1)Write a method

public static void downsize(LinkedList employeeNames, int n)

that removes every nth employee from a linked list.

2)Implement the sieve of Eratosthenes: a method for computing prime numbers, known to the ancient Greeks. This method will compute all prime numbers up to n.

Choose an n. First insert all numbers from 2 to n into a set. Then erase all multiples of 2 (except 2); that is, 4, 6, 8, 10, 12, . . . . Erase all multiples of 3; that is, 6, 9, 12, 15, . . . . Go up to ?n. Then print the set.

3)Write a program that keeps a map in which both keys and values are stringsthe names of students and their course grades. Prompt the user of the program to add or remove students, to modify grades, or to print all grades. The printout should be sorted by name and formatted like this:

Carl: B+ Joe: C Sarah: A

4)Insert all words from a large file (such as the novel War and Peace) into a hash set and a tree set. Time the results. Which data structure is more efficient?