LARGEST returns a maximum element chosen from $A.$

$1$a$.(5$ points.$)$ What is the cost and count of each line in LARGEST? A line's cost is its run time. Its count is the number of times it is executed. Replace the question marks in the table shown above.

Briefly explain your answer.

In questions $2$a through $2$d$,$ use a loop invariant to prove that LARGEST is correct. Your invariant, and your proof, may be written in mathematics, in English, or in a mixture of the two.

$2$a$.(5$ points.$)$ Show a loop invariant for LARGEST. Hint: Your invariant may optionally use logical connectives like not,${?}^{{?}^{?}},v,,$ etc.

$2$b$.(5$ points.$)$ Prove that your invariant from $2a$ is true at initialization.

$2$c$.(10$ points.$)$ Prove that your invariant from $2$a is true during maintenance.

$2$d$.(5$ points.$)$ Prove that your invariant from $2$a shows that LARGEST is correct at termination.