动态规划_LCS

#coding=utf-8

# 最长公共子序列

# s1[m] = s2[n]
#     LSC(m,n) = LSC(m-1,n-1) + 1
# s1[m] != s2[n]
#     LSC= max(LSC(m-1,n),LSC(m,n-1))

class Solution(object):
    def findlcs(self, s1, s2):

        if not s1 or not s2:
            return 0

        m = len(s1)
        n = len(s2)

        lsc = [[0 for i in range(n)] for i in range(m)]


        # for i in range(m):
        #     if s1[i] == s2[0]:
        #         lsc[i][0] = 1
        #
        # for i in range(n):
        #     if s2[i] == s1[0]:
        #         lsc[0][i] = 1

        if s1[0] == s2[0]:
            lsc[0][0] = 1



        for i in range(m):
            for j in range(n):
                if s1[i] == s2[j]:
                    if i-1 >=0 and j-1>=0:
                        lsc[i][j] = lsc[i-1][j-1]+1
                else:
                    if i-1 >= 0:
                        lsc[i][j] = lsc[i-1][j]
                    if j-1 >= 0:
                        lsc[i][j] = max(lsc[i][j],lsc[i][j-1])


        return lsc[m-1][n-1]



s = Solution()

s1 = "abcd"
s2 = "aebd"

print s.findlcs(s1,s2)