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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