Order of the functions according to their growth rate is:
2/N < 37 < √N <N < NloglogN < N logN ≤ N log(N^2) < Nlog^2(N) < N^1.5 < N^2 < N^(2) logN < N^3 < 2^(N/2) < 2^N
Functions having same rate are N log N and N log (N^2):
N log(N^2) = 2N logN = Θ(N logN)
Order the following functions by growth rate: N, squrerootN, N1.5, N2, NlogN, N log logN, Nlog2N,...
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
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
Order the following functions by asymptotic growth rate: 4n, 2^log(n), 4nlog(n)+2n, 2^10, 3n+100log(n), 2^n, n^2+10n, n^3, nlog(n) You should state the asymptotic growth rate for each function in terms of Big-Oh and also explicitly order those functions that have the same asymptotic growth rate among themselves.
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.
Here are some common orders of growth, ranked from no growth to fastest growth: Θ(1) — constant time takes the same amount of time regardless of input size Θ(log n) — logarithmic time Θ(n) — linear time Θ(n log n) — linearithmic time Θ(n2 ) — quadratic time Θ(n3 ), etc. — polynomial time Θ(2n), Θ(3n), etc. — exponential time (considered “intractable”; these are really, really horrible) In addition, some programs will never terminate if they get stuck in an...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci number. By definition Fibonnaci(0) is 1, Fibonnaci(1) is 1, Fibonnaci(2) is 2, Fibonnaci(3) is 3, Fibonnaci(4) is 5, and so on. Your function may only use a constant amount of memory (i.e. no auxiliary array). Argue that the running time of the function is Θ(n), i.e. the function is linear in n. 2. (10 points) Order the following functions by growth rate: N, \N,...
Need help with 1,2,3 thank you. 1. Order of growth (20 points) Order the following functions according to their order of growth from the lowest to the highest. If you think that two functions are of the same order (Le f(n) E Θ(g(n))), put then in the same group. log(n!), n., log log n, logn, n log(n), n2 V, (1)!, 2", n!, 3", 21 2. Asymptotic Notation (20 points) For each pair of functions in the table below, deternme whether...
Compare the following pairs of functions f, g. In each case, say whether f- o(g) f-w(g), or f = Θ(g), and prove your claim. 157. f(n) -100n+logn, gn) (logn)2. 158,介f(n) = logn, g(n) = log log(n2). 159. . f(n)-n2/log n, g(n) = n(log n)2. 160·介介f(n)-(log n)106.9(n)-n10-6 . 161. (n)logn, g(n) (log nlog n 162. f(n) n2, gn) 3. Compare the following pairs of functions f, g. In each case, say whether f- o(g) f-w(g), or f = Θ(g), and prove...
What is the order of the following growth function? t(n)= 5 nlog n + 20n +20 O(log n) Oin log n) o O(n2) 0(1)
JAVA: Which of the following shows a list of Big-Oh running times in order from slowest to fastest? O(1), O(N), O(N2), O(logN), O(2N) O(1), O(N), O(N3), O(2N), O(N!) O(logN), O(N!), O(N2), O(N3), O(2N) O(N!), O(2N), O(N2), O(N), O(logN)