Dec 00 Challenge Volume Number: 16 (2000)
Issue Number: 12
Column Tag: Programmer's Challenge

# Programmer's Challenge

By Bob Boonstra, Westford, MA

### Crutches

Crutches? What an odd topic for a Programmer's Challenge, you might think. Let me explain. This month's problem was actually suggested by my wife, whose connection with the Challenge has until now been limited to the patience required to put up with the amount of time I spend running the contest. She recently had the misfortune to break her foot, which has, you guessed it, put her on crutches for six or so weeks. Being on crutches gives one a new perspective on distance, particularly distance between points around the house. And while she tries to stay off the foot as much as possible, she still has to get from place to place, so the broken foot also motivates one to find ways to minimize distance. Which leads us to this month's Challenge, a practical extension of the well-known Traveling Salesperson problem.

The prototype for the code you should write is:

```typedef long Node;
typedef long Weight;

typedef struct Connection {
Node node1;         /* a connection exists between node1 ... */
Node node2;         /* ... and node2 .... */
long distance;      /* ... separated by this distance */
} Connection;

Weight weight;   /* you need to carry an object with this weight ... */
Node fromNode;   /* ... from fromNode ... */
Node toNode;      /* ... to toNode */

typedef enum {kPickUpObject=1, kDropOffObject, kMoveTo} ActionType;

typedef struct Action {
ActionType action,   /* actions comprising the solution */
long object,            /* kPickUpObject or kDropOffObject this object */
Node node               /* kMoveTo this node */
} Action;

long /* actions in solution */ Crutches (
const Node nodes[],            /* Nodes defining the problem */
long numNodes,
const Connection connections[],   /* Connections between nodes */
long numConnections,
const Task objectsToMove[],   /* objects to be moved */
long numObjects,
Node startingNode,            /* start from this node */
Weight maxWeightToCarry,   /* maximum weight that you can carry */
Action solutionPath[]      /* return your solution here */
);
```

Your job is to write code that will perform a set of Tasks and minimize the distance traveled in doing so. Each Task consists of moving an object of a specified weight from one place (Node) to another. You can travel from one Node to another only if a Connection exists between the Nodes, and moving between a pair of Nodes requires traveling the associated distance along that Connection.

At the start of the problem, you are located at the startingNode. You are given the numNodes Nodes describing the problem space and the numConnections Connections between them. You are also given numObjects objectsToMove, each of which needs to be transported from the fromNode to the toNode. You can carry more than one object along your journey, provided the sum of the weights of the objects being carried does not exceed the maxWeightToCarry. The solution is described as a sequence of Actions. An Action consists of picking up an object (kPickUpObject) from the current Node, dropping off an Object at the current Node (kDropOffObject), or moving to an adjacent Node (kMoveTo) and carrying all objects that have been picked up to that Node. You may not pick up an object if doing so would cause the maxWeightToCarry to be exceeded. The sequence of Actions that transports all of the objectsToMove to the appropriate Nodes should be returned as the solutionPath, and Crutches should return the number of Actions in your solution.

None of the Tasks will be impossible to perform. No object will have a weight greater than maxWeightToCarry, so it will be possible to carry each object. It will be possible to reach each fromNode and each toNode by traversing Connections from the startingNode. Connections may not satisfy the triangle inequality, that is, it may be the case that a direct Connection between two Nodes is not the shortest path between them. No other a priori information about the Connections, Nodes, or Tasks is available.

Your solution will be evaluated first on correctness (as always), and then on score. Your score for this Challenge will be the total distance traveled to perform the required Tasks, plus a 10% penalty for each second of execution time expended. Lower scores are, of course, better.

The Challenge prize will be divided between the overall winner and the best scoring entry from a contestant that has not won the Challenge recently. If you have wanted to compete in the Challenge, but have been discouraged from doing so by the quality of the entries from our veteran contestants, perhaps this is your chance at some recognition and a share of the Challenge prize.

This will be a native PowerPC Challenge, using the CodeWarrior Pro 5 environment. Solutions may be coded in C, C++, or Pascal.

Next month, perhaps we'll solve the problem of how to motivate a couple of teenage children to perform these Tasks, allowing the broken foot more time to rest and heal. But perhaps that would be too difficult, even for Challenge readers. (Actually, the kids are being very helpful with the household chores.)

### Three Months Ago Winner

Congratulations to Claes Wihlborg (Sweden) for submitting the winning entry to the September Busy Beaver Challenge. This Challenge required contestants to do two things. First, contestants were to produce a 5-state "Busy Beaver" Turing Machine that writes as large a number of 1s as possible when given a blank input tape. Second, they had to write a general Turing Machine simulator that executes this Busy Beaver as quickly as possible. The problem statement provided a reference to a Turing Machine demonstrating that BB(5), the maximum number of 1s produced by any 5-state Busy Beaver, is at least 4098. Alas, none of the nine entries in this Challenge broke new ground in Busy Beaver research by providing a Busy Beaver that produced more than 4098 1s. So this competition was based on how quickly the Busy Beaver could be executed.

Claes' solution is extraordinarily fast, five times faster than the second place solution, and more than sixty times faster than the third-place solution. Upon investigation, while somewhat difficult to understand because of sparse commentary, Claes' entry is fascinating. To fully understand it, I inserted some debugging code and watched it in operation. I'll try to compensate for the terseness of the code by providing some additional explanation here.

The first thing Claes does is to call the CreateOptimizedTMRules routine to compile the Turing Machine rules into OptimizedTMRules. Two OptimizedTMRules are created for each Turing Machine rule, encoding both the rule and the associated binary input symbol. Each OptimizedTMRule contains a OneBitActionRoutines action field that combines two elements of the original Turing Machine rule: the move direction, and whether the output symbol is unchanged, 0, or 1. These actions are encoded as follows:

abaLeft, abaRight , abaHalt - leave the input unchanged and move left, right, or halt

abaLeftSet, abaRightSet, abaHaltSet - write a 1 and move left, right, or halt

abaLeftClear, abaRightClear, abaHaltClear - write a 0 and move left, right, or halt

This optimization allows Claes to factor out some logic tests during the Turing Machine simulation, and to avoid modifying the output tape when it doesn't change.

The runNBitTuringMachine performs the Turing Machine simulation. This routine processes the input tape in chunks of either 6 bits or 8 bits in size, trying the former first, and the latter if the former fails. It creates and uses two additional data structures, the TapeSegment structure that encodes a segment of the Turing Machine tape, and the MacroNTMRule data structure that further encodes the OptimizedTMRules. The TapeSegment data structure takes advantage of the fact that repeating sequences can occur on a Turing Machine tape, and do occur on Busy Beaver Turing Machines. It contains a symbol field, which is a 6- or 8-bit section of the tmTape, an exponent that contains a repetition count for that section, and left and right pointers to adjacent tape segments.

The MacroNTMRule is a little more difficult to explain. The 256 Turing Machine states that the problem statement requires entries to support are expanded into 512 OptimizedTMRules, and further expand into 512*256 MacroNTMRules. A MacroNTMRule is indexed by 8 bits that identify the OptimizedTMRule, plus of the TapeSegment symbol value (6 or 8 bits). In effect, the MacroNTMRule expands the symbol set from 1 bit to 6 or 8 bits, and expands the set of Turing Machine states accordingly.

When runNBitTuringMachine executes the Turing Machine, it first looks to see if the MacroNTMRule corresponding to the current state has been created. If not, it calls the createNbitMacroRule routine to create it. This routine simulates the effect of the OptimizedTMRules on the current input symbol, determines what newSymbol output is produced, counts the number of OptimizedTMRules executed for this one MacroNTMRule, characterizes the nature of the rule into an NBitActionRoutines action, and stores a pointer to the new MacroNTMRule state.

The NBitActionRoutines field characterizes the MacroNTMRule by encoding the move direction, whether the output is different from the input, and whether the state is changed after processing this chunk of input. The most interesting values for this NBitActionRoutines field are as follows:

• tbaBounceLeft, tbaBounceRight - leave the input unchanged and reverse direction left or right
• tTbaBounceLeftChange, tbaBounceRightChange - write changed output and reverse direction left or right
• tTbaThruLeft, tbaThruRight - leave the input unchanged, continue moving left or right, and modify the state
• tTbaThruLeftChange, tbaThruRightChange - write changed output, continue moving left or right, and modify the state
• tTbaThruOptimized tbaThruRightOptimized - leave the input unchanged, continue moving left or right, and stay in the same state
• tTbaThruChangeOptimized tbaThruRightChangeOptimized - write changed output, continue moving left or right, and stay in the same state

The optimizations in the runNBitTuringMachine code allow the final output of Claes' Busy Beaver to be represented in a few TapeSegments:

 Segment Symbol (Hex) Exponent (Hex) 0 0 180 1 1 1 2 36 1023 3 37 1 4 0 395

When runNBitTuringMachine returns, it indicates whether the attempt to execute with 6-bit tape segments succeeded or failed. If it failed, it is run again using 8-bit segments. While the 6-bit optimization is clearly intended to speed up the 5-state Busy Beaver Turing machines, it also kicks in for other machines. More importantly, the program meets the requirement of correctly simulating any Turing Machine with up to 256 states, without hard-coding any particulars of the Busy Beaver problem.

Before RunTuringMachine returns, it copies the TapeSegments back to the Turing Machine tape. (Until this point, the output of the Turing Machine exists only in the TapeSegment database.) For the 6-bit tape segment case, Claes uses an unrolled loop. For the 8-bit case, he uses memset. In both cases, the exponent field in the TapeSegment controls the number of times a TapeSegment symbol is copied.

I'd encourage you to take a look at Claes solution. I found it to be very clever.

The table below lists, for each of the solutions submitted, the number of 1s generated by the entry's Busy Beaver Turing Machine, the number of rules executed by that machine, the execution time of the Busy Beaver in milliseconds, and cumulative test case execution time. It also provides the code size, data size, and programming language used for each entry. As usual, the number in parentheses after the entrant's name is the total number of Challenge points earned in all Challenges prior to this one.

 Name # of 1s # of Rules BB Time (msecs) Time (msecs) Code Size Data Size Lang Claes Wihlborg (9) 4098 11798826 0.93 3.04 6680 1080033 C Ernst Munter (651) 4098 11798826 5.10 22.82 4764 749 C++ Mike Miller 4098 11798826 61.49 306.93 2044 410 C Rob Shearer (51) 4098 11798826 64.92 311.59 1432 716 C++ Randy Boring (133) 4098 11798826 213.09 1066.58 4456 94 C++ Willeke Rieken (112) 4098 11798826 489.74 2456.34 912 16 C Tom Saxton (165) 4098 11798826 734.27 3678.83 708 180 C++ Yung-Lueng Lan 4098 11798826 743.58 3726.49 1372 28 C Ladislav Hala (7) 4098 47176870 2954.95 5922.87 1520 750 C

### Top Contestants...

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

 Rank Name Points 1. Munter, Ernst 231 2. Saxton, Tom 106 3. Maurer, Sebastian 68 4. Rieken, Willeke 65 5. Boring, Randy 52 6. Shearer, Rob 48 7. Taylor, Jonathan 36 8. Wihlborg, Charles 29 9. Brown, Pat 20

### ... and the Top Contestants Looking For a Recent Win

Starting this month, in order to give some recognition to other participants in the Challenge, we are also going to list the high scores for contestants who have accumulated points without taking first place in a Challenge. Listed here are all of those contestants who have accumulated 6 or more points during the past two years.

 10 Downs, Andrew 12 11 Jones, Dennis 12 12 Day, Mark 10 13 Duga, Brady 10 14 Fazekas, Miklos 10 15 Selengut, Jared 10 16 Strout, Joe 10 17 Hala, Ladislav 7 18 Miller, Mike 7 19 Nicolle, Ludovic 7 20 Schotsman, Jan 7 21 Widyyatama, Yudhi 7 22 Heithcock, JG 6

There are three ways to earn points: (1) scoring in the top 5 of any Challenge, (2) being the first person to find a bug in a published winning solution or, (3) being the first person to suggest a Challenge that I use. The points you can win are:

 1st place 20 points 2nd place 10 points 3rd place 7 points 4th place 4 points 5th place 2 points finding bug 2 points suggesting Challenge 2 points

Here is Claes' winning Busy Beaver solution:

```BusyBeaver.c
Claes Wihlborg

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

#include "BusyBeaver.h"

BusyBeaver5
ulong /* return number of rules */ BusyBeaver5(
TMRule theTMRules[]
/* preallocated storage, return the rules for your BB machine */
)
{
TMRule tm01[] = {
{0,0, 1,1,kMoveRight},
{0,1, 0,1,kMoveRight},
{1,0, 2,1,kMoveLeft},
{1,1, 1,1,kMoveLeft},
{2,0, 0,1,kMoveRight},
{2,1, 3,1,kMoveLeft},
{3,0, 0,1,kMoveRight},
{3,1, 4,1,kMoveLeft},
{4,0, 1,1,kHalt},
{4,1, 2,0,kMoveLeft}
};

memcpy( theTMRules, tm01, 10*sizeof(TMRule) );
return 5*2;
}

TYPES
typedef enum {obaNotYetDefined,
obaLeft, obaLeftSet, obaLeftClear,
obaHalt, obaHaltSet, obaHaltClear,
obaRight, obaRightSet, obaRightClear } OneBitActionRoutines;

typedef struct OptimizedTMRule {
OneBitActionRoutines action;
struct OptimizedTMRule *newState;
/* set current state to newState when this rule fires */
} OptimizedTMRule;

typedef enum {tbaNotYetDefined, tbaUndefined,
tbaHaltFromLeft, tbaHaltFromRight,
tbaBounceLeft, tbaBounceRight,
tbaBounceLeftChange, tbaBounceRightChange,
tbaThruLeft, tbaThruRight,
tbaThruLeftChange, tbaThruRightChange,
tbaThruLeftOptimized, tbaThruRightOptimized,
tbaThruLeftChangeOptimized,
tbaThruRightChangeOptimized } NBitActionRoutines;

typedef struct MacroNTMRule {
NBitActionRoutines action;
unsigned char newSymbol;
unsigned short ruleCount;
struct MacroNTMRule *newState;
/* set current state to newState when this rule fires */
} MacroNTMRule;

typedef struct TapeSegment {
unsigned int symbol;
unsigned int exponent;
struct TapeSegment *left,*right;
} TapeSegment;

GLOBAL VARIABLES
static OptimizedTMRule optimizedTMRules[512];
static unsigned int highestState;

static    MacroNTMRule rules[256*2*256];

static unsigned int nBit, maxBit;

#define tapeDim 1520
static int nxtTapeIx;
static TapeSegment myTape[tapeDim], *freeSegment, *rightmostSegment, *leftmostSegment;

static unsigned char *TheTapeCenter;
static ulong allocatedLeft, maxALeft, allocatedRight, maxARight;
static ulong numberOf1sOnInputTape;

static int aLotOfZeroes[] = {
0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0,
0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0,
0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0,
0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0,
0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0      };

FUNCTION PROTOTYPES
static Boolean CreateOptmizedTMRules(
TMRule theTMRules[],     /* contains the rules for your BB machine */
ulong numberOfTMRules);

static void createNbitMacroRule( unsigned int inSymbol, MacroNTMRule *inState );

static Boolean MoreSegments( void );
static TapeSegment *GetFreeSegment( void );
static TapeSegment *expandLeft( void );
static TapeSegment *expandRight( void );

static Boolean runNBitTuringMachine(
ulong *numberOf1sGenerated,
ulong *numberOfRulesExecuted
);

CreateOptmizedTMRules
static Boolean CreateOptmizedTMRules(
TMRule theTMRules[],     /* contains the rules for your BB machine */
ulong numberOfTMRules)
{
unsigned int i,state,inputSymbol;
OptimizedTMRule *destRule;

highestState = 0;
memset( optimizedTMRules, 0x00, 512*sizeof(OptimizedTMRule) );

for(i=0; i<numberOfTMRules; i++)
{
if ((state = theTMRules[i].oldState) > highestState)
highestState = state;
destRule = optimizedTMRules + ((theTMRules[i].oldState << 1) +
(inputSymbol=theTMRules[i].inputSymbol));
if (destRule->action != obaNotYetDefined)
{
printf("State: %d  Input: %d multiply defined\n",
theTMRules[i].oldState,inputSymbol);
return false;
}
destRule->newState = optimizedTMRules +
(theTMRules[i].newState << 1);
destRule->action = obaHalt + 3*theTMRules[i].moveDirection;
if (inputSymbol != theTMRules[i].outputSymbol)
if (theTMRules[i].inputSymbol) destRule->action+=2;
else destRule->action++;
}
return true;
}

createNbitMacroRule
static void createNbitMacroRule( unsigned int inSymbol,
MacroNTMRule *inState )
{
int   mySymbol = inSymbol;
int bit;
OptimizedTMRule *state;
int iState;
OneBitActionRoutines action;
int   ruleCount = 0;
MoveDir inDir,outDir;

iState = (inState - rules) >> nBit;
state = optimizedTMRules + (iState & 0xfffe);

if (iState & 1)
{
bit = 1;
inDir = kMoveLeft;
}
else
{
bit = maxBit;
inDir = kMoveRight;
}

loop:
ruleCount++;
if (mySymbol & bit)
{
action = state[1].action;
state = state[1].newState;
}
else
{
action = state->action;
state = state->newState;
}
switch (action)
{
case obaNotYetDefined:
inState->ruleCount = ruleCount;
inState->newSymbol = mySymbol;
inState->action = tbaUndefined;
return;
case obaLeft:
if ((bit <<= 1) <= maxBit) goto loop;
break;
case obaLeftSet:
mySymbol |= bit;
if ((bit <<= 1) <= maxBit) goto loop;
break;
case obaLeftClear:
mySymbol &= -1 - bit;
if ((bit <<= 1) <= maxBit) goto loop;
break;
case obaHalt:
inState->ruleCount = ruleCount;
inState->newSymbol = mySymbol;
inState->action = (inDir == kMoveRight)?
tbaHaltFromLeft : tbaHaltFromRight;
return;
case obaHaltSet:
mySymbol |= bit;
inState->ruleCount = ruleCount;
inState->newSymbol = mySymbol;
inState->action = (inDir == kMoveRight)?
tbaHaltFromLeft : tbaHaltFromRight;
return;
case obaHaltClear:
mySymbol &= -1 - bit;
inState->ruleCount = ruleCount;
inState->newSymbol = mySymbol;
inState->action = (inDir == kMoveRight)?
tbaHaltFromLeft : tbaHaltFromRight;
return;
case obaRight:
if (bit >>= 1) goto loop;
break;
case obaRightSet:
mySymbol |= bit;
if (bit >>= 1) goto loop;
break;
case obaRightClear:
mySymbol &= -1 - bit;
if (bit >>= 1) goto loop;
break;
}

inState->ruleCount = ruleCount;
inState->newSymbol = mySymbol;
inState->action = tbaBounceLeft;
if (!bit)
{
outDir = kMoveRight;
inState->action++;
}
else
{
outDir = kMoveLeft;
state++;
}
if (mySymbol != inSymbol)
inState->action += 2;

inState->newState = ((state - optimizedTMRules) << nBit) +
rules;
if (outDir == inDir)
{
inState->action += 4;
if ((state - optimizedTMRules) == iState)
inState->action += 4;
}

return;
}

MoreSegments
static Boolean MoreSegments( void )
{
int end;
if (nBit == 6) return false;
if (nxtTapeIx < tapeDim)
{
end = nxtTapeIx + 149;
freeSegment = myTape + nxtTapeIx;
do
{
myTape[nxtTapeIx].right = myTape + nxtTapeIx + 1;
}
while (++nxtTapeIx < end);
myTape[nxtTapeIx++].right = 0;
return true;
}
//  printf("Segments finito!!!!\n");
return false;
}

GetFreeSegment
static TapeSegment *GetFreeSegment( void )
{
TapeSegment *tmp;

if (freeSegment || MoreSegments())
{
tmp = freeSegment;
freeSegment = tmp->right;
return tmp;
}
return 0;
}

expandLeft
static TapeSegment *expandLeft( void )
{
ulong delta;
TapeSegment *tmp, *newCurrent, *oldLeftmost;
unsigned char *p,*pOld;
ulong oneCount, oldValue;

if (!(delta = (((maxALeft - allocatedLeft) >300) ?
300 : (maxALeft - allocatedLeft))))
return 0;

allocatedLeft += delta;
p = TheTapeCenter - allocatedLeft;

if (!(newCurrent = GetFreeSegment()))
return 0;
newCurrent->left = 0;
oldLeftmost = leftmostSegment;
leftmostSegment = newCurrent;

if (!memcmp( p, aLotOfZeroes, delta))
{
newCurrent->symbol = 0;
newCurrent->exponent = 8*delta / nBit;
}
else
if (nBit == 8)
{
newCurrent->symbol = *p;
newCurrent->exponent = 1;
pOld = p + delta;
while (++p < pOld)
{
if (*p == newCurrent->symbol)
{
newCurrent->exponent++;
}
else
{
tmp = newCurrent;
if (!(newCurrent = GetFreeSegment()))
return 0;
newCurrent->left = tmp;
tmp->right = newCurrent;
newCurrent->symbol = *p;
newCurrent->exponent = 1;
}
}
tmp = newCurrent;
do
{
if ((oldValue = tmp->symbol)!=0)
{
oneCount = 0;
do {
++oneCount;
} while (oldValue = oldValue & (oldValue-1));
numberOf1sOnInputTape += oneCount*tmp->exponent;
}
}
while (tmp = tmp->left);
}
else/*nBit==6*/
{
return 0;
}

newCurrent->right = oldLeftmost;
if (oldLeftmost)
{
oldLeftmost->left = newCurrent;
}
else
{
rightmostSegment = newCurrent;
}
return newCurrent;
}

expandRight
static TapeSegment *expandRight( void )
{
ulong delta;
TapeSegment *tmp, *newCurrent, *oldRightmost;
unsigned char *p,*pOld;
ulong oneCount, oldValue;

if (!(delta = (((maxARight - allocatedRight) >300) ?
300 : (maxARight - allocatedRight))))
return 0;

pOld = TheTapeCenter + allocatedRight;
allocatedRight += delta;

if (!(newCurrent = GetFreeSegment()))
return 0;
newCurrent->right = 0;
oldRightmost = rightmostSegment;
rightmostSegment = newCurrent;

if (!memcmp( pOld, aLotOfZeroes, delta))
{
newCurrent->symbol = 0;
newCurrent->exponent = 8*delta / nBit;
}
else
if (nBit == 8)
{
p = pOld + delta -1;
newCurrent->symbol = *p;
newCurrent->exponent = 1;
while (—p >= pOld)
{
if (*p == newCurrent->symbol)
{
newCurrent->exponent++;
}
else
{
tmp = newCurrent;
if (!(newCurrent = GetFreeSegment()))
return 0;
newCurrent->right = tmp;
tmp->left = newCurrent;
newCurrent->symbol = *p;
newCurrent->exponent = 1;
}
}
tmp = newCurrent;
do
{
if ((oldValue = tmp->symbol)!=0)
{
oneCount = 0;
do {
++oneCount;
} while (oldValue = oldValue & (oldValue-1));
numberOf1sOnInputTape += oneCount*tmp->exponent;
}
}
while (tmp = tmp->right);
}
else/*nBit==6*/
{
return 0;
}

newCurrent->left = oldRightmost;
oldRightmost->right = newCurrent;
return newCurrent;
}

runNBitTuringMachine
static Boolean runNBitTuringMachine(
ulong *numberOf1sGenerated,
ulong *numberOfRulesExecuted
)
{
// Local data areas
ulong oneCount;
ulong ruleCount = 0;
int oldValue,i;
MacroNTMRule *state;
TapeSegment *currentSegment, *tmp;
Boolean resultat = false;

// Init

*numberOf1sGenerated = 0;
numberOf1sOnInputTape = 0;

memset( rules, 0x00,
(highestState+1)*2*(1<<nBit)*sizeof(MacroNTMRule) );
state = rules;

for (i=0;i<19;i++)
{
myTape[i].right = myTape + i + 1;
}
myTape[19].right = 0;
freeSegment = myTape;

rightmostSegment = 0;
leftmostSegment = 0;
allocatedLeft = 0;
allocatedRight = 0;

expandLeft();
currentSegment = expandRight();

mainLoop:
state += currentSegment->symbol;
loop:
ruleCount += state->ruleCount;
switch (state->action)
{
case tbaNotYetDefined:
createNbitMacroRule( currentSegment->symbol, state );
goto loop;

case tbaUndefined:
goto avsluta;

case tbaHaltFromLeft:
if (currentSegment->exponent > 1)
{
tmp = currentSegment;
if (!(currentSegment = freeSegment))
{
if (!MoreSegments()) goto avsluta;
currentSegment = freeSegment;
}
freeSegment = currentSegment->right;
currentSegment->left = tmp->left;
currentSegment->left->right = currentSegment;
currentSegment->right = tmp;
tmp->left = currentSegment;
currentSegment->exponent = 1;
tmp->exponent—;
}
currentSegment->symbol = state->newSymbol;
break;

case tbaHaltFromRight:
if (currentSegment->exponent > 1)
{
tmp = currentSegment;
if (!(currentSegment = freeSegment))
{
if (!MoreSegments()) goto avsluta;
currentSegment = freeSegment;
}
freeSegment = currentSegment->right;
currentSegment->left = tmp;
currentSegment->right = tmp->right;
tmp->right->left = currentSegment;
tmp->right = currentSegment;
currentSegment->exponent = 1;
tmp->exponent—;
}
currentSegment->symbol = state->newSymbol;
break;

case tbaBounceLeft:
state = state->newState;
currentSegment = currentSegment->left;
goto mainLoop;

case tbaBounceRight:
currentSegment = currentSegment->right;
state = state->newState;
goto mainLoop;

case tbaBounceLeftChange:
if (currentSegment->exponent > 1)
{
tmp = currentSegment;
if (!(currentSegment = freeSegment))
{
if (!MoreSegments()) goto avsluta;
currentSegment = freeSegment;
}
freeSegment = currentSegment->right;
currentSegment->left = tmp->left;
currentSegment->right = tmp;
tmp->left->right = currentSegment;
tmp->left = currentSegment;
currentSegment->exponent = 1;
tmp->exponent—;
}
currentSegment->symbol = state->newSymbol;
state = state->newState;
currentSegment = currentSegment->left;
goto mainLoop;

case tbaBounceRightChange:
if (currentSegment->exponent > 1)
{
tmp = currentSegment;
if (!(currentSegment = freeSegment))
{
if (!MoreSegments()) goto avsluta;
currentSegment = freeSegment;
}
freeSegment = currentSegment->right;
currentSegment->left = tmp;
currentSegment->right = tmp->right;
tmp->right->left = currentSegment;
tmp->right = currentSegment;
currentSegment->exponent = 1;
tmp->exponent—;
}
currentSegment->symbol = state->newSymbol;
currentSegment = currentSegment->right;
state = state->newState;
goto mainLoop;

case tbaThruLeft:
if (currentSegment->exponent > 1)
{
tmp = currentSegment;
if (!(currentSegment = freeSegment))
{
if (!MoreSegments()) goto avsluta;
currentSegment = freeSegment;
}
freeSegment = currentSegment->right;
currentSegment->left = tmp;
currentSegment->right = tmp->right;
tmp->right->left = currentSegment;
tmp->right = currentSegment;
currentSegment->exponent = 1;
tmp->exponent—;
}
state = state->newState;
if (currentSegment = currentSegment->left)
goto mainLoop;
if (currentSegment = expandLeft()) goto mainLoop;
break;

case tbaThruRight:
if (currentSegment->exponent > 1)
{
tmp = currentSegment;
if (!(currentSegment = freeSegment))
{
if (!MoreSegments()) goto avsluta;
currentSegment = freeSegment;
}
freeSegment = currentSegment->right;
currentSegment->left = tmp->left;
currentSegment->right = tmp;
tmp->left->right = currentSegment;
tmp->left = currentSegment;
currentSegment->exponent = 1;
tmp->exponent—;
}
state = state->newState;
if (currentSegment = currentSegment->right)
goto mainLoop;
if (currentSegment = expandRight()) goto mainLoop;
break;

case tbaThruLeftChange:
if (currentSegment->exponent > 1)
{
tmp = currentSegment;
if (!(currentSegment = freeSegment))
{
if (!MoreSegments()) goto avsluta;
currentSegment = freeSegment;
}
freeSegment = currentSegment->right;
currentSegment->left = tmp;
currentSegment->right = tmp->right;
tmp->right->left = currentSegment;
tmp->right = currentSegment;
currentSegment->exponent = 1;
tmp->exponent—;
}
currentSegment->symbol = state->newSymbol;
state = state->newState;
if (currentSegment = currentSegment->left)
goto mainLoop;
if (currentSegment = expandLeft()) goto mainLoop;
break;

case tbaThruRightChange:
if (currentSegment->exponent > 1)
{
tmp = currentSegment;
if (!(currentSegment = freeSegment))
{
if (!MoreSegments()) goto avsluta;
currentSegment = freeSegment;
}
freeSegment = currentSegment->right;
currentSegment->left = tmp->left;
currentSegment->right = tmp;
tmp->left->right = currentSegment;
tmp->left = currentSegment;
currentSegment->exponent = 1;
tmp->exponent—;
}
currentSegment->symbol = state->newSymbol;
state = state->newState;
if (currentSegment = currentSegment->right)
goto mainLoop;
if (currentSegment = expandRight()) goto mainLoop;
break;

case tbaThruLeftOptimized:
while ((tmp = currentSegment->left) &&
(currentSegment->symbol == tmp->symbol))
{
currentSegment->exponent += tmp->exponent;
tmp->right = freeSegment;
freeSegment = tmp;
currentSegment->left = tmp->left;
if (currentSegment->left)
currentSegment->left->right = currentSegment;
else
leftmostSegment = currentSegment;
}
ruleCount += state->ruleCount*
(currentSegment->exponent-1);
state = state->newState;
if (currentSegment = currentSegment->left)
goto mainLoop;
if (currentSegment = expandLeft()) goto mainLoop;
break;

case tbaThruRightOptimized:
while ((tmp = currentSegment->right) &&
(currentSegment->symbol == tmp->symbol))
{
currentSegment->exponent += tmp->exponent;
currentSegment->right = tmp->right;
tmp->right = freeSegment;
freeSegment = tmp;
if (currentSegment->right)
currentSegment->right->left = currentSegment;
else
rightmostSegment = currentSegment;
}
ruleCount += state->ruleCount*
(currentSegment->exponent-1);
state = state->newState;
if (currentSegment = currentSegment->right)
goto mainLoop;
if (currentSegment = expandRight()) goto mainLoop;
break;

case tbaThruLeftChangeOptimized:
while ((tmp = currentSegment->left) &&
(currentSegment->symbol == tmp->symbol))
{
currentSegment->exponent += tmp->exponent;
tmp->right = freeSegment;
freeSegment = tmp;
currentSegment->left = tmp->left;
if (currentSegment->left)
currentSegment->left->right = currentSegment;
else
leftmostSegment = currentSegment;
}
currentSegment->symbol = state->newSymbol;
ruleCount += state->ruleCount*
(currentSegment->exponent-1);
state = state->newState;
if (currentSegment = currentSegment->left)
goto mainLoop;
if (currentSegment = expandLeft()) goto mainLoop;
break;

case tbaThruRightChangeOptimized:
while ((tmp = currentSegment->right) &&
(currentSegment->symbol == tmp->symbol))
{
currentSegment->exponent += tmp->exponent;
currentSegment->right = tmp->right;
tmp->right = freeSegment;
freeSegment = tmp;
if (currentSegment->right)
currentSegment->right->left = currentSegment;
else
rightmostSegment = currentSegment;
}
currentSegment->symbol = state->newSymbol;
ruleCount += state->ruleCount*
(currentSegment->exponent-1);
state = state->newState;
if (currentSegment = currentSegment->right) goto mainLoop;
if (currentSegment = expandRight()) goto mainLoop;
}

if (currentSegment)
{
resultat = true;
}

avsluta:

*numberOfRulesExecuted = ruleCount;

for (currentSegment = leftmostSegment; currentSegment;
currentSegment=currentSegment->right)
{
if ((oldValue = currentSegment->symbol)!=0)
{
oneCount = 0;
do {
++oneCount;
} while (oldValue = oldValue & (oldValue-1));
*numberOf1sGenerated += oneCount*currentSegment->exponent;
}
}
// bug in following line corrected by JRB, doesn't affect results
//   numberOf1sGenerated -= numberOf1sOnInputTape;
*numberOf1sGenerated -= numberOf1sOnInputTape;

return resultat;
}

RunTuringMachine
Boolean /* return true for success */ RunTuringMachine(
TMRule theTMRules[],
/* contains the rules for your BB machine */
ulong numberOfTMRules,
/* the number of rules in theTMRules */
ulong numBytesInHalfTape,
/* half-size of the "infinite" Turing Machine tape */
unsigned char *tmTape,
/* pointer to preallocated Turing Machine tape storage */
/* Each byte contains 8 tape symbols, each symbol is 0 or 1. */
/* The tape extends from tmTape[-numBytesInHalfTape] to
tmTape[numBytesInHalfTape -1] */
/* Tape position 0 is (tmTape[0] & 0x80),
tape position 1 is (tmTape[0] & 0x40)
tape position -1 is (tmTape[-1] & 0x01), etc. */
ulong *numberOf1sGenerated,
/* return the number of 1s placed on the tape */
ulong *numberOfRulesExecuted
/* return the number of rules executed when running BB, including the halt rule */
)
{

// Local data areas
unsigned char *p;
ulong myDoubleSymbol;
Boolean resultat;
TapeSegment *currentSegment;

// Init data areas
if (!CreateOptmizedTMRules( theTMRules, numberOfTMRules))
{
return false;
}

TheTapeCenter = tmTape;

nBit = 6;
maxBit = 0x20;

maxALeft = numBytesInHalfTape - numBytesInHalfTape%3;
maxARight = maxALeft;

resultat = runNBitTuringMachine( numberOf1sGenerated,
numberOfRulesExecuted );

if (resultat)
{
p = tmTape - allocatedLeft;
currentSegment = leftmostSegment;

#define CHECK_SEGMENT \
if (—(currentSegment->exponent) == 0) \
currentSegment=currentSegment->right

while (currentSegment)
{
myDoubleSymbol  = currentSegment->symbol << 18;
CHECK_SEGMENT;
myDoubleSymbol |= currentSegment->symbol << 12;
CHECK_SEGMENT;
myDoubleSymbol |= currentSegment->symbol << 6;
CHECK_SEGMENT;
myDoubleSymbol |= currentSegment->symbol;
CHECK_SEGMENT;
*p++ = myDoubleSymbol>>16;
*p++ = myDoubleSymbol>>8;
*p++ = myDoubleSymbol;
}

return true;
}

nBit = 8;
maxBit = 0x80;

maxALeft = numBytesInHalfTape;
maxARight = maxALeft;
nxtTapeIx = 20;

resultat = runNBitTuringMachine( numberOf1sGenerated,
numberOfRulesExecuted );

p = tmTape - allocatedLeft;
for (currentSegment = leftmostSegment; currentSegment;
currentSegment=currentSegment->right)
{
memset( p, currentSegment->symbol, currentSegment->exponent );
p += currentSegment->exponent;
}

return resultat;
}
```

Community Search:
MacTech Search:

Capto 1.2.9 - \$29.99
Capto (was Voila) is an easy-to-use app that takes capturing, recording, video and image editing to the next level. With an intelligent file manager and quick sharing options, Capto is perfect for... Read more
Opera 51.0.2830.40 - 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
GarageSale 7.0.13 - Create outstanding e...
GarageSale is a slick, full-featured client application for the eBay online auction system. Create and manage your auctions with ease. With GarageSale, you can create, edit, track, and manage... 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
Evernote 7.0.1 - Create searchable notes...
Evernote allows you to easily capture information in any environment using whatever device or platform you find most convenient, and makes this information accessible and searchable at anytime, from... Read more
MacUpdate Desktop 6.2.0 - \$20.00
MacUpdate Desktop brings seamless 1-click app installs and version updates to your Mac. With a free MacUpdate account and MacUpdate Desktop 6, Mac users can now install almost any Mac app on... Read more
HoudahSpot is a versatile desktop search tool. Use HoudahSpot to locate hard-to-find files and keep frequently used files within reach. HoudahSpot will immediately feel familiar. It works just the... Read more
EtreCheck 4.0.4 - For troubleshooting yo...
EtreCheck is an app that displays the important details of your system configuration and allow you to copy that information to the Clipboard. It is meant to be used with Apple Support Communities to... Read more
WhatsApp 0.2.8361 - Desktop client for W...
WhatsApp is the desktop client for WhatsApp Messenger, a cross-platform mobile messaging app which allows you to exchange messages without having to pay for SMS. WhatsApp Messenger is available for... Read more
iClock is a menu-bar replacement for Apple's default clock but with 100x features. Have your Apple or Google calendar in the menubar. Have the day, date, and time in different fonts and colors in the... Read more

## Latest Forum Discussions

The best games like Florence
Florence is a great little game about relationships that we absolutely adored. The only problem with it is it's over a little too soon. If you want some other games with some emotional range like Florence, check out these suggestions: [Read more] | Read more »
Angry Birds Champions adds cash prizes t...
Collaborating with developer Rovio Entertainment, GSN Games has released a twist on the Angry Birds formula. Angry Birds Champions features the same bird-flinging gameplay, but now you can catapult Red and co for cash. | Read more »
Around the Empire: What have you missed...
148Apps is part of a family. A big family of sites that make sure you're always up to date with all the portable gaming news. Just like a real family, I guess. I don't know, my mum never told me anything about Candy Crush to be fair. [Read more] | Read more »
The Battle of Polytopia Guide - Tips for...
The addition of multiplayer to The Battle of Polytopia has catapulted the game from a fun enough time waster to a fully-fledged 4X experience on your phone. We've been playing quite a few matches over the past week or so, and we've put together a... | Read more »
All the best games on sale for iPhone an...
Hi there, and welcome to our round up of all the best games that are on sale for iOS at the moment. It's not a vintage week in terms of numbers, but I'm pretty sure that every single one of these is worth picking up if you haven't already played... | Read more »
Disc Drivin' 2 Guide - Tips for the...
We're all still playing quite a bit of Disc Drivin' 2 over here at 148Apps, and we've gotten pretty good at it. Now that we've spent some more time with the game and unlocked more powerups, check out some of these more advanced tips: | Read more »
Alto's Odyssey Guide - How to Tackl...
Alto’s Odyssey is a completely stunning and serene runner, but it can also be a bit tricky. Check out these to try and keep your cool while playing this endless runner: Don’t focus too much on tasks [Read more] | Read more »
Here's everything you need to know...
Alto's Odyssey is a really, really good game. If you don't believe me, you should definitely check out our review by clicking this link right here. It takes the ideas from the original Alto's Adventure, then subtly builds on them, creating... | Read more »
Alto's Odyssey (Games)
Alto's Odyssey 1.0.1 Device: iOS Universal Category: Games Price: \$4.99, Version: 1.0.1 (iTunes) Description: Just beyond the horizon sits a majestic desert, vast and unexplored. Join Alto and his friends and set off on an endless... | Read more »
Vainglory 5v5: Everything you need to kn...

## Price Scanner via MacPrices.net

Apple AirPods in stock today for \$159, free s...
Adorama reports stock of Apple AirPods today for \$159 including free shipping, plus pay no sales tax outside of NY & NJ. See our Apple AirPod Price Tracker for the latest prices and stock status... Read more
Saturday Sale: Amazon offers 12″ 1.3GHz MacBo...
Amazon has Silver and Gold 2017 12″ 1.3GHz Retina MacBooks on sale for \$250 off MSRP. Shipping is free: – 12″ 1.3GHz Silver MacBook: \$1349.99 \$250 off MSRP – 12″ 1.3GHz Gold MacBook: \$1349.99 \$250... Read more
Use your Apple Education discount and save up...
Purchase a new Mac using Apple’s Education discount, and take up to \$400 off MSRP. All teachers, students, and staff of any educational institution with a .edu email address qualify for the discount... Read more
Apple Canada offers 2017 21″ and 27″ iMacs fo...
Canadian shoppers can save up to \$470 on the purchase of a 2017 current-generation 21″ or 27″ iMac with Certified Refurbished models at Apple Canada. Apple’s refurbished prices are the lowest... Read more
9″ iPads available online at Walmart for \$50...
Walmart has 9.7″ Apple iPads on sale for \$50 off MSRP for a limited time. Sale prices are for online orders only, in-store prices may vary: – 9″ 32GB iPad: \$279.99 \$50 off – 9″ 128GB iPad: \$379.99 \$... Read more
15″ Apple MacBook Pros, Certified Refurbished...
Save \$360-\$420 on the purchase of a 2017 15″ MacBook Pro with Certified Refurbished models at Apple. Apple’s refurbished prices are the lowest available for each model from any reseller. An standard... Read more
Amazon restocks MacBook Pros with models avai...
Amazon has restocked 15″ and 13″ Apple MacBook Pros with models on sale for up to \$251 off MSRP. Shipping is free. Note that stock of some Macs may come and go (and some sell out quickly), so check... Read more
Lowest price of the year: 15″ 2.8GHz Apple Ma...
Amazon has the 2017 Space Gray 15″ 2.8GHz MacBook Pro on sale today for \$251 off MSRP. Shipping is free: – 15″ 2.8GHz Touch Bar MacBook Pro Space Gray (MPTR2LL/A): \$2148, \$251 off MSRP Their price is... Read more
Apple restocks full line of Certified Refurbi...
Apple has restocked a full line of Apple Certified Refurbished 2017 13″ MacBook Pros for \$200-\$300 off MSRP. A standard Apple one-year warranty is included with each MacBook, and shipping is free.... Read more
Lowest sale price available for 13″ 1.8GHz Ma...
Focus Camera has the 2017 13″ 1.8GHz/128GB Apple MacBook Air on sale today for \$829 including free shipping. Their price is \$170 off MSRP, and it’s the lowest price available for a current 13″... Read more

## Jobs Board

*Apple* Retail - Multiple Positions - Apple,...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, 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
*Apple* Retail - Multiple Positions - Apple,...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
*Apple* Solutions Consultant - Apple (United...
# Apple Solutions Consultant Job Number: 113523441 Orange, CA, California, United States Posted: 21-Feb-2018 Weekly Hours: 40.00 **Job Summary** Are you passionate 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