TweetFollow Us on Twitter

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

Programmer’s Challenge

by Bob Boonstra


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.


Community Search:
MacTech Search:

Software Updates via MacUpdate

World of Tanks Generals guide - Tips and...
World of Tanks Generals is a brand new card game by the developer behind the World of Tanks shooter franchise. It plays like a cross between chess and your typical card game. You have to keep in consideration where you place your tanks on the board... | Read more »
TruckSimulation 16 guide: How to succeed...
Remember those strangely enjoyable truck missions in Grand Theft Auto V whereit was a disturbing amount of fun to deliver cargo? TruckSimulation 16 is reminiscent of that, and has you play the role of a truck driver who has to deliver various... | Read more »
The best GIF making apps
Animated GIFs have exploded in popularity recently which is likely thanks to a combination of Tumblr, our shorter attention spans, and the simple fact they’re a lot of fun. [Read more] | Read more »
The best remote desktop apps for iOS
We've been sifting through the App Store to find the best ways to do computer tasks on a tablet. That gave us a thought - what if we could just do computer tasks from our tablets? Here's a list of the best remote desktop apps to help you use your... | Read more »
Warhammer 40,000: Freeblade guide - How...
Warhammer 40,000: Freebladejust launched in the App Store and it lets you live your childhood dream of blowing up and slashing a bunch of enemies as a massive, hulking Space Marine. It's not easy being a Space Marine though - and particularly if... | Read more »
Gopogo guide - How to bounce like the be...
Nitrome just launched a new game and, as to be expected, it's a lot of addictive fun. It's called Gopogo, and it challenges you to hoparound a bunch of platforms, avoiding enemies and picking up shiny stuff. It's not easy though - just like the... | Read more »
Sago Mini Superhero (Education)
Sago Mini Superhero 1.0 Device: iOS Universal Category: Education Price: $2.99, Version: 1.0 (iTunes) Description: KAPOW! Jack the rabbit bursts into the sky as the Sago Mini Superhero! Fly with Jack as he lifts impossible weights,... | Read more »
Star Wars: Galaxy of Heroes guide - How...
Star Wars: Galaxy of Heroes is all about collecting heroes, powering them up, and using them together to defeat your foes. It's pretty straightforward stuff for the most part, but increasing your characters' stats can be a bit confusing because it... | Read more »
The best cooking apps (just in time for...
It’s that time of year again, where you’ll be gathering around the dinner table with your family and a huge feast in front of you. [Read more] | Read more »
Square Rave guide - How to grab those te...
Square Rave is an awesome little music-oriented puzzle game that smacks of games like Lumines, but with its own unique sense of gameplay. To help wrap your head around the game, keep the following tips and tricks in mind. [Read more] | Read more »

Price Scanner via

Cyber Monday: Apple MacBooks on sale for up t...
Apple resellers have MacBook Pros, MacBook Airs, and MacBooks on sale for up to $250 off MSRP for Cyber Monday 2015. The following is a roundup of the lowest prices available for new models from any... Read more
Cyber Monday: 15% off Apple products, and sto...
Use code CYBER15 on Cyber Monday only to take 15% on Apple products at Target, and store-wide. Choose free shipping or free local store pickup (if available). Sale prices for online orders only, in-... Read more
iPad Air 2 And iPad mini Among Top Five Black...
Adobe has released its 2015 online shopping data for Black Friday and Thanksgiving Day. The five best selling electronic products on Black Friday were Samsung 4K TVs, Apple iPad Air 2, Microsoft Xbox... Read more
All-in-one PC Shipments Projected To Drop Ove...
Digitimes’ Aaron Lee and Joseph Tsai report that all-in-one (AIO) PC shipments may drop a double-digit percentage on-year in 2015 due to weaker-than-expected demand, although second-largest AIO make... Read more
Sprint Offers iPad Pro
Sprint now offers Apple’s new iPad Pro with Wi-Fi + Cellular, featuring a 12.9-inch Retina display with 5.6 million pixels. Customers can pick up iPad Pro at select Sprint retail locations. It can... Read more
Cyber Monday: Target offers 15% discount on A...
Target has discounted Apple Watches by 15% for Cyber Monday. Choose free shipping or free local store pickup (if available). Sale prices for online orders only, in-store prices may vary: - Apple... Read more
Sunday roundup of Holiday weekend Mac sales:...
Take up to $500 off MSRP on the price of a new Mac at B&H Photo today as part of their Black Friday/Holiday weekend sale. Shipping is free, and B&H charges NY tax only. These prices are... Read more
Holiday weekend: Apple Watch on sale for $50-...
B&H Photo has the Apple Watch on sale today for $50-$100 off MSRP. Shipping is free, and B&H charges NY sales tax only: - Apple Watch Sport: $50 off - Apple Watch: $50-$100 off Read more
Holiday weekend: iPad Air 2s on sale for up t...
B&H Photo has iPad Air 2s on sale for up to $80 off MSRP including free shipping plus NY sales tax only: - 16GB iPad Air 2 WiFi: $459 $40 off - 64GB iPad Air 2 WiFi: $569 $30 off - 128GB iPad Air... Read more
Holiday weekend Mac sales roundup: B&H Ph...
B&H Photo continues to have all new Macs on sale for up to $500 off MSRP as part of their Black Friday/Holiday weekend sale. Shipping is free, and B&H charges NY tax only: - 15″ 2.2GHz Retina... Read more

Jobs Board

Technical Program Manager, Strategic Merchant...
# Technical Program Manager, Strategic Merchants - Apple Pay Job Number: 44001177 Santa Clara Valley, Califo ia, United States Posted: Oct. 30, 2015 Weekly Hours: 40.00 Read more
Frameworks Engineer, *Apple* Watch - Apple...
# Frameworks Engineer, Apple Watch Job Number: 41403122 Santa Clara Valley, Califo ia, United States Posted: Jul. 1, 2015 Weekly Hours: 40.00 **Job Summary** Join the Read more
Software Engineer - *Apple* Pay - Apple (Un...
# Software Engineer - Apple Pay Job Number: 44003246 Santa Clara Valley, Califo ia, United States Posted: Nov. 16, 2015 Weekly Hours: 40.00 **Job Summary** Apple Pay Read more
Merchant Operations Manager: *Apple* Pay -...
# Merchant Operations Manager: Apple Pay Job Number: 43593822 Santa Clara Valley, Califo ia, United States Posted: Nov. 10, 2015 Weekly Hours: 40.00 **Job Summary** The Read more
Product Design Engineer - *Apple* Watch - A...
# Product Design Engineer - Apple Watch Job Number: 41727161 Santa Clara Valley, Califo ia, United States Posted: Jul. 22, 2015 Weekly Hours: 40.00 **Job Summary** Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.