f = np.zeros((len(a), len(b)))

for j in xrange(len(b)):

f[0, j] = d * j

for i in xrange(len(a)):

f[i, 0] = d * i

for i in xrange(1, len(a)):

for j in xrange(1, len(b)):

match = f[i-1, j-1] + sim(a[i], b[j])

delete = f[i-1, j] + d

insert = f[i, j-1] + d

f[i, j] = max(match, delete, insert)

f = create_f(a, b)

al_a = ''

al_b = ''

i = len(a) - 1

j = len(b) - 1

while i > 0 or j > 0:

sim_val = sim(a[i], b[j])

if i > 0 and j > 0 and f[i, j] == f[i-1, j-1] + sim_val:

al_a = a[i] + al_a

al_b = b[j] + al_b

i -= 1

j -= 1

elif i > 0 and f[i, j] == f[i-1, j] + d:

al_a = a[i] + al_a

al_b = GAP + al_b

i -= 1

else:

al_a = GAP + al_a

al_b = b[j] + al_b

j -= 1