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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Capture One Pro 8 is a professional RAW converter offering you ultimate image quality with accurate colors and incredible detail from more than 300 high-end cameras -- straight out of the box. It... Read more
Backblaze 4.0.0.872 - Online backup serv...
Backblaze is an online backup service designed from the ground-up for the Mac.With unlimited storage available for \$5 per month, as well as a free 15-day trial, peace of mind is within reach with... Read more
Little Snitch gives you control over your private outgoing data. Track background activity As soon as your computer connects to the Internet, applications often have permission to send any... Read more
Monolingual 1.6.4 - Remove unwanted OS X...
Monolingual is a program for removing unnecesary language resources from OS X, in order to reclaim several hundred megabytes of disk space. If you use your computer in only one (human) language, you... Read more
CleanApp 5.0 - Application deinstaller a...
CleanApp is an application deinstaller and archiver.... Your hard drive gets fuller day by day, but do you know why? CleanApp 5 provides you with insights how to reclaim disk space. There are... Read more
Fantastical 2.0 - Create calendar events...
Fantastical is the Mac calendar you'll actually enjoy using. Creating an event with Fantastical is quick, easy, and fun: Open Fantastical with a single click or keystroke Type in your event details... Read more
Cocktail 8.2 - General maintenance and o...
Cocktail is a general purpose utility for OS X that lets you clean, repair and optimize your Mac. It is a powerful digital toolset that helps hundreds of thousands of Mac users around the world get... Read more
Direct Mail 4.0.4 - Create and send grea...
Direct Mail is an easy-to-use, fully-featured email marketing app purpose-built for OS X. It lets you create and send great looking email campaigns. Start your newsletter by selecting from a gallery... Read more

## Latest Forum Discussions

These are All the Apple Watch Apps and G...
The Apple Watch is less than a month from hitting store shelves, and once you get your hands on it you're probably going to want some apps and games to install. Fear not! We've compiled a list of all the Apple Watch apps and games we've been able to... | Read more »
Appy to Have Known You - Lee Hamlet Look...
Being at 148Apps these past 2 years has been an awesome experience that has taught me a great deal, and working with such a great team has been a privilege. Thank you to Rob Rich, and to both Rob LeFebvre and Jeff Scott before him, for helping me... | Read more »
Hands-On With Allstar Heroes - A Promisi...
Let’s get this out of the way quickly. Allstar Heroes looks a lot like a certain other recent action RPG release, but it turns out that while it’s not yet available here, Allstar Heroes has been around for much longer than that other title. Now that... | Read more »
Macho Man and Steve Austin Join the Rank...
WWE Immortals, by Warner Bros. Interactive Entertainment and WWE, has gotten a superstar update. You'll now have access to Macho Man Randy Savage and Steve Austin. Both characters have two different versions: Macho Man Randy Savage Renegade or Macho... | Read more »
Fearless Fantasy is Fantastic for the iF...
I actually had my first look at Fearless Fantasy last year at E3, but it was on a PC so there wasn't much for me to talk about. But now that I've been able to play with a pre-release version of the iOS build, there's quite a bit for me to talk... | Read more »
MLB Manager 2015 (Games)
MLB Manager 2015 5.0.14 Device: iOS Universal Category: Games Price: \$4.99, Version: 5.0.14 (iTunes) Description: Guide your favorite MLB franchise to glory! MLB Manager 2015, officially licensed by MLB.com and based on the award-... | Read more »
Breath of Light (Games)
Breath of Light 1.0.1421 Device: iOS Universal Category: Games Price: \$2.99, Version: 1.0.1421 (iTunes) Description: Hold a quiet moment. Breath of Light is a meditative and beautiful puzzle game with a hypnotic soundtrack by... | Read more »
WWE WrestleMania Tags into the App Store
Are You ready to rumble? The official WWE WrestleMania app, by World Wrestling Entertainment, is now available. Now you can get all your WrestleMania info in one place before anyone else. The app offers details on superstar signings, interactive... | Read more »
Bio Inc's New Expansion is Infectin...
Bio Inc., by DryGin Studios, is the real time strategy game where you infect a human body with the worst virus your evil brain can design. Recently, the game was updated to add a whole lot of new features. Now you can play the new “Lethal”... | Read more »
The Monocular Minion is Here! Despicable...
Despicable Me: Minion Rush, by Gameloft, is introducing a new runner to the mix in their latest update. Now you can play as Carl, the prankster minion. Carl has a few new abilities to play with, including running at a higher speed from the start.... | Read more »

## Price Scanner via MacPrices.net

13-inch 2.5GHz MacBook Pro (refurbished) avai...
The Apple Store has Apple Certified Refurbished 13″ 2.5GHz MacBook Pros available for \$829, or \$270 off the cost of new models. Apple’s one-year warranty is standard, and shipping is free: - 13″ 2.... Read more
Save up to \$80 on iPad Air 2s, NY tax only, f...
B&H Photo has iPad Air 2s on sale for \$80 off MSRP including free shipping plus NY sales tax only: - 16GB iPad Air 2 WiFi: \$469.99 \$30 off - 64GB iPad Air 2 WiFi: \$549.99 \$50 off - 128GB iPad... Read more
iMacs on sale for up to \$205 off MSRP
B&H Photo has 21″ and 27″ iMacs on sale for up to \$205 off MSRP including free shipping plus NY sales tax only: - 21″ 1.4GHz iMac: \$1019 \$80 off - 21″ 2.7GHz iMac: \$1189 \$110 off - 21″ 2.9GHz... Read more
Färbe Technik Offers iPhone Battery Charge LI...
Färbe Technik, which manufactures and markets of mobile accessories for Apple, Blackberry and Samsung mobile devices, is offering tips on how to keep your iPhone charged while in the field: •... Read more
Electronic Recyclers International CEO Urges...
Citing a recent story on CNBC about concerns some security professionals have about the forthcoming Apple Watch, John Shegerian, Chairman and CEO of Electronic Recyclers International (ERI), the... Read more
Save up to \$380 with Apple refurbished iMacs
The Apple Store has Apple Certified Refurbished iMacs available for up to \$380 off the cost of new models. Apple’s one-year warranty is standard, and shipping is free: - 27″ 3.5GHz 5K iMac – \$2119 \$... Read more
Mac minis on sale for up to \$75 off, starting...
MacMall has Mac minis on sale for up to \$75 off MSRP including free shipping. Their prices are the lowest available for these models from any reseller: - 1.4GHz Mac mini: \$459.99 \$40 off - 2.6GHz Mac... Read more
College Student Deals: Additional \$50 off Mac...
Take an additional \$50 off all MacBooks and iMacs at Best Buy Online with their College Students Deals Savings, valid through April 11, 2015. Anyone with a valid .EDU email address can take advantage... Read more
Mac Pros on sale for up to \$260 off MSRP
B&H Photo has Mac Pros on sale for up to \$260 off MSRP. Shipping is free, and B&H charges sales tax in NY only: - 3.7GHz 4-core Mac Pro: \$2799, \$200 off MSRP - 3.5GHz 6-core Mac Pro: \$3719.99... Read more
13-inch 2.5GHz MacBook Pro on sale for \$100 o...
B&H Photo has the 13″ 2.5GHz MacBook Pro on sale for \$999 including free shipping plus NY sales tax only. Their price is \$100 off MSRP. Read more

## Jobs Board

DevOps Software Engineer - *Apple* Pay, iOS...
**Job Summary** Imagine what you could do here. At Apple , great ideas have a way of becoming great products, services, and customer experiences very quickly. Bring Read more
*Apple* Retail - Multiple Positions (US) - A...
Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, you're also the Read more
Sr. Technical Services Consultant, *Apple*...
**Job Summary** Apple Professional Services (APS) has an opening for a senior technical position that contributes to Apple 's efforts for strategic and transactional Read more
Lead *Apple* Solutions Consultant - Retail...
**Job Summary** Job Summary The Lead ASC is an Apple employee who serves as the Apple business manager and influencer in a hyper-business critical Reseller's store Read more
*Apple* Pay - Site Reliability Engineer - Ap...
**Job Summary** Imagine what you could do here. At Apple , great ideas have a way of becoming great products, services, and customer experiences very quickly. Bring Read more