Suppose that we wish to keep track of a point of maximum overlap in a set of

Question:

Suppose that we wish to keep track of a point of maximum overlap in a set of intervals—a point that has the largest number of intervals in the database overlapping it.
a. Show that there will always be a point of maximum overlap which is an endpoint of one of the segments.
b. Design a data structure that efficiently supports the operations INTERVAL-INSERT, INTERVAL-DELETE, and FIND-POM, which returns a point of maximum overlap.