Consider the following pseudocode for Bubble Sort on $A[1..n]$ :

$($a$)$ Show an example of this algorithm being executed on an array of size $6.$

$($b$)$ For an array of size $n,$ how many key comparisons $($line $3)$ does this algorithm do$?$ How

many swaps $($line $4)$ will it do in the best case? in the worst case?