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:

FileMaker Pro 19.4.2 - Quickly build cus...
FileMaker Pro is the tool you use to create a custom app. You also use FileMaker Pro to access your app on a computer. Start by importing data from a spreadsheet or using a built-in Starter app to... Read more
WhatRoute 2.4.9 - Geographically trace o...
WhatRoute is designed to find the names of all the routers an IP packet passes through on its way from your Mac to a destination host. It also measures the round-trip time from your Mac to the router... Read more
Notion 2.0.20 - A unified workspace for...
Notion is the unified workspace for modern teams. Notion Features: Integration with Slack Documents Wikis Tasks Release notes were unavailable when this listing was updated. Download Now]]> Read more
Monterey Cache Cleaner 17.0.2 - Clear ca...
Monterey Cache Cleaner is an award-winning general-purpose tool for macOS X. MCC makes system maintenance simple with an easy point-and-click interface to many macOS X functions. Novice and expert... Read more
Firetask Pro represents the next generation of easy-to-use, project-oriented task management apps. By combining David Allen's powerful Getting Things Done (GTD®) approach with classical task... Read more
Smultron 13.0.4 - Easy-to-use, powerful...
Smultron 13 is the text editor for all of us. Smultron is powerful and confident without being complicated. Its elegance and simplicity helps everyone being creative and to write and edit all sorts... Read more
Box Sync 4.0.8057 - Online synchronizati...
Box Sync gives you a hard-drive in the Cloud for online storage. Note: You must first sign up to use Box. What if the files you need are on your laptop -- but you're on the road with your iPhone? No... Read more
Audio Hijack 3.8.10 - Record and enhance...
Audio Hijack (was Audio Hijack Pro) drastically changes the way you use audio on your computer, giving you the freedom to listen to audio when you want and how you want. Record and enhance any audio... Read more
Direct Mail 6.0.1 - Create and send grea...
Direct Mail is an easy-to-use, fully-featured email marketing app purpose-built for macOS. Create, send, and track great looking email campaigns that get results. Start your newsletter by selecting... Read more

## Latest Forum Discussions

Hopefully Not Jared’s Last Show – The To...
My suspicions from last week were correct, and after my two kids tested positive for Covid last week both my wife and I have now tested positive as well. It seems you just can’t escape this stuff lately. Thankfully the two little ones are pretty... | Read more »
TouchArcade Game of the Week: ‘Micro RPG...
I feel like idle games are one of those perfect fits for the mobile platform. Not that they replace more involved gaming experiences when you’re in the mood for that, but they do fit in alongside other types of games just fine as a “go to" when you... | Read more »
Phantom Blade: Executioners is holding a small-scale technical test that lets players get first dibs on the KungFuPunk action RPG. Offered to selected players only, S-Game’s first Closed Beta Test will provide players with limited edition in-game... | Read more »
New ‘Warhammer 40,000: Tacticus’ Video S...
Back in September Snowprint Studios, who you may know from their previous Legend of Solgard or Rivengard, announced that they’d partnered up with Games Workshop to put out a new tactical game in the Warhammer 40,000 universe titled Warhammer 40,000... | Read more »
Hello gentle readers, and welcome to the SwitchArcade Round-Up for January 28th, 2022. We’ve got a bunch of new releases to look at today, with a few big hitters, a few mid-level diversions, and a healthy supply of compost. Since it’s Friday, we... | Read more »
S-Game has kicked off its first Closed Beta Test for Phantom Blade: Executioners, inviting a selected few to get first dibs on the upcoming KungFuPunk action RPG on mobile. The CBT officially begins this January 28th, and beta testers will receive... | Read more »
‘Infinite Galaxy’ First Anniversary: Cel...
Cultivating a new generation of valiant commanders across 240 countries worldwide, Infinite Galaxy has quenched players’ thirst to explore the vastness of space – and there are only more intergalactic adventures to embark on from here on out. Camel... | Read more »
War and Order: How to brave the cold in...
War and Order's 6th-anniversary celebrations are underway, and all in good time too - this season not only brings about fabulous festivities, but it also lets players experience the harsh winter in an entirely new way. [Read more] | Read more »
‘Hidden Folks+’ Is This Week’s New Apple...
The original Hidden Folks from Adriaan de Jongh is an excellent hidden objects game featuring hand drawn visuals. It is an absolute joy to play, and it has now released on Apple Arcade in the form of Hidden Folks+ () as an App Store great. If you’... | Read more »
Mini Metro’s First Big Update of 2022 Ad...
Last year saw great updates for Dinosaur Polo Club’s Mini Metro (\$3.99) which is also available on Apple Arcade as an App Store Great. | Read more »

## Price Scanner via MacPrices.net

Apple has clearance 2020 13″ MacBook Airs ava...
Apple has clearance, Certified Refurbished, 2020 13″ Intel-based MacBook Airs in stock today starting at only \$719 and up to \$370 off original MSRP. Each MacBook features a new outer case, comes with... Read more
The cheapest iPhones for sale today at Apple...
Apple has restocked Apple Certified Refurbished iPhone 8 models starting at only \$359. Each refurbished iPhone comes with a fresh external case, standard Apple 1-year warranty, and free shipping.... Read more
14″ MacBook Pro with Apple M1 Max CPU now in...
Looking for a new 14″ MacBook Pro with an Apple M1 Max CPU? Stock is finally trickling into Apple resellers. B&H has Silver 14″ M1 Max MacBook Pros in stock today for \$2899 including free 1-2 day... Read more
14″ MacBook Pros with Apple M1 Pro CPUs are i...
Amazon is reporting stock of 14″ MacBook Pros with M1 Pro CPUs today with a \$50 discount. Shipping is free, and delivery is available by February 1st for most configurations. Be sure to make your... Read more
Apple has restocked 13″ M1 MacBook Pros for \$...
Apple has restocked a full line of 13″ M1 MacBook Pros available Certified Refurbished, starting at only \$1099 and up to \$230 off original MSRP. These are the cheapest M1 MacBook Pros for sale today... Read more
Apple’s AirPods Max headphones are on sale fo...
Amazon has Silver, Blue, and Space Gray Apple AirPods Max headphones on sale today for \$100 off MSRP. Shipping is free, and all models are in stock today. Their price is the lowest currently... Read more
Open a new line of service at Verizon and get...
Verizon is giving away 64GB Apple iPhone 12 minis or your choice of an iPhone 11 to customers who choose one of these phones and open a new line of service. Offer is available online only, and no... Read more
Open-box 13″ M1 MacBook Airs now available st...
QuickShip Electronics has open-box return 13″ M1 MacBook Airs in stock and on sale for \$200-\$400 off MSRP on their eBay store right now with free express delivery. According to QuickShip, “The item... Read more
Verizon’s 2022 iPad promo: \$100-\$310 off any...
Verizon has cellular-capable iPads on sale for \$100-\$310 off MSRP when purchased with an Unlimited service plan. Sale price is applied to your account monthly over a 24 or 30 month period, depending... Read more
Sunday Sale: Apple AirPods are on sale for up...
Amazon has Apple AirPods on sale for \$10-\$100 off MSRP today, depending on the model. All are in stock today with free delivery: – AirPods Max headphones (Blue): \$449 \$100 off MSRP – AirPods Max... Read more

## Jobs Board

Registered Nurse (RN) Employee Health PSJH -...
…is calling for a Registered Nurse (RN) Employee Health PSJH to our location in Apple Valley, CA.** We are seeking a Registered Nurse (RN) Employee Health PSJH to be Read more
Systems Administrator - Pearson (United State...
…and troubleshoot Windows operating systems (workstation and server), laptop computers, Apple iPads, Chromebooks and printers** + **Administer and troubleshoot all Read more
IT Assistant Level 1- IT Desktop Support Anal...
…providing tier-1 or better IT help desk support in a large Windows and Apple environment * Experience using IT Service Desk Management Software * Knowledge of IT Read more
Human Resources Business Partner PSJH - Provi...
…**is calling a** **Human Resources Business Partner, PSJH** **to our location in Apple Valley, CA.** **Applicants that meet qualifications will receive a text with Read more
Manager Community Health Investment Programs...
…is calling a Manager Community Health Investment Programs PSJH to our location in Apple Valley, CA.** **Qualified candidates will be invited to do a self-paced video Read more