Implementing kd-tree for fast range-search, nearest-neighbor search and k-nearest-neighbor search algorithms in 2D in Java and python


The following problem appeared as an assignment in the coursera course Algorithm-I by Prof.Robert Sedgewick from the Princeton University few years back (and also in the course cos226 offered at Princeton). The problem definition and the description is taken from the course website and lectures. The original assignment was to be done in java, where in this article both the java and a corresponding python implementation will also be described. The idea is to build a BST with points in the nodes, using the x– and y-coordinates of the points as keys in strictly alternating sequence, starting with the x-coordinates, as shown in the next figure. The following figures and animations show how the 2-d-tree is grown with recursive space-partioning for a few sample datasets.