503FinalExam_F03

503FinalExam_F03 - UML CS 91.503 Final Exam Fall, 2003...

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UML CS 91.503 Final Exam Fall, 2003 NAME:____________________________________ FINAL EXAM This exam is open books, notes and closed neighbors, calculators The upper bound on exam time is 3 hours. Please put all your work on the exam paper. (Partial credit will only be given if your work is shown.) General Hint : Graph duality is sometimes helpful. The dual G’=(V’,E’) of a graph G=(V,E) is formed by creating a vertex in V’ for each edge of E and creating an edge (u’,v’) in E’ if u’ and v’ share a common vertex in V. Good luck! 1 of 16
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UML CS 91.503 Final Exam Fall, 2003 1: (10 points) Function Order of Growth (a) (6 points) List the 4 functions below in nondecreasing asymptotic order of growth: ( 29 3 lg lg 2 2 2 n n n n n - 1) 2) 3) 4) smallest largest Given: Circle TRUE or FALSE for each statement below b) (1 point) )) ( ( ) ( 3 4 n f n f TRUE FALSE c) (1 point) )) ( ( ) ( 4 1 n f O n f TRUE FALSE d) (1 point) )) ( ( ) ( 1 2 n f O n f TRUE FALSE e) (1 point) )) ( ( ) ( 2 1 n f n f Θ TRUE FALSE 2 of 16 ) 16 ( ) ( ) 3 lg 3 n n f Θ ( 29 ( 29 2 2 4 lg ) ( ) 4 n n n f Θ ( 29 ) lg lg( ) ( ) 1 4 4 1 n n n n f ( 29 ) lg lg( ) ( ) 2 4 4 2 n n n O n f
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503FinalExam_F03 - UML CS 91.503 Final Exam Fall, 2003...

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