For the following problem, the input consists of two arrays X[1 .. k] and Y[1..n] where k n.

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.