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//! [Vantage-point trees](https://en.wikipedia.org/wiki/Vantage-point_tree).
use super::{Metric, NearestNeighbors, Neighborhood};
use std::iter::FromIterator;
/// A node in a VP tree.
#[derive(Debug)]
struct VpNode<T> {
/// The vantage point itself.
item: T,
/// The radius of this node.
radius: f64,
/// The subtree inside the radius, if any.
inside: Option<Box<Self>>,
/// The subtree outside the radius, if any.
outside: Option<Box<Self>>,
}
impl<T: Metric> VpNode<T> {
/// Create a new VpNode.
fn new(mut items: Vec<T>) -> Option<Box<Self>> {
if items.is_empty() {
return None;
}
let item = items.pop().unwrap();
items.sort_by_cached_key(|a| item.distance(a));
let mid = items.len() / 2;
let outside: Vec<T> = items.drain(mid..).collect();
let radius = items.last().map(|l| item.distance(l).into()).unwrap_or(0.0);
Some(Box::new(Self {
item,
radius,
inside: Self::new(items),
outside: Self::new(outside),
}))
}
}
trait VpSearch<'a, T, U, N> {
/// Recursively search for nearest neighbors.
fn search(&'a self, neighborhood: &mut N);
/// Search the inside subtree.
fn search_inside(&'a self, distance: f64, neighborhood: &mut N);
/// Search the outside subtree.
fn search_outside(&'a self, distance: f64, neighborhood: &mut N);
}
impl<'a, T, U, N> VpSearch<'a, T, U, N> for VpNode<T>
where
T: 'a,
U: Metric<&'a T>,
N: Neighborhood<&'a T, U>,
{
fn search(&'a self, neighborhood: &mut N) {
let distance = neighborhood.consider(&self.item).into();
if distance <= self.radius {
self.search_inside(distance, neighborhood);
self.search_outside(distance, neighborhood);
} else {
self.search_outside(distance, neighborhood);
self.search_inside(distance, neighborhood);
}
}
fn search_inside(&'a self, distance: f64, neighborhood: &mut N) {
if let Some(inside) = &self.inside {
if neighborhood.contains(distance - self.radius) {
inside.search(neighborhood);
}
}
}
fn search_outside(&'a self, distance: f64, neighborhood: &mut N) {
if let Some(outside) = &self.outside {
if neighborhood.contains(self.radius - distance) {
outside.search(neighborhood);
}
}
}
}
/// A [vantage-point tree](https://en.wikipedia.org/wiki/Vantage-point_tree).
#[derive(Debug)]
pub struct VpTree<T> {
root: Option<Box<VpNode<T>>>,
}
impl<T: Metric> FromIterator<T> for VpTree<T> {
fn from_iter<I: IntoIterator<Item = T>>(items: I) -> Self {
Self {
root: VpNode::new(items.into_iter().collect::<Vec<_>>()),
}
}
}
impl<T, U> NearestNeighbors<T, U> for VpTree<T>
where
T: Metric,
U: Metric<T>,
{
fn search<'a, 'b, N>(&'a self, mut neighborhood: N) -> N
where
T: 'a,
U: 'b,
N: Neighborhood<&'a T, &'b U>,
{
if let Some(root) = &self.root {
root.search(&mut neighborhood);
}
neighborhood
}
}
/// An iterator that moves values out of a VP tree.
#[derive(Debug)]
pub struct IntoIter<T> {
stack: Vec<Box<VpNode<T>>>,
}
impl<T> IntoIter<T> {
fn new(node: Option<Box<VpNode<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.inside);
self.stack.extend(node.outside);
node.item
})
}
}
impl<T> IntoIterator for VpTree<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;
#[test]
fn test_vp_tree() {
test_nearest_neighbors(VpTree::from_iter);
}
}
|
