TweetFollow Us on Twitter

Feb 00 Challenge

Volume Number: 16 (2000)
Issue Number: 2
Column Tag: Programmer's Challenge

Programmer's Challenge

by Bob Boonstra, Westford, MA

Web apps with Lasso and FileMaker Pro

Latin Squares

A Latin Square of order N is an NxN array of numbers, where each number from 0..N-1 occurs exactly once in each row and in each column. Your Challenge this month is to construct Latin Squares that are minimal, in the sense that each must form the smallest NxN digit base N number, where the digits are read off column by column, one row at a time.

The prototype for the code you should write is:

#if defined(__cplusplus)
extern "C" {
#endif

void LatinSquares(
  short n,	/* dimension of the Latin Square to be generated */
  short *latinSquare	/* set latinSquare[c + r*n] to square value row r, col c */
);

#if defined(__cplusplus)
}
#endif

For example, 

				1234
				2341
				4123
				3412

is a Latin Square with the value 1234234141233412. It is not the minimal Latin Square of order 4, however, since the following Latin Square,

				1234
				2143
				3412
				4321

forms the number 1234214334124321.

The dimension of the squares you must generate will be less than 2**16. The winner will be the solution that correctly computes minimal Latin Squares in the least amount of execution time. Code size and code elegance, in that order, will be the tiebreakers, in the event two solutions are within 1% of one another in execution time. All Latin Squares must be computed at execution time - entries that precompute solutions will be disqualified.

This month's Challenge was suggested by Aaron Montgomery, who earns 2 Challenge points for making the suggestion

This will be a native PowerPC Challenge, using the CodeWarrior Pro 5 environment. Solutions may be coded in C, C++, or Pascal. Solutions in Java will also be accepted, but Java entries must be accompanied by a test driver that uses the interface provided in the problem statement.

Three Months Ago Winner

Congratulations to Tom Saxton for taking first place in the November, 1999, Putting Green Challenge. While I'm not sure that the next Ryder Cup teams will be beating a path to his door for his four-putting green skills, Tom did soundly beat the three other entries.

The Putting Green Challenge required contestants to analyze a sequence of greens described as three-dimensional points connected into adjoining triangles. Each green had a fixed pin position, and several holes were played on each green from varying initial ball positions. Complicating the Challenger's job was the fact that the propagation model was unknown, available only by observing the results of a putt. For each green, the contestants were given several practice holes that could be used to puzzle out the propagation model. Scoring was based on an award of 100 points for each hole successfully completed, minus 10 points for each stroke taken (not counting practice holes), and minus 10 points for each second of execution time (including practice time).

Two of the solutions submitted did not manage to sink a putt for any of the holes played in my test match. One of those solutions simply hit the ball at the hole very hard, trying to take advantage of a possible ambiguity about ball velocity in the problem statement. I heard from enough real golfers who had rimmed the cup a few times that I had to close the velocity loophole. Tom's winning solution is fairly straightforward. He takes 10 practice shots on the first hole of the first green to estimate the drag coefficients. It does not attempt to analyze the contours of the green or to model the effect of gravity. But the drag model is good enough to put the ball in the hole with only one putt on a level green, and with one or two putts on a flat but gently sloping green.

I used three greens in my test cases, a perfectly flat and level green, a flat but gently sloping green, and a green with more varied terrain. Five practice holes were played on each green, five scored holes on each of the first two greens, and 20 holes on the final green. On the interesting terrain of the last hole, Tom's solution completed each hole successfully, taking up to seven putts to complete the hole.

The table below lists, for each of the solutions submitted, the number of holes successfully completed, the total number of strokes taken on nonpractice holes, total execution time, the total score, and the size and language code parameters. 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 Holes Strokes Time Score Code Data Lang
Tom Saxton (138) 30 117 3.148 1829.969 2224 432 C
Brady Duga 10 49 2.435 509.976 1660 380 C
R. S. 0 60 0.42 -600.004 568 93 C++
J. T. 0 210 197.47 -2101.975 2580 255 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 237
2. Saxton, Tom 146
3. Maurer, Sebastian 67
4. Rieken, Willeke 51
5. Heithcock, JG 43
6. Shearer, Rob 41
7. Boring, Randy 39
8. Brown, Pat 20
9. Hostetter, Mat 20
10. Jones, Dennis 12
11. Hart, Alan 11
12. Duga, Brady 10
13. Hewett, Kevin 10
14. Murphy, ACC 10
14. Selengut, Jared 10
16. Smith, Brad 10
17. Strout, Joe 10
18. Varilly, Patrick 10

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 Tom's winning Putting Green solution:

PuttingGreen.c
Copyright © 1999 Tom Saxton

#include "PuttingGreen.h"

#include <stdlib.h>
#include <math.h>

enum
{
	fFalse = 0,
	fTrue = TRUE
};
#define DIM(a) (sizeof(a)/sizeof((a)[0]))

// disable asserts
#define Assert(f)

// vector types and constants
typedef struct Point3DDouble VEC;
static const double epsilon = 1.0e-7;
static const VEC s_normalZ = { 0, 0, 1.0 };
static const VEC s_vecZero;

// this green

static Point3DDouble *s_paposGrid;
static int s_cposGrid;
static MyTriangle *s_patri;
static int s_ctri;
static int s_itriPin;
static Point3DDouble s_posPin;

static int s_cholePractice;			// number of practice putts
static int s_choleScored;				// number of scored putts

// computed physical constants for this green
static int s_fGetDrag = fTrue;
static double mDrag, bDrag;

// current state

static int s_ihole;						// which hole are we on?
static int s_cputt;						// which putt is this
static int s_fPractice;				// is this a practice putt?
static Point3DDouble s_posCur;	// where's the ball?

// the current putt

static double s_svInitial;
static double s_distExpect;

// vector utilities

static void _SubVec(VEC pos1, VEC pos2, VEC *pposResult);
static double _DotVec(VEC vec1, VEC vec2);
static double _LenVec(VEC vec);
static void _ScaleVec(VEC vec, double s, VEC *pvecResult);

// triangle utilities

static void _GetMidTriPos(int itri, Point3DDouble *ppos);

//
// Entry Points
//
#if 0
static void ___Entry_Points(){}
#endif

InitGreen

void InitGreen(
	Point3DDouble paposGrid[],	/* green terrain description */
	long cposGrid,	/* number of points */
	MyTriangle patri[],	/* triangles comprising the green */
	int ctri,	/* number of triangles */
	long itriPin,	/* index in triangles[] of the pin on this green */
	long cholePractice,	/* number of unscored (but timed) holes to 			   practice on this green */
	long choleScored	/* number of holes to be scored on this green */
)

{
	s_paposGrid = paposGrid;
	s_cposGrid = cposGrid;
	s_patri = patri;
	s_ctri = ctri;
	s_itriPin = itriPin;
	
	s_cholePractice = cholePractice;
	s_choleScored = choleScored;
	
	_GetMidTriPos(itriPin, &s_posPin);
	
	s_ihole = 0;
}
	
#pragma warn_unusedarg off

StartHole

void StartHole(	/* called to start play on this hole */
	Point3DDouble posStart, 	/* initial ball position on the green */
	Boolean fPractice	/* TRUE if this hole is practice */
)
{
	++s_ihole;
	
	s_posCur = posStart;
	s_cputt = 0;
	s_fPractice = fPractice;
}

#pragma warn_unusedarg reset

#define cputtPractice 10
#define cputtScore    10

typedef struct SD SD;
struct SD
{
	double speed;
	double dist;
};
static SD s_asd[cputtPractice];
static int s_csd;

MakePutt

Boolean 		/* quit */ MakePutt(
	Velocity2DDouble *pvXY		/* return initial ball velocity in the z==0 plane */
)
{
	double dist;
	Point3DDouble vXY;
		
	if (s_cputt >= (s_fPractice ? cputtPractice : cputtScore))
	{
		if (s_fGetDrag)
		{
			int isd;
			double sumX, sumY, sumXY, sumXX;
			
			Assert(s_csd > 0);

			// do linear regression on the data

			sumX = sumY = sumXY = sumXX = 0;
			for (isd = 0; isd < s_csd; ++isd)
			{
				SD *psd = &s_asd[isd];
				double y = psd->dist;
				double x = fabs(psd->speed);
				
				sumXX += x * x;
				sumXY += x * y;
				sumX += x;
				sumY += y;
			}
			
			mDrag = (sumX*sumY - s_csd*sumXY)/(sumX*sumX - s_csd*sumXX);
			bDrag = (sumY - mDrag*sumX)/s_csd;
			
			Assert(0.0 <= mDrag && mDrag <= 5.0);
			Assert(-5.0 <= bDrag && bDrag <= 5.0);

			s_fGetDrag = fFalse;
		}
		
		// give up

		return fTrue;
	}
	
	// just give up after we've finished with practice shots

	if (s_fPractice && !s_fGetDrag)
		return fTrue;

	_SubVec(s_posPin, s_posCur, &vXY);
	vXY.z = 0;
	dist = _LenVec(vXY);
	
	if (s_fGetDrag)
	{
		s_svInitial = 3.0*(1.0 + s_cputt/2);
		if (s_cputt % 2)
			s_svInitial = -s_svInitial;
	}
	else
	{
		s_svInitial = (dist + 0.03 - bDrag) / mDrag;
		s_distExpect = dist;
	}
	_ScaleVec(vXY, s_svInitial/dist, &vXY);
	
	pvXY->x = vXY.x;
	pvXY->y = vXY.y;

	return fFalse; // keep going
}

BallMovement

void BallMovement(
	BallPosition papos4[],	/* provides ball movement in response to MakePutt */
	int cpos,	/* number of ball positions provided */
	Boolean fInHole	/* true if the ball went into the hole */
)
{
	Point3DDouble posNew;
	
	posNew = papos4[cpos-1].pt;
	
	if (!fInHole)
	{
		double dist;
		Point3DDouble vecMove;
			
		_SubVec(posNew, s_posCur, &vecMove);
		dist = _LenVec(vecMove);

		if (s_fGetDrag)
		{
			Assert(0 <= s_csd && s_csd < DIM(s_asd));
			s_asd[s_csd].speed = fabs(s_svInitial);
			s_asd[s_csd].dist = dist;
			++s_csd;
		}
	}

	s_posCur = posNew;
		
	++s_cputt;
}

//
// Vector Functions
//

#if 0
static void ___Vector_Functions(){}
#endif

_SubVec

static void _SubVec(VEC pos1, VEC pos2, VEC *pposResult)
{
	pposResult->x = pos1.x - pos2.x;
	pposResult->y = pos1.y - pos2.y;
	pposResult->z = pos1.z - pos2.z;
}

_DotVec

static double _DotVec(VEC vec1, VEC vec2)
{
	return vec1.x * vec2.x + vec1.y * vec2.y + vec1.z * vec2.z;
}

_LenVec

static double _LenVec(VEC vec)
{
	return sqrt(_DotVec(vec, vec));
}
_ScaleVec

static void _ScaleVec(VEC vec, double s, VEC *pvecResult)
{
	pvecResult->x = s * vec.x;
	pvecResult->y = s * vec.y;
	pvecResult->z = s * vec.z;

}

_GetMidTriPos

static void _GetMidTriPos(int itri, Point3DDouble *pposMid)
{
	MyTriangle tri;
	int iipos;
	
	Assert(0 <= itri && itri < s_ctri);
	tri = s_patri[itri];
	
	*pposMid = s_vecZero;
	
	for (iipos = 0; iipos < DIM(tri.pointIndices); ++iipos)
	{
		Point3DDouble *ppos;
		
		Assert(0 <= tri.pointIndices[iipos] && 
										tri.pointIndices[iipos] < s_cposGrid);
		ppos = &s_paposGrid[tri.pointIndices[iipos]];
		
		pposMid->x += ppos->x;
		pposMid->y += ppos->y;
		pposMid->z += ppos->z;
	}
	
	pposMid->x *= 1.0/3.0;
	pposMid->y *= 1.0/3.0;
	pposMid->z *= 1.0/3.0;
}
 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Bookends 12.5.8 - Reference management a...
Bookends is a full-featured bibliography/reference and information-management system for students and professionals. Access the power of Bookends directly from Mellel, Nisus Writer Pro, or MS Word (... Read more
Chromium 44.0.2403.125 - Fast and stable...
Chromium is an open-source browser project that aims to build a safer, faster, and more stable way for all Internet users to experience the web. Version 44.0.2403.125: This release contains a number... Read more
iMazing 1.2.2 - Complete iOS device mana...
iMazing (was DiskAid) is the ultimate iOS device manager with capabilities far beyond what iTunes offers. With iMazing and your iOS device (iPhone, iPad, or iPod), you can: Copy music to and from... Read more
Audio Hijack 3.2.0 - 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
FontExplorer X Pro 5.0.1 - Font manageme...
FontExplorer X Pro is optimized for professional use; it's the solution that gives you the power you need to manage all your fonts. Now you can more easily manage, activate and organize your... Read more
Calcbot 1.0.2 - Intelligent calculator a...
Calcbot is an intelligent calculator and unit converter for the rest of us. Featuring an easy-to-read history tape, expression view, intuitive conversion, and much more! Features History Tape -... Read more
MTR 5.0.0.1 - The Mac's oldest and...
MTR (was MacTheRipper)--the Mac's oldest and smartest DVD-backup app--is now updated to version 5.001 MTR -- the complete toolbox, not a one-trick, point-and-click extractor. MTR is intended for... Read more
LibreOffice 4.4.5.2 - Free, open-source...
LibreOffice is an office suite (word processor, spreadsheet, presentations, drawing tool) compatible with other major office suites. The Document Foundation is coordinating development and... Read more
Adobe Lightroom 6.1.1 - Import, develop,...
Adobe Lightroom is available as part of Adobe Creative Cloud for as little as $9.99/month bundled with Photoshop CC as part of the photography package. Lightroom 6 is also available for purchase as a... Read more
File Juicer 4.41 - Extract images, video...
File Juicer is a drag-and-drop can opener and data archaeologist. Its specialty is to find and extract images, video, audio, or text from files which are hard to open in other ways. It finds and... Read more

Pac-Man Championship Edition DX has brou...
Bandai Namco has released Pac-Man Championship Edition DX on iOS and Android, which features the classic arcade gameplay that we've all grown to love. Pac-Man Championship Edition DX can be enjoyed in much shorter bursts than the arcade versions... | Read more »
Cosmonautica (Games)
Cosmonautica 1.1 Device: iOS Universal Category: Games Price: $6.99, Version: 1.1 (iTunes) Description: Cast off! Are you ready for some hilarious adventures in outer space? | Read more »
Rescue humanity from a Demon horde in An...
Angel Stone is Fincon's follow up to the massively successful Hello Hero and is out now on iOS and Android. You play as a member of The Resistance, a group of mighty human warriors who have risen up in defiance of the Demon horde threatening to... | Read more »
Gallery Doctor (Photography)
Gallery Doctor 1.0 Device: iOS iPhone Category: Photography Price: $2.99, Version: 1.0 (iTunes) Description: Free up valuable iCloud and iPhone storage with Gallery Doctor, the only iPhone cleaner that automatically identifies the... | Read more »
You Against Me (Games)
You Against Me 1.0 Device: iOS Universal Category: Games Price: $.99, Version: 1.0 (iTunes) Description: A simple game… You. Me. Claim, steal, lock, score, win! | Read more »
Yep, it's True - Angry Birds 2 is O...
The not exactly rumors were true and the birds are back. Angry Birds 2 has come to the App Store and the world will... well I suppose it'll still be the same, but now we have more bird-flinging options! [Read more] | Read more »
You Could Design Your Own Card for Chain...
If you've ever wanted to create your own item, weapon, trap, or even monster for Chainsaw Warrior: Lords of the Night, this is your chance. Auroch Digital is currently holding a contest so that fans can fight to the death (not really) to see which... | Read more »
Bitcoin Billionaire is Going Back in Tim...
If you thought you managed to buy everything there is to buy in Bitcoin Billionaire and make all the money, well you though wrong. Those of you who made it far enough might remember investing in time travel - and it looks like that investment is... | Read more »
Domino Drop (Games)
Domino Drop 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: Domino Drop is a delightful new puzzle game with dominos and gravity!Learn how to play it in a minute, master it day by day.Your... | Read more »
OPERATION DRACULA (Games)
OPERATION DRACULA 1.0.1 Device: iOS Universal Category: Games Price: $5.99, Version: 1.0.1 (iTunes) Description: 25% off launch sale!!! 'Could prove to be one of the most accurate representations of the Japanese bullet hell shmup... | Read more »

Price Scanner via MacPrices.net

Sale! 13-inch MacBook Pros on sale for $100 o...
B&H Photo has 13″ MacBook Pros on sale for $100 off MSRP. Shipping is free, and B&H charges NY sales tax only: - 13″ 2.5GHz/500GB MacBook Pro: $999.99 save $100 - 13″ 2.7GHz/128GB Retina... Read more
Sale! Save $100 on 13-inch MacBook Airs this...
B&H Photo has the 13″ 1.6GHz/128GB MacBook Air on sale for $899.99 including free shipping plus NY tax only. Their price is $100 off MSRP, and it’s the lowest price available for this model.... Read more
Worldwide Tablet Market Decline Continues, Ap...
The worldwide tablet market declined -7.0% year-over-year in the second quarter of 2015 (2Q15) with shipments totaling 44.7 million units according to preliminary data from the International Data... Read more
TP-LINK TL-PA8030P KIT Powerline Featuring Ho...
Consumer and business networking products provider TP-LINK is now shipping its TL-PA8030P KIT AV1200 3-Port Gigabit Passthrough Powerline Starter Kit that expands your home’s network over its... Read more
Apple refurbished iPad Air 2s available for u...
The Apple Store has Apple Certified Refurbished iPad Air 2s available for up to $140 off the price of new models. Apple’s one-year warranty is included with each model, and shipping is free: - 128GB... Read more
Updated Apple iPad Price Trackers
We’ve updated our iPad Air Price Tracker and our iPad mini Price Tracker with the latest information on prices and availability from Apple and other resellers. Read more
Apple refurbished 2014 13-inch 128GB MacBook...
The Apple Store has Apple Certified Refurbished 2014 13″ MacBook Airs available starting at $759. An Apple one-year warranty is included with each MacBook, and shipping is free: - 13″ 1.4GHz/128GB... Read more
Apple’s Education discount saves up to $300 o...
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
Save up to $600 with Apple refurbished Mac Pr...
The Apple Store has Apple Certified Refurbished Mac Pros available for up to $600 off the cost of new models. An Apple one-year warranty is included with each Mac Pro, and shipping is free. The... Read more
Mac Pros on sale for up to $260 off MSRP
B&H Photo has Mac Pros on sale for up to $260 off MSRP. Shipping is free, and B&H charges sales tax in NY only: - 3.7GHz 4-core Mac Pro: $2799, $200 off MSRP - 3.5GHz 6-core Mac Pro: $3719.99... Read more

Jobs Board

Executive Administrative Assistant, *Apple*...
…supporting presentation development for senior leadership. * User experience with Apple hardware and software is preferred. Additional Requirements The following list Read more
*Apple* Bus Company is now hirin - Apple Bus...
Apple Bus Company is now hiring school bus drivers in the Pettis County area. Class B CDL preferred. Free training provided. No nights or weekends required. Flexible Read more
*Apple* Certified Mac Technician - Updated 6...
…and friendly, hands-on technical support to customers troubleshooting and repairing Apple /Mac products with courtesy, speed and skill. Use your problem-solving skills Read more
Infrastructure Engineer - *Apple* /Mac Envir...
…a part of a team Requires proven problem solving skills Preferred Additional Apple Certified System Administrator (ACSA) Apple Certified Technical Coordinator (ACTC) 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.