Solved: Exercises 6–9 each contain a while loop annotated

Chapter 5, Problem 7E

(choose chapter or problem)

Problem 7E

Exercises 6–9 each contain a while loop annotated with a preand a post-condition and also a loop invariant. In each case, use the loop invariant theorem to prove the correctness of the loop with respect to the pre- and post-conditions.

[Pre-condition: largest = A[1] and i = 1]

while ( i ≠ m)

1. i := i + 1

2. ifA[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.”