def back_spaceeff_dyna(x, y, c):
"""
Find the LCS_length end value with a linear space backward algorithm
"""
n = len(y)
m = len(x)
for i in range(m - 1, -1, -1):
c[n][1] = 0
for j in range(n - 1, -1, -1):
if x[i] == y[j]:
c[j][1] = c[j + 1][0] + 1
else:
cbottom = c[j][0]
cright = c[j + 1][1]
cbottomright = c[j + 1][0]
c[j][1], d = max3(cbottomright, cbottom, cright)
for k in range(len(c)):
c[k][0] = c[k][1]
def spaceeff_dyna(x, y, c):
"""
Find the LCS_length end value with a linear space forward algorithm
"""
n = len(y)
m = len(x)
for i in range(1, m + 1):
c[0][1] = 0
for j in range(1, n + 1):
if x[i - 1] == y[j - 1]:
c[j][1] = c[j - 1][0] + 1
else:
ctop = c[j][0]
cleft = c[j - 1][1]
ctopleft = c[j - 1][0]
c[j][1], d = max3(ctopleft, ctop, cleft)
for k in range(len(c)):
c[k][0] = c[k][1]
def approximated_dp_ed(x, y, k, ed):
"""
Compute the ED with an approximated divide and conquer LCS algorithm
"""
if not (k < len(x) and k < len(y)) or k < 1:
raise Exception('BAD K')
m = len(x)
n = len(y)
c = [[0 for _ in range(n + 1)] for _ in range(m + 1)]
b = [[0 for _ in range(n)] for _ in range(m)]
diff = m - n
left = -k // 2
right = k // 2 + k % 2
if diff > 0: # m > n -> x longer than y
left -= diff
else: # m > n -> y longer than x
right += -diff # (-) because diff < 0
# building b and c
for i in range(m):
for j in range(max(1, left), min(n, right)):
if x[i] == y[j]:
c[i + 1][j + 1] = c[i][j] + 1
b[i][j] = 0 # TOPLEFT
else:
ctop = c[i][j + 1]
cleft = c[i + 1][j]
ctopleft = c[i][j]
c[i + 1][j + 1], b[i][j] = max3(ctopleft, ctop, cleft)
left += 1
right += 1
# building answer
i = m - 1
j = n - 1
while i >= 0 and j >= 0:
ed.add_marker(i, j)
if b[i][j] == 0: # TOPLEFT
i -= 1
j -= 1
elif b[i][j] == 1: # TOP
i -= 1
else:
j -= 1
while i >= 0 or j >= 0:
if i >= 0:
ed.add_marker(i, j)
i -= 1
if j >= 0:
ed.add_marker(i, j)
j -= 1
ed.add_marker(i, j)