24. An algorithm is called optimal for the solution of a prob- lem with respect to a specified operation if there is no al- gorithm for solving this problem using fewer operations. a) Show that Algorithm 1 in Section 3.1 is an optimal algorithm with respect to the number of comparisons of integers. [Note: Comparisons used for bookkeep- ing in the loop are not of concern here.] b) Is the linear search algorithm optimal with respect to 0 the number of comparisons of integers (not including çomparisons used for bookkeeping in the loop)? ba
24. An algorithm is called optimal for the solution of a prob- lem with respect to a specified operation if there is no al- gorithm for solving this problem using fewer operations. a) Show that Algorithm 1 in Section 3.1 is an optimal algorithm with respect to the number of comparisons of integers. [Note: Comparisons used for bookkeep- ing in the loop are not of concern here.] b) Is the linear search algorithm optimal with respect to 0 the number of comparisons of integers (not including çomparisons used for bookkeeping in the loop)? ba
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 45E
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Question
An algorithm is called optimal for the solution of a problem with respect to a specified operation if there is no algorithm for solving this problem using fewer operations.
(THE FIRST ATTACHMENT IS FROM SECTION 3.1)
Please answer parts a & b.
![oms
oved gonsnps
ALGORITHM 1 Finding the Maximum Element in a Finite Sequence.
init
procedure max(a,, a2, ... , a„: integers)
cbe suq
тах :- а
for i := 2 to n
if max < a; then max := a;
return max{max is the largest element}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4f752fd-e2b5-4a98-8d20-a9cf3e4d111d%2F32a958fc-4538-4acf-9568-6312d666d2aa%2Fh24odbn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:oms
oved gonsnps
ALGORITHM 1 Finding the Maximum Element in a Finite Sequence.
init
procedure max(a,, a2, ... , a„: integers)
cbe suq
тах :- а
for i := 2 to n
if max < a; then max := a;
return max{max is the largest element}
![24. An algorithm is called optimal for the solution of a prob-
lem with respect to a specified operation if there is no al-
gorithm for solving this problem using fewer operations.
a) Show that Algorithm 1 in Section 3.1 is an optimal
algorithm with respect to the number of comparisons
of integers. [Note: Comparisons used for bookkeep-
ing in the loop are not of concern here.]
guil b) Is the linear search algorithm optimal with respect to
18:(6) the number of comparisons of integers (not including
comparisons used for bookkeeping in the loop)?
bas (s)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4f752fd-e2b5-4a98-8d20-a9cf3e4d111d%2F32a958fc-4538-4acf-9568-6312d666d2aa%2Fxiksnf8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:24. An algorithm is called optimal for the solution of a prob-
lem with respect to a specified operation if there is no al-
gorithm for solving this problem using fewer operations.
a) Show that Algorithm 1 in Section 3.1 is an optimal
algorithm with respect to the number of comparisons
of integers. [Note: Comparisons used for bookkeep-
ing in the loop are not of concern here.]
guil b) Is the linear search algorithm optimal with respect to
18:(6) the number of comparisons of integers (not including
comparisons used for bookkeeping in the loop)?
bas (s)
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