plz explain clearly, will upvote if correct

In this problem, we explore some common DNA problems that arise in Biology.

Given two strings of characters X $($of length n$)$ and Y $($of length m$),$ we care

to compute the length of their longest common subsequence. If there is no

common subsequence, the answer is of course $0.$

A subsequence of a string is a new string generated from the original

string with some characters deleted without changing the relative order of the

remaining characters. A common subsequence of two strings is a subsequence

that is common to both strings.

Examples: $$ace$$ is a subsequence of $$abcde$.$ Another example is that

$$abc$,$abg$,$bdf$,$aeg$,$acefg$,$ all are subsequences of $$abcdefg$$

A$)$ Describe an algorithm that finds the length of the longest common sub$-$

sequence between two strings X and Y $.$ What$$s the runtime of your

algorithm? Your algorithm should not be of exponential time and you

should clearly define any subproblems needed and$/$or any recursions that

you write down $($Hint: Dynamic Programming$)$

B$)$ Given two strings X $($of length n$)$ and Y $($of length m$),$ we ask you to find

the length of the shortest string that has both X and Y as subsequences.

Here are two examples: If X is $$beek$,$ and Y is $$eke$,$ then the answer

is $5,$ because the string $$beeke$$ has both string $$beek$$ and $$eke$$ as

subsequences and is shortest possible. For another example, take X to be

$$AGGTAB$,$ and Y to be $$GXTXAYB$,$ then the answer is $9,$ because the

string $$AGXGTXAYB$$ has both strings $$AGGTAB$$ and $$GXTXAYB$$

as subsequences and is shortest possible. $($Hint: try to figure out what$$s

the connection with the longest common subsequence problem.$)$