$($a$)$ Recall in class that there are two possible $($costs$)$ penalties: mismatch for $1$ and gap

for $2.$ Now, suppose that the gap penalty is $\backslash$delta $>0$ and the mismatch penalty for

lining up xi with yj is $\backslash$alpha ij $>0$ if xi $=$ yj and $\backslash$alpha ij $=0$ if xi $=$ yj $.$ Please revisit the

sequence alignment problem and derive the recurrence relation for the optimal cost,

c$($i$,$ j$).$