The cost of a multiple sequence alignment is defined
as the summation of the costs of all columns in the alignment.
This treats spaces in the alignment independently. Discuss how to
modify the definition to take into account gap penalties. More
specifically,

* Explain how to modify the formulations of SP alignment and tree
alignment to incorporate gap penalties. Observe that gap penalties are
well defined for pairwise alignment, and both SP and tree alignments can
be viewed as a combination of some pairwise alignments. (For tree
alignment, we have to use the sequence reconstruction formulation.)

* Give an efficient algorithm to compute the modified (gap-based) 
SP cost of an input multiple sequence alignment.

* Give an efficient dynamic programming algorithm in pseudo-code to
compute an optimal SP alignment of 3 sequences with gap penalties. You
need provide the recurrence relations.

* Give an efficient algorithm to compute 
the modified (gap-based) tree cost of an input multiple sequence alignment.