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mt1c - CS 373 U Conict Midterm 1 Questions Spring 2004...

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CS 373 U Conflict Midterm 1 Questions (February 24, 2004) Spring 2004 Write your answers in the separate answer booklet. 1. Multiple Choice: Each question below has one of the following answers. A: Θ(1) B: Θ(log n ) C: Θ( n ) D: Θ( n log n ) E: Θ( n 2 ) X: I don’t know. For each question, write the letter that corresponds to your answer. You do not need to justify your answers. Each correct answer earns you 1 point. Each X earns you 1 4 point. Each incorrect answer costs you 1 2 point. Your total score will be rounded down to an integer. Negative scores will be rounded up to zero. (a) What is n i =1 n i ? (b) What is lg n i =1 4 i ? (c) How many bits are required to write n ! in binary? (d) What is the solution of the recurrence T ( n ) = 4 T ( n/ 2) + n log n ? (e) What is the solution of the recurrence T ( n ) = T ( n - 3) + 5 n ? (f) What is the solution of the recurrence T ( n ) = 9 T (ceilingleftbig n +13 3 ceilingrightbig) + 10 n - 7 n - lg 3 n lg lg n ? (g) How long does it search for a value in an n -node binary search tree?
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