Kd-trees can be used for partial match queries. A 2-dimensional partial match query specifies a value for one of the coordinates and asks for all points that have that value for the specified coordinate. In higher dimensions we specify values for a subset of the coordinates. Here we allow multiple points to have equal values for coordinates.

a. Show that 2-dimensional kd-trees can answer partial match queries in O(n + k) time, where k is the number of reported answers.

b. Explain how to use a 2-dimensional range tree to answer partial match queries. What is the resulting query time?

c. Describe a data structure that uses linear storage and solves 2-dimen- sional partial match queries in O(log n + k) time.