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HW4-W07-full - Homework Four CS 191 Discrete Structures I...

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Homework Four CS 191 : Discrete Structures I Mar. 6 , Winter 2007 Due Date: Mar. 20, 2007, Tuesday, before the class meeting. Section 4.2, p155 ___________________________________________________ Exercise (15) Write an algorithm whose input is a sequence s 1 , …, s n sorted in nondecreasing order and a value x . (Assume that all the values are real numbers.) The algorithm inserts x into the sequence so that the resulting sequence is sorted in nondecreqsing order. Example: If the sequence is 2, 6, 12, 14, and x = 5, the resulting sequence is 2, 5, 6, 12, 14. ____________________________________________________ Exercise (18) Describe the worst case input for algorithm 4.2.1. _____________________________________________________ Section 4.3, p168 Select a theta notation from Table 4.3.3 for each expression in exercises 1-12. Exercise (6) 4 6 6 + + n n _______________________________________________________________ Exercise (9) (6 n + 4)(1+lg n ) __________________________________________________________ Exercise (11) n n n n n 2 2 ) 1 )( lg ( + + + _______________________________________________________ Exercise (12) 2+4+8+16+…+ 2 n 1
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__________________________________________________ In Exercises 13-15, select a theta notation for f(n) + g(n). Exercise (15) f ( n ) = Θ ( n 3/2 ), g ( n ) = Θ ( n 5/2 ), _________________________________________________ In exercises 16-26, select a theta notation from among Θ (1), Θ (lg n ), Θ ( n ), Θ ( n lg n ), Θ ( n 2 ), Θ ( n 3 ), Θ (2 n ), or Θ ( n !).
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