【问题】 求两字符序列的最长公共字符子序列
1 def lcs_length(x,y):
2 m = len(x)
3 n = len(y)
4 c = [[0 for _ in range(n+1)] for _ in range(m+1)]
5 for i in range(1,m+1):
6 for j in range(1,n+1):
7 if x[i-1] == y[j-1]:
8 c[i][j] = c[i-1][j-1] + 1
9 else:
10 c[i][j] = max(c[i-1][j],c[i][j-1])
11 return c[m][n]
12
13 def lcs(x,y):
14 m = len(x)
15 n = len(y)
16 c = [[0 for _ in range(n+1)] for _ in range(m+1)]
17 b = [[0 for _ in range(n+1)] for _ in range(m+1)]
18 for i in range(1,m+1):
19 for j in range(1,n+1):
20 if x[i-1] == y[j-1]:
21 c[i][j] = c[i-1][j-1] +1
22 b[i][j] = 1
23 elif c[i-1][j] > c[i][j-1]:
24 c[i][j] = c[i-1][j]
25 b[i][j] = 2
26 else:
27 c[i][j] = c[i][j-1]
28 b[i][j] = 3
29 return c[m][n],b
30
31 def lcs_trackback(x,y):
32 c,b = lcs(x,y)
33 i = len(x)
34 j = len(y)
35 res = []
36 while i>0 and j>0:
37 if b[i][j] == 1: #来自左上方=>匹配
38 res.append(x[i-1])
39 i-=1
40 j-=1
41 elif b[i][j] == 2:#来自于上方=>不匹配
42 i-=1
43 else: #==3来自于左方=>不匹配
44 j-=1
45 return "".join(reversed(res))
