From af325f5a4ff967314fb484b77b33406d21133393 Mon Sep 17 00:00:00 2001
From: Tavian Barnes <tavianator@tavianator.com>
Date: Wed, 27 May 2020 14:49:32 -0400
Subject: kd: Implement flat k-d trees

---
 src/kd.rs | 155 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 155 insertions(+)

(limited to 'src')

diff --git a/src/kd.rs b/src/kd.rs
index 97616e7..4f591f9 100644
--- a/src/kd.rs
+++ b/src/kd.rs
@@ -333,6 +333,156 @@ where
     V: Coordinates,
 {}
 
+/// A node in a flat k-d tree.
+#[derive(Debug)]
+struct FlatKdNode<T> {
+    /// The vantage point itself.
+    item: T,
+    /// The size of the left subtree.
+    left_len: usize,
+}
+
+impl<T: Coordinates> FlatKdNode<T> {
+    /// Create a new FlatKdNode.
+    fn new(item: T) -> Self {
+        Self {
+            item,
+            left_len: 0,
+        }
+    }
+
+    /// Create a balanced tree.
+    fn balanced<I: IntoIterator<Item = T>>(items: I) -> Vec<Self> {
+        let mut nodes: Vec<_> = items
+            .into_iter()
+            .map(Self::new)
+            .collect();
+
+        Self::balance_recursive(&mut nodes, 0);
+
+        nodes
+    }
+
+    /// Create a balanced subtree.
+    fn balance_recursive(nodes: &mut [Self], level: usize) {
+        if !nodes.is_empty() {
+            nodes.sort_by_cached_key(|x| Ordered::new(x.item.coord(level)));
+
+            let mid = nodes.len() / 2;
+            nodes.swap(0, mid);
+
+            let (node, children) = nodes.split_first_mut().unwrap();
+            let (left, right)  = children.split_at_mut(mid);
+            node.left_len = left.len();
+
+            let next = (level + 1) % node.item.dims();
+            Self::balance_recursive(left, next);
+            Self::balance_recursive(right, next);
+        }
+    }
+}
+
+impl<'a, K, V, N> KdSearch<K, &'a V, N> for &'a [FlatKdNode<V>]
+where
+    K: KdProximity<&'a V>,
+    V: Coordinates,
+    N: Neighborhood<K, &'a V>,
+{
+    fn item(self) -> &'a V {
+        &self[0].item
+    }
+
+    fn left(self) -> Option<Self> {
+        let end = self[0].left_len + 1;
+        if end > 1 {
+            Some(&self[1..end])
+        } else {
+            None
+        }
+    }
+
+    fn right(self) -> Option<Self> {
+        let start = self[0].left_len + 1;
+        if start < self.len() {
+            Some(&self[start..])
+        } else {
+            None
+        }
+    }
+}
+
+/// A [k-d tree] stored as a flat array.
+///
+/// A FlatKdTree is always balanced and usually more efficient than a [KdTree], but doesn't support
+/// dynamic updates.
+///
+/// [k-d tree]: https://en.wikipedia.org/wiki/K-d_tree
+#[derive(Debug)]
+pub struct FlatKdTree<T> {
+    nodes: Vec<FlatKdNode<T>>,
+}
+
+impl<T: Coordinates> FlatKdTree<T> {
+    /// Create a balanced tree out of a sequence of items.
+    pub fn balanced<I: IntoIterator<Item = T>>(items: I) -> Self {
+        Self {
+            nodes: FlatKdNode::balanced(items),
+        }
+    }
+}
+
+impl<T: Coordinates> FromIterator<T> for FlatKdTree<T> {
+    fn from_iter<I: IntoIterator<Item = T>>(items: I) -> Self {
+        Self::balanced(items)
+    }
+}
+
+/// An iterator that moves values out of a flat k-d tree.
+#[derive(Debug)]
+pub struct FlatIntoIter<T>(std::vec::IntoIter<FlatKdNode<T>>);
+
+impl<T> Iterator for FlatIntoIter<T> {
+    type Item = T;
+
+    fn next(&mut self) -> Option<T> {
+        self.0.next().map(|n| n.item)
+    }
+}
+
+impl<T> IntoIterator for FlatKdTree<T> {
+    type Item = T;
+    type IntoIter = FlatIntoIter<T>;
+
+    fn into_iter(self) -> Self::IntoIter {
+        FlatIntoIter(self.nodes.into_iter())
+    }
+}
+
+impl<K, V> NearestNeighbors<K, V> for FlatKdTree<V>
+where
+    K: KdProximity<V>,
+    V: Coordinates,
+{
+    fn search<'k, 'v, N>(&'v self, mut neighborhood: N) -> N
+    where
+        K: 'k,
+        V: 'v,
+        N: Neighborhood<&'k K, &'v V>,
+    {
+        if !self.nodes.is_empty() {
+            let mut closest = neighborhood.target().as_vec();
+            self.nodes.as_slice().search(0, &mut closest, &mut neighborhood);
+        }
+        neighborhood
+    }
+}
+
+impl<K, V> ExactNeighbors<K, V> for FlatKdTree<V>
+where
+    K: KdMetric<V>,
+    V: Coordinates,
+{}
+
 #[cfg(test)]
 mod tests {
     use super::*;
@@ -354,4 +504,9 @@ mod tests {
             tree
         });
     }
+
+    #[test]
+    fn test_flat_kd_tree() {
+        test_nearest_neighbors(FlatKdTree::from_iter);
+    }
 }
-- 
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