Question 2 For each of the following pairs of functions, either f(n) is O(g(n)). f(n) is (g(n)), or f(n) is (g(n)). For each pair, determine which relationship is correct. Justify your answer. # f(n) g(n) (a) 4n log n + n² logn (b) 8 log n² (log n)2 (c) logn²+n³ log n +3 (d) n√n+logn log n² (e) 2+10 10n² (8) log² n log n (h) n log2 n (1) √n log n (i) 4n 5" (k) n" 3"

Question 2 For each of the following pairs of functions, either f(n) is O(g(n)). f(n) is (g(n)), or f(n) is (g(n)). For each pair, determine which relationship is correct. Justify your answer. # f(n) g(n) (a) 4n log n + n² logn (b) 8 log n² (log n)2 (c) logn²+n³ log n +3 (d) n√n+logn log n² (e) 2+10 10n² (8) log² n log n (h) n log2 n (1) √n log n (i) 4n 5" (k) n" 3"

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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f(n) = O(f(n)g(n)) Indicate whether the below is true or false. Explain your reasoning. For all functions f(n) and g(n):
6. Suppose functions f(n) > 0 and g(n) > 0 satisfy f(n) = 0(9(n)). Prove or give a counterexample to each of the following. (a) log, f(n) = O(log, 9(n)). To avoid an obscure special case, assume that g(n) > 2 for all n. (b) 2/(n) = 0(29(n)) %3D %3D (c) (f(n))² = 0(g(n))")
For each of the following pairs of functions, either f(n) is O(g(n)), f(n) is Ω(g(n)), or f(n) is θ(g(n)). For each pair, determine which relationship is correct. Briefly justify your answer (no formal proofs needed). i) f(n) = n^4 + (log n)^2 g(n) = log(log n) ii) f(n) = 2log n^2 g(n) = (log n)^2 iii) f(n) = n! + n g(n) = 2^n iv) f(n) = ?√? + log ? g(n) = log n^2 v) f(n) = 2^(2n) + 10^n g(n) = 10n^n vi) f(n) = n! g(n) = n^n vii) f(n) = 2^(n*2n) g(n) = n^n viii) f(n) = n g(n) = log^(2) (n) ix) f(n) = √? g(n) = log n x) f(n) = 2^n g(n) = n^(3n) ANSWER PLS
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True or False? Justify your answer accordingly: 1. For any two functions f(n) and g(n), if f(n) = Θ(g(n)), then nf(n) = Θ(ng(n)). 2. O(f(n)+g(n))=O(max(f(n),g(n))).
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