TweetFollow Us on Twitter

Dec 96 Challenge
Volume Number:12
Issue Number:12
Column Tag:Programmer’s Challenge

Programmer’s Challenge

by Bob Boonstra

Tangrams

The Challenge this month is to write code that will solve a tangram puzzle - that is, reassemble a two-dimensional shape that has been cut into a number of smaller shapes. The classic tangram consists of five right triangles of three different sizes, a square, and a rhomboid that are to be reassembled into a larger square. Your code will have to deal with a more general set of polygons. The prototype for the code you should write is:

#define kMaxVertices 10

typedef struct MyVertex {
 float  h;/* horizontal coordinate of vertex */
 float  v;/* vertical coordinate of vertex */
} MyVertex;

typedef struct MyPolygon {
    long     numVertices;/* number of vertices in polygon */
    MyVertex vertex[kMaxVertices];        /* vertex coordinates */
} MyPolygon;

typedef struct MyTransform {
    float     flipH;         /* optionally flip polygon about this horiz coordinate */
    float     rotateClockwise;      /* then rotate polygon clockwise by this many                                        
    radians */
    float     rotateCenterH;   /* around the point with this horiz coordinate */
    float     rotateCenterV;   /* and with this vertical coordinate */
    float     translateH;    /* then translate horizontally by this amount */
 float  translateV;/* then translate vertically by this amount */
    Boolean doFilp;                /* only perform flip if this is TRUE */
} MyTransform;

void SolveTangram(
    MyPolygon     *theShape,          /* shape to be reassembled */
    long     numHoles,            /* shape has this many holes (>=0) */
    MyPolygon     *theHoles[],  /* pointers to polygons that form the holes */
    long     numPieces,   /* number of pieces to reassemble */
    MyPolygon     *thePieces[],      /* shape and position of pieces to reassemble */
    MyTransform *theXForms[]      /* reassembly transforms corresponding to  thePieces */
);

The shape to be reassembled is a polygon pointed to by theShape, except that the reassembled shape may have some holes in it. The number of holes, which might be zero, is provided by numHoles, and the shape of the i-th hole is a polygon pointed to by theHoles[i]. You are to reassemble theShape using numPieces polygons pointed to by thePieces[]. For each piece, you should transform it to its correct position by optionally flipping it about a vertical axis, rotating it, and translating it, in that order. For the j-th piece, you should store the required transformation in the structure pointed to by theXForms[j]. Set doFilp to FALSE if no flip is needed, otherwise set doFilp to TRUE to flip the horizontal coordinates about the vertical axis with horizontal coordinate flipH. Set rotateClockwise to the number of radians that the piece should be rotated about the point (rotateCenterH, rotateCenterV). Finally, set translateH and translateV to the amount that the piece should be moved in the horizontal and vertical directions, respectively.

Calculations should be accurate to .00001, meaning that when I apply your transformations using the sin() and cos() library functions, the resulting positions should agree with theShape to within that accuracy.

All of the polygons will be legal polygons - no edge formed by a pair of adjacent vertices will intersect any other edge in the same polygon except at a vertex. The last vertex in each polygon connects to the first vertex (i.e., a square will have four vertices, not a fifth that is the same as the first). All of theHoles in the shape to be reassembled will be strictly inside theShape, not intersecting the edges. No hole will intersect any other hole. You may allocate up to 10MB of memory for your own use, provided you deallocate any allocated memory prior to returning.

This will be a native PowerPC Challenge, using the latest CodeWarrior environment. Solutions may be coded in C, C++, or Pascal. The winner will be the solution that solves my set of test tangrams in the shortest amount of time. And thanks go out to Ernst Munter for suggesting this Challenge - he wins two contest points for the suggestion.

Two Months Ago Winner

Congratulations to... Well, that is what you would normally read in this part of the column. Alas, the realities of publication deadlines have forced us to make a change in when we publish the winning solution. Perhaps an example of the publishing schedule for this, the December issue which ships in mid-November, would help me explain. Most of the articles for this issue were due to the editorial staff on September 23. Now, if that seems like a lot of lead time to you, it does to me also. However, people who know a lot more about publishing than I do assure me that This Is The Way It Is (e.g., most monthlies have 4-6 month lead times). I believe them - what does a software guy know about publishing deadlines anyway?

Well, I know enough simple arithmetic to realize that it is difficult to include a solution submitted on October 1 in an article due on September 23. The publishers, being just as good at arithmetic, also figured this out, so they have always given me a little extra time to write the Challenge column. That presented the magazine with a Challenge of its own, in that the Challenge column is very unpredictable in length, making magazine layout difficult.

We always try to guess how long the column is going to be, but that means guessing how long the winning solutions are going to be. Sometimes the solutions do not cooperate by being predictable in length. The Challenge deadlines (mine, not yours) kept creeping toward the 1st-of-the-month solution submission deadline. Sometimes there was only one day to compile the solutions, score them, select the winner, and write the column. Sometimes that one day was a day when that Real Job got in the way. (That’s right kids, you can’t make a living writing the Programmer’s Challenge column.) Soooo, in undeniable recognition of publishing reality and our continued goal of improving the magazine, we have reluctantly decided that we need to publish the winning solution three months after we publish the puzzle, instead of two. That is why you are reading this explanation instead of a description of the winning solution to the DNA Match Challenge.

Seriously though, this change will provide me with a more reasonable amount of time to analyze submitted solutions and hopefully point out more interesting and useful features of competitive solutions. For Challenge contestants, we will be announcing the identity of the winner on the CHALLENGE email list at approximately the time that we would have published under the previous arrangement. We hope that this change, in addition to restoring some sanity to the publishing schedule, will allow us to produce a more informative and interesting column. See you next month.


 
AAPL
$100.86
Apple Inc.
-0.77
MSFT
$46.76
Microsoft Corpora
+0.52
GOOG
$579.95
Google Inc.
+6.85

MacTech Search:
Community Search:

Software Updates via MacUpdate

Capture One Pro 8.0.0.433 - RAW workflow...
Capture One Pro 8 is a professional RAW converter offering you ultimate image quality with accurate colors and incredible detail from more than 300 high-end cameras -- straight out of the box. It... Read more
Adobe Acrobat Pro 11.0.09 - Powerful PDF...
Adobe Acrobat allows users to communicate and collaborate more effectively and securely. Unify a wide range of content in a single organized PDF Portfolio. Collaborate through electronic document... Read more
Adobe Reader 11.0.09 - View PDF document...
Adobe Reader allows users to view PDF documents. You may not know what a PDF file is, but you've probably come across one at some point. PDF files are used by companies and even the IRS to... Read more
iFFmpeg 4.6.1 - Convert multimedia files...
iFFmpeg is a graphical front-end for FFmpeg, a command-line tool used to convert multimedia files between formats. The command line instructions can be very hard to master/understand, so iFFmpeg does... Read more
NTFS 11.3.62 - Provides full read and wr...
Paragon NTFS breaks down the barriers between Windows and OS X. Paragon NTFS effectively solves the communication problems between the Mac system and NTFS, providing full read and write access to... Read more
OS X Yosemite 10.10 DP8 - Developer Prev...
Note: This is a Developer Preview. You must be a registered Apple Mac Developer to download this update. You can also sign up for the free OS X Beta Program to download and preview public beta... Read more
FotoMagico 4.5 - Powerful slideshow crea...
FotoMagico lets you create professional slideshows from your photos and music with just a few, simple mouse clicks. It sports a very clean and intuitive yet powerful user interface. High image... Read more
Screenshot Path 1.2.1 - Change the defau...
Screenshot Path lets you change the folder where OS X saves screenshots. Screenshots are saved by default to the user’s desktop. This is handy for the occasional screenshot but those looking to take... Read more
Fantastical 1.3.16 - Create calendar eve...
Fantastical is the Mac calendar you'll actually enjoy using. Creating an event with Fantastical is quick, easy, and fun: Open Fantastical with a single click or keystroke Type in your event details... Read more
GIMP 2.8.14 - Powerful, free image editi...
GIMP is a multi-platform photo manipulation tool. GIMP is an acronym for GNU Image Manipulation Program. The GIMP is suitable for a variety of image manipulation tasks, including photo retouching,... Read more

Latest Forum Discussions

See All

Zynga Unveils First Look at Looney Tunes...
Zynga Unveils First Look at Looney Tunes Dash! Posted by Ellis Spice on September 16th, 2014 [ permalink ] Be vewy, vewy qwiet. I’m hunting wunners featuwing wabbits, and luckily, it’s duck season wunner season. | Read more »
Guardians on the Go – How to Connect to...
At this point I’m relatively certain most of the country is familiar with Destiny. And for those looking to augment their game a bit, Bungie has changed their Bungie Mobile Companion App to Destiny Companion. | Read more »
Kunin Review
Kunin Review By Jordan Minor on September 16th, 2014 Our Rating: :: SHURIKEN DO ITUniversal App - Designed for iPhone and iPad Kunin is a nervous test of ninja reflexes.   Developer: Dodreams Price: FREE Version Reviewed: 1.0.1... | Read more »
4 KEMCO Titles are Just $0.99 for a Limi...
4 KEMCO Titles are Just $0.99 for a Limited Time Posted by Jessica Fisher on September 16th, 2014 [ permalink ] KEMCO RPGs Destiny Fantasia, Infinite Dunamis, Bonds of the Sk | Read more »
Introducing Flash, the Latest Wearable F...
Introducing Flash, the Latest Wearable Fitness Monitor from Misfit Posted by Jessica Fisher on September 16th, 2014 [ permalink ] The Misfit Flash is the newly-released fitness and sleep monitor from | Read more »
Hyper Trip Review
Hyper Trip Review By Jennifer Allen on September 16th, 2014 Our Rating: :: HYPER TWITCHYUniversal App - Designed for iPhone and iPad Tough and unforgiving, Hyper Trip is a bit like Snake – if Snake was really harsh.   | Read more »
Collectible Card Game Earthcore: Shatter...
Collectible Card Game Earthcore: Shattered Elements is Set to Arrive on iOS in 2015 Posted by Ellis Spice on September 16th, 2014 [ permalink ] Polish developers | Read more »
Boogey Boy Review
Boogey Boy Review By Jennifer Allen on September 16th, 2014 Our Rating: :: PRETTY BUT BASICUniversal App - Designed for iPhone and iPad It looks delightful but lack of Game Center support and more variety really affects the fun... | Read more »
Vizzywig 4K (Photography)
Vizzywig 4K 1.0 Device: iOS iPhone Category: Photography Price: $999.99, Version: 1.0 (iTunes) Description: REQUIRES: iOS 7 on iPhone 5S with 32GB or 64GB. (Do not use iOS 8)The world's FIRST mobile 4K video capture, editing and... | Read more »
The Sleeping Prince Review
The Sleeping Prince Review By Jennifer Allen on September 15th, 2014 Our Rating: :: RESTRICTIVE KINGDOM SAVINGUniversal App - Designed for iPhone and iPad The Sleeping Prince looks and feels great to play, but its lack of peril and... | Read more »

Price Scanner via MacPrices.net

Sprint offers 16GB iPad mini for $199.99 with...
Sprint is offering 1st generation 16GB iPad minis for $199.99 with a 2-year service agreement. Standard MSRP for this iPad is $429. Their price is the lowest available for this model. Read more
2.5GHz Mac mini remains on sale for $549, sav...
B&H Photo has the 2.5GHz Mac mini on sale for $549.99 including free shipping. That’s $50 off MSRP, and B&H will also include a free copy of Parallels Desktop software. NY sales tax only. Read more
Apple refurbished iMacs available for up to $...
The Apple Store has Apple Certified Refurbished iMacs available for up to $300 off the cost of new models. Apple’s one-year warranty is standard, and shipping is free. These are the best prices on... Read more
13″ 2.5GHz MacBook Pro offered for $100 off M...
B&H Photo has the 13″ 2.5GHz MacBook Pro on sale for $999.99 including free shipping plus NY sales tax only. Their price is $100 off MSRP. Read more
Free GIMP Professional Grade Graphics App Ver...
The latest 2.8.14 version of the oddly-named GIMP (acronym for: GNU Image Manipulation Program) open source, high-end image editing and creation alternative to Adobe’s Photoshop and refuge from... Read more
Apple Announces Record Pre-orders for iPhone...
Apple has released metrics showing a record number of first day pre-orders of iPhone 6 and iPhone 6 Plus, with over four million sold in the first 24 hours. Demand for the new iPhones exceeds the... Read more
10% off iPhone 6 and 6 Plus Otterbox cases
Get 10% off on popular Otterbox iPhone 6 and iPhone 6 Plus cases at MacMall through September 19th. Use code OTTERBOX10 to see the discount. Read more
15-inch MacBook Pros on sale for up to $125 o...
Amazon has the new 2014 15″ Retina MacBook Pros on sale for up to $125 off MSRP including free shipping: - 15″ 2.2GHz Retina MacBook Pro: $1899.99 save $100 - 15″ 2.5GHz Retina MacBook Pro: $2374... Read more
27-inch 3.2GHz iMac on sale for $1698, $101 o...
Abt has the 27″ 3.2GHz iMac on sale for $1698 including free shipping. Their price is $101 off MSRP. Read more
More To Making A Larger iPad Than Expanded Sc...
CNET’s Ross Rubin has posted a thoughtful analysis of prospects for a larger display iPad Pro, noting that Microsoft and Samsung currently have the large-display touchscreen tablet category to... Read more

Jobs Board

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