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.
What is the worst-case time complexity of the following algorithm? Select the tightest bound.
Consider the undirected graph G (V,E,W) with V representing the nodes and E representing theundirected 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.
What is the worst-case time complexity of the following algorithm? Select the tightest bound.
- 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?
What is the minimum total weight of unscheduled tasks when there is one processor, no preemption isallowed, 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)?
What is the time complexity of the dynamic programming approach for solving the Matrix ChainMultiplication problem? Select the tightest bound.
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?
Given the pattern BBABBCBBABBA, compute the lps[] array used by the Knuth-Morris-Pratt algorithm. Type your answers in the boxes provided:
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| lps[]: |
Note that 12 entries need to be filled in. If you don't see all 12 entries, maximize your window!
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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