# Question: Suppose that we wish to keep track of a point

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.

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.

**View Solution:**## Answer to relevant Questions

a. Suppose that m is a constant. Describe an O (n)-time algorithm that, given an integer n, outputs the (n, m)-Josephus permutation.b. Suppose that m is not a constant. Describe an O (n lg n)-time algorithm that, given ...There are four basic operations on red-black trees that perform structural modifications: node insertions, node deletions, rotations, and color modifications. We have seen that RB-INSERT and RB-DELETE use only O (1) ...Suppose that we have a set of activities to schedule among a large number of lecture halls. We wish to schedule all the activities using as few lecture halls as possible. Give an efficient greedy algorithm to determine which ...A sequence of n operations is performed on a data structure. The ith operation costs i if i is an exact power of 2, and 1 otherwise. Use aggregate analysis to determine the amortized cost per operation.Given a weighted, directed graph G = (V, E) with no negative-weight cycles, let m be the maximum over all pairs of vertices u, v ¬ V of the minimum number of edges in a shortest path from u to v. (Here, the shortest ...Post your question