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https://github.com/geocrystal/kd_tree
Crystal implementation of "K-Dimensional Tree" and "N-Nearest Neighbors"
https://github.com/geocrystal/kd_tree
crystal data-structures k-dimensional priority-queue tree-structure
Last synced: 2 months ago
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Crystal implementation of "K-Dimensional Tree" and "N-Nearest Neighbors"
- Host: GitHub
- URL: https://github.com/geocrystal/kd_tree
- Owner: geocrystal
- License: mit
- Created: 2018-08-10T15:13:37.000Z (almost 6 years ago)
- Default Branch: master
- Last Pushed: 2024-04-12T21:51:46.000Z (3 months ago)
- Last Synced: 2024-04-14T07:48:20.340Z (3 months ago)
- Topics: crystal, data-structures, k-dimensional, priority-queue, tree-structure
- Language: Crystal
- Homepage:
- Size: 59.6 KB
- Stars: 17
- Watchers: 3
- Forks: 3
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Lists
- awesome-crystal - kd_tree - An implementation of "K-Dimensional Tree" and "N-Nearest Neighbors" (Algorithms and Data structures)
- awesome-crystal - kd_tree - An implementation of "K-Dimensional Tree" and "N-Nearest Neighbors" (Algorithms and Data structures)
README
# Kd::Tree
[](https://github.com/geocrystal/kd_tree/actions/workflows/crystal.yml)
[](https://github.com/geocrystal/kd_tree/releases)
[](https://geocrystal.github.io/kd_tree/)
[](https://github.com/geocrystal/kd_tree/blob/master/LICENSE)
Crystal implementation of "K-Dimensional Tree" and "N-Nearest Neighbors"
based on .
## Installation
Add this to your application's `shard.yml`:
```yaml
dependencies:
kd_tree:
github: geocrystal/kd_tree
```
## Usage
```crystal
require "kd_tree"
```
For example, construct a new tree where each point is represented as a two-dimensional array in the form [x, y], where x and y are numbers (such as Int32, Float64, etc).
```crystal
kd = Kd::Tree(Array(Int32)).new(points)
```
Find the nearest point to `[x, y]`. Returns an array with one point:
```crystal
kd.nearest([x, y])
```
Find the nearest `k` points to `[x, y]`. Returns an array of points:
```crystal
kd.nearest([x, y], k)
```
## Example
```crystal
require "kd_tree"
points = [
[2.0, 3.0],
[5.0, 4.0],
[4.0, 7.0],
[7.0, 2.0],
[8.0, 1.0],
[9.0, 6.0],
]
kd = Kd::Tree(Array(Float64)).new(points)
kd.nearest([1.0, 1.0])
# => [[2.0, 3.0]])
kd_tree.nearest([1.0, 1.0], 2)
# => [[2.0, 3.0], [5.0, 4.0]])
```
### Complex objects
`Kd::Tree(T)` can accept any object that responds to `#size` and `#[](i : Int)` methods.
```crystal
class GeoLocation
property name : String
property longitude : Float64
property latitude : Float64
getter size = 2 # Assuming all GeoLocation objects are 2-dimensional
def initialize(@name : String, @longitude : Float64, @latitude : Float64)
end
# Define an indexer to allow easy access by index for longitude and latitude
def [](index : Int32) : Float64
case index
when 0 then @longitude
when 1 then @latitude
else raise "Index out of bounds"
end
end
end
# Create an array of GeoLocation points
points = [
GeoLocation.new("New York", -73.935242, 40.730610),
GeoLocation.new("Los Angeles", -118.243683, 34.052235),
GeoLocation.new("London", -0.127647, 51.507322),
GeoLocation.new("Tokyo", 139.691711, 35.689487),
]
# Initialize the KD-tree with these points
kd_tree = Kd::Tree(GeoLocation).new(points)
# Find the nearest point to London
target = GeoLocation.new("Near London", -0.125740, 51.508530)
nearest_point = kd_tree.nearest(target, 1)
puts "Nearest to London: #{nearest_point.first.name} (longitude #{nearest_point.first.longitude}, latitude #{nearest_point.first.latitude})"
# Nearest to London: London (longitude -0.127647, latitude 51.507322)
```
### Distance
For distance calculations, the squared Euclidean distance is used. However, you can easily monkey-patch the `Kd::Tree#distance` method to implement another algorithm, such as the Haversine formula, to calculate distances between two points given their latitudes and longitudes.
```crystal
require "haversine"
module Kd
class Tree(T)
private def distance(m : T, n : T)
# Calling `Haversine.distance` with 2 pairs of latitude/longitude coordinates.
# Returns a distance in meters.
Haversine.distance({m.latitude, m.longitude}, {n.latitude, n.longitude}).to_meters
end
end
end
points = [
GeoLocation.new("New York", -73.935242, 40.730610),
GeoLocation.new("Los Angeles", -118.243683, 34.052235),
GeoLocation.new("London", -0.127647, 51.507322),
GeoLocation.new("Tokyo", 139.691711, 35.689487),
]
kd_tree = Kd::Tree(GeoLocation).new(points)
# Find the nearest point to London
target = GeoLocation.new("Near London", -0.125740, 51.508530)
nearest_point = kd_tree.nearest(target, 1)
puts "Nearest to London: #{nearest_point.first.name} (longitude #{nearest_point.first.longitude}, latitude #{nearest_point.first.latitude})"
# Nearest to London: London (longitude -0.127647, latitude 51.507322)
```
## Performance
Using a tree with 1 million points `[x, y] of Float64` on my i7-8550U CPU @ 1.80GHz:
`crystal run benchmark/benchmark.cr --release`
```console
Benchmarking KD-Tree with 1 million points
build(init): 3.43 seconds
user system total real
nearest point 1 0.000021 0.000000 0.000021 ( 0.000022)
nearest point 5 0.000014 0.000000 0.000014 ( 0.000014)
nearest point 10 0.000011 0.000000 0.000011 ( 0.000012)
nearest point 50 0.000061 0.000000 0.000061 ( 0.000061)
nearest point 100 0.000083 0.000001 0.000084 ( 0.000084)
nearest point 255 0.000238 0.000002 0.000240 ( 0.000240)
nearest point 999 0.000981 0.000009 0.000990 ( 0.000990)
```
## Contributing
1. Fork it ()
2. Create your feature branch (`git checkout -b my-new-feature`)
3. Commit your changes (`git commit -am 'Add some feature'`)
4. Push to the branch (`git push origin my-new-feature`)
5. Create a new Pull Request
## Contributors
- [mamantoha](https://github.com/mamantoha) Anton Maminov - creator, maintainer