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36. G = (V, E) is an undirected simple graph in which each edge has a distinct weight, and e is a particular edge of G. Which of the following statements about the minimum spanning trees (MSTS) of G is/are TRUE? I. If e is the lightest edge of some cycle in G, then every MST of G includes e. II. If e is the heaviest edge of some cycle in G, then every MST of G excludes e.
I only
II only
both I and II
neither I nor II
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37. Consider the undirected graph below: Using Prim's algorithm to construct a minimum spanning tree starting with node A, which one of the following sequences of edges represents a possible order in which the edges would be added to construct the minimum spanning tree?
(E,G), (C,F), (F,G), (A,D), (A,B), (A,C)
(A,D), (A,B), (A,C), (CP), (G,E), (F,G)
(A,B), (A,D), (D,F), (F,G), (G,E), (F,C)
(A,D), (A,B), (D,F), (F,C), (F,G), (G,E)
38. The following are the starting and ending times of activities A, B, C, D, E, F, G and H respectively in chronological order: “asbscsaedsceesfsbedegseefehsgehe” Here, xs denotes the starting time and xe denotes the ending time of activity X. W need to schedule the activities in a set of rooms available to us. An activity can be scheduled in a room only if the room is reserved for the activity for its entire duration. What is the minimum number of rooms required?
3
4
5
6
39. Are all tasks completed in the schedule that gives maximum profit?
All tasks are completed
T1 and T6 are left out
T1 and T8 are left out
T4 and T6 are left out
40. What is the maximum profit earned?
147
165
167
175
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