Take a look at the following pseudocode.

Input: An array $A[1..n]$ of $n$ integers

Output: $[$an appropriate description of the output$]$

Mystery$1($A$[1..$n$])$

returnValue larr$0$

for ilarr$1$ to $n-1$ do

for jlarri$+1$ to $n$ do

if $|A[i]-A[j]|>$ returnValue then

returnValue larr$|A[i]-A[j]|$

return returnValue

a$.$ Provide an English description of the output of the algorithm. Don't just say what

each line of the code does. Instead, describe what property the output has. For example,

for the maximum algorithm mentioned in class, an appropriate description of the output

would be "The maximum element in array $..n."$ An inappropriate description of

the output would be "Compares each element to the maximum element seen so far and

then updates the current maximum. Return the current maximum at the end."

b$.$ Identify the line $($or lines$)$ in the pseudocode gets executed the most. You may assume

that $n$ is a large number.

c$.$ Write a mathematical expression $($probably involving summations$)$ for the number of

times that the line from part b gets executed $($as a function of $n),$ and then simplify it into

closed form $($no summations left in the simplified expression$).$ Show all of your work.