Chapter 8, Problem 17SE

In Exercises 15-18 we develop a dynamic programming algorithm for finding a longest common subsequence of two sequences $a_1,a_2,\mathrm{....},a_m$ and $b_1,b_2,\mathrm{....},b_n$, an important problem in the comparison of DNA of different organisms.

Use Exercise 16 to construct a dynamic programming algorithm for computing the length of a longest common subsequence of two sequences $a_1,a_2,\mathrm{....},a_m$ and $b_1,b_2,\mathrm{....},b_n$, storing the values of L(I,J) as they are found.