$($COMPUTER$-$SCIENCE$)$

For each of the following problems, the input consists of two arrays X $[1..$ k$]$

and Y $[1..$ n$]$ where k $$ n$.$

$($b$)$ Describe a recursive backtracking algorithm to find the smallest number

of symbols that can be removed from Y so that X is no longer a

subsequence. Equivalently, your algorithm should find the longest

subsequence of Y that is not a supersequence of X$.$ For example, after

removing removing two symbols from the string PENPINEAPPLEAPPLEPEN,

the string PPAP is no longer a subsequence.