Problem $3.$ points$)$ Row$-$column ordered arrays

We say that an $nn2-D$ array $A$ of integers is row$-$column ordered if it satisfies the following

property: the entries of each row are sorted from left to right and the entries of each column are

sorted from top to bottom. Thus, for any $1in,$ we have

$A[i,1]A[i,2]$dots$A[i,n]$

and for $1jn,$ we have

$A[1,j]A[2,j]$dots$A[n,j]$

For each of the tasks below, present your algorithm in pseudocode.

$($a$)$ Third$-$Min$((A)$ : returns the $3$rd smallest element in $A.$ Your algorithm should use at most

$10$ comparisons among the elements of $A.$

$($b$)$ CHAnge$-$Key $(A,i,j,k)$ : changes the value of $A[i,j]$ to $k$ and updates $A$ so that it continues

to be row$-$column ordered. Your algorithm must make at most $2n$ comparisons among the

elements in $A.$

Solution: Type your solution here.