Suppose you are given three strings of characters: X, Y , and Z, where |X| = n, |Y | = m, and |Z| = n + m. Z is said to be a shuffle of X and Y iff Z can be formed by interleaving the characters from X and Y in a way that maintains the left-to-right ordering of the characters from each string.

(a) Show that cchocohilaptes is a shuffle of chocolate and chips, but chocochilatspe is not.

(b) Give an efficient dynamic-programming algorithm that determines whether Z is a shuffle of X and Y.