Question: Show that log _ 2 ( n ! ) < = nlog _ 2 ( n )

Show that log_2(n!)<= nlog_2(n)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Q:

Fundamentals of the Analysis of Algorithm Efficiency A ( 2 k ) = A ( 2 k 1 ) + 1 for k > 0 , A ( 2 0 ) = 0 . Now backward substitutions encounter no problems: A ( 2 k ) = A ( 2 k 1 ) + 1 substitute A...

Q:

=+4.12. (a) Show (see Example 4.21) that log2 n + log2 log 2 n + 0 log, log, log2 n is an outer boundary if 0 > 1. Generalize.

Q:

Problem 1 Design an algorithm to find all the common elements in two sorted lists of numbers. For example, for the lists 2 , 5 , 5 , 5 and 2 , 2 , 3 , 5 , 5 , 7 , the output should be 2 , 5 , 5 ....

Q:

Let f ( n ) = 1 0 0 n 2 log n f ( n ) = 1 0 0 n 2 logn and g ( n ) = 2 2 log 2 ( n ) g ( n ) = 2 2 log 2 ( n ) The following multiple - choice options contain math elements, so you may need to read...

Q:

Below are seven functions of integer variable n. Sort these functions in increasing order of their running times. (a) n' log, n+n (b) 0.1.n5.5 ( c ) r 1.5 + - 4 -n! (d) log 2 n + 7vn (e) 7 .(log2 n)3...

Q:

C++ - Recursion - Binary Trees Background: War is a very simple 2-player card game that requires no strategy, but lots of patience. It works as follows. A single deck of cards is shuffled and dealt...

Q:

Java 2) Order each of the following functions from fastest to slowest in terms of asymptotic growth. (By fastest, we mean which function increases the most rapidly as n increases.) a) log n 2 + log 2...

Q:

Java 2) Order each of the following functions from fastest to slowest in terms of asymptotic growth. (By fastest, we mean which function increases the most rapidly as n increases.) a) log n 2 + log 2...

Q:

The first unit of construction is completed in 10,000 hours. A learning rate of 80 percent is expected on doubled units (always assume doubled units unless specifically stated otherwise). How much...

Q:

In the worst case, the number of comparisons needed to search a singly linked list of length n for a given element is (GATE CS 2002) A. log 2 n B. n/2 C. log 2 n 1 D. n\

Q:

(a) Determine the number of distinct ways one can color the vertices of an equilateral triangle using the colors red and white, if the triangle is free to move in three dimensions. (b) Answer part...

Q:

E and F were partners in firm sharing profits in the ratio of 3: 1. They admitted G and will share future profits equally. G brought Rs.50,000 in cash and machinery worth Rs.70,000 fir his share of...

Q:

Corey has a vested account balance in his employer-sponsored qualified money purchase pension plan of $60,000. He has two years of service with his employer and the plan follows the least generous...

Q:

Required information [The following information applies to the questions displayed below.] Pam's Creations had the following sales and purchase transactions during Year 2. Beginning inventory...

Q:

2. Do you find change a. invigorating? b. stressful? _______

Q:

10. Are you a. a leader? b. a follower? _______

Q:

5. Would you prefer a job that a. is pretty much the same from day to day? b. changes constantly? _______