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Add K-D Tree (#3210)

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AmirMohammad Hosseini Nasab
2022-08-13 15:30:00 +04:30
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parent 854b900257
commit 05660dae92
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src/main/java/com/thealgorithms/datastructures/trees/KDTree.java Normal file
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package com.thealgorithms.datastructures.trees;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Objects;
import java.util.Optional;
/*
* K-D Tree Implementation
* Wikipedia: https://en.wikipedia.org/wiki/K-d_tree
*
* Author: Amir Hosseini (https://github.com/itsamirhn)
*
* */
public class KDTree {
private Node root;
private final int k; // Dimensions of the points
/**
* Constructor for empty KDTree
*
* @param k Number of dimensions
*/
KDTree(int k) {
this.k = k;
}
/**
* Builds the KDTree from the specified points
*
* @param points Array of initial points
*/
KDTree(Point[] points) {
if (points.length == 0) throw new IllegalArgumentException("Points array cannot be empty");
this.k = points[0].getDimension();
for (Point point : points) if (point.getDimension() != k) throw new IllegalArgumentException("Points must have the same dimension");
this.root = build(points, 0);
}
/**
* Builds the KDTree from the specified coordinates of the points
*
* @param pointsCoordinates Array of initial points coordinates
*
*/
KDTree(int[][] pointsCoordinates) {
if (pointsCoordinates.length == 0) throw new IllegalArgumentException("Points array cannot be empty");
this.k = pointsCoordinates[0].length;
Point[] points = Arrays.stream(pointsCoordinates)
.map(Point::new)
.toArray(Point[]::new);
for (Point point : points) if (point.getDimension() != k) throw new IllegalArgumentException("Points must have the same dimension");
this.root = build(points, 0);
}
static class Point {
int[] coordinates;
public int getCoordinate(int i) {
return coordinates[i];
}
public int getDimension() {
return coordinates.length;
}
public Point(int[] coordinates) {
this.coordinates = coordinates;
}
@Override
public boolean equals(Object obj) {
if (obj instanceof Point other) {
if (other.getDimension() != this.getDimension()) return false;
return Arrays.equals(other.coordinates, this.coordinates);
}
return false;
}
@Override
public String toString() {
return Arrays.toString(coordinates);
}
/**
* Find the comparable distance between two points (without SQRT)
*
* @param p1 First point
* @param p2 Second point
*
* @return The comparable distance between the two points
*/
static public int comparableDistance(Point p1, Point p2) {
int distance = 0;
for (int i = 0; i < p1.getDimension(); i++) {
int t = p1.getCoordinate(i) - p2.getCoordinate(i);
distance += t * t;
}
return distance;
}
/**
* Find the comparable distance between two points with ignoring specified axis
*
* @param p1 First point
* @param p2 Second point
* @param axis The axis to ignore
*
* @return The distance between the two points
*/
static public int comparableDistanceExceptAxis(Point p1, Point p2, int axis) {
int distance = 0;
for (int i = 0; i < p1.getDimension(); i++) {
if (i == axis) continue;
int t = p1.getCoordinate(i) - p2.getCoordinate(i);
distance += t * t;
}
return distance;
}
}
static class Node {
private Point point;
private int axis; // 0 for x, 1 for y, 2 for z, etc.
private Node left = null; // Left child
private Node right = null; // Right child
Node(Point point, int axis) {
this.point = point;
this.axis = axis;
}
public Point getPoint() {
return point;
}
public Node getLeft() {
return left;
}
public Node getRight() {
return right;
}
public int getAxis() {
return axis;
}
/**
* Get the nearest child according to the specified point
*
* @param point The point to find the nearest child to
*
* @return The nearest child Node
*/
public Node getNearChild(Point point) {
if (point.getCoordinate(axis) < this.point.getCoordinate(axis)) return left;
else return right;
}
/**
* Get the farthest child according to the specified point
*
* @param point The point to find the farthest child to
*
* @return The farthest child Node
*/
public Node getFarChild(Point point) {
if (point.getCoordinate(axis) < this.point.getCoordinate(axis)) return right;
else return left;
}
/**
* Get the node axis coordinate of point
*
* @return The axis coordinate of the point
*/
public int getAxisCoordinate() {
return point.getCoordinate(axis);
}
}
public Node getRoot() {
return root;
}
/**
* Builds the KDTree from the specified points
*
* @param points Array of initial points
* @param depth The current depth of the tree
*
* @return The root of the KDTree
*/
private Node build(Point[] points, int depth) {
if (points.length == 0) return null;
int axis = depth % k;
if (points.length == 1) return new Node(points[0], axis);
Arrays.sort(points, Comparator.comparingInt(o -> o.getCoordinate(axis)));
int median = points.length >> 1;
Node node = new Node(points[median], axis);
node.left = build(Arrays.copyOfRange(points, 0, median), depth + 1);
node.right = build(Arrays.copyOfRange(points, median + 1, points.length), depth + 1);
return node;
}
/**
* Insert a point into the KDTree
*
* @param point The point to insert
*
*/
public void insert(Point point) {
if (point.getDimension() != k) throw new IllegalArgumentException("Point has wrong dimension");
root = insert(root, point, 0);
}
/**
* Insert a point into a subtree
*
* @param root The root of the subtree
* @param point The point to insert
* @param depth The current depth of the tree
*
* @return The root of the KDTree
*/
private Node insert(Node root, Point point, int depth) {
int axis = depth % k;
if (root == null) return new Node(point, axis);
if (point.getCoordinate(axis) < root.getAxisCoordinate()) root.left = insert(root.left, point, depth + 1);
else root.right = insert(root.right, point, depth + 1);
return root;
}
/**
* Search for Node corresponding to the specified point in the KDTree
*
* @param point The point to search for
*
* @return The Node corresponding to the specified point
*/
public Optional<Node> search(Point point) {
if (point.getDimension() != k) throw new IllegalArgumentException("Point has wrong dimension");
return search(root, point);
}
/**
* Search for Node corresponding to the specified point in a subtree
*
* @param root The root of the subtree to search in
* @param point The point to search for
*
* @return The Node corresponding to the specified point
*/
public Optional<Node> search(Node root, Point point) {
if (root == null) return Optional.empty();
if (root.point.equals(point)) return Optional.of(root);
return search(root.getNearChild(point), point);
}
/**
* Find a point with minimum value in specified axis in the KDTree
*
* @param axis The axis to find the minimum value in
*
* @return The point with minimum value in the specified axis
*/
public Point findMin(int axis) {
return findMin(root, axis).point;
}
/**
* Find a point with minimum value in specified axis in a subtree
*
* @param root The root of the subtree to search in
* @param axis The axis to find the minimum value in
*
* @return The Node with minimum value in the specified axis of the point
*/
public Node findMin(Node root, int axis) {
if (root == null) return null;
if (root.getAxis() == axis) {
if (root.left == null) return root;
return findMin(root.left, axis);
} else {
Node left = findMin(root.left, axis);
Node right = findMin(root.right, axis);
Node[] candidates = {left, root, right};
return Arrays.stream(candidates)
.filter(Objects::nonNull)
.min(Comparator.comparingInt(a -> a.point.getCoordinate(axis))).orElse(null);
}
}
/**
* Find a point with maximum value in specified axis in the KDTree
*
* @param axis The axis to find the maximum value in
*
* @return The point with maximum value in the specified axis
*/
public Point findMax(int axis) {
return findMax(root, axis).point;
}
/**
* Find a point with maximum value in specified axis in a subtree
*
* @param root The root of the subtree to search in
* @param axis The axis to find the maximum value in
*
* @return The Node with maximum value in the specified axis of the point
*/
public Node findMax(Node root, int axis) {
if (root == null) return null;
if (root.getAxis() == axis) {
if (root.right == null) return root;
return findMax(root.right, axis);
} else {
Node left = findMax(root.left, axis);
Node right = findMax(root.right, axis);
Node[] candidates = {left, root, right};
return Arrays.stream(candidates)
.filter(Objects::nonNull)
.max(Comparator.comparingInt(a -> a.point.getCoordinate(axis))).orElse(null);
}
}
/**
* Delete the node with the given point.
*
* @param point the point to delete
* */
public void delete(Point point) {
Node node = search(point).orElseThrow(() -> new IllegalArgumentException("Point not found"));
root = delete(root, node);
}
/**
* Delete the specified node from a subtree.
*
* @param root The root of the subtree to delete from
* @param node The node to delete
*
* @return The new root of the subtree
*/
private Node delete(Node root, Node node) {
if (root == null) return null;
if (root.equals(node)) {
if (root.right != null) {
Node min = findMin(root.right, root.getAxis());
root.point = min.point;
root.right = delete(root.right, min);
} else if (root.left != null) {
Node min = findMin(root.left, root.getAxis());
root.point = min.point;
root.left = delete(root.left, min);
} else return null;
}
if (root.getAxisCoordinate() < node.point.getCoordinate(root.getAxis())) root.left = delete(root.left, node);
else root.right = delete(root.right, node);
return root;
}
/**
* Finds the nearest point in the tree to the given point.
*
* @param point The point to find the nearest neighbor to.
* */
public Point findNearest(Point point) {
return findNearest(root, point, root).point;
}
/**
* Finds the nearest point in a subtree to the given point.
*
* @param root The root of the subtree to search in.
* @param point The point to find the nearest neighbor to.
* @param nearest The nearest neighbor found so far.
* */
private Node findNearest(Node root, Point point, Node nearest) {
if (root == null) return nearest;
if (root.point.equals(point)) return root;
int distance = Point.comparableDistance(root.point, point);
int distanceExceptAxis = Point.comparableDistanceExceptAxis(root.point, point, root.getAxis());
if (distance < Point.comparableDistance(nearest.point, point)) nearest = root;
nearest = findNearest(root.getNearChild(point), point, nearest);
if (distanceExceptAxis < Point.comparableDistance(nearest.point, point))
nearest = findNearest(root.getFarChild(point), point, nearest);
return nearest;
}
}

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src/test/java/com/thealgorithms/datastructures/trees/KDTreeTest.java Normal file
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package com.thealgorithms.datastructures.trees;
import org.junit.jupiter.api.Test;
import static org.junit.jupiter.api.Assertions.assertEquals;
public class KDTreeTest {
KDTree.Point pointOf(int x, int y) {
return new KDTree.Point(new int[]{x, y});
}
@Test
void findMin() {
int[][] coordinates = {
{30, 40},
{5, 25},
{70, 70},
{10, 12},
{50, 30},
{35, 45}
};
KDTree kdTree = new KDTree(coordinates);
assertEquals(5, kdTree.findMin(0).getCoordinate(0));
assertEquals(12, kdTree.findMin(1).getCoordinate(1));
}
@Test
void delete() {
int[][] coordinates = {
{30, 40},
{5, 25},
{70, 70},
{10, 12},
{50, 30},
{35, 45}
};
KDTree kdTree = new KDTree(coordinates);
kdTree.delete(pointOf(30, 40));
assertEquals(35, kdTree.getRoot().getPoint().getCoordinate(0));
assertEquals(45, kdTree.getRoot().getPoint().getCoordinate(1));
}
@Test
void findNearest() {
int[][] coordinates = {
{2, 3},
{5, 4},
{9, 6},
{4, 7},
{8, 1},
{7, 2}
};
KDTree kdTree = new KDTree(coordinates);
assertEquals(pointOf(7, 2), kdTree.findNearest(pointOf(7, 2)));
assertEquals(pointOf(8, 1), kdTree.findNearest(pointOf(8, 1)));
assertEquals(pointOf(2, 3), kdTree.findNearest(pointOf(1, 1)));
assertEquals(pointOf(5, 4), kdTree.findNearest(pointOf(5, 5)));
}
}