Algorithms - Algorithm Design Techniques

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.

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37. Consider the undirected graph below:

  • Option : D
  • Explanation :
    Option “A” and “B” produce disconnected components which is never allowed by primes algorithm In option “C” if vertex “A” is randomly chosen, then first edge must be (A,D) so option “D” is correct.
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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?

  • Option : B
  • Explanation :
    So total 4 rooms are required.
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39. Are all tasks completed in the schedule that gives maximum profit?

  • Option : D
  • Explanation :
    T1T2T3T5T7T8T9
    T4 and T6 are left out
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40. What is the maximum profit earned?

  • Option : A
  • Explanation :
    Total profit = 15 + 20 + 30 + 18 + 26 + 16 + 25 = 147
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