Modify the Perl script for sequence alignment that we wrote in class to work
with affine gaps (see recurrence below). You only need to modify how the matrix
V is computed. The traceback remains the same.

Submit your assignment by copying it into the directory
/afs/cad/courses/bnfo/f18/bnfo/601/001/<ucid>.
For example if your ucid is abc12 then copy your Perl script into 
/afs/cad/courses/bnfo/f18/bnfo/601/001/abc12.

Submit your solution to your course directory by 
midnight Sept 30th.

Input: Sequences X and Y of lengths m and n respectively

Output: Optimal alignment of X and Y with affine gaps

Use costs m=5, mm=-4, g=-26, e=-1.

Pseudocode for affine gap alignment:

Define the matrices V, E, F, and M as follows:

M(i,j) = Optimal sequence alignment of X1X2...Xi and Y1Y2...Yj such
	 that Xi is aligned to Yj
E(i,j) = Optimal sequence alignment of X1X2...Xi and Y1Y2...Yj such
	 that Yj is aligned to a gap
F(i,j) = Optimal sequence alignment of X1X2...Xi and Y1Y2...Yj such
	 that Xi is aligned to a gap
V(i,j) = Optimal sequence alignment of X1X2...Xi and Y1Y2...Yj 

Initialization:

V(0,0) = M(0,0) = 0
E(0,0) = F(0,0) = -Inf
M(i,0) = M(0,i) = E(i,0) = F(0,i) = -Inf
V(i,0) = V(0,i) = E(0,i) = F(i,0) = g+(i-1)e

Recurrence:

V(i,j) = max{ E(i,j), F(i,j), M(i,j) )
M(i,j) = V(i-1,j-1) + m/mm
F(i,j) = max{ M(i-1,j) + g, F(i-1,j) + e }
E(i,j) = max{ M(i,j-1) + g, E(i,j-1) + e }

Traceback:
T(i,j)= 'd' if V(i,j)==M(i,j)
	'l' if V(i,j)==E(i,j)
	'u' if V(i,j)==F(i,j)