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:

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:

#### Chinese Checkers.c Copyright © 1999 J. Robert Boonstra

/*
*  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 is a professional RAW converter offering you ultimate image quality with accurate colors and incredible detail from more than 400 high-end cameras -- straight out of the box. It offers... Read more
GraphicConverter 10.5.4 - \$39.95
GraphicConverter is an all-purpose image-editing program that can import 200 different graphic-based formats, edit the image, and export it to any of 80 available file formats. The high-end editing... Read more
Dash 4.1.3 - Instant search and offline...
Dash is an API documentation browser and code snippet manager. Dash helps you store snippets of code, as well as instantly search and browse documentation for almost any API you might use (for a full... Read more
Microsoft OneNote 16.9 - Free digital no...
OneNote is your very own digital notebook. With OneNote, you can capture that flash of genius, that moment of inspiration, or that list of errands that's too important to forget. Whether you're at... Read more
DEVONthink Pro 2.9.17 - Knowledge base,...
Save 10% with our exclusive coupon code: MACUPDATE10 DEVONthink Pro is your essential assistant for today's world, where almost everything is digital. From shopping receipts to important research... Read more
OmniGraffle 7.6 - Create diagrams, flow...
OmniGraffle helps you draw beautiful diagrams, family trees, flow charts, org charts, layouts, and (mathematically speaking) any other directed or non-directed graphs. We've had people use Graffle to... Read more
iFinance 4.3.7 - Comprehensively manage...
iFinance allows you to keep track of your income and spending -- from your lunchbreak coffee to your new car -- in the most convenient and fastest way. Clearly arranged transaction lists of all your... Read more
Opera 50.0.2762.58 - High-performance We...
Opera is a fast and secure browser trusted by millions of users. With the intuitive interface, Speed Dial and visual bookmarks for organizing favorite sites, news feature with fresh, relevant content... Read more

## Latest Forum Discussions

Around the Empire: What have you missed...
Around this time every week we're going to have a look at the comings and goings on the other sites in Steel Media's pocket-gaming empire. We'll round up the very best content you might have missed, so you're always going to be up to date with the... | Read more »
Everything about Hero Academy 2: Part 4...
In this part of our Hero Academy 2 guide, we're going to have a look at some of the tactics you're going to need to learn if you want to rise up the ranks. We're going to start off slow, then get more advanced in the next section. [Read more] | Read more »
All the best games on sale for iPhone an...
Another week has flown by. Sometimes it feels like the only truly unstoppable thing is time. Time will make dust of us all. But before it does, we should probably play as many awesome mobile videogames as we can. Am I right, or am I right? [Read... | Read more »
The 7 best games that came out for iPhon...
Well, it's that time of the week. You know what I mean. You know exactly what I mean. It's the time of the week when we take a look at the best games that have landed on the App Store over the past seven days. And there are some real doozies here... | Read more »
Popular MMO Strategy game Lords Mobile i...
Delve into the crowded halls of the Play Store and you’ll find mobile fantasy strategy MMOs-a-plenty. One that’s kicking off the new year in style however is IGG’s Lords Mobile, which has beaten out the fierce competition to receive Google Play’s... | Read more »
Blocky Racing is a funky and fresh new k...
Blocky Racing has zoomed onto the App Store and Google Play this week, bringing with it plenty of classic kart racing shenanigans that will take you straight back to your childhood. If you’ve found yourself hooked on games like Mario Kart or Crash... | Read more »
Cytus II (Games)
Cytus II 1.0.1 Device: iOS Universal Category: Games Price: \$1.99, Version: 1.0.1 (iTunes) Description: "Cytus II" is a music rhythm game created by Rayark Games. It's our fourth rhythm game title, following the footsteps of three... | Read more »
JYDGE (Games)
JYDGE 1.0.0 Device: iOS Universal Category: Games Price: \$4.99, Version: 1.0.0 (iTunes) Description: Build your JYDGE. Enter Edenbyrg. Get out alive. JYDGE is a lawful but awful roguehate top-down shooter where you get to build your... | Read more »
Tako Bubble guide - Tips and Tricks to S...
Tako Bubble is a pretty simple and fun puzzler, but the game can get downright devious with its puzzle design. If you insist on not paying for the game and want to manage your lives appropriately, check out these tips so you can avoid getting... | Read more »
Everything about Hero Academy 2 - The co...
It's fair to say we've spent a good deal of time on Hero Academy 2. So much so, that we think we're probably in a really good place to give you some advice about how to get the most out of the game. And in this guide, that's exactly what you're... | Read more »

## Price Scanner via MacPrices.net

Deals on clearance 15″ Apple MacBook Pros wit...
B&H Photo has clearance 2016 15″ MacBook Pros available for up to \$800 off original MSRP. Shipping is free, and B&H charges NY & NJ sales tax only: – 15″ 2.7GHz Touch Bar MacBook Pro... Read more
Apple restocked Certified Refurbished 13″ Mac...
Apple has restocked a full line of Certified Refurbished 2017 13″ MacBook Airs starting at \$849. An Apple one-year warranty is included with each MacBook, and shipping is free: – 13″ 1.8GHz/8GB/128GB... Read more
How to find the lowest prices on 2017 Apple M...
Apple has Certified Refurbished 13″ and 15″ 2017 MacBook Pros available for \$200 to \$420 off the cost of new models. Apple’s refurbished prices are the lowest available for each model from any... Read more
The lowest prices anywhere on Apple 12″ MacBo...
Apple has Certified Refurbished 2017 12″ Retina MacBooks available for \$200-\$240 off the cost of new models. Apple will include a standard one-year warranty with each MacBook, and shipping is free.... Read more
Apple now offering a full line of Certified R...
Apple is now offering Certified Refurbished 2017 10″ and 12″ iPad Pros for \$100-\$190 off MSRP, depending on the model. An Apple one-year warranty is included with each model, and shipping is free: –... Read more
27″ iMacs on sale for \$100-\$130 off MSRP, pay...
B&H Photo has 27″ iMacs on sale for \$100-\$130 off MSRP. Shipping is free, and B&H charges sales tax for NY & NJ residents only: – 27″ 3.8GHz iMac (MNED2LL/A): \$2199 \$100 off MSRP – 27″ 3.... Read more
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B&H Photo has the 2.8GHz Mac mini (model number MGEQ2LL/A) on sale for \$899 including free shipping plus NY & NJ sales tax only. Their price is \$100 off MSRP. Read more
Apple offers Certified Refurbished iPad minis...
Apple has Certified Refurbished 128GB iPad minis available today for \$339 including free shipping. Apple’s standard one-year warranty is included. Their price is \$60 off MSRP. Read more
Amazon offers 13″ 256GB MacBook Air for \$1049...
Amazon has the 13″ 1.8GHz/256B #Apple #MacBook Air on sale today for \$150 off MSRP including free shipping: – 13″ 1.8GHz/256GB MacBook Air (MQD42LL/A): \$1049.99, \$150 off MSRP Read more
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B&H Photo has 9.7″ 2017 WiFi #Apple #iPads on sale for \$30 off MSRP for a limited time. Shipping is free, and pay sales tax in NY & NJ only: – 32GB iPad WiFi: \$299, \$30 off – 128GB iPad WiFi... Read more

## Jobs Board

AppleCare Support Engineer for *Apple* Medi...
# AppleCare Support Engineer for Apple Media Products Job Number: 113222855 Santa Clara Valley, California, United States Posted: 14-Nov-2017 Weekly Hours: 40.00 Read more
QA Automation Engineer, *Apple* Pay - Apple...
# QA Automation Engineer, Apple Pay Job Number: 113202642 Santa Clara Valley, California, United States Posted: 11-Dec-2017 Weekly Hours: 40.00 **Job Summary** At Read more
*Apple* Video Partnerships - Apple (United S...
# Apple Video Partnerships Job Number: 113059126 Santa Clara Valley, California, United States Posted: 15-Nov-2017 Weekly Hours: 40.00 **Job Summary** Partnerships Read more
Sr. Engineering Manager- *Apple* Media Produ...
# Sr. Engineering Manager- Apple Media Products Job Number: 113335268 Santa Clara Valley, California, United States Posted: 17-Jan-2018 Weekly Hours: 40.00 **Job Read more
*Apple* Retail - Multiple Positions - Apple,...
Job Description:SalesSpecialist - Retail Customer Service and SalesTransform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
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