Q1. Give a big-O estimate for each of these functions. For the function g in yourestimate that f(x) is O(g(x)), use a simple function g of the smallest order.a. n log(n? + 1) + n² log nb. (n log n + 1)² + (log n + 1)(n² + 1)

given: Give a big-O estimate for each of these functions. For the function g in your estimate that…

Answered: Q1. Give a big-0 estimate for each of…

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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For each of the following pairs of functions fln)f(n) and g(n)g(n), determine whether Ofin))=0(g(n)). Don't just indicate “yes" or "no"; provide your reasoning. a. f(n) = log n² g(n) = log n + 5. b. f(n) = Vn g(n) = log n². c. f(n) = log² n g(n) = log n. d. f(n) = n g(n) = log² n.
Problem 4. Let f(n) and g(n) be asymptotically positive functions. Prove or disprove each of the following conjectures. 1. f(n) = O(g(n)) implies g(n) = O(f(n)) 2. f(n)+g(n) = (min(f(n), g(n))) 3. f(n) = (f()) 4. f(n) = O(g(n)) implies g(n) = N(f(n)) 5. f(n) = O((f(n))²)
Q7. The big O bound for the following functions is T(n)= nlogn2+ nlogn OO (log(log n)) OO (nlogn) 00 (n² log n) 00 (n²)
Please answer it asap. both questions.
Wilson's Theorem states that for any natural number n > 1, n is prime if and only if Python (n – 1)! = -1 (mod n) Write a function wilson (n) that accepts a natural number n, and returns the remainder of (n – 1)! + 1 after division by n.
The factorial function f(n) = n! is defined by n! = 1 2 3... n whenever n is a positive integer, and O! = 1. Provide big-O estimates for the factorial function and the logarithm of the factorial function. As an illustration, 1! = 1, 2! = 1 2=2, 3! = 1 23 = 6, and 4! = 1 234=24.Take note of how quickly the function n! expands. Consider the following: 20! = 2,432,902,008,176,640,000.
Let f(n) y g(n) two positive asymptotic functions. Prove or disprove the following conjectures: a) f(n) = O(g(n)) implies 2f(n) = O(29(n)). b) f(n) = O(g(n)) implies g(n) = N(f(n)). c) g(n) = O((g(n))²).
4. Show that 6n + 3n log(n)= O(n logn). Find the appropriate values of C and no
for i=1 to n/2: for j-i to n-i : for k=1 to j do print("hello") Let T(n) denote the number of times "hello" is printed as a function of n. 1- Find a function f(n) -> T(n)=0(f(n)) 2- Explain T(n) as three nested summations, and simplify them by step by step
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we are assuming f(n) and g(n) are asymptotically positive functions. Prove/ disproveeach of the following.

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Q1. Give a big-0 estimate for each of these functions. For the function g in your estimate that f(x) is O(g(x)), use a simple function g of the smallest order. a. n log(n? + 1)+n² log n b. (n log n + 1)² + (log n + 1)(n² + 1)