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;
}
 
AAPL
$111.78
Apple Inc.
-0.87
MSFT
$47.66
Microsoft Corpora
+0.14
GOOG
$516.35
Google Inc.
+5.25

MacTech Search:
Community Search:

Software Updates via MacUpdate

Monolingual 1.6.2 - Remove unwanted OS X...
Monolingual is a program for removing unnecesary language resources from OS X, in order to reclaim several hundred megabytes of disk space. It requires a 64-bit capable Intel-based Mac and at least... Read more
NetShade 6.1 - Browse privately using an...
NetShade is an Internet security tool that conceals your IP address on the web. NetShade routes your Web connection through either a public anonymous proxy server, or one of NetShade's own dedicated... Read more
calibre 2.13 - Complete e-library manage...
Calibre is a complete e-book library manager. Organize your collection, convert your books to multiple formats, and sync with all of your devices. Let Calibre be your multi-tasking digital librarian... Read more
Mellel 3.3.7 - Powerful word processor w...
Mellel is the leading word processor for OS X and has been widely considered the industry standard since its inception. Mellel focuses on writers and scholars for technical writing and multilingual... Read more
ScreenFlow 5.0.1 - Create screen recordi...
Save 10% with the exclusive MacUpdate coupon code: AFMacUpdate10 Buy now! ScreenFlow is powerful, easy-to-use screencasting software for the Mac. With ScreenFlow you can record the contents of your... Read more
Simon 4.0 - Monitor changes and crashes...
Simon monitors websites and alerts you of crashes and changes. Select pages to monitor, choose your alert options, and customize your settings. Simon does the rest. Keep a watchful eye on your... Read more
BBEdit 11.0.2 - Powerful text and HTML e...
BBEdit is the leading professional HTML and text editor for the Mac. Specifically crafted in response to the needs of Web authors and software developers, this award-winning product provides a... Read more
ExpanDrive 4.2.1 - Access cloud storage...
ExpanDrive builds cloud storage in every application, acts just like a USB drive plugged into your Mac. With ExpanDrive, you can securely access any remote file server directly from the Finder or... Read more
Adobe After Effects CC 2014 13.2 - Creat...
After Effects CC 2014 is available as part of Adobe Creative Cloud for as little as $19.99/month (or $9.99/month if you're a previous After Effects customer). After Effects CS6 is still available... Read more
Evernote 6.0.5 - 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

Latest Forum Discussions

See All

Make your own Tribez Figures (and More)...
Make your own Tribez Figures (and More) with Toyze Posted by Jessica Fisher on December 19th, 2014 [ permalink ] Universal App - Designed for iPhone and iPad | Read more »
So Many Holiday iOS Sales Oh My Goodness...
The holiday season is in full-swing, which means a whole lot of iOS apps and games are going on sale. A bunch already have, in fact. Naturally this means we’re putting together a hand-picked list of the best discounts and sales we can find in order... | Read more »
It’s Bird vs. Bird in the New PvP Mode f...
It’s Bird vs. Bird in the New PvP Mode for Angry Birds Epic Posted by Jessica Fisher on December 19th, 2014 [ permalink ] Universal App - Designed for iPhone and iPad | Read more »
Telltale Games and Mojang Announce Minec...
Telltale Games and Mojang Announce Minecraft: Story Mode – A Telltale Games Series Posted by Jessica Fisher on December 19th, 2014 [ permalink ] | Read more »
WarChest and Splash Damage Annouce Their...
WarChest and Splash Damage Annouce Their New Game: Tempo Posted by Jessica Fisher on December 19th, 2014 [ permalink ] WarChest Ltd and Splash Damage Ltd are teaming up again to work | Read more »
BulkyPix Celebrates its 6th Anniversary...
BulkyPix Celebrates its 6th Anniversary with a Bunch of Free Games Posted by Jessica Fisher on December 19th, 2014 [ permalink ] BulkyPix has | Read more »
Indulge in Japanese cuisine in Cooking F...
Indulge in Japanese cuisine in Cooking Fever’s new sushi-themed update Posted by Simon Reed on December 19th, 2014 [ permalink ] Lithuanian developer Nordcurrent has yet again updated its restaurant simulat | Read more »
Badland Daydream Level Pack Arrives to C...
Badland Daydream Level Pack Arrives to Celebrate 20 Million Downloads Posted by Ellis Spice on December 19th, 2014 [ permalink ] | Read more »
Far Cry 4, Assassin’s Creed Unity, Desti...
Far Cry 4, Assassin’s Creed Unity, Destiny, and Beyond – AppSpy Takes a Look at AAA Companion Apps Posted by Rob Rich on December 19th, 2014 [ permalink ] These day | Read more »
A Bunch of Halfbrick Games Are Going Fre...
A Bunch of Halfbrick Games Are Going Free for the Holidays Posted by Ellis Spice on December 19th, 2014 [ permalink ] Universal App - Designed for iPhone and iPad | Read more »

Price Scanner via MacPrices.net

The Apple Store offering free next-day shippi...
The Apple Store is now offering free next-day shipping on all in stock items if ordered before 12/23/14 at 10:00am PT. Local store pickup is also available within an hour of ordering for any in stock... Read more
It’s 1992 Again At Sony Pictures, Except For...
Techcrunch’s John Biggs interviewed a Sony Pictures Entertainment (SPE) employee, who quite understandably wished to remain anonymous, regarding post-hack conditions in SPE’s L.A office, explaining “... Read more
Holiday sales this weekend: MacBook Pros for...
 B&H Photo has new MacBook Pros on sale for up to $300 off MSRP as part of their Holiday pricing. Shipping is free, and B&H charges NY sales tax only: - 15″ 2.2GHz Retina MacBook Pro: $1699... Read more
Holiday sales this weekend: MacBook Airs for...
B&H Photo has 2014 MacBook Airs on sale for up to $120 off MSRP, for a limited time, for the Thanksgiving/Christmas Holiday shopping season. Shipping is free, and B&H charges NY sales tax... Read more
Holiday sales this weekend: iMacs for up to $...
B&H Photo has 21″ and 27″ iMacs on sale for up to $200 off MSRP including free shipping plus NY sales tax only. B&H will also include a free copy of Parallels Desktop software: - 21″ 1.4GHz... Read more
Holiday sales this weekend: Mac minis availab...
B&H Photo has new 2014 Mac minis on sale for up to $80 off MSRP. Shipping is free, and B&H charges NY sales tax only: - 1.4GHz Mac mini: $459 $40 off MSRP - 2.6GHz Mac mini: $629 $70 off MSRP... Read more
Holiday sales this weekend: Mac Pros for up t...
B&H Photo has Mac Pros on sale for up to $500 off MSRP. Shipping is free, and B&H charges sales tax in NY only: - 3.7GHz 4-core Mac Pro: $2599, $400 off MSRP - 3.5GHz 6-core Mac Pro: $3499, $... Read more
Save up to $400 on MacBooks with Apple Certif...
The Apple Store has Apple Certified Refurbished 2014 MacBook Pros and MacBook Airs available for up to $400 off the cost of new models. An Apple one-year warranty is included with each model, and... Read more
Save up to $300 on Macs, $30 on iPads with Ap...
Purchase a new Mac or iPad at The Apple Store for Education and take up to $300 off MSRP. All teachers, students, and staff of any educational institution qualify for the discount. Shipping is free,... Read more
iOS and Android OS Targeted by Man-in-the-Mid...
Cloud services security provider Akamai Technologies, Inc. has released, through the company’s Prolexic Security Engineering & Research Team (PLXsert), a new cybersecurity threat advisory. The... Read more

Jobs Board

*Apple* Store Leader Program (US) - Apple, I...
…Summary Learn and grow as you explore the art of leadership at the Apple Store. You'll master our retail business inside and out through training, hands-on experience, Read more
Project Manager, *Apple* Financial Services...
**Job Summary** Apple Financial Services (AFS) offers consumers, businesses and educational institutions ways to finance Apple purchases. We work with national and Read more
*Apple* Retail - Multiple Positions (US) - A...
Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, you're also the Read more
*Apple* Retail - Multiple Positions (US) - A...
Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, you're also the Read more
*Apple* Retail - Multiple Positions (US) - A...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.