【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))