Rank the following functions in terms of asymptotic growth. Please, explain your answer using limits.
√n*ln(n) ln(ln(n^2)) 2ln^2(n) n! n0.001 22ln(n) (ln(n))!
Rank the following functions in terms of asymptotic growth. Please, explain your answer using limits. √n*ln(n) ln(ln(n^2)) 2ln^2(n) n! n0.001 22ln(n) (ln(n))!
3-3 Ordering by asymptotic growth rates a. Rank the following functions by order of growth; that is, find an arrangement 81,82, 830 of the functions satisfying gi = Ω(82), g2 Ω(83), , g29 = Ω(g30). Partition your list into equivalence classes such that functions f(n) and g(n) are in the same class if and only if f(n) = Θ(g(n)) Chaptr3 Growth of Functions 1n In Inn lg* g nn-2" n'ln Ig nIn n 2" nlgn 22+1 b. Give an example...
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.
Compare the asymptotic orders of growth of the following pairs of functions. log2 n and . n (n+1)/2 and n2. 2n and 3n
Arrange the following functions in ascending order of asymptotic growth rate; that is if function g(n) immediately follows function f(n) in your list, then it should be the case that f(n) is O(g(n)): 2 Squareroot log n, 2^n, n^4/3, n(log n)^3, n log n, 2 2^n, 2^n^2. Justify your answer.
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
Order of Growth Rate Order the following functions by asymptotic growth: (i) fi(n) 3" (ii) f2(n) ni (iii) fa(n) 12 (iv) fa(n) 2log2 n (v) fs(n) Vn (vi) f6(n) 2" (vii) fr(n) log2 n (viii) fs(n) 2V (ix) fo(n) n3
1. Asymptotic Bounds la) Rank the following functions at ascending order; that is, find an arrangement fi, f2,..., fg of the functions satisfying f1 = O(f2), fz = O(fz), ...,f7= O(fy). Briefly show your work for this problem. (2pts) Ign n n n? (lg n) len 21gn n? +n nlgign 1b) Partition your list into equivalence classes such that f(n) and g(n) are in the same class if and only if f(n) = (g(n)). (2pts)
Provide a closed-form expression for the asymptotic growth of n + n/2 + n/3 + … + 1. Determine the big-O growth of the function f(n-WTgn. Explain and show work.
Rank the following functions in order from smallest asymptotic running time to largest. Addi- tionally, identify all pairs x, y where fæ(n) = (fy(n)). Please note n! ~ V2an(m)". i. fa(n) = na? ii. f6(n) = 210! iii. fe(n) = log2 n iv. fa(n) = log² n v. fe(n) = {i=i&j=i+1 vi. ff(n) = 4log2 n vii. fg(n) = log(n!) viii. fn(n) = (1.5)” ix. fi(n) = 21
Using the pseudocode answer these questions Algorithm 1 CS317FinalAlgorithm (A[O..n-1]) ito while i<n - 2 do if A[i]A[i+1] > A[i+2) then return i it i+1 return -1 6. Use limits to show that, for best case inputs, the asymptotic growth of the number of comparisons is (1). Show your work. 7. Use limits to show that, for worst case inputs, the asymptotic growth of the number of comparisons is O(n). Show your work.