A file is a sequence of strings where the $i-$th element $($string$)$ corresponds to line $i$ in

the file. The task is to compare $($text$)$ files containing program code, such as Python

or Java code. Specifically, compare files A and B by counting the number of

operations required to transform A into $B.$ It is assumed that there are three types of

editing operations: i$)$ adding a new line, ii$)$ deleting a line, and iii$)$ swapping two

adjacent lines. Swapping adjacent lines is cheap as they are in memory, whereas

adding and deleting lines are expensive.

Example: To transform A into B$,$ one can add line $2$ from B to A $($expensive$)$ and swap

lines $4$ and $5$ in $A($cheap$).$

A

B

def fib$(n)$ :

if $n1$ :

return $n$

return fib$(n-1)+$fib$(n-2)$

else:

def fib$(n)$:

#Fibonacci

if $n1$ :

return $n$

else:

return fib$(n-1)+$fib$(n-2)$

Present an efficient algorithm $($pseudocode$)$ that utilizes dynamic programming to

determine the minimum number of changes, other than swaps, needed to transform

an $n-$line file A into an $n-$line file $B($i$.$e$.,$ excluding swap operations$).$ Assume that

there are at most $k$ unique lines, each line can $be$ swapped only once, and the

lines being swapped are adjacent $in$ both A and $B.$ Clearly specify what kind $of$ data

structures you use $in$ the algorithm.