
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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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.)
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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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