Answered: If f = (log n)^2, g = n log n; what is…

If f = (log n)^2, g = n log n; what is the relationship between f and g? Choose all that applies. a. g= O(f) b. f = O(g) c. g= Ω(f) d. f = Ω(g)

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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3. I: II T(n) = 27)+n², then T(n) = O(nlogn). II: If T(n) = ! 27()+nlogn, then T(n) = O(nlogn). III: If T(n) = 2T(√) + logn, then T(n) = O(logn log n). (A) Only I is TRUE. (B) Only II is TRUE. (C) Only III is TRUE. (D)All of LII and III are TRUE. 4. (a) 5%Show that the lower bound for the sorting problem is (nlogn). (b) 3% The least signifcant digit first RadixSort sorts n numbers in O(n) and it beats the (nlogn) lower bound. What went wrong? (c) 5% Prove correctness of the O(n) time least significant digit first RadixSort. (d) 4% Show that finding the convex hull of n points in 2D space needs at least (nlogn) time. (e) 3% Show that finding the convex hull of n points in 3D spaceneeds at least (nlogn) time.
T(n) = T(n - 1) + 3n and T(0)=0. Then T(n) is e (n³1 ө (п) e (n lg n) e (2")
Big-O notation is defined as follows: The function f(n) is O(g(n)) if there are positive integers c and N such that f(n) ≤ c · g(n) for all n > N. Is the relation “f(n) is O(g(n))” reflexive? symmetric? transitive? Justify your answers. “Θ(g(n))” is defined as follows: f(n) is Θ(g(n)) if and only if (f(n) is O(g(n)) & g(n) is O(f(n))). Is the relation “f(n) is Θ(g(n))” reflexive? symmetric? transitive? Justify your answers
Correct answer will be upvoted else downvoted. Computer science. Polycarp recalled the 2020-th year, and he is content with the appearance of the new 2021-th year. To recall such a great second, Polycarp needs to address the number n as the amount of a specific number of 2020 and a specific number of 2021. For instance, if: n=4041, then, at that point, the number n can be addressed as the total 2020+2021; n=4042, then, at that point, the number n can be addressed as the total 2021+2021; n=8081, then, at that point, the number n can be addressed as the total 2020+2020+2020+2021; n=8079, then, at that point, the number n can't be addressed as the amount of the numbers 2020 and 2021. Assist Polycarp with seeing if the number n can be addressed as the amount of a specific number of numbers 2020 and a specific number of numbers 2021. Input The primary line contains one integer t (1≤t≤104) — the number of experiments. Then, at that point, t experiments follow.…
4.Consider F = {BC -> D, B -> E, CE -> D, E -> CA, BF -> G} and R(A,B,C,D,E,F,G) a)Find all many keys for R
Let Tk (n) denote the value returned by A(k, n). This gives T0(n) = 2 + n, T1(0) = 0, Tk (0) = 1 for k ≥ 2, and Tk (n) = Tk−1(Tk (n − 1)) for k > 0 and n > 0.
1.Show that f(n)= n2 +2n+1 is not O(n). Compute c and no. 2.Show that f(n)= n2+2n+1 is O (n2).
If the first number in a sequence is a positive integer, x Let ao= x, an is defined as follows if an is even, then an+1 = an/2 if an is odd, then an+1 =3 *an+ 1 Then there exists an integer k, such that ak =1 For example, if: 75, then k = 14 and the numbers in the sequence are: 75, 226, 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1. The largest number in the sequence is 340 and it is a position 4 in the sequence (assuming 75 is at position 1) Design and implement a complete C++ program that will • read a series of integers (greater than 0) from a file and for each integer display (to the screen) − the integer − the number of steps it takes to reach 1 − the largest value in the sequence and its position
* In C language the word (sum) is invalid identifier True False In C language the word ...... is a valid identifier asd$ c4_5 8abd In C language the word (scanf) is not reserved word True False In C language the word (main) is not reserved word False True
You are given the following definitions to help you: O(g(n)) = {f(n): there exist positive constants c and no such that 0 ≤ f(n) ≤ cg(n) for all n ≥ no} . N(g(n)) = {f(n): there exist positive constants c and no such that 0 ≤ cg (n) ≤ f(n) for all n ≥ no} . ©(g(n)) = {f(n): there exist positive constants C₁, C2, and no such that 0 ≤ c₁g(n) ≤ f(n) ≤ c₂g (n) for all n ≥ no} . Using above definitions, prove that: 5. T(n) = 6n + 4n+ 3 € 0 (n) 6. T(n) = 100n + 10000 € O(n²) 7. T(n) = 5n² - 2n + 16 € O(n³) 8. T(n)=5n² - 2n + 16 is not € O(n) 9. T(n) = n³ + 20n € №(n² ) 10. T(n) = 2n³ - 7n + 1 € ☺(n³)
Question 2: Let f = 100n and g(n) = n+. Show that f = 0(g).
Suppose, T(n) = 12+22+32+…..+n2. Show that, T(n) is in Θ(n3 ).