Dynamic Programming: Give a Dynamic programming Solution

So I've tried to study my book to solve this as best I can without much luck. If someone could assist in helping me understand this, I would be grateful.

Question:

(a) Define an array of subclasses (b) give a recurrence based on solving each subproblem in terms of simpler subproblems

(c) Give an algorithm for computing the recurrence

If u, v, and w are strings over an alphabet , then w is a shufe of u and provided there are (possibly empty) strings ri and yi such that u -r1r2.rk and v - yyyk and w = x1y1x2y2 . . .Xkyk. A shuffle is sometimes instead called a "merge" or an "interleaving." The intuition for the definition is that w can be obtained from u and v by an operation similar to shuffling two decks of cards. We use w = u O v to denote that w is a shuffle of u and v; note, however, that in spite of the notation there can be many different shuffles w of u and v. The string w is called a square provided it is equal to a shuffle of a string u with itself, namely rovided w = 110 u for some string u The idea behind the algorithm of is to construct a grid graph, with (1) x (y1) nodes; the lower-left node is represented with (0,0) and the upper-right node is represented with (Ixl, ly!). For any i