Write pseudocode for a program that will take an unordered list of distinct integers $A(1)A(n),$ and output a new list $B(1)-B(n)$ such that;

$B(1)$ is the largest number in list $A,B(2)$ is the smallest number in $A$

$B(3)$ is the second largest number in $A,B(4)$ is the second smallest number in $A$

$B(5)$ is the third largest, etc.

$A(1)=1,A(2)=3,A(3)=4,A(4)=2,N(5)=8,A(6)=10,A(2)=2$

The following gives pseudocode for a "binary search". We have a list of $n$ integers $A(1)-A(n),$ in order starting with the lowest. We are given a value $"x"$ to search for in the list. If $"x"$ is in the list, we Return its position. If $"x"$ is not in the list, Return $-1.$

$($a$)$ Trace the program using $n=7,$ A value $1,3,4,7,8,10,12,$ and $x-$value $10.$ Give me the values of low, hi and mid each time the mid value is calculated $($by mid: $={|}_{{?}_{?}}\frac{\text{l}\text{o}\text{w}+hi}{2_{{?}_{?}}}|,$ and give the final output Returned.

$($b$)$ Same as $($a$),$ but now use $x-$value $2.$

Program Binary Search

Input: positive integer $n,$ list of $n$ integers $A(1)-A(n),$ number $x$

Output: location of $x$ if it is in the list, otherwise $-1.$

$|)|$