Consider the task of aligning two sequences where the score matrix is filled using dynamic programming. If you need to find the optimum $($i$)$global$,($ii$)$local$,($iii$)$semiglobal$$ alignment of two sequences, explain for each case:

How do you initialize the scoring matrix?

Which cell$($s$)$ in the matrix would give you the score of these alignments?

What would your trace back strategy $($beginning cell, ending cell$)$ be in each case?

Would they all have the same recursion rule to determine the score of each cell? If not, which one is different and how? Explain briefly, you do not need to write the entire recurrence rule.