The university has hired you to write an algorithm to schedule their final exams. each quarter, the university offers n different classes. there are r different rooms on campus and t different time slots in which exams can be offered. you are given two arrays e[1..n] and s[1..r] where e[i] is the number of students enrolled in the ith class, and s[j] is the number of seats in the jth room. at most one final exam can be held in each room during each time slot. class i can hold its final exam in room j only if e[i] < s[j].

a. (9 pts) write an algorithm to assign a room and a time slot to each class (or report correctly that no such assignment is possible).

b. (3 pts) provide time complexity analysis.

c. (3 pts) explain why your algorithm is correct.