DISCRETE MATHEMATICS AND ITS APPLICATIONS - DOC by GEYv2dL

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									CECS 228 – Group Exercise on 12/2/04
Due 12/7/04
Group members:____________________________________________________________________________

1. Problem 8 in Section 2.2
   Find the least integer n such that f(x) is O(xn) for each of the following functions. Support your answer.
a) f(x) = 2 x2 + x3 log x




b) f(x) = 3 x5 + (log x)4




c) f(x) = (x4 + x2 + 1) / ((x4 + 1)




d) f(x) = (x3 + 5 log x) / (x4 + 1)
2. Problem 18 in Section 2.2
   Let k be a positive integer. Show that 1k + 2k + … + nk is O(nk+1).




3. Problem 22 in Section 2.1
   Describe an algorithm to find the longest word in an English sentence (where a word is a string of letters
   and a sentence is a list of words, separated by blanks).

								
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