(a) Rank the following three functions: log N, log (N2), log2N. Explain.
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(a) Rank the following three functions: log N, log (N2), log2N. Explain.
Rank the following functions from slowest growing to fastest growing (i.e. fastest to slowest) 1 (constant) log2n (logarithmic) n (linear) n * log2 n (“n log n”) n2 (quadratic)
Order the following functions by growth rate: N, squrerootN, N1.5, N2, NlogN, N log logN, Nlog2N, Nlog(N2), 2/N,2N, 2N/2, 37, N2 logN, N3. Indicate which functions grow at the same rate.
Order the following functions by asymptotic growth rate. 2n log n + 2n, 210, 2 log n, 3n + 100 log n, 4n, 2n, n2 + 10n, n3, n log n2
Which of the following could be false? A. n2/(log(n)) = O(n2). B. (log n)1000 = O(n1//1000). C. 1/n = O(1/(log(n))). D. 2(log(n))^2 = O(n2). E. None of the above.
76. Arrange the following functions in ascending or- der of growth rate: 4000 log n, 2n2 + 13n - 8, 1,036, 3n log n, 2" - n2, 2n! - n, n2 – 4n.
***Please answer all the following (Computer science) Discrete math question completely.*** Q2. Growth of functions. In each of the following cases, either construct a function /(/n) that satisfies the specified constraints or state that no such function exists. (2pt each) b, (n)-Ω(n2) and/(n)-O (n + n') In the following two questions, arrange the functions in a list so that each function is a big-O of the next function. (2pt each) d. nlog n, V', log n, (log2n+log n+n), 12 n,...
Needs to be explained also, like what method you used to compare the growth rate. Thank you 4) Order the following functions by growth rate. Indicate which functions grow at the same rate (15 points) N, N2, log N, N log N, log(N2), log2 N, N log2N, 2, 2N, 37, N2 log N, 5logN, N3, 10N log N2
if possible solve part d in detail. a) fi(n) n2+ 45 n log n b) f:(n)-1o+ n3 +856 c) f3(n) 16 vn log n 2. Use the functions in part 1 a) Isfi(n) in O(f(n)), Ω(fg(n)), or Θ((6(n))? b) Isfi(n) in O(f(n)), Ω(f,(n)), or Θ((fs(n))? c) Ísf3(n) in O(f(n)), Ω(f(n)), or Θ(f(n))? d) Under what condition, if any, would the "less efficient" algorithm execute more quickly than the "more efficient" algorithm in question c? Explain Give explanations for your answers...
Figure out the comparisons of the sizes of these functions as n gets big: f1(n) ∼ 0.9n log(n), f2(n) ∼ 1.1n , f3(n) ∼ 10n, f4(n) ∼ n2 ? Your answer should allow you to put them in order, from smallest to biggest
2. [6 marks] Are the following functions O(n)? Justify your answer. a) n log n b) f(n) = Vn (log n)