1 # 最长公共子序列问题
 2 __author__ = 'ice'
 3
 4
 5 # arr_x,arr_y [0 ~ length-1]
 6 # subarr_len [0,1~x_length][0,1~y_length]
 7 # flag [0 ~ x_length-1][0 ~ y_length]
 8
 9
10 def lcs_length(arr_x, arr_y):
11     x_length = len(arr_x)
12     y_length = len(arr_y)
13     subarr_len = [[0 for j in range(y_length + 1)] for i in range(x_length + 1)]
14     flag = [[0 for j in range(y_length)] for i in range(x_length)]
15     for i in range(1, x_length + 1):
16         for j in range(1, y_length + 1):
17             if arr_x[i - 1] == arr_y[j - 1]:
18                 subarr_len[i][j] = subarr_len[i - 1][j - 1] + 1
19                 flag[i - 1][j - 1] = 1
20             elif subarr_len[i - 1][j] >= subarr_len[i][j - 1]:
21                 subarr_len[i][j] = subarr_len[i - 1][j]
22                 flag[i - 1][j - 1] = 2
23             else:
24                 subarr_len[i][j] = subarr_len[i][j - 1]
25                 flag[i - 1][j - 1] = 3
26     return {'subarr_length': subarr_len[x_length][y_length], 'flag': flag}
27
28
29 def lcs(arr_x, x_i, y_j, flag, result):
30     if x_i < 0 or y_j < 0:
31         return
32     if flag[x_i][y_j] == 1:
33         lcs(arr_x, x_i - 1, y_j - 1, flag, result)
34         result.append(arr_x[x_i])
35     elif flag[x_i][y_j] == 2:
36         lcs(arr_x, x_i - 1, y_j, flag, result)
37     elif flag[x_i][y_j] == 3:
38         lcs(arr_x, x_i, y_j - 1, flag, result)
39
40
41 array_x = ['a', 'b', 'c', 'b', 'd', 'a', 'b']
42 array_y = ['b', 'd', 'c', 'a', 'b', 'a']
43 longest_common_subsequence = []
44 lcs_info = lcs_length(array_x, array_y)
45 lcs(array_x, len(array_x) - 1, len(array_y) - 1, lcs_info['flag'], longest_common_subsequence)
46 print(longest_common_subsequence)