def __path(V, D, k):
if D == 0:
return [(xy, xy) for xy in irange(V[0][0])]
tx = V[D][k]
if k == -D or (k != D and V[D][k - 1] < V[D][k + 1]):
x = V[D][k + 1]
y = x - (k + 1)
k = k + 1
y = y + 1
else:
x = V[D][k - 1]
y = x - (k - 1)
k = k - 1
x = x + 1
return __path(V, D - 1, k) + [(x + d, y + d) for d in irange(tx - x)]
def path(a, b, eq = __eq):
"""
Finds the path through the match grid of sequence a and b,
using the function eq to determine equality.
Returns path
"""
m = len(a)
n = len(b)
mn = m + n
if mn == 0: # two empty sequences
return [(0, 0)]
Vd = []
V = {1: 0}
for D in irange(mn):
for k in irange(-D, D, 2):
if k == -D or (k != D and V[k - 1] < V[k + 1]):
x = V[k + 1]
else:
x = V[k - 1] + 1
y = x - k
while x < m and y < n and eq(a[x], b[y]):
x += 1
y += 1
V[k] = x
if x >= m and y >= n:
Vd.append(V.copy())
return __path(Vd, D, k)
Vd.append(V.copy())
raise Exception("lcs should not reach here")
