Purchase Solution

Method of Iteration

Not what you're looking for?

Ask Custom Question

1) Use the method of Iteration to find a formula expressing S(n) as a function of n for the given recurrence relation and initial condition: S(n) = S(n-1) - 3, S(0)=5.

2) How many elementary operations are used in the following algorithm? The elementary operations are comparison operations (such as > and < ) and mathematical operations (such as addition, subtraction, multiplication, division etc.).

Step 1: Set S=a, k=0, and t=a.

Step 2: while k < n
(a) Replace t with t+d
(b) Replace S with S+t
(c) Replace k with k+1
endwhile

Step 3: Print S.

3) How many elementary operations are used in the following algorithm? The elementary operations are comparison operations (such as > and < ) and mathematical operations (such as addition, subtraction, multiplication, division etc.).

Step 1: Set a=1, b=1, c=2, and k=1.

Step 2: while k < n
(a) Replace c with a+b
(b) Replace a with b
(c) Replace b with c
(d) Replace k with k+1
endwhile

Step 3: Print b.

Purchase this Solution

Solution Summary

Detailed explanations included to help the reader understand the process leading to answers.

Solution Preview

1) S(n) = S(n-1) - 3 = S(n-1) - [1*3]
= (S(n-2) - 3) - 3 = S(n-2) - [3 + 3] = S(n-2) - [2*3]
= (S(n-3) - 3) - [3 + 3] = S(n-3) - [3 + 3 + 3] = S(n-3) - [3*3]

We can easily notice that number of 3s in [summation] at any stage during expansion is same as K in S(n-K) in the expansion at that stage.

So, we can say that

S(n) = S(n-n) - [n*3]
= S(0) - 3n
= 5 - 3n

2) We can count elementary operations in the given ...

Purchase this Solution


Free BrainMass Quizzes
Inserting and deleting in a linked list

This quiz tests your understanding of how to insert and delete elements in a linked list. Understanding of the use of linked lists, and the related performance aspects, is an important fundamental skill of computer science data structures.

Excel Introductory Quiz

This quiz tests your knowledge of basics of MS-Excel.

Word 2010: Tables

Have you never worked with Tables in Word 2010? Maybe it has been a while since you have used a Table in Word and you need to brush up on your skills. Several keywords and popular options are discussed as you go through this quiz.

Basic Networking Questions

This quiz consists of some basic networking questions.

Word 2010: Table of Contents

Ever wondered where a Table of Contents in a Word document comes from? Maybe you need a refresher on the topic? This quiz will remind you of the keywords and options used when working with a T.O.C. in Word 2010.