitive yet powerful user interface. High image... Read more

Latest Forum Discussions

See All

SwitchArcade Round-Up: ‘Chained Echoes’,...
Hello gentle readers, and welcome to the SwitchArcade Round-Up for December 8th, 2022. Today is Thursday, and that usually means an absolute deluge of new releases on the eShop. But the year is winding down, so we’ve only got ten or so to look at... | Read more »
‘Awaken Legends: Idle RPG’ Celebrates th...
Awaken Legends: Idle RPG is adding its first update since the game was soft-launched in November, letting players get their hands on a new hero “Hera Valen". Players can also look forward to the Covenant of the Dark Knight event and the Wishing Well... | Read more »
‘Horizon Chase 2’ Japan World Tour Expan...
Horizon Chase 2 () from Aquiris is getting a major expansion today on Apple Arcade. The Japan World Tour expansion brings in 11 new races across 9 cities and it should be rolling out now as of this writing. I expect it to be available worldwide... | Read more »
Dark Fantasy Visual Novel ‘The 13th Mont...
Originally announced for release in August, The 13th Month from Japanese developer Kobayashimaru and publisher Kodansha released on PC via Steam worldwide this month. The dark fantasy visual novel that reimagines the classic Sleeping Beauty tale, is... | Read more »
Tom Clancey’s The Divison Resurgence ann...
Ubisoft has announced the latest Live Test dates for Tom Clancy’s The Division Resurgence, the hotly anticipated mobile entry in the Divison series. Starting December 8th and ending on the 22nd, the test will offer a huge amount of content for the... | Read more »
‘Easy Come Easy Golf’ New Update Adds St...
Easy Come Easy Golf () from Clap Hanz is one of my favorite games on Apple Arcade. It has been updated quite a bit since launch bringing in new modes and improvements. It recently launched on Nintendo Switch as well. | Read more »
Out Now: ‘Magic vs Metal’, ‘Suzerain’, ‘...
Each and every day new mobile games are hitting the App Store, and so each week we put together a big old list of all the best new releases of the past seven days. Back in the day the App Store would showcase the same games for a week, and then... | Read more »
SwitchArcade Round-Up: Reviews Featuring...
Hello gentle readers, and welcome to the SwitchArcade Round-Up for December 7th, 2022. Today can be accurately described as Mikhail Madness, with a whopping four reviews from our pal-est of pals. Football Manager 2023 Touch, Wobbledogs, Soccer Story... | Read more »
Alchemy Stars celebrates 1 and a half ye...
It has been one and a half years since Alchemy Stars launched, and Level Infinite is celebrating in style with a host of new content. There will be a new story mission and even a store to explore, and a whole new mode for those budding idol... | Read more »
Fighting Game ‘Art of Fighting 2’ ACA Ne...
Last week, side-scrolling shooter Pulstar hit mobile platforms as the newest ACA NeoGeo series release from Hamster and SNK. Read Shaun’s review of it here. Today, fighting game Art of Fighting 2 has launched on iOS and Android. Art of Fighting 2... | Read more »

Price Scanner via MacPrices.net

New! Details on Verizon’s Christmas/Holiday p...
Verizon is offering discounts on iPhones, Apple Watch models, and iPads with specific promo codes as part of their Christmas/Holiday 2022 offerings. Codes are valid when adding a new line of service... Read more
Apple MagSafe accessories are back on Holiday...
Amazon has Apple MagSafe Chargers and Apple’s MagSafe Battery on sale for up to 24% off MSRP again as part of their Christmas/Holiday sale. Shipping is free, and all models are in stock: – MagSafe... Read more
13″ M2 MacBook Airs on sale again for the low...
Amazon has 13″ MacBook Airs with M2 CPUs in stock today and on sale for $150 off MSRP as part of their Christmas/Holiday Sale, prices start at $1049. Shipping is free. They are the lowest prices... Read more
Get an Apple 16″ MacBook Pro for $400 off MSR...
16″ MacBook Pros with Apple’s M1 Pro CPUs are in stock and on sale today at B&H Photo for $300-$400 off Apple’s MSRP for a limited time. Prices start at $2099 for M1 Pro models with 512GB or 1TB... Read more
Holiday clearance sale! Previous-generation A...
Amazon has 2nd generation 32GB and 64GB 4K Apple TVs with Siri remotes and 32GB Apple TV HDs on clearance sale for $80-$90 off original MSRP. Shipping is free, and delivery is available in time for... Read more
Christmas sale at Verizon: Apple AirPods Pro...
Verizon has first-generation Apple AirPods Pro on sale for $159.99 on their online store as part of their continuing Christmas/Holiday sale. Their price is $90 off Apple’s original MSRP, and it’s the... Read more
New Christmas/New Years promo at Xfinity Mobi...
Switch to Xfinity Mobile and open a new line of service, and take $400 off the price of a new iPhone, no trade-in required, through January 10, 2023. The $400 is applied to your account as credits... Read more
Apple iPad Smart Keyboard Folio prices drop u...
Apple iPad Smart Keyboard Folio prices have dropped up to $60 off MSRP at Amazon and Walmart as part of their Christmas/Holiday sales. These are the cheapest prices currently available for these iPad... Read more
Today is the final day for Xfinity Mobile’s $...
If you switch to Xfinity Mobile and open a new line of service, they will take $500 off the price of a new iPhone, no trade-in required. This is the best no trade-in Cyber Monday Apple iPhone 14 deal... Read more
Amazon restocks 10.2″ 64GB 9th-generation iPa...
Amazon has Apple’s 9th generation 10.2″ 64GB WiFi iPads (Silver) in stock and on sale for $269.99 shipped as part of their Christmas/Holiday Sale. Their price is $60 off Apple’s MSRP. Free delivery... Read more

Jobs Board

*Apple* Systems Administrator - JAMF - Activ...
…Administration **Duties and Responsibilities** + Configure and maintain the client's Apple Device Management (ADM) solution. The current solution is JAMF supporting Read more
Cashier - *Apple* Blossom Mall - JCPenney (...
Cashier - Apple Blossom Mall Location:Winchester, VA, United States (https://jobs.jcp.com/jobs/location/191170/winchester-va-united-states) - Apple Blossom Mall Read more
Omnichannel Associate - *Apple* Blossom Mal...
Omnichannel Associate - Apple Blossom Mall Location:Winchester, VA, United States (https://jobs.jcp.com/jobs/location/191170/winchester-va-united-states) - Apple Read more
Sephora Beauty Advisor - *Apple* Blossom Ma...
Sephora Beauty Advisor - Apple Blossom Mall Location:Winchester, VA, United States (https://jobs.jcp.com/jobs/location/191170/winchester-va-united-states) - Apple Read more
Operations Associate - *Apple* Blossom Mall...
Operations Associate - Apple Blossom Mall Location:Winchester, VA, United States (https://jobs.jcp.com/jobs/location/191170/winchester-va-united-states) - Apple Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.