TweetFollow Us on Twitter

Sep 97 Challenge

Volume Number: 13 (1997)
Issue Number: 9
Column Tag: Programmer's Challenge

Programmer's Challenge

by Bob Boonstra, Westford, MA

Image Locator

Imagine yourself with a collection satellite images and the task of finding a particular item in those images. Rather than look for a needle in this image haystack manually, you might call on your PowerMac to narrow down the choices for you. We'll enlist the aid of our Programmer's Challenge participants to help you do that job quickly. The Challenge this month is to detect the presence of a target pattern inside a larger background image. Because the background has been detected by an imperfect sensor, there is noise present in the background image. Your code will need to detect the target in the background despite this noise.

The prototype for the code you should write is:

#define topLeft(r)    (((Point *) &(r))[0])

void InitTarget(
  BitMap pattern,    /* image to be detected */
  BitMap mask      /* bits in image that we care about */
);

long /* numFound */ ImageDetect(
  BitMap backgroundImage,  /* find the target image in backgroundImage */
  Point locations[],    /* return topLeft of matching locations here */
  long maxLocations,    /* max number of locations to return */
  float noise        /* allow this fraction of mismatched bits */
);

void CleanUp(void);  /* deallocate any memory allocated by InitTarget */

Image location will take place in two steps. First, your InitTarget routine will be called with the target pattern that you will be looking for. Next, the ImageDetect routine will be called multiple times with a different background image and an associated noise threshold. ImageDetect should locate all occurrences of the target in the background, allowing for mismatched bits up to the noise threshold, and return the location of the pattern matches. Finally, the CleanUp routine will be called to allow you to deallocate any memory allocated by InitTarget.

InitTarget will be called with two BitMaps that describe the target pattern to be detected. The pattern BitMap identifies bits that should be set to 1, and the mask BitMap describes the bits that you care about (1s and 0s). Any bits not in the mask are not part of the target image, and the corresponding values in the background image are to be ignored. InitTarget should process the target image as desired and allocate memory to remember it.

ImageDetect will then be called multiple times (5-10 on average for each call to InitTarget). You should locate each occurrence of the target image in backgroundImage and return the coordinate in the background of topLeft(pattern.bounds) in the locations array. The noise parameter describes the fraction of target bits where the backgroundImage is allowed to differ from the target and still be considered a match. Up to noise times the number of 1s in the mask, rounded down, bits may be mismatched. Normally, locations will be large enough to hold all of the matches found, but you should not return more than the maxLocations matches for which storage has been allocated. The pattern matches may be returned in any order. If the maxLocations limit is exceeded, the choice of which matches to report is yours. ImageDetect should return the number of matches found.

Other information: The bounds rectangle for the pattern and the mask will be identical. All bits set in the pattern will also be set in the mask (but not the converse). The backgroundImage will typically be the size of a large monitor (e.g., 1024x768, or 1600x1200).

This will be a native PowerPC Challenge, using the latest CodeWarrior environment. In keeping with tradition, September is assembly language month here at the Programmer's Challenge. Solutions may be coded in PowerPC or 68K assembly language, C, C++, or Pascal.

Finally, we should note that the Programmer's Challenge began its sixth year last month. During that time, the Challenge has changed development environments, moved from 68K to PowerPC, and expanded its selection of languages. We appreciate the participation of our readers, without which the Challenge would not be possible. Happy belated birthday, Programmer's Challenge.

Three Months Ago Winner

The June Challenge was to implement a Turing Machine, a finite state machine augmented with an infinite amount of external storage. Twenty people submitted entries, and 17 of those worked correctly. Congratulations to Ernst Munter (Kanata, Ontario) for submitting the fastest solution and returning to the Challenge winner's circle.

The key to success in this Challenge was being able to quickly find the rule that applied to the current machine state and the current input symbol. A variety of techniques were used to find the applicable rule. Hashing was used by many of the faster entries. Ernst uses either hashing or a simple lookup table, depending on memory availability. Others sorted the rules and used a binary search. The slower solutions typically used a brute force approach of simply searching linearly through the rule set.

I used two types of test cases to stress the solutions. The first case involved a Turing Machine of approximately 2300 rules that sorted an input tape with an alphabet of 30 symbols and tape lengths of about 100 symbols. This case required over 113,000 Turing Machine state changes. The second test case was a Universal Turing Machine. A UTM is an interesting creature. Its input tape has two parts, an encoded version of the rules (program) for another Turing Machine, which it is to execute, and the input tape for that emulated program. The tape also contains an area where the Universal TM maintains the state for the program being emulated. The UTM operates by looking up the rule (or program instruction) that applies given the current state of the machine being emulated, remembering that instruction while it moves to the current input for the emulated machine, and then executing that instruction. The Universal Turing Machine I used operated on a binary alphabet and consisted of 184 rules, operating on an input tape that described a simple unary addition machine. This test case required just under 240,000 state changes to execute.

The table below lists for each entry the execution times in milliseconds for the sort test case and the Universal Turing Machine case, total execution time, code and data sizes, and the programming language used. The number in parentheses after the entrant's name is the total number of Challenge points earned in all Challenges to date prior to this one.

NameTime1Time2Total TimeCodeDataLanguage
Ernst Munter (246) 28.1 29.3 57.6 920 8 C++
Russ Webb 30.9 33.0 64.2 1696 140 C
Devon Carew 33.4 35.6 79.5 976 28 C
Gary Beith (24) 39.6 39.9 86.9 592 32 C
Mason Thomas (4) 47.9 40.5 89.1 740 8 C
Kevin Cutts (57) 42.4 43.9 89.7 620 32 C++
Simon Holmes à Court 44.1 42.3 90.0 744 32 C++
Juerg Wullschleger 48.5 50.4 99.7 476 8 C
Daniel Harding 96.0 63.0 159.7 2612 406 C++
Zach Thompson 93.2 64.8 161.3 1076 48 C++
Gregory Cooper (54) 107.8 84.6 192.7 668 40 C
Graham Herrick 137.0 107.2 244.8 820 16 C
Andy Scheck (17) 3239.0 158.3 3397.0 212 8 C++
Charles Higgins (20) 3238.0 167.8 3406.0 276 8 C
David Whitney 4174.0 272.3 4449.0 19800 2745 C++
Bjorn Davidsson (6) 6565.0 165.6 6731.0 224 8 C++
Terry Noyes 6737.0 198.3 6936.0 200 8 C
R.B. 2736 99 C
S.A. 840 448 C
W.R. 1148 8 C++

Top 20 Contestants

Here are the Top Contestants for the Programmer's Challenge. The numbers below include points awarded over the 24 most recent contests, including points earned by this month's entrants.

RankNamePoints
1. Munter, Ernst 196
2. Gregg, Xan 83
3. Cooper, Greg 54
4. Lengyel, Eric 40
5. Boring, Randy 37
6. Lewis, Peter 32
7. Mallett, Jeff 30
8. Murphy, ACC 30
9. Larsson, Gustav 27
10. Antoniewicz, Andy 24
11. Nicolle, Ludovic 21
12. Picao, Miguel Cruz 21
13. Brown, Jorg 20
14. Day, Mark 20
15. Gundrum, Eric 20
16. Higgins, Charles 20
17. Slezak, Ken 20
18. Studer, Thomas 20
19. Karsh, Bill 19
20. Nevard, John 19

Here is Ernst's winning solution:

Turing.cp ® 1997 Ernst Munter

Problem Statement
Implement the engine for a Turing Machine, a state machine which, at each step, reads a symbol from a tape, consults a rule which is a function of the current state and the symbol. The rule specifies a new state, a symbol to output, and the direction in which to move the tape, or to halt.
Solution
I first try to build a lookup table as an index into the rules array. But this may require an "unreasonable" amount of memory.

First, I scan the rules to determine the amount of table memory required for a simple lookup index. If this appears to be too much, I go to plan B: a hashed index.

The hash table uses linear open addressing: when the table is built and an index location is needed which is already in use we have a collision. To resolve it, I scan linearly through the index array until a free location is found. The size of the index array is larger than the number of rules, so a free location will always be found.

Optimization of hash table lookup
The majority of rules will hash to unique index addresses.

Rules which hash to the same value can be seen as a sequence of index table entries, with the primary location containing the first rule address to be found.

When the Turing Machine is executing, any colliding rule that is encountered will have its index moved to the primary index location, on the assumption that it will be used again, and will then be found more quickly.

Assumptions
A minimum amount of table memory of 8K entries is always provided. But for larger rule sets, an index table that will occupy about 1/2 to 3/4 the amount of memory taken by the rules array itself may be allocated.

The memory allocated for the simple lookup table will be the number_of_states * number_of_symbols, rounded up to a power of 2, but not more than 8K entries, or 2 * number_of_rules, whichever is larger.

If the memory required for the simple index would exceed those rules, for example if there are a lot of holes in the symbol/state space, the hashed index is used.

The memory allocated for the hash index array will be the larger of 8K entries or 2 * number_of_rules, rounded up to the nearest power of 2.

For example, a rule set of up to 2K rules may result in a 32K byte index; a rule set of 50,000 rules which occupy 1M of rules memory may get an index table of 512K bytes.

#include <stdio.h>

#include <stdlib.h>
#include <string.h>
#include "turing.h"

const enum {    // constants controlling min size of index
  EXPANSION  = 2,
  MIN_BITS   = 13,
  MIN_SIZE    = 1L<<MIN_BITS };  
  
typedef const TMRule* TMRulePtr;

Boolean TuringMachine(
  const TMRule theRules[],
  ulong numRules,
  ulong *theTape,
  ulong tapeLen,
  long rwHeadPos,
  TMMoveProc ReportMove
)  {
  TMRulePtr* index;
  ulong    state=0;
  ulong    symbol;
  int    direction;
  ulong*  tape=theTape+rwHeadPos;
  ulong*  tapeEnd=theTape+tapeLen;

  ulong    mask;
  TMRulePtr rule=theRules;

// The function contains 2 very similar sections,
// one section uses a plain lookup table for an index,
// the other uses a hash table.

// Try to construct a collision-free index of rule addresses

// compute table size
  ulong   maxState=rule->oldState;
  ulong   maxSym=rule->inputSymbol;
  ulong   minSym=rule->inputSymbol;
  rule++;
  for (int i=1;i<numRules;i++) {
    if (maxState<rule->oldState) maxState=rule->oldState;
    if (maxSym<rule->inputSymbol) maxSym=rule->inputSymbol;
    else
    if (minSym>rule->inputSymbol) minSym=rule->inputSymbol;
    rule++;
  }
  ulong numSyms=maxSym-minSym+1;
  ulong numStates=maxState+1;
  ulong numIndex=(numStates)*(numSyms);

  if ((numIndex<numStates)               // overflow
    || ((numIndex > MIN_SIZE)
    && (numIndex > EXPANSION*numRules)))  // too large
      goto try_hash;

// increase size to the next power of 2
  ulong dummy=1;
  while (numIndex) {
    numIndex>>=1;
    dummy<<=1;
  }
  numIndex=dummy;

// Allocate the table memory
  index=(TMRulePtr*)malloc(numIndex*sizeof(TMRulePtr));

// Always expect to get the memory, but just in case ...
  if (index==0)
    return FALSE;

// All unused index locations will remain 0
  memset(index,0,numIndex*sizeof(TMRulePtr));
  mask=numIndex-1;

// Scan the rules and populate the index array
  rule=theRules;
  for (int i=0;i<numRules;i++) {
    ulong addr=
      mask & (rule->oldState*numSyms+rule->inputSymbol);
    index[addr]=rule++;
  }
// Using the collision-free index table:
// Loop until the tape halts or we fail on error
  do {
      symbol=*tape;
      ulong addr=mask & (state*numSyms+symbol);
      rule=index[addr];
      if (rule == 0)    // illegal symbol, no rule
        break;
      symbol=rule->outputSymbol;
      state=rule->newState;
      direction=rule->moveDirection;

      ReportMove(symbol,state,MoveDir(direction));
      *tape=symbol;

      if (direction==kHalt) {
        free(index);
        return TRUE;  
    }  
    
      tape+=direction;
  } while ((tape>=theTape) && (tape<tapeEnd));
  free(index);
  return FALSE;

try_hash:
// Section 2
// If we get here, we could not make a simple table
// and have to go with a hash table, collisions are possible

// Find table size >= minimum size
  numIndex=MIN_SIZE;
  while (numIndex < EXPANSION*numRules) {
    numIndex*=2;
  }

// Allocate the table memory
  index=(TMRulePtr*)malloc(numIndex*sizeof(TMRulePtr));

// Always expect to get the memory, but just in case ...
  if (index==0)
    return FALSE;

// All unused index locations will remain 0
  memset(index,0,numIndex*sizeof(TMRulePtr));

  mask=numIndex-1;
  ulong   hFactor=1 | (numIndex/numStates);
  long     hDelta=1 | (hFactor>>1);

// Scan the rules and populate the index array
  rule=theRules;
  for (int i=0;i<numRules;i++) {
    ulong addr=
      mask & (rule->oldState*hFactor+rule->inputSymbol);

// if primary location is not empty: find next free location
    while (index[addr])   
      addr=mask & (addr+hDelta);
    index[addr]=rule++;
  }

// Using the hash index table:
// Loop until the tape halts or we fail on error.
// This loop is the same as the loop in the first section
// except we have to check for possible collisions with each rule..
  do {
      symbol=*tape;
      ulong addr=mask & (state*hFactor+symbol);
      rule=index[addr];
      if (rule == 0)          // illegal symbol, no rule
        break;
  
// check if we have the right rule, or a collision  
    if ((symbol != rule->inputSymbol)
      || (state != rule->oldState)) {  
       const TMRule* rule0=rule;
        ulong addr0=addr;

      do {          // resolve the collision
        addr=mask & (addr+hDelta);
        rule=index[addr];
          if (rule == 0) {      // could not find rule
        free(index);
      return FALSE;
      }  
  
      } while ((symbol != rule->inputSymbol)
      || (state != rule->oldState));
      index[addr]=rule0;        // move last-used rule
      index[addr0]=rule;        // up in chain
  
    }
  
// now we have the correct rule  
      symbol=rule->outputSymbol;
      state=rule->newState;
      direction=rule->moveDirection;

      ReportMove(symbol,state,MoveDir(direction));

      *tape=symbol;
      if (direction==kHalt) {    // normal stop
        free(index);
        return TRUE;  
        }

        tape+=direction;
  } while ((tape>=theTape) && (tape<tapeEnd));

  free(index);
  return FALSE;
}
 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Latest Forum Discussions

See All

Top Mobile Game Discounts
Every day, we pick out a curated list of the best mobile discounts on the App Store and post them here. This list won't be comprehensive, but it every game on it is recommended. Feel free to check out the coverage we did on them in the links... | Read more »
Price of Glory unleashes its 1.4 Alpha u...
As much as we all probably dislike Maths as a subject, we do have to hand it to geometry for giving us the good old Hexgrid, home of some of the best strategy games. One such example, Price of Glory, has dropped its 1.4 Alpha update, stocked full... | Read more »
The SLC 2025 kicks off this month to cro...
Ever since the Solo Leveling: Arise Championship 2025 was announced, I have been looking forward to it. The promotional clip they released a month or two back showed crowds going absolutely nuts for the previous competitions, so imagine the... | Read more »
Dive into some early Magicpunk fun as Cr...
Excellent news for fans of steampunk and magic; the Precursor Test for Magicpunk MMORPG Crystal of Atlan opens today. This rather fancy way of saying beta test will remain open until March 5th and is available for PC - boo - and Android devices -... | Read more »
Prepare to get your mind melted as Evang...
If you are a fan of sci-fi shooters and incredibly weird, mind-bending anime series, then you are in for a treat, as Goddess of Victory: Nikke is gearing up for its second collaboration with Evangelion. We were also treated to an upcoming... | Read more »
Square Enix gives with one hand and slap...
We have something of a mixed bag coming over from Square Enix HQ today. Two of their mobile games are revelling in life with new events keeping them alive, whilst another has been thrown onto the ever-growing discard pile Square is building. I... | Read more »
Let the world burn as you have some fest...
It is time to leave the world burning once again as you take a much-needed break from that whole “hero” lark and enjoy some celebrations in Genshin Impact. Version 5.4, Moonlight Amidst Dreams, will see you in Inazuma to attend the Mikawa Flower... | Read more »
Full Moon Over the Abyssal Sea lands on...
Aether Gazer has announced its latest major update, and it is one of the loveliest event names I have ever heard. Full Moon Over the Abyssal Sea is an amazing name, and it comes loaded with two side stories, a new S-grade Modifier, and some fancy... | Read more »
Open your own eatery for all the forest...
Very important question; when you read the title Zoo Restaurant, do you also immediately think of running a restaurant in which you cook Zoo animals as the course? I will just assume yes. Anyway, come June 23rd we will all be able to start up our... | Read more »
Crystal of Atlan opens registration for...
Nuverse was prominently featured in the last month for all the wrong reasons with the USA TikTok debacle, but now it is putting all that behind it and preparing for the Crystal of Atlan beta test. Taking place between February 18th and March 5th,... | Read more »

Price Scanner via MacPrices.net

AT&T is offering a 65% discount on the ne...
AT&T is offering the new iPhone 16e for up to 65% off their monthly finance fee with 36-months of service. No trade-in is required. Discount is applied via monthly bill credits over the 36 month... Read more
Use this code to get a free iPhone 13 at Visi...
For a limited time, use code SWEETDEAL to get a free 128GB iPhone 13 Visible, Verizon’s low-cost wireless cell service, Visible. Deal is valid when you purchase the Visible+ annual plan. Free... Read more
M4 Mac minis on sale for $50-$80 off MSRP at...
B&H Photo has M4 Mac minis in stock and on sale right now for $50 to $80 off Apple’s MSRP, each including free 1-2 day shipping to most US addresses: – M4 Mac mini (16GB/256GB): $549, $50 off... Read more
Buy an iPhone 16 at Boost Mobile and get one...
Boost Mobile, an MVNO using AT&T and T-Mobile’s networks, is offering one year of free Unlimited service with the purchase of any iPhone 16. Purchase the iPhone at standard MSRP, and then choose... Read more
Get an iPhone 15 for only $299 at Boost Mobil...
Boost Mobile, an MVNO using AT&T and T-Mobile’s networks, is offering the 128GB iPhone 15 for $299.99 including service with their Unlimited Premium plan (50GB of premium data, $60/month), or $20... Read more
Unreal Mobile is offering $100 off any new iP...
Unreal Mobile, an MVNO using AT&T and T-Mobile’s networks, is offering a $100 discount on any new iPhone with service. This includes new iPhone 16 models as well as iPhone 15, 14, 13, and SE... Read more
Apple drops prices on clearance iPhone 14 mod...
With today’s introduction of the new iPhone 16e, Apple has discontinued the iPhone 14, 14 Pro, and SE. In response, Apple has dropped prices on unlocked, Certified Refurbished, iPhone 14 models to a... Read more
B&H has 16-inch M4 Max MacBook Pros on sa...
B&H Photo is offering a $360-$410 discount on new 16-inch MacBook Pros with M4 Max CPUs right now. B&H offers free 1-2 day shipping to most US addresses: – 16″ M4 Max MacBook Pro (36GB/1TB/... Read more
Amazon is offering a $100 discount on the M4...
Amazon has the M4 Pro Mac mini discounted $100 off MSRP right now. Shipping is free. Their price is the lowest currently available for this popular mini: – Mac mini M4 Pro (24GB/512GB): $1299, $100... Read more
B&H continues to offer $150-$220 discount...
B&H Photo has 14-inch M4 MacBook Pros on sale for $150-$220 off MSRP. B&H offers free 1-2 day shipping to most US addresses: – 14″ M4 MacBook Pro (16GB/512GB): $1449, $150 off MSRP – 14″ M4... Read more

Jobs Board

All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.