Respuesta :
A Python implementation of the dynamic programming algorithm for finding the longest common subsequence of two binary strings:
def longest_common_subsequence(s1, s2):
"""
Dynamic programming algorithm for finding the longest common subsequence of two binary strings.
"""
m = len(s1)
n = len(s2)
dp = [[0] * (n + 1) for _ in range(m + 1)]
for i in range(1, m + 1):
for j in range(1, n + 1):
if s1[i - 1] == s2[j - 1]:
dp[i][j] = dp[i - 1][j - 1] + 1
else:
dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
# reconstruct the longest common subsequence
lcs = ""
i = m
j = n
while i > 0 and j > 0:
if s1[i - 1] == s2[j - 1]:
lcs = s1[i - 1] + lcs
i -= 1
j -= 1
elif dp[i - 1][j] > dp[i][j - 1]:
i -= 1
else:
j -= 1
return lcs
# Test the algorithm
s1 = "1001010"
s2 = "0101110"
lcs = longest_common_subsequence(s1, s2)
print(f"Longest common subsequence of {s1} and {s2}: {lcs}")
Using dynamic programming, the longest common subsequence function takes two binary strings, s1 and s2, and returns the longest common subsequence. The function first fills the 2D array dp with zeros, where dp[i][j] is the longest common subsequence of the first I characters of s1 and the first j characters of s2, and is the length of the longest common subsequence. The dp array is then filled up by iterating over the letters in s1 and s2.
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