Tree and Center Star Alignment $[25$ points$]$

$v_1$: CGGGAGTGA

$v_2$: CGTTAGGGA

$v_3$: CGTTGGA

$v_4$: AGTTGGGAA

Here are their pre$-$computed optimal pairwise alignments with a cost of $0$ for matches

and $1$ otherwise:

b$.$ Find an alignment of v$\_(1),$v$\_(2),$v$\_(3),$v$\_(4)$ consistent with the tree v$\_(2)-$v$\_(3)-$v$\_(4)-$v$\_(1).$

Present your answer by $($i$)$ indicating which two sequences you are aligning at

each step, and $($ii$)$ provide all intermediate multiple alignments as well as the

final multiple alignment of the strings. $[10$ points$]$

Consider the following four strings v$\_(1),$v$\_(2),$v$\_(3),$v$\_(4)$ :