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//! [k-d trees](https://en.wikipedia.org/wiki/K-d_tree).
use super::{Metric, NearestNeighbors, Neighborhood};
use ordered_float::OrderedFloat;
use std::iter::FromIterator;
/// A point in Cartesian space.
pub trait Cartesian: Metric<[f64]> {
/// Returns the number of dimensions necessary to describe this point.
fn dimensions(&self) -> usize;
/// Returns the value of the `i`th coordinate of this point (`i < self.dimensions()`).
fn coordinate(&self, i: usize) -> f64;
}
/// Blanket [Cartesian] implementation for references.
impl<'a, T: Cartesian> Cartesian for &'a T {
fn dimensions(&self) -> usize {
(*self).dimensions()
}
fn coordinate(&self, i: usize) -> f64 {
(*self).coordinate(i)
}
}
/// Blanket [Metric<[f64]>](Metric) implementation for [Cartesian] references.
impl<'a, T: Cartesian> Metric<[f64]> for &'a T {
type Distance = T::Distance;
fn distance(&self, other: &[f64]) -> Self::Distance {
(*self).distance(other)
}
}
/// Standard cartesian space.
impl Cartesian for [f64] {
fn dimensions(&self) -> usize {
self.len()
}
fn coordinate(&self, i: usize) -> f64 {
self[i]
}
}
/// Marker trait for cartesian metric spaces.
pub trait CartesianMetric<T: ?Sized = Self>:
Cartesian + Metric<T, Distance = <Self as Metric<[f64]>>::Distance>
{
}
/// Blanket [CartesianMetric] implementation for cartesian spaces with compatible metric distance
/// types.
impl<T, U> CartesianMetric<T> for U
where
T: ?Sized,
U: ?Sized + Cartesian + Metric<T, Distance = <U as Metric<[f64]>>::Distance>,
{
}
/// A node in a k-d tree.
#[derive(Debug)]
struct KdNode<T> {
/// The value stored in this node.
item: T,
/// The left subtree, if any.
left: Option<Box<Self>>,
/// The right subtree, if any.
right: Option<Box<Self>>,
}
impl<T: Cartesian> KdNode<T> {
/// Create a new KdNode.
fn new(i: usize, mut items: Vec<T>) -> Option<Box<Self>> {
if items.is_empty() {
return None;
}
items.sort_unstable_by_key(|x| OrderedFloat::from(x.coordinate(i)));
let mid = items.len() / 2;
let right: Vec<T> = items.drain((mid + 1)..).collect();
let item = items.pop().unwrap();
let j = (i + 1) % item.dimensions();
Some(Box::new(Self {
item,
left: Self::new(j, items),
right: Self::new(j, right),
}))
}
/// Recursively search for nearest neighbors.
fn search<'a, U, N>(&'a self, i: usize, closest: &mut [f64], neighborhood: &mut N)
where
T: 'a,
U: CartesianMetric<&'a T>,
N: Neighborhood<&'a T, U>,
{
neighborhood.consider(&self.item);
let target = neighborhood.target();
let ti = target.coordinate(i);
let si = self.item.coordinate(i);
let j = (i + 1) % self.item.dimensions();
let (near, far) = if ti <= si {
(&self.left, &self.right)
} else {
(&self.right, &self.left)
};
if let Some(near) = near {
near.search(j, closest, neighborhood);
}
if let Some(far) = far {
let saved = closest[i];
closest[i] = si;
if neighborhood.contains_distance(target.distance(closest)) {
far.search(j, closest, neighborhood);
}
closest[i] = saved;
}
}
}
/// A [k-d tree](https://en.wikipedia.org/wiki/K-d_tree).
#[derive(Debug)]
pub struct KdTree<T> {
root: Option<Box<KdNode<T>>>,
}
impl<T: Cartesian> FromIterator<T> for KdTree<T> {
/// Create a new k-d tree from a set of points.
fn from_iter<I: IntoIterator<Item = T>>(items: I) -> Self {
Self {
root: KdNode::new(0, items.into_iter().collect()),
}
}
}
impl<T, U> NearestNeighbors<T, U> for KdTree<T>
where
T: Cartesian,
U: CartesianMetric<T>,
{
fn search<'a, 'b, N>(&'a self, mut neighborhood: N) -> N
where
T: 'a,
U: 'b,
N: Neighborhood<&'a T, &'b U>,
{
let target = neighborhood.target();
let dims = target.dimensions();
let mut closest: Vec<_> = (0..dims).map(|i| target.coordinate(i)).collect();
if let Some(root) = &self.root {
root.search(0, &mut closest, &mut neighborhood);
}
neighborhood
}
}
/// An iterator that the moves values out of a k-d tree.
#[derive(Debug)]
pub struct IntoIter<T> {
stack: Vec<Box<KdNode<T>>>,
}
impl<T> IntoIter<T> {
fn new(node: Option<Box<KdNode<T>>>) -> Self {
Self {
stack: node.into_iter().collect(),
}
}
}
impl<T> Iterator for IntoIter<T> {
type Item = T;
fn next(&mut self) -> Option<T> {
self.stack.pop().map(|node| {
self.stack.extend(node.left);
self.stack.extend(node.right);
node.item
})
}
}
impl<T> IntoIterator for KdTree<T> {
type Item = T;
type IntoIter = IntoIter<T>;
fn into_iter(self) -> Self::IntoIter {
IntoIter::new(self.root)
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::metric::tests::{test_nearest_neighbors, Point};
use crate::metric::SquaredDistance;
impl Metric<[f64]> for Point {
type Distance = SquaredDistance;
fn distance(&self, other: &[f64]) -> Self::Distance {
self.0.distance(other)
}
}
impl Cartesian for Point {
fn dimensions(&self) -> usize {
self.0.dimensions()
}
fn coordinate(&self, i: usize) -> f64 {
self.0.coordinate(i)
}
}
#[test]
fn test_kd_tree() {
test_nearest_neighbors(KdTree::from_iter);
}
}
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