| № | Пользователь | Рейтинг |
|---|---|---|
| 1 | tourist | 4009 |
| 2 | jiangly | 3831 |
| 3 | Radewoosh | 3646 |
| 4 | jqdai0815 | 3620 |
| 4 | Benq | 3620 |
| 6 | orzdevinwang | 3529 |
| 7 | ecnerwala | 3446 |
| 8 | Um_nik | 3396 |
| 9 | gamegame | 3386 |
| 10 | ksun48 | 3373 |
| Страны | Города | Организации | Всё → |
| № | Пользователь | Вклад |
|---|---|---|
| 1 | cry | 164 |
| 1 | maomao90 | 164 |
| 3 | Um_nik | 163 |
| 4 | atcoder_official | 160 |
| 5 | -is-this-fft- | 158 |
| 6 | awoo | 157 |
| 7 | adamant | 156 |
| 8 | TheScrasse | 154 |
| 8 | nor | 154 |
| 10 | Dominater069 | 153 |
Does anyone know an algorithm to solve the following problem:
Given a sequence of points in the plane that represent a polygon (not necessarily convex), output the maximum possible radius of a circle that can fit inside this polygon.
It would be good if it was below O(n2), but any references are welcome. Thanks ahead.
Auto comment: topic has been updated by kowalsk1 (previous revision, new revision, compare).
If it was convex, you could make inequalities of form Ax+By+Cr>=0. For non-convex you need something different.
Binary search for R. if you choose R to be your radius check if size R circle fits inside.
You probably will need veronoi diagrams.
How do you determine in which point should be center of the circle?
All right, I already understand how. If somebody still curious — visit this article.
In each vertex with reflex angle generate two new polygons without that vertex. Black is non-convex. Red and green are new polygons. And after having only convex ones get maximum of circles in each polygon. Algorithm at emaxx for convex.
Where's O(2^n) subpolygons...
Btw, why did you not just google your question? I found answer for that in few minutes.