# Question: Given a set of n numbers we wish to find the i largest

Given a set of n numbers, we wish to find the i largest in sorted order using a comparison based algorithm. Find the algorithm that implements each of the following methods with the best asymptotic worst-case running time, and analyze the running times of the algorithms in terms of n and i.

a. Sort the numbers, and list the i largest.

b. Build a max-priority queue from the numbers, and call EXTRACT-MAX i times.

c. Use an order-statistic algorithm to find the ith largest number, partition around that number, and sort the i largest numbers.

a. Sort the numbers, and list the i largest.

b. Build a max-priority queue from the numbers, and call EXTRACT-MAX i times.

c. Use an order-statistic algorithm to find the ith largest number, partition around that number, and sort the i largest numbers.

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

For n distinct elements x1, x2, ..., xn with positive weights w1, w2, ..., wn such that Σni =1 wi = 1, the weighted (lower) median is the element xk satisfying a. Argue that the median of x1, x2, ..., xn is the ...During the course of an algorithm, we sometimes find that we need to maintain past versions of a dynamic set as it is updated. Such a set is called persistent. One way to implement a persistent set is to copy the entire set ...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) ...Not just any greedy approach to the activity-selection problem produces a maximum-size set of mutually compatible activities. Give an example to show that the approach of selecting the activity of least duration from those ...Suppose we wish not only to increment a counter but also to reset it to zero (i.e., make all bits in it 0). Show how to implement a counter as an array of bits so that any sequence of n INCREMENT and RESET operations takes ...Post your question