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Consider the following algorithm segment. Assume that n is a positive integer such that n2 4. for k:- 3 to n for j:- 1 to 5n x:- a[k] - b[j] next / next k (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 11.3.3 and exercises 11.3.11a and 11.3.14a 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 n2

Consider the following algorithm segment. Assume that n is a positive integer such that n2 4. for k:- 3 to n for j:- 1 to 5n x:- a[k] - b[j] next / next k (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 11.3.3 and exercises 11.3.11a and 11.3.14a 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 n2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 52E
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Consider the following algorithm segment. Assume that n is a positive integer such that n2 4. for k:= 3 to n for j:= 1 to 5n x := a[k] – b[j] next / next k (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 11.3.3 and exercises 11.3.11a and 11.3.14a in the "Read It" link.) n² – n 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 n2v
Transcribed Image Text:Consider the following algorithm segment. Assume that n is a positive integer such that n2 4. for k:= 3 to n for j:= 1 to 5n x := a[k] – b[j] next / next k (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 11.3.3 and exercises 11.3.11a and 11.3.14a in the "Read It" link.) n² – n 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 n2v
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