32 lines
1 KiB
Markdown
32 lines
1 KiB
Markdown
## Problem statement
|
|
|
|
This solves the following problem:
|
|
```
|
|
Given a set of rectilinear rectangles in the plane, each by coordinates of opposing corners,
|
|
calculate the area of their union.
|
|
```
|
|
It was a task to show that this is solvable in `O(n^2)` on one of my exercise sheets.
|
|
Because I had some spare time, I decided to implement this.
|
|
|
|
Actually, this can be done in `O(nlog n)` time using a sweepline algorithm
|
|
that makes use of [segment trees][st].
|
|
|
|
The implementation tries to be reasonably fast and respects `nlog n` running time,
|
|
but is certainly not too optimized and more of a showcase.
|
|
|
|
|
|
## Build
|
|
A standard `C++` installation along with `CMake` should to the job.
|
|
Remove the benchmark targets if you do not need them.
|
|
|
|
|
|
## Benchmark
|
|
|
|
Just for fun, I played around with the [Google Benchmark Library][gl-benchmark].
|
|
You will have to install the library and statically link to it to run the
|
|
benchmarks.
|
|
See the github page of the benchmark library for details.
|
|
|
|
|
|
[gl-benchmark]: https://github.com/google/benchmark
|
|
[st]: https://en.wikipedia.org/wiki/Segment_tree
|