final(1) - CS 373 1 True False or Maybe Final Exam Fall...

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Final Exam (December 15, 2000) Fall 2000 1. True, False, or Maybe Indicate whether each of the following statments is always true, sometimes true, always false, or unknown. Some of these questions are deliberately tricky, so read them carefully. Each correct choice is worth +1 , and each incorrect choice is worth 1 . Guessing will hurt you! (a) Suppose SMARTALGORITHM runs in Θ( n 2 ) time and DUMBALGORITHM runs in Θ(2 n ) time for all inputs of size n . (Thus, for each algorithm, the best-case and worst-case running times are the same.) SMARTALGORITHM is faster than DUMBALGORITHM. True False Sometimes Nobody Knows (b) QUICKSORT runs in O ( n 6 ) time. True False Sometimes Nobody Knows (c) log 2 n ⌋ ≥ ⌈ log 2 n True False Sometimes Nobody Knows (d) The recurrence F ( n ) = n + 2 n · F ( n ) has the solution F ( n ) = Θ( n log n ) . True False Sometimes Nobody Knows (e) A Fibonacci heap with n nodes has depth Ω(log n ) . True False Sometimes Nobody Knows (f) Suppose a graph G is represented by an adjacency matrix. It is possible to determine whether G is an independent set without looking at every entry of the adjacency matrix. True False Sometimes Nobody Knows (g) NP n = co-NP True False Sometimes Nobody Knows (h) Finding the smallest clique in a graph is NP-hard. True False Sometimes Nobody Knows (i) A polynomial-time reduction from X to 3SAT proves that X is NP-hard. True False Sometimes Nobody Knows (j) The correct answer for exactly three of these questions is “False”. True
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  • Spring '09
  • A
  • Computational complexity theory, Convex hull, Conjunctive normal form, disjunctive normal form, NP-complete, Algebraic normal form

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final(1) - CS 373 1 True False or Maybe Final Exam Fall...

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