The python implementation of the longest common substring and subsequence, with illustration.

Use a matrix to record the correspondence between the characters in each of the two substrings.

Oldest string : The largest number in the matrix is the length of the oldest string. If the corresponding position character is the same, then c[i][j] = c[i-1][j-1] + 1

1 deflongsubstr (STR1,STR2):2Len1 =Len (str1)3Len2 =Len (str2)4Longest,start1,start2 =0,0,05c = [[0 forIinchRange (len2+1)] forIinchRange (len1+1)]6      forIinchRange (len1+1):7          forJinchRange (len2+1):8             ifi = = 0orj = =0:9C[I][J] =0Ten             elifStr1[i-1] = = Str2[j-1]: OneC[I][J] = c[i-1][j-1]+1 A             Else: -C[I][J] =0 -             if(Longest <C[i][j]): theLongest =C[i][j] -Start1 = iLongest -Start2 = JLongest -               +     returnStr1[start1:start1+longest],start1,start2

Oldest sequence : if the corresponding position character is the same, then c[i][j] = c[i-1][j-1] + 1, if different, then Max (C[i][j-1],c[i-1][j]).

1 defPrintlcs (flag,a,i,j):2     ifI==0orj==0:3         return  4     ifflag[i][j]=='OK':  5Printlcs (flag,a,i-1,j-1)  6         PrintA[i-1],7     elifflag[i][j]==' Left':  8Printlcs (flag,a,i,j-1)  9     Else:  TenPrintlcs (flag,a,i-1, J) One  A defLongsubseq (STR1,STR2): -Len1 =Len (str1) -Len2 =Len (str2) theLongest =0 -c = [[0 forIinchRange (len2+1)] forIinchRange (len1+1)] -flag = [[0 forIinchRange (len2+1)] forIinchRange (len1+1)]   -      forIinchRange (len1+1): +          forJinchRange (len2+1): -             ifi = = 0orj = =0: +C[I][J] =0 A             elifStr1[i-1] = = Str2[j-1]: atC[I][J] = c[i-1][j-1]+1 -FLAG[I][J] ='OK' -Longest =Max (Longest,c[i][j]) -             elifC[i][j-1] > C[i-1][j]: -C[I][J] =c[i][j-1] -FLAG[I][J] =' Left' in             Else: -C[I][J] =c[i-1][j] toFLAG[I][J] =' up' + Printlcs (FLAG,STR1,LEN1,LEN2) -     returnLongest theA='Abcbdab'   *b='Bdcaba'   $ PrintLongsubseq (A, B)

The python implementation of the longest common substring and subsequence, with illustration.