Given two strings X = x1,x2,…,xn and Y = y1,y2,…,ym give adynamic programming algorithm to find the length k of the longeststring Z = z1, . . . , zk where Z appears as a substring of X andas a subsequence of Y . Recall, a substring means consecutiveelements.
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 andit is also a subsequence of Y). You do not need to output theactual substring, just its length.
(Faster (and correct) in asymptotic O(ยท) notation is worth morecredit.)
(a) Define
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