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//! [Vantage-point trees](https://en.wikipedia.org/wiki/Vantage-point_tree).
use super::{Metric, NearestNeighbors, Neighborhood, Ordered};
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 size of the subtree inside the radius.
inside_len: usize,
}
impl<T: Metric> VpNode<T> {
/// Create a new VpNode.
fn new(item: T) -> Self {
Self {
item,
radius: 0.0,
inside_len: 0,
}
}
/// Build a VP tree recursively.
fn build(slice: &mut [VpNode<T>]) {
if let Some((node, children)) = slice.split_first_mut() {
let item = &node.item;
children.sort_by_cached_key(|n| Ordered(item.distance(&n.item)));
let (inside, outside) = children.split_at_mut(children.len() / 2);
if let Some(last) = inside.last() {
node.radius = item.distance(&last.item).into();
}
node.inside_len = inside.len();
Self::build(inside);
Self::build(outside);
}
}
/// Recursively search for nearest neighbors.
fn recurse<'a, U, N>(slice: &'a [VpNode<T>], neighborhood: &mut N)
where
T: 'a,
U: Metric<&'a T>,
N: Neighborhood<&'a T, U>,
{
let (node, children) = slice.split_first().unwrap();
let (inside, outside) = children.split_at(node.inside_len);
let distance = neighborhood.consider(&node.item).into();
if distance <= node.radius {
if !inside.is_empty() && neighborhood.contains(distance - node.radius) {
Self::recurse(inside, neighborhood);
}
if !outside.is_empty() && neighborhood.contains(node.radius - distance) {
Self::recurse(outside, neighborhood);
}
} else {
if !outside.is_empty() && neighborhood.contains(node.radius - distance) {
Self::recurse(outside, neighborhood);
}
if !inside.is_empty() && neighborhood.contains(distance - node.radius) {
Self::recurse(inside, neighborhood);
}
}
}
}
/// A [vantage-point tree](https://en.wikipedia.org/wiki/Vantage-point_tree).
#[derive(Debug)]
pub struct VpTree<T>(Vec<VpNode<T>>);
impl<T: Metric> FromIterator<T> for VpTree<T> {
fn from_iter<I: IntoIterator<Item = T>>(items: I) -> Self {
let mut nodes: Vec<_> = items.into_iter().map(VpNode::new).collect();
VpNode::build(nodes.as_mut_slice());
Self(nodes)
}
}
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 !self.0.is_empty() {
VpNode::recurse(&self.0, &mut neighborhood);
}
neighborhood
}
}
/// An iterator that moves values out of a VP tree.
#[derive(Debug)]
pub struct IntoIter<T>(std::vec::IntoIter<VpNode<T>>);
impl<T> Iterator for IntoIter<T> {
type Item = T;
fn next(&mut self) -> Option<T> {
self.0.next().map(|n| n.item)
}
}
impl<T> IntoIterator for VpTree<T> {
type Item = T;
type IntoIter = IntoIter<T>;
fn into_iter(self) -> Self::IntoIter {
IntoIter(self.0.into_iter())
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::metric::tests::test_nearest_neighbors;
#[test]
fn test_vp_tree() {
test_nearest_neighbors(VpTree::from_iter);
}
}
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