Given two strings X = x1,x2,...,xn and Y = y1,y2,...,ym give a dynamic programming algorithm to find the length k of the longest string Z = z1, . . . , zk where Z appears as a substring of X and as a subsequence of Y . Recall, a substring means consecutive elements.

For example, for the following input: X = a,b,d,b,a,b,f,g,d

Y = b,e,t,f,d,b,f,a,f,r

then the answer is 4 (since, b, d, b, a is a substring of X and it is also a subsequence of Y). You do not need to output the actual substring, just its length.

(Faster (and correct) in asymptotic O() notation is worth more credit.)

(a) Define the entries of your table in words. E.g., T (i) or T (i, j) is ....

(b) State recurrence for entries of table in terms of smaller subproblems.

(c) Write pseudocode for your algorithm to solve this problem.