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Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Consider the following algorithm segment. Assume that n is a positive integer such that n 2 6. max := a[4] for i := 5 ton if max < a[i] then max := a[i] next i (a) What is the actual number of elementary operations (additions, subtractions, multiplications, divisions, and comparisons) that are performed when the algorithm segment is executed? For simplicity, count only comparisons that occur within if-then statements, and ignore those implied by for-next loops. Express your answer in terms of n. (Hint: See Example 11.3.2 and Exercise 11.3.6a in the "Read It" link.) The number of operations is (b) Apply the theorem on polynomial orders to the expression in part (a) to find that an order for the algorithm segment is n
Transcribed Image Text:Consider the following algorithm segment. Assume that n is a positive integer such that n 2 6. max := a[4] for i := 5 ton if max < a[i] then max := a[i] next i (a) What is the actual number of elementary operations (additions, subtractions, multiplications, divisions, and comparisons) that are performed when the algorithm segment is executed? For simplicity, count only comparisons that occur within if-then statements, and ignore those implied by for-next loops. Express your answer in terms of n. (Hint: See Example 11.3.2 and Exercise 11.3.6a in the "Read It" link.) The number of operations is (b) Apply the theorem on polynomial orders to the expression in part (a) to find that an order for the algorithm segment is n
Example 11.3.2 Computing an Order of an Algorithm Segment Assume n is a positive integer and consider the following algorithm segment: p:= 0, x := 2 for i := 2 to n p:= (p+i)•x next i a. Compute the actual number of elementary operations that are performed when this algorithm segment is executed. b. Use the theorem on polynomial orders to find an order for this algorithm segment. Solution a. This algorithm segment has just one loop, which goes from 2 to n, and so there are as many iterations of the loop as there are integers from 2 to n, namely n – 2+1=n- 1. During each iteration, one multiplication and one addition are performed. Thus twice as many elementary operations are performed as there are iterations of the loop, and hence 2(n – 1) = 2n- 2 elementary operations are performed when the algorithm segment is executed. b. By the theorem on polynomial orders, 2n - 2 is 6(n),
Transcribed Image Text:Example 11.3.2 Computing an Order of an Algorithm Segment Assume n is a positive integer and consider the following algorithm segment: p:= 0, x := 2 for i := 2 to n p:= (p+i)•x next i a. Compute the actual number of elementary operations that are performed when this algorithm segment is executed. b. Use the theorem on polynomial orders to find an order for this algorithm segment. Solution a. This algorithm segment has just one loop, which goes from 2 to n, and so there are as many iterations of the loop as there are integers from 2 to n, namely n – 2+1=n- 1. During each iteration, one multiplication and one addition are performed. Thus twice as many elementary operations are performed as there are iterations of the loop, and hence 2(n – 1) = 2n- 2 elementary operations are performed when the algorithm segment is executed. b. By the theorem on polynomial orders, 2n - 2 is 6(n),
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