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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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.
Transcribed Image Text: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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