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Algorithms-Lecture,Section-2-Spring 2025

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What is the worst-case time complexity of the following algorithm? Select the tightest bound. 

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What is the worst-case time complexity of the following algorithm? Select the tightest bound. 

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Consider the undirected graph G (V,E,W) with V representing the nodes and E representing the

undirected edges, and W representing the edge weights. What is the computational complexity for Kruskals’s MST algorithm to find the MST? Select the tightest bound. 

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What is the worst-case time complexity of the following algorithm? Select the tightest bound. 

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  • If any NP-complete problem can be solved in polynomial time, then P = NP.
  • An NP-complete problem cannot be verified in polynomial time.
  • If a problem is NP-hard, it must also be in NP.
  • A problem X is NP-complete then every problem in NP can be reduced to X in polynomial-time

How many of the above statements are true?

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What is the minimum total weight of unscheduled tasks when there is one processor, no preemption is

allowed, and there are 5 tasks with equal lengths of 1, with given weights and deadlines as follows: t1: (w1 = 2, d1 = 2), t2: (w2 = 3, d2 = 2), t3: (w3 = 8, d3 = 3), t4: (w4 = 4, d4 = 2), t5: (w5 = 5, d5 = 2)?

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What is the time complexity of the dynamic programming approach for solving the Matrix Chain

Multiplication problem? Select the tightest bound. 

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You are given a text T = aabbabaaabba and a pattern P = abaa. Based on our lecture discussions, which state will the finite automaton (for the pattern matching problem) be in after processing the first six characters of the text T?

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Given the pattern BBABBCBBABBA, compute the lps[] array used by the Knuth-Morris-Pratt algorithm. Type your answers in the boxes provided:

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lps[]: 

Note that 12 entries need to be filled in. If you don't see all 12 entries, maximize your window!

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Assume that you perform the following operations in the given order on an initially empty min-heap (priority queue):

  • Insert(5)
  • Insert(3)
  • Insert(8)
  • ExtractMin()
  • Insert(2)
  • Insert(6)
  • ExtractMin()

After these operations, what is the left child of the root of the min-heap?

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