LCS 最长公共子序列

 1 ‘‘‘
 2 LCS 最长公共子序列
 3 ‘‘‘
 4 
 5 
 6 def LCS_len(x, y):
 7     m = len(x)
 8     n = len(y)
 9     dp = [[0] * (n + 1) for i in range(m + 1)]
10     B = [[‘ ‘] * (n + 1) for i in range(m + 1)]
11     for i in range(1, m + 1):
12         for j in range(1, n + 1):
13             if x[i - 1] == y[j - 1]:
14                 dp[i][j] = dp[i - 1][j - 1] + 1
15                 B[i][j] = ‘X‘
16             elif dp[i - 1][j] > dp[i][j - 1]:
17                 dp[i][j] = dp[i - 1][j]
18                 B[i][j] = ‘L‘
19             else:
20                 dp[i][j] = dp[i][j - 1]
21                 B[i][j] = ‘T‘
22     print(dp)
23     return dp, B
24 
25 
26 def LCS_str(B, x, i, j):
27     if i == 0 or j == 0:
28         return
29     if B[i][j] == ‘X‘:
30         print(x[i - 1])
31         LCS_str(B, x, i - 1, j - 1)
32 
33     elif B[i][j] == ‘L‘:
34         LCS_str(B, x, i - 1, j)
35     else:
36         LCS_str(B, x, i, j - 1)
37 
38 
39 def main():
40     x = ‘ABDC‘
41     y = ‘AFBC‘
42     dp, B = LCS_len(x, y)
43     LCS_str(B, x, len(x), len(y))
44 main()