Question: (a) Explain why computing the factorial of (n) by multiplying all values from 1 to (n) together is an exponential time algorithm. (b) Explain why

(a) Explain why computing the factorial of $n$ by multiplying all values from 1 to $n$ together is an exponential time algorithm.

(b) Explain why computing an approximation to the factorial of $n$ by making use of Stirling's formula (see Section 2.2) is a polynomial time algorithm.

Step by Step Solution

★★★★★

3.48 Rating (151 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Time Complexity Analysis a Computing Factorial using Multiplication When you calculate the factorial of n denoted by n 1 cdot 2 cdot 3 cdots n you per... View full answer

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 Practical Introduction To Data Structures Questions!

When a machine is bought for $ 8 0 0 0 0 0 , post the journalentry required, cash is paid

Prepare the journal entries to record payroll for the employee and record the employer's contribution. Assume the employee was paid immediately. For transactions with more than one credit, enter the...

Explain why computing the proximity between two attributes is often simpler than computing the similarity between two objects.

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

re Regular Languages and Finite Automata (a) Let L be the set of all strings over the alphabet {a, b} that end in a and do not contain the substring bb. Describe a deterministic finite automaton...

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

ANSI-SPARC6 Programming Language Compilation Write notes on each of the following topics: (a) the implementation of labels and jumps in a recursive, block structured programming language [7 marks]...

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

For monotone functions f, f0: P Q between posets (P, vP ) and (Q, vQ), let f v f(i) Prove that the binary relation v is a partial order. [3 marks] (ii) For monotone functions between posets p : P 0...

A hollow cylinder, of radius R and mass M, rolls without slipping down a loop-the-loop track of radius r. The cylinder starts from rest at a height h above the horizontal section of track. What is...

How will the shift from nonmilitary civil service positions to contract positions affect HR issues for the impacted organizations? Will this impact differ depending on the type of contracting...

What are typical factors that might suggest the use of chance events in capacity expansion analyses? What economic criteria would be appropriate under such circumstances?

What impact did Mr. Meyers personal situation (visa and tenure issues) have on his desire to carry through with his concerns?? p-9687

Distinguish between CM and CMTS.

Repeat Problem P14-7 using a cable modem (consider the minimum rates). Problem P14-7 Calculate the minimum time required to download one million bytes of information using a 56K modem.

What is the relationship between SONET and SDH?

Current Attempt in Progress BAK Corp, is considering purchasing one of two new diagnostic machines. Either machine would make it possible for the company to bid on jobs that it currently isn't...

You are considering an investment in a new start-up company, Over Armour, Inc., an Internet service provider. A review of the company's financial statements reveals a negative retained earnings. In...

Suppose r RF = 5 % rRF=5%, r M = 10 % rM=10%, and r A = 12 % rA=12%. Calculate Stock As beta. If Stock As beta were 2.0, then what would be As new required rate of return?