① This kind of topic is called longest common subsequence, which is very famous and widely used in computer and biotechnology (such as gene pairing mentioned above). The latter involves a wide range of mathematical problems. You can search if you are interested.

② The method to solve the problem is generally "dynamic programming", which is also a common method. It is hard to say clearly in a few words. The basic idea is: given a problem, solve it by decomposing sub-problems and then merge them. Usually, many subproblems have high similarity, and dynamic programming tries to solve each subproblem only once, thus reducing the amount of calculation: once the solution of a given subproblem is calculated, it is memorized and stored, so that the table can be directly looked up next time the solution of the same subproblem is needed. -You can search it if you are interested.

③ The demonstration code is as follows:

Program? lcs _ seq

Use? Mathematics;

defined variable

s 1，？ s2？ :? String;

dp？ :? Array? Yes? Array? Yes? Integer;

Me? j，？ m，？ n？ :? Integer;

begin

readln(s 1)；

readln(S2)；

m？ :=? Length (s1); ? n？ :=? Length (S2);

Set the length (dp, m+ 1,? n+ 1)；

For what? Me? :=? 1? Where to? m？ Do what?

For what? j？ :=? 1? Where to? n？ Do what?

Start?

What if? (me? =? 0)? Or? (j？ =? 0)? then what dp[i][j]？ :=? 0

Or what? What if? (s 1[i]？ =? s2[j])？ then what dp[i][j]？ :=? dp[i- 1][j- 1]？ +? 1

Or what? dp[i][j]？ :=? max(dp[i- 1][j]，？ DP[I][j- 1])；

End;

writeln(DP[M][N])；

End. Run:

1 122 1 12 122

1222 1 122 1 1

seven