4. (6 points): Individual assignment For two strings 81 and 82, let OPTsi (S1, S2) denote an optimal global alignment path reported using the scoring scheme (S1): ma = r, m; = y and g = 2, for some arbitrary integers r > 0, y 0; (S3): me = r +d, m;= y +d, and g = 2 +d, where d > 0; For the same two strings si and S2, how would the optimal alignment paths com- puted under scoring schemes S2 and S3 individually compare with OPTSI(S1, S2)? Are they guaranteed to be the same as OPTSI (S1,S2) or could they possibly differ from OPTSI(S1, S2)? Justify your answers. For simplicity, assume that the two strings are such that there exists only one unique optimal path under each of three scoring schemes. PS: Note that the emphasis on this question is on the optimal path and not the score itself, as the latter will obviously change with any change in the scoring scheme. 4. (6 points): Individual assignment For two strings 81 and 82, let OPTsi (S1, S2) denote an optimal global alignment path reported using the scoring scheme (S1): ma = r, m; = y and g = 2, for some arbitrary integers r > 0, y 0; (S3): me = r +d, m;= y +d, and g = 2 +d, where d > 0; For the same two strings si and S2, how would the optimal alignment paths com- puted under scoring schemes S2 and S3 individually compare with OPTSI(S1, S2)? Are they guaranteed to be the same as OPTSI (S1,S2) or could they possibly differ from OPTSI(S1, S2)? Justify your answers. For simplicity, assume that the two strings are such that there exists only one unique optimal path under each of three scoring schemes. PS: Note that the emphasis on this question is on the optimal path and not the score itself, as the latter will obviously change with any change in the scoring scheme