This exercise contains a while loop annotated with a pre- and a post-condition and also a loop invariant. Use the loop invariant theorem to prove the correctness of the loop with respect to the pre- and post-conditions. [Pre-condition: m is a positive integer, largest = A[1] and i = 1] while (i + m) 1. i := i+1 2. if Ali] > largest then largest :- A[i] end while [Post-condition: largest = maximum value of A[1], A[2], ... A[m]] loop invariant: I(n) is "largest = maximum value of A[1], A[2], .. A[n + 1] and i = n+ 1." Proof: 1. Basis Property: Select I(0) from the choices below. O largest = 0. O largest = the maximum value of A[1] and i = 1. O largest = the maximum value of A[1]. O largest = the maximum value of A[O + 1] and 0 + 1.
This exercise contains a while loop annotated with a pre- and a post-condition and also a loop invariant. Use the loop invariant theorem to prove the correctness of the loop with respect to the pre- and post-conditions. [Pre-condition: m is a positive integer, largest = A[1] and i = 1] while (i + m) 1. i := i+1 2. if Ali] > largest then largest :- A[i] end while [Post-condition: largest = maximum value of A[1], A[2], ... A[m]] loop invariant: I(n) is "largest = maximum value of A[1], A[2], .. A[n + 1] and i = n+ 1." Proof: 1. Basis Property: Select I(0) from the choices below. O largest = 0. O largest = the maximum value of A[1] and i = 1. O largest = the maximum value of A[1]. O largest = the maximum value of A[O + 1] and 0 + 1.
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![This exercise contains a while loop annotated with a pre- and a post-condition and also a loop invariant. Use the loop invariant theorem to prove the
correctness of the loop with respect to the pre- and post-conditions.
[Pre-condition: m is a positive integer, largest = A[1] and i = 1]
while (i + m)
1. i := i +1
2. if A[i] > largest then largest := A[i]
end while
[Post-condition: largest = maximum value of A[1], A[2], ..., A[m]]
loop invariant: I(n) is "largest = maximum value of A[1], A[2],
A[n + 1] and i = n+ 1."
Proof: 1. Basis Property: Select I(0) from the choices below.
O largest = 0.
O largest = the maximum value of A[1] and i = 1.
O largest = the maximum value of A[1].
O largest = the maximum value of A[O + 1] and 0 + 1.
O largest = 1.
O largest =
According to the pre-condition
this statement is true.
Complete the proof by constructing proofs for each of the following: II. Inductive Property, III. Eventual Falsity of Guard, and IV. Correctness of the Post-
Condition. Submit your answer as a free response. (Submit a file with a maximum size of 1 MB.)
Choose File No file chosen](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee9a8d9c-e0d7-484d-a7f1-66eab1606065%2Ff0052d8b-198b-4f89-b53c-bb27bbaee081%2F5cve3qb_processed.png&w=3840&q=75)
Transcribed Image Text:This exercise contains a while loop annotated with a pre- and a post-condition and also a loop invariant. Use the loop invariant theorem to prove the
correctness of the loop with respect to the pre- and post-conditions.
[Pre-condition: m is a positive integer, largest = A[1] and i = 1]
while (i + m)
1. i := i +1
2. if A[i] > largest then largest := A[i]
end while
[Post-condition: largest = maximum value of A[1], A[2], ..., A[m]]
loop invariant: I(n) is "largest = maximum value of A[1], A[2],
A[n + 1] and i = n+ 1."
Proof: 1. Basis Property: Select I(0) from the choices below.
O largest = 0.
O largest = the maximum value of A[1] and i = 1.
O largest = the maximum value of A[1].
O largest = the maximum value of A[O + 1] and 0 + 1.
O largest = 1.
O largest =
According to the pre-condition
this statement is true.
Complete the proof by constructing proofs for each of the following: II. Inductive Property, III. Eventual Falsity of Guard, and IV. Correctness of the Post-
Condition. Submit your answer as a free response. (Submit a file with a maximum size of 1 MB.)
Choose File No file chosen
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