a) Adapt Algorithm 1 in Section 3.1 to find the maximum and the minimum of a sequence of elements by employing a temporary maximum and a temporary minimum that is updated as each successive element is examined.

b) Describe the algorithm from part (a) in pseudocode.

c) How many comparisons of elements in the sequence are carried out by this algorithm? (Do not count comparisons used to determine whether the end of the sequence has been reached.)

Question

Accepted Answer

(a) We add a variable “min” which keeps track of the minimum. We assigns the

first element as the minimum “ min” . then it checks if each element is smaller than

the maximum, the value of the element is assigned as the new value of the

maximum.

(b) procedure last largest $(a_{1}, a_{2}, . . . a_{n} : integers with n \geq 2)$

$m a x : = a_{1}$

$m i n : = a_{1}$

for $i : = 2$ to n

if $a_{i} > m a x$ then $m a x : = a_{1}$

if $a_{i} < m i n$ then $\min : = a_{1}$

return max, min

(c) $2 n - 2$ comparisons

Short Answer