# P5 KD Trees.docx

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Programming Assignment 5: Kd-Trees Write a data type to represent a set of points in the unit square (all points have x - and y -coordinates between 0 and 1) using a 2d-tree to support efficient range search (find all of the points contained in a query rectangle) and nearest neighbor search (find a closest point to a query point). 2d-trees have numerous applications, ranging from classifying astronomical objects to computer animation to speeding up neural networks to mining data to image retrieval. Geometric primitives. To get started, use the following geometric primitives for points and axis-aligned rectangles in the plane. Use the immutable data type Point2D.java (part of algs4.jar ) for points in the plane. Here is the subset of its API that you may use:

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public class Point2D implements Comparable<Point2D> { public Point2D(double x, double y) // construct the point (x, y) public double x() // x-coordinate public double y() // y-coordinate public double distanceTo(Point2D that) // Euclidean distance between two points public double distanceSquaredTo(Point2D that) // square of Euclidean distance between two points public int compareTo(Point2D that) // for use in an ordered symbol table public boolean equals(Object that) // does this point equal that? public void draw() // draw to standard draw public String toString() // string representation } Use the immutable data type RectHV.java (not part of algs4.jar ) for axis-aligned rectanges. Here is the subset of its API that you may use: public class RectHV { public RectHV(double xmin, double ymin, // construct the rectangle [xmin, xmax] x [ymin, ymax] double xmax, double ymax) // throw a java.lang.IllegalArgumentException if (xmin > xmax) or (ymin > ymax) public double xmin() // minimum x-coordinate of rectangle public double ymin() // minimum y-coordinate of rectangle public double xmax() // maximum x-coordinate of rectangle public double ymax() // maximum y-coordinate of rectangle public boolean contains(Point2D p) // does this rectangle contain the point p (either inside or on boundary)?
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• Winter '18
• Dr Sibt
• Euclidean space, Nearest neighbor search, set of points

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