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What is a big-O estimate of the function f(n)= n logan +n!? On!) (2") (log2n) Oln...
What is the average running time for quicksort? O(1) O(log10N) O(log2N) O(log2N) O(N) O(N log N) O(N2) O(N3) O(Nk) O(2N) O(N!)
What is the worst case running time of a linear search? O(1) O(log10N) O(log2N) O(log2N) O(N) O(N log N) O(N2) O(N3) O(Nk) O(2N) O(N!)
What is the worst case running time of a binary search? O(1) O(log10N) O(log2N) O(log2N) O(N) O(N log N) O(N2) O(N3) O(Nk) O(2N) O(N!)
1. What is the best asymptotic ("big-O”) characterization of the following function: f(n) = (14logn)2 + log (3) a) 0(3) Show steps. b) O(n) c) 0(n) d) 0(21) e) O(logn)
For each of the following g(n), which are legitimate Big-O, Big-Theta, or Big-Omega for f(n) = n^2 + 2n. List all that apply. a) n^2 b) n^3 c) n d) 2^n e) lg n
Suppose that the function f satisfies the recurrence rela- tion f (n)2f(Vn)+1 whenever n is a perfect square greater than 1 and f (2) 1. a) Find f(16). . b) Give a big-O estimate for f(n). [Hint: Make the sub- stitution m log n
Assume that an O(log2N) algorithm runs for 10 milliseconds when the input size (N) is 32. What is input size makes the algorithm run for 14 milliseconds?
Formal Definitions of Big-Oh, Big-Theta and Big-Omega:
1. Use the formal definition of Big-Oh to prove that if f(n) is a decreasing function, then f(n) = 0(1). A decreasing function is one in which f(x1) f(r2) if and only if xi 5 r2. You may assume that f(n) is positive evervwhere Hint: drawing a picture might make the proof for this problem more obvious 2. Use the formal definition of Big-Oh to prove that if f(n) = 0(g(n)) and g(n)...
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?
What is the order of the following growth function expressed using Big-Oh notation: T(N)=7*N3 + N/2 + 2 * log N + 38 ? O(2N) O(N3) O(N/2) O(N3 + log N)