Question

. The manager of a large student union on campus comes to you with the following problem. She’s in charge of a group of n students, each of whom is scheduled to work one shift during the week. There are different jobs associated with these shifts (tending the main desk, helping with package delivery, rebooting cranky information kiosks, etc.), but.we can view each shift as a single contiguous interval of time. There can be multiple shifts going on at once. She’s trying to choose a subset of these n students to form a supervising committee that she can meet with once a week. She considers such a committee to be complete if, for every student not on the committee, that student’s shift overlaps (at least partially) the shift of some student who is on the committee. In this way, each student’s performance can be observed by at least one person who’s serving on the committee. Give an efficient algorithm that takes the schedule of n shifts and produces a complete supervising committee containing as few students as possible. Example. Suppose n = 3, and the shifts are Monday 4 p.M.-Monday 8 P.M., Monday 6 p.M.-Monday 10 P.M., Monday 9 P.M.-Monday 1I P.M.. Then the smallest complete supervising committee would consist of just the second student, since the second shift overlaps both the first and the third

Answer 1