Battle of the Brains

Preparing for World Finals in Poland? Interested in computer programming?  Try your hand at this practice problem, straight from the 2011 World Finals in Orlando, FL!   You can find this set and more problems on the ACM ICPC website.

Trash Removal - Problem ID: trash

Allied Chute Manufacturers is a company that builds trash chutes. A trash chute is a hollow tube installed in buildings so that trash dropped in at the top will fall down and be collected in the basement. Designing trash chutes is actually highly nontrivial. Depending on what kind of trash people are expected to drop into them, the trash chute needs to have an appropriate size. And since the cost of manufacturing a trash chute is proportional to its size, the company always would like to build a chute that is as small as possible. Choosing the right size can be tough though.

We will consider a 2-dimensional simplification of the chute design problem. A trash chute points straight down and has a constant width. Objects that will be dropped into the trash chute are modeled as polygons. Before an object is dropped into the chute it can be rotated so as to provide an optimal fit. Once dropped, it will travel on a straight path downwards and will not rotate in flight. The following figure shows how an object is first rotated so it fits into the trash chute.

Your task is to compute the smallest chute width that will allow a given polygon to pass through.

Input

The input contains several test cases. Each test case starts with a line containing an integer n (3 ≤  n ≤  100), the number of points in the polygon that models the trash item. The next n lines then contain pairs of integers xi and yi (0 ≤ xi; yi ≤ 10^4), giving the coordinates of the polygonvertices in order. All points in one test case are guaranteed to be mutually distinct and the polygon sides will never intersect. (Technically, there is one inevitable exception of two neighboring sides sharing their common vertex. Of course, this is not considered an intersection.)

The last test case is followed by a line containing a single zero.

Output

For each test case, display its case number followed by the width of the smallest trash chute through which it can be dropped. Display the minimum width with exactly two digits to the right of the decimal point, rounding up to the nearest multiple of 1/100. Answers within 1/100 of the correct rounded answer will be accepted.

Follow the format of the sample output.

Sample Input                      Output for the Sample Input

3                                                     Case 1: 2.40

0  0                                                Case 2: 14.15

3  0

0  4

4

0  10

10 0

20 10

10 20

0

For the first podcast of 2012, we're treating you to a behind-the-scenes look at what - and who - makes our regionals competitions so successful.  Podcast host Christine Guerrini catches up with IBM intern Jeremy Lavergne (bottom, left) about how he got involved as an ICPC regional contest system administrator, as well as what he's working on now with IBM Software Group.  She also gets the inside scoop from former Speed Team member and current IBMer Jon Wedaman (bottom, right) on how his time as a volunteer system administrator helped his programming career.

Visit the World Finals website for the latest on this year's competition and to brush up on practice problems.  Have a fun picture of your teammates?  Tweet us @BrainBattleICPC!

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Happy Holidays from the Battle of the Brains!

Today, we're introducing a new voice to our series:  Salvatore Vella, Vice President of Architecture and Technology for IBM Software Group.  With over 20 years of experience in the IT industry, he understands both the technical aspects and the business strategy behind a successful technology company.  Podcast host Christine Guerrini catches up with Sal on how his career developed, as well as how students can utilize the ACM ICPC to take their own careers to the next level.

If you're headed to World Finals and would like to be featured on our podcast series, leave us a message in the comment section. And as always, be sure to follow us on Twitter. See you in 2012!

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When we last spoke with Steve Dale, he was on site at the 2011 World Finals in Orlando, Florida.  Now that he’s back at IBM’s DEMOCentral, Steve walks postcast host Amanda Carl through a day in the life of an IBMer and how he’s seen the industry evolve over the past decade.  He also shares fresh insights on what top technology companies are looking for in new recruits.

Check out the ACM-ICPC website for the latest updates on Regionals around the world.  We also love hearing your suggestions for new podcast topics, so give us a shout out on Twitter!

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Celebrating our fifth year on the web, we’re excited to kick off what we know will be our best season yet.

Today, we dive into the regionals phase of the competition, which is heating up in almost 90 countries across the globe.  Host Christine Guerrini caught up with podcast favorite Doug Heintzman, Director of Strategy for IBM Software Group and Sponsorship Executive of the ICPC, to relive some of the most exciting moments of World Finals 2011.  New to the ACM ICPC competition?  No problem.  Doug also discusses the competition structure and what teams need to succeed at the regional level.

Check back for more podcasts with all the inside tips and tidbits from contest executives, past World Finals participants, and IT professionals.  You can also brush up on practice problems and follow us on Twitter.

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With just days away from the IBM-sponsored Battle of the Brains, podcast host Amanda Carl chats with Sponsorship Manager Brenda Chow on-site in Orlando, at the Peabody Hotel about what contestants can expect when they arrive in sunny Florida. From great food to exciting excursions, Brenda shares with our listeners the events to come during the upcoming weekend.

Want to keep up with the contest? Follow us on twitter or check out the live cast at www.acmicpc.org.

Member of the press and interested in attending the World Finals? Contact Amanda Carl.

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With two weeks remaining until the World Finals in Orlando, podcast host Amanda Carl sat down with Dr. Michael Karasick, vice president of architecture and technology for IBM Software Group to discuss his thoughts surrounding the software technology industry and what students can do to prepare for the business world and beyond. Business analytics, cloud computing, system optimization – Dr. Karasick covers it all in this pre-World Finals chat.

Want to keep up with the World Finals from home? Follow us on Twitter for photos, videos, and contest updates throughout the week.

Best of luck to the contestants!

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As executive director of the IBM-sponsored ACM-ICPC and a former co-coach and contest judge, Dr. Bill Poucher knows the World Finals inside and out.  Since 1977, he has watched teams from around the world – Prague to Canada, Russia to the US – take home the coveted World’s Smartest Trophy.  What predictions does he have for the 2011 competition? Podcast host Christine Guerrini catches Bill during a rare free moment to talk last-minute tips, World Finals contenders, and even a few inside details on this year’s IBM Tech Trek.

Use your last few weeks of preparation to the fullest by checking out practice problems on our website.  And whether you’re a first-time competitor, returning champion, or simply interested in the contest, don’t forget to follow us on Twitter!

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