Looking at the big O of functions, If f1(N)=O(NlogN) and f2(N)=O(log N), then what is "big O" of f1 +f2?
Give a good big-Oh characterization in terms of n of the running time of the following. Provide brief justification for your answer (in terms of finding a k and n_0). 4n^5 + 3n^3 + 7 15n^12 + 3n log n + 2n 3n log n + 2log n + n 12n*3^n + 50n
Consider the given functions bellow. Sort all of them using the asymptotic order (big-O). Provide short explanation for your answer. 3 log n 3 log log n nlog n 5n nn^(1/4) (n/4)(n/4)
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
Choose the equivalent Big Oh notation for the functions given below. If there is more than one option, circle the tightest asymptotic bound. function f(n) = 5n - 10 belongs to a) O(1) b) O(n) c) O(n2) d) O(log n) function f(n) = 4n2 + 4n + 1 belongs to a) O(1) b) O(n) c) O(n2) d) O(log n) function f(n) = n2 + 100 log n belongs to a) O(1) b) O(n) c) O(n2) d) O(log n)
Give a big-O estimate of the following functions. Try to find estimates that are as simple as possible. (2^n + n^2)(n^3 + 2n + 3) (n^2 + n log n)(n^2 + 2n + 1)
Give a Big-Oh Estimate for (x-7)log(x3+4x+1) + 3x7. Please break down steps used. I am mostly unsure how to address the log.
Use the definition of 0 to show that 5n^5 +4n^4 + 3n^3 + 2n^2 + n 0(n^5).Use the definition of 0 to show that 2n^2 - n+ 3 0(n^2).Let f,g,h : N 1R*. Use the definition of big-Oh to prove that if/(n) 6 0(g{n)) and g(n) 0(h{n)) then/(n) 0(/i(n)). You should use different letters for the constants (i.e. don't use c to denote the constant for each big-Oh).
1. a) Let f(n) = 6n2 - 100n + 44 and g(n) = 0.5n3 . Prove that f(n) = O(g(n)) using the definition of Big-O notation. (You need to find constants c and n0). b) Let f(n) = 3n2 + n and g(n) = 2n2 . Use the definition of big-O notation to prove that f(n) = O(g(n)) (you need to find constants c and n0) and g(n) = O(f(n)) (you need to find constants c and n0). Conclude that...
[6 marks] Arrange the functions (1.5)n , n100, log n, n!, and n99 + n98 in a list so that each is a big-O of the next. Ans: log n, (n99+n98), n100, (1.5)n , n!