动态规划及LCS

LCS的python实现：

 #!/usr/bin/env python
 #-*- coding: utf-8 -*-
 import sys

 reload(sys)
 sys.setdefaultencoding('utf-8')

 class LCS(object):
     """Long Common Subsequence算法
     """
     def __init__(self, str1, str2):
         self.s1 = str1
         self.s2 = str2
         self.lcs = [['' for i in range(len(self.s2) + 1)] for j in range(len(self.s1) + 1)] # 另一种写法

     def get_lcs_len(self):
         """递归计算lcs的长度
         """
         for i in xrange(len(self.s1) + 1):
             for j in xrange(len(self.s2) + 1):
                 if i == 0 or j == 0:
                     self.lcs[i, j] = 0
                 elif self.s1[i - 1] == self.s2[j - 1]:
                     self.lcs[i, j] = self.lcs[i - 1][j - 1] + 1
                 else:
                     self.lcs[i, j] = max(self.lcs[i - 1][j], self.lcs[i][j - 1])
         return self.lcs[len(self.s1), len(self.s2)]

     def get_lcs(self):
         """递归计算lcs(直接获取lCS)
         """
         for i in xrange(len(self.s1) + 1):
             for j in xrange(len(self.s2) + 1):
                 if i == 0 or j == 0:
                     self.lcs[i][j] = ''
                 elif self.s1[i - 1] == self.s2[j - 1]:
                     self.lcs[i][j] = self.lcs[i - 1][j - 1] + self.s1[i - 1]
                 else:
                     self.lcs[i][j] = self.lcs[i - 1][j] if len(self.lcs[i - 1][j]) > \
                             len(self.lcs[i][j - 1]) else self.lcs[i][j - 1]
         return self.lcs[len(self.s1)][len(self.s2)]

 if __name__ == '__main__':
     s1 = 'abcdefgw'
     s2 = 'bdfgegwe'
     model = LCS(s1, s2)
     print model.get_lcs()