a) Show that log (n!) is in O(n log nb) Express the runtime of the following loop as a Theta () bound in terms of n:k = nwhile k > 1if k is evenk = k/ 4elsek = 2 * kc) Is the following statement true? If f(n) is NOT in Omega(g(n)), then f(n) is in O(g(n)).Prove the statement or provide a counterexample.

Remember that log(n!) = log(1) + log(2) + ... + log(n-1) + log(n) You can get the upper bound by…

Answered: Show that log (n!) is in O(n log n)

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Show that log (n!) is in O(n log n)

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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Question

a) Show that log (n!) is in O(n log n
b) Express the runtime of the following loop as a Theta () bound in terms of n:
k = n
while k > 1
if k is even
k = k/ 4
else
k = 2 * k
c) Is the following statement true? If f(n) is NOT in Omega(g(n)), then f(n) is in O(g(n)).
Prove the statement or provide a counterexample.

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