Comments on: Polygonous Party Games

By: strauss

strauss — Tue, 23 Mar 2010 21:12:44 +0000

We use this trick all the time in Differential Topology class!

By: jyoak

jyoak — Tue, 23 Mar 2010 17:26:53 +0000

I remembered this one from when I was in college competing in the ACM programming competition. The idea was that your team was given a number of problems in terms of input and output required ranging from very simple to very hard and the team that could complete the most of them in a day won. The simplest was that your program would receive six arguments to be interpreted as three ordered pairs on the plane and determine whether or not they formed a triangle and output yes or no. For this one, you received an unknown number of ordered pairs and were assured that all but the last formed a polygon and you were to report whether the last was inside or outside the polygon. I happened to implement that solution for our team and did it essentially as all the comments above did. I projected a ray from that final point, ensuring that it didn't pass through any previously provided point, and counted the number of segments it intersected.

By: Blaine

Blaine — Tue, 23 Mar 2010 16:41:27 +0000

I think this would work: [spoiler]Just run straight to the clubhouse, as quickly as possible. Count the number of times you cross under a rope. Each rope crossing will toggle you from inside to outside or vice versa. If you count an odd number of crossings, you were inside. If you count an even number of crossings, you were outside.[/spoiler]

By: Krister Jonsson

Krister Jonsson — Tue, 23 Mar 2010 16:41:03 +0000

I think I remember how to do this.

[spoiler]Go in a straight line as fast as possible towards the clubhouse, and keep count of how many ropes you pass. If you pass an even number of ropes you started outside of the polygon, and if you pass an odd number you started inside. [/spoiler]

By: Jonathan Harford

Jonathan Harford — Tue, 23 Mar 2010 15:04:10 +0000

Assuming I could see the clubhouse, I’d head straight for it, counting the number of times I pass under (or over) a rope. If the count ends at an odd number, I was inside the shape. Otherwise, outside.

By: Blaise Pascal

Blaise Pascal — Tue, 23 Mar 2010 05:26:56 +0000

This one’s easy, assuming you know where the top of the hill is in relation to where you start.