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def lcs_length(x, y):
m = len(x)
n = len(y)
c = [[0 for _ in range(n + 1)] for _ in range(m + 1)]
for i in range(1, m + 1):
for j in range(1, n + 1):
if x[i - 1] == y[j - 1]:
c[i][j] = c[i - 1][j - 1] + 1
else:
c[i][j] = max(c[i - 1][j], c[i][j - 1])
for _ in c:
print(_)
return c[m][n]
print("==========================最长公共子序列的长度==========================")
print(f'最长公共子序列的长度为:{lcs_length("ABCBDAB", "BDCABA")}')
def lcs(x, y):
m = len(x)
n = len(y)
c = [[0 for _ in range(n + 1)] for _ in range(m + 1)]
b = [[0 for _ in range(n + 1)] for _ in range(m + 1)]
for i in range(1, m + 1):
for j in range(1, n + 1):
if x[i - 1] == y[j - 1]:
c[i][j] = c[i - 1][j - 1] + 1
b[i][j] = 1
elif c[i - 1][j] > c[i][j - 1]:
c[i][j] = c[i - 1][j]
b[i][j] = 2
else:
c[i][j] = c[i][j - 1]
b[i][j] = 3
return c[m][n], b
def lcs_trackback(x, y):
c, b = lcs(x, y)
for _ in b:
print(_)
i = len(x)
j = len(y)
res = []
while i > 0 and j > 0:
if b[i][j] == 1:
res.append(x[i - 1])
i -= 1
j -= 1
elif b[i][j] == 2:
i -= 1
else:
j -= 1
return "".join(reversed(res))
print("===============================最长公共子序列===============================")
print(lcs_trackback("ABCBDAB", "BDCABA"))
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