May 99 Challenge

Volume Number: 15 (1999)
Issue Number: 5
Column Tag: Programmer's Challenge

# May 99 Challenge

by Bob Boonstra, Westford, MA

### Piper

Every once in a while, good fortune not only comes your way, but actually reaches out of your computer monitor, and grabs you by the throat. I felt a little like that while reading a recent issue of TidBITS. In it was a column by Rick Holzgrafe reflecting on the increasing speed of computers, in which Rick described a program he wrote for a PDP-11/60 to solve a word puzzle. The idea behind the puzzle was to take a phrase and map it onto a rectangular grid, with the objective being to map the phrase into a rectangle of the smallest possible area. The word puzzle looked like a good idea for a Challenge, and Rick and TidBITS agreed to let me use it.

In more detail, the puzzle works like this. To start, you are given a null-terminated string consisting of printable characters. You process the characters in order, ignoring any non-alphabetic characters and ignoring case. The first alphabetic character can be mapped to any square in the grid. The next letter can be mapped to any adjacent square, where adjacent is any of the eight neighboring squares in a horizontal, vertical, or diagonal direction. You may reuse a square if it is adjacent and already has the letter you are mapping. If the same letter occurs twice in a row in the input string, the letters must still be mapped to adjacent (but distinct) squares.

The prototype for the code you should write is:

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

typedef struct GridPoint {
long x;
long y;
} GridPoint;

void Piper (
char *s,
GridPoint pt[]
);

#if defined(__cplusplus)
}
#endif
```

For example, your Piper routine might be provided with the string:

```            How much wood would a woodchuck chuck if a woodchuck
could chuck wood?
```

You might place the letters of that string into a 4x14 rectangle like:

```                  ULD  ADLU
HDOAIUCOHWUHOD
UCOWFKHDOMCWOW
K   WO
```

Or, you might compact them into an 4x4 rectangle:

```               HWMU
OOCH
UDWK
LAFI
```

You must return the GridPoint coordinates of where each character is mapped, with pt[i] containing the coordinates of input character s[i]. The origin of your coordinate system should be the cell where the first character is placed. The winner will be the solution that stores the input string in a rectangle of minimal area. Note that you are minimizing rectangle area, not the number of occupied squares. A time penalty of 1% for each second of execution time will be added

This will be a native PowerPC Challenge, using the latest CodeWarrior environment. Solutions may be coded in C, C++, or Pascal.

### Three Months Ago Winner

The February Challenge invited readers to write a player for the game of Chinese Checkers. Played on a hexagonal board with six appended triangles, Chinese Checkers pits between 2 and 6 players against one another, with the objective being to move one's pieces from the home triangle to the opposite triangle. In the traditional game, the home triangles are usually 3 or 4 positions on a side; the Challenge extended the game to triangles of up to 64 positions. Pieces can either be moved to an immediately adjacent position or jumped over an adjacent piece. A single piece is permitted to make a sequence of jumps in a single move.

As simple as the game sounds, readers found it to be very difficult, so difficult that no solutions were submitted for the Chinese Checkers Challenge. Which left Yours Truly in something of a difficult spot. I could stop the column at this point, which wouldn't be very interesting for readers, not to mention not very satisfying for the magazine. Or I could write a solution for the Challenge myself, something I haven't done since I retired from Competition four plus years ago. Somewhat against my better judgement, I selected the latter option.

The first thing I noticed in solving the Challenge was that the board coordinate system specified in the problem wasn't very useful in generating a solution. I needed a coordinate system that could be easily rotated in 60-degree increments, enabling my solution to play any of the six possible player positions. After some thought, I came up with a more symmetric coordinate system, called CanonPosition in the code, along with conversion routines ConvertPositionToCanonPosition and ConvertCanonPositionToPosition. The commentary in the code illustrates the coordinate system for a board of size 4. Then I needed a way to evaluate board positions. I decided on a simple metric that summed the distances of all pieces from the apex of their goal triangle. That metric could be improved upon by taking possible jump moves into account. The solution starts by computing all possible moves for our player. It then tries each of those moves, and then recursively calls MakeNextMove to process the next player. It computes and tries all moves for that player, and recurses for the next player. Recursion terminates when kMaxPlys turns have been taken for all players. Positions are evaluated using a min-max technique, where each player selects the position that maximizes his position relative to the best position of the other players.

The code could be improved in many ways. Instead of trying all possible positions, it could prune some obviously bad moves in the backward direction. This is complicated by the fact that some good jump multi-moves can include individual jumps that appear to be moving backward. The code might also be improved by evaluating moves by progressive deepening, rather than the depth-first search currently used, and by ordering move evaluation based on the scores at the prior depth. This technique is used in chess programs to prune the move tree to a manageable size. These and other optimizations are left to the reader. :-)

Remember, you can't win if you don't play. To ensure that you have as much time as possible to solve the Challenge, subscribe to the Programmer's Challenge mailing list. To subscribe, see the Challenge web page at <http://www.mactech.com/mactech/progchallenge/>. The Challenge is sent to the list around the 12th of the month before the solutions are due, often in advance of when the physical magazine is delivered.

Here is our sample Chinese Checkers solution:

```/*
*  Example solution for the February 1999 Programmer's Challenge
*
*  This solution is provided because no solutions were submitted
*  for the ChineseCheckers Challenge.  This solution leaves a
*  great deal to be desired: it is not optimized, it does not
*  prune prospective moves efficiently, and it does not employ
*  any of the classic alpha-beta techniques for efficiently
*  selecting a move.
*/

#include <stdio.h>
#include <stdlib.h>
#include <Quickdraw.h>

#include "ChineseCheckers.h"

/* Position coordinates specified in problem (size==4)

0:                           0
1:                         0   1
2:                      -1   0   1
3:                    -1   0   1   2
4:  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6
5:    -5  -4  -3  -2  -1   0   1   2   3   4   5   6
6:      -5  -4  -3  -2  -1   0   1   2   3   4   5
7:        -4  -3  -2  -1   0   1   2   3   4   5
8:          -4  -3  -2  -1   0   1   2   3   4
9:        -4  -3  -2  -1   0   1   2   3   4   5
10:      -5  -4  -3  -2  -1   0   1   2   3   4   5
11:    -5  -4  -3  -2  -1   0   1   2   3   4   5   6
12:  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6
13:                    -1   0   1   2
14:                      -1   0   1
15:                         0   1
16:                           0
*/

#define kMaxPlys 1
#define kEmpty -1

/* CanonPosition uses units with (0,0) at the middle of the board */
typedef struct CanonPosition {
long row;
long col;
} CanonPosition;

/* Canonical position coordinates (size==4)

-8:                           0
-7:                        -1   1
-6:                      -2   0   2
-5:                    -3  -1   1   3
-4: -12 -10  -8  -6  -4  -2   0   2   4   6   8  10  12
-3:   -11  -9  -7  -5  -3  -1   1   3   5   7   9  11
-2:     -10  -8  -6  -4  -2   0   2   4   6   8  10
-1:        -9  -7  -5  -3  -1   1   3   5   7   9
0:          -8  -6  -4  -2   0   2   4   6   8
1:        -9  -7  -5  -3  -1   1   3   5   7   9
2:     -10  -8  -6  -4  -2   0   2   4   6   8  10
3:   -11  -9  -7  -5  -3  -1   1   3   5   7   9  11
4: -12 -10  -8  -6  -4  -2   0   2   4   6   8  10  12
5:                    -3  -1   1   3
6:                      -2   0   2
7:                        -1   1
8:                           0
*/

/* PlayerPos is used to store the location of each of a players pieces */
typedef struct PlayerPos {
CanonPosition pos;
} PlayerPos;

typedef char *CanonBoard;

static long myNumPlayers,myNumPieces,myIndex,myGameSize,
myPlayerPosition[6],myMinDist;
static PlayerPos *myPositions;

/* global board */
static CanonBoard myBoard;

/* moveIncrement is added to a CanonPosition to find the adjacent square in the
* six possible directions 0..6, with 0==horizontal right, 1==down right, ...
* 5==up right
*/
static CanonPosition moveIncrement[6] =
{ { 0, 2}, { 1, 1}, { 1,-1}, { 0,-2}, {-1,-1}, {-1, 1} };

/* macros to access the board */
#define CanonRowSize(size) (6*(size)+1)
#define CanonBoardPos(row,col) (3*(myGameSize) +    \
(2*(myGameSize)+(row))*(CanonRowSize(myGameSize)) + (col))
#define CanonBoardVal(board,row,col)          \
board[CanonBoardPos(row,col)]
#define IsEmpty(board,row,col)             \
(kEmpty == board[CanonBoardPos(row,col)])

ConvertPositionToCanonPosition
/* Convert coordinates from problem statement to canonical coordinates */
static CanonPosition ConvertPositionToCanonPosition (
Position *pos, long size) {
CanonPosition canon;
canon.row = pos->row - 2 * size;
if (pos->row == 2 * (int)(pos->row/2)) {
canon.col = 2 * pos->col;
} else {
canon.col = 2 * pos->col - 1;
}
return canon;
}

ConvertCanonPositionToPosition
/* Convert canonical coordinates to coordinates from problem statement */
static Position ConvertCanonPositionToPosition (CanonPosition *canon, long size) {
Position pos;
pos.row = canon->row + 2 * size;
if (canon->row == 2 * (int)(canon->row/2)) {
pos.col = canon->col / 2;
} else {
pos.col = (canon->col + 1) / 2;
}
return pos;
}

RotateCanonPosition0ToN
/* rotate board by posNum increments of player positions (60 degrees) */
static CanonPosition RotateCanonPosition0ToN(
CanonPosition oldPos, long posNum) {
CanonPosition newPos;
while (posNum<0) posNum+=6;   /* normalize to 0..5 */
while (posNum>5) posNum-=6;
switch (posNum) {
case 0:
newPos.row = oldPos.row;
newPos.col = oldPos.col;
break;
case 1:
newPos.row = (oldPos.row + oldPos.col)/2;
newPos.col = (oldPos.col - 3*oldPos.row)/2;
break;
case 2:
newPos.row =  (oldPos.col - oldPos.row)/2;
newPos.col = -(oldPos.col + 3*oldPos.row)/2;
break;
case 3:
newPos.row = -oldPos.row;
newPos.col = -oldPos.col;
break;
case 4:
newPos.row = -(oldPos.row + oldPos.col)/2;
newPos.col = -(oldPos.col - 3*oldPos.row)/2;
break;
case 5:
newPos.row = -(oldPos.col - oldPos.row)/2;
newPos.col =  (oldPos.col + 3*oldPos.row)/2;
break;
}
return newPos;
}

MaxColInRow
/* return the max column number in a given row */
static long MaxColInRow(long row, long size) {
long maxCol;
if (row<-size) {
maxCol = row+2*size;
} else if (row<0) {
maxCol = 2*size-row;
} else if (row<=size) {
maxCol = row+2*size;
} else /* if (row<=2*size) */ {
maxCol = 2*size-row;
}
return maxCol;
}

IsLegalPosition
/* determine if a row,col coordinate represents a legal position */
static Boolean IsLegalPosition(CanonPosition *pos) {
long maxCol;
if ((pos->row<-2*myGameSize) || (pos->row>2*myGameSize))
return false;
if ((pos->row + pos->col) !=
2 * (int)((pos->row + pos->col)/2))
return false;
maxCol = MaxColInRow(pos->row,myGameSize);
if ((pos->col<-maxCol) || (pos->col>maxCol))
return false;
return true;
}

MoveFromTo
/* move a piece between positions from and to, does not check legality of move */
static void MoveFromTo(CanonBoard b,CanonPosition *from,CanonPosition *to,long newValue) {
PlayerPos *p = &myPositions[newValue*myNumPieces];
long oldValue = CanonBoardVal(b,from->row,from->col);
int i;

if (oldValue != newValue) {
DebugStr("\p check err");
}
if ( IsLegalPosition(from) && IsLegalPosition(to) ) {
CanonBoardVal(b,from->row,from->col) = kEmpty;
CanonBoardVal(b,to->row,to->col) = (char)newValue;
for (i=0; i<myNumPieces; i++) {
if (    (p[i].pos.row == from->row) &&
(p[i].pos.col == from->col)) {
p[i].pos.row = to->row;
p[i].pos.col = to->col;
break;
}
}
}
}

PositionDistFromGoal
/* return the distance of a given position from a goal postion for player 0 */
static long PositionDistFromGoal (const CanonPosition *a, const CanonPosition *goal) {
long rowDelta,colDelta;
rowDelta = a->row - goal->row;
if (rowDelta<0) rowDelta = -rowDelta;
colDelta = a->col - goal->col;
if (colDelta<0) colDelta = -colDelta;
if (rowDelta>=colDelta) return rowDelta;
else return rowDelta + (colDelta-rowDelta)/2;
}

PlayerDistFromGoal
/* return the cumulative distance of a player from his goal postion */
static long PlayerDistFromGoal(long player) {
long cumDist;
int i;
CanonPosition goal;
PlayerPos *p = &myPositions[player*myNumPieces];
goal.row = -2*myGameSize;
goal.col = 0;
goal =
RotateCanonPosition0ToN(goal,(myPlayerPosition[player]+3)%6);
for (i=0, cumDist=0; i<myNumPieces; i++) {
CanonPosition *cp = &p[i].pos;
long dist = PositionDistFromGoal(cp,&goal);
cumDist += dist;
}
return cumDist;
}

InitPlayer
/* initialize the positions for a player at a given position */
static void InitPlayer(char *b,PlayerPos *piecePositions, long player, long position,long size) {
CanonPosition pos,newPos;
int col,maxCol,pieceCount;
PlayerPos *piecePos;

pieceCount = 0;
for (maxCol=0; maxCol<size; maxCol++) {
pos.row = -2*size+maxCol;
maxCol = maxCol;
for (col=-maxCol; col<=maxCol; col+=2) {
pos.col = col;
newPos = RotateCanonPosition0ToN(pos,position);
CanonBoardVal(b,newPos.row,newPos.col) = (char)player;
piecePos = &piecePositions[myNumPieces*player + pieceCount];
piecePos->pos = newPos;
++pieceCount;
}
}
}

/* some variables to record the history of multi-jump moves, to
prevent them from repeating infinitely */
static CanonPosition gMoveHistoryPos[6*64];
static long gMoveHistoryDirection[6*64];
static long gMoveHistoryCtr = -1;

CalcMove
/* Calculate a move for a given piece for a given player in a given moveDir.
* Return true there is a legal move.
* Return doneWithThisDirection==true if there are no more moves in this direction.
*/
static Boolean CalcMove(
CanonBoard b, long player, long pieceNum, long moveDir,
CanonPosition *p1, CanonPosition *p2,
Boolean *doneWithThisDirection, long iterationLimit) {
Boolean legalMove = true;
if (gMoveHistoryCtr<0) {
PlayerPos *p = &myPositions[player*myNumPieces];
*p2 = *p1 = p[pieceNum].pos;
p2->row += moveIncrement[moveDir].row;
p2->col += moveIncrement[moveDir].col;
if (!IsLegalPosition(p2)) legalMove = false;
else if (IsEmpty(b,p2->row,p2->col)) {
} else {
long oldVal = CanonBoardVal(b,p2->row,p2->col);
p2->row += moveIncrement[moveDir].row;
p2->col += moveIncrement[moveDir].col;
if (!IsLegalPosition(p2)) legalMove = false;
else if (IsEmpty(b,p2->row,p2->col)) {
if (gMoveHistoryCtr>iterationLimit)
DebugStr("\p limit exceeded");
gMoveHistoryPos[++gMoveHistoryCtr] = *p1;
gMoveHistoryDirection[gMoveHistoryCtr] = 6;
gMoveHistoryPos[++gMoveHistoryCtr] = *p2;
gMoveHistoryDirection[gMoveHistoryCtr] = -1;
} else {
legalMove = false;
}
}
} else {
CanonPosition pStart,pTemp;
long newDir;
++gMoveHistoryDirection[gMoveHistoryCtr];
pStart = pTemp = gMoveHistoryPos[gMoveHistoryCtr];
while (   (gMoveHistoryCtr>=0) &&
(gMoveHistoryDirection[gMoveHistoryCtr]>=6) ) {
gMoveHistoryCtr-;
}
if (gMoveHistoryCtr>0) {
newDir = gMoveHistoryDirection[gMoveHistoryCtr];
pTemp.row += moveIncrement[newDir].row;
pTemp.col += moveIncrement[newDir].col;
if (!IsLegalPosition(&pTemp)) legalMove=false;
else if (IsEmpty(b,pTemp.row,pTemp.col)) legalMove=false;
else {
pTemp.row += moveIncrement[newDir].row;
pTemp.col += moveIncrement[newDir].col;
if (!IsLegalPosition(&pTemp)) legalMove=false;
else if (!IsEmpty(b,pTemp.row,pTemp.col)) legalMove=false;
else {
int i;
for (i=0; i<=gMoveHistoryCtr; i++)
if (   (pTemp.row == gMoveHistoryPos[i].row) &&
(pTemp.col == gMoveHistoryPos[i].col) )
legalMove=false;
if (legalMove) {
gMoveHistoryDirection[++gMoveHistoryCtr] = -1;
gMoveHistoryPos[gMoveHistoryCtr] = pTemp;
*p1 = gMoveHistoryPos[0];
*p2 = pTemp;
}
}
}
} else {
legalMove=false;
}

}
*doneWithThisDirection = (gMoveHistoryCtr<0);
return legalMove;
}

/* multiplier to determine how much storage to reserves for moves for each piece */
#define kMemAllocFudge 12

EnumerateMoves
static long EnumerateMoves(CanonBoard b, long player, CanonPosition moveFrom[], CanonPosition moveTo[]) {
long numMoves = 0;
int piece,moveDir;
Boolean legalMove,doneWithThisDirection;
for (piece=0; piece<myNumPieces; piece++) {
int pieceCounter=0;
int firstPieceMoveIndex = numMoves;
moveDir = 0;
do {
legalMove = CalcMove(b,player,piece,moveDir,
&moveFrom[numMoves],&moveTo[numMoves],
&doneWithThisDirection,6*myGameSize);
if (doneWithThisDirection)
++moveDir;
if (!legalMove) continue;
if (numMoves>=kMemAllocFudge*myNumPieces-1) {
DebugStr("\pnumMoves limit exceeded");
break;
} else {
int i;
for (i=firstPieceMoveIndex; i<numMoves; i++)
if ( (moveTo[i].row==moveTo[numMoves].row) &&
(moveTo[i].col==moveTo[numMoves].col) )
legalMove = false;
if (!legalMove) continue;
++numMoves;
}
} while (moveDir<6);
}
return numMoves;
}

MakeNextMove
/*
* Recursive routine to explore move tree.
* MakeNextMove iterates over all possible moves for a player.
* If ply limit is not yet reached, it recurses by calling for the next player.
* Ply limit is decreased by 1 when the "me" player is called.
* Recursion terminates when ply limit is reached.
* Score is assigned on return based on the perspective of the player making the move.
* Simple-minded score algorithm is used:
*   difference between player score and the best other player score, where
*   a player's score is the number of spaces he is away from the final state
* No alpha-beta pruning is employed - search is exhaustive.
*/

static long MakeNextMove(CanonBoard b, long me, long player, long playerDistances[6], long numPlys,
Boolean firstTime, CanonPosition *from, CanonPosition *to) {
long theMove,nextPlayer,numMoves,
bestScore=0x7FFFFFFF, myBestDistance=0x7FFFFFFF;
CanonPosition pFrom,pTo,bestFrom,bestTo;
int newPlys;
CanonPosition *moveFrom,*moveTo;

/* allocate storage for possible moves */
moveFrom = (CanonPosition *)
malloc(kMemAllocFudge*myNumPieces*sizeof(CanonPosition));
if (0==moveFrom)
DebugStr("\pproblem allocation moveFrom memory");
moveTo = (CanonPosition *)
malloc(kMemAllocFudge*myNumPieces*sizeof(CanonPosition));
if (0==moveTo)
DebugStr("\pproblem allocation moveTo memory");

/* prime best move with starting move */
bestFrom = *from;
bestTo = *to;
/* enumerate all legal moves for this player */
numMoves = EnumerateMoves(b,player,moveFrom,moveTo);
/* examine all of the enumerated moves */
for (theMove=0; theMove<numMoves; theMove++) {
long opponent,scoreDifference,minOpponentDistance,
myDistance,returnedDistances[6];
int thePlayer;
pFrom = moveFrom[theMove];
pTo = moveTo[theMove];
if (firstTime) {
*from = pFrom;
*to = pTo;
}
nextPlayer = (player+1)%myNumPlayers;
newPlys = (player==me) ? numPlys-1 : numPlys;

/* record move in the simulated board */
MoveFromTo(b,&pFrom,&pTo,player);

myDistance = PlayerDistFromGoal(player);

/* recurse if ply limit not reached */
if ( (newPlys>=0) && (myDistance>myMinDist) ){
/* MakeNextMove returns each player's distance from the goal in
returnedDistances, and the score from nextPlayer's perspective in
returnScore.
returnScore is ignored except by nonrecursive callers to MakeNextMove
*/
long returnScore;
returnScore =
MakeNextMove(b, me, nextPlayer, returnedDistances,
newPlys, false, from, to);
} else /*if (player==me)*/ {
/* terminating recursion, calculate position values for each player */
/* compute distances for all players */
for (thePlayer=0; thePlayer<myNumPlayers; thePlayer++)
returnedDistances[thePlayer] =
PlayerDistFromGoal(thePlayer);
}
/* compute best opponent score from this player perspective */
for (thePlayer=0,minOpponentDistance=0x7fffffff;
thePlayer<myNumPlayers; thePlayer++) {
if (   (thePlayer != player) &&
(returnedDistances[thePlayer]<minOpponentDistance) )
minOpponentDistance = returnedDistances[thePlayer];
}
scoreDifference =
returnedDistances[player]-minOpponentDistance;
/* Save score if it is the best for this player.
This move is best if
(1) our distance from goal minus best opponents distance is smallest, or
(2) goal distance difference is equal, but our absolute distance is smallest, or
(3) goal distance difference is equal, and coin flip says pick this move
(commented out) */
if ( (scoreDifference < bestScore) ||
((scoreDifference==bestScore) &&
(returnedDistances[player]<myBestDistance)) /*||
((scoreDifference==bestScore) && ((rand()&0x0080)==1))*/ ) {
bestScore = scoreDifference;
myBestDistance = returnedDistances[player];
for (opponent=0; opponent<myNumPlayers; opponent++)
playerDistances[opponent] = returnedDistances[opponent];
bestFrom = pFrom;
bestTo = pTo;
}
/* reverse move to clear board for mext move */
MoveFromTo(b,&pTo,&pFrom,player);
}
/* free dynamically allocated move storage */
free(moveTo);
free(moveFrom);

/* return best move */
*from = bestFrom;
*to = bestTo;

return bestScore;
}

FindBestMove
/* find best move for player me from this position on the board */
static long FindBestMove(CanonBoard b, long me, long numPlys, CanonPosition *from, CanonPosition *to) {
long playerDistances[6];

return MakeNextMove(b,me,me,playerDistances,numPlys,true,from,to);
}

InitChineseCheckers
void InitChineseCheckers(
long numPlayers,      /* 2..6  */
long gameSize, /* base of home triangle, 3..63, you have size*(size+1)/2 pieces */
long playerPosition[6],   /* 0..5, entries 0..numPlayers-1 are valid */
long yourIndex /* 0..numPlayers-1, your position is playerPosition[yourIndex] */
) {
int i,numPositions;
/* allocate memory for board */
numPositions = 6*(1+gameSize)*4*(1+gameSize);
myBoard = (char *)malloc(numPositions*sizeof(char));
if (myBoard==0) DebugStr("\p could not allocate board");
myNumPieces = gameSize*(gameSize+1)/2;
myPositions = (PlayerPos *)
malloc(6*myNumPieces*sizeof(PlayerPos));
if (myPositions==0)
DebugStr("\p could not allocate myPositions");

/* copy parameters */
for (i=0;i<6; i++) myPlayerPosition[i] = playerPosition[i];
myIndex = yourIndex;
myNumPlayers = numPlayers;
myGameSize = gameSize;
/* initialize board */
for (i=0; i<numPositions; i++) myBoard[i] = kEmpty;
for (i=0; i<numPlayers; i++) {
InitPlayer(myBoard,myPositions,i,playerPosition[i],gameSize);
}

/* calculate distance metric at goal position */
for (i=1, myMinDist=0; i<gameSize; i++) myMinDist += i*(i+1);
}

YourMove
void YourMove(
Position *fromPos,   /* originating position */
Position *toPos   /* destination position */
) {
CanonPosition from,to;
long numPlys = kMaxPlys;
FindBestMove(myBoard,myIndex,numPlys,&from,&to);
MoveFromTo(myBoard,&from,&to,myIndex);
*fromPos = ConvertCanonPositionToPosition(&from,myGameSize);
*toPos = ConvertCanonPositionToPosition(&to,myGameSize);
}

OpponentMove
void OpponentMove(
long opponent,   /* index in playerPosition[] of the player making move */
Position fromPos,   /* originating position */
Position toPos      /* destination position */
) {
CanonPosition from,to;
from = ConvertPositionToCanonPosition(&fromPos,myGameSize);
to =   ConvertPositionToCanonPosition(&toPos,myGameSize);
MoveFromTo(myBoard,&from,&to,opponent);
}

TermChineseCheckers
void TermChineseCheckers(void) {
free (myPositions);
free (myBoard);
}
```

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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 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
Affinity Photo 1.10.6 - Digital editing...
Affinity Photo - redefines the boundaries for professional photo editing software for the Mac. With a meticulous focus on workflow it offers sophisticated tools for enhancing, editing and retouching... Read more

## Latest Forum Discussions

‘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 »
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 »
‘Genshin Impact’ Version 3.3 Update Now...
HoYoverse recently revealed the next major update for Genshin Impact (Free) in the form of version 3.3 ‘All Senses Clear, All Existence Void’. | 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