IN THIS TUTORIAL YOU WILL LEARN DESCRIPTIVELY ABOUT LONGEST COMMON SUBSTRING AND LONGEST COMMON SUBSEQUENCE.Video tutorial is also available in bangla-(https://youtu.be/0w-MbvTtj_c)

1. Longest
Common
Subsequence
(LCS)
Lecture By
Md. Nakib Rahaman ,Student ,CSE ,BRACU

2. Longest Common Subsequence
(LCS)
– Y= “ABCE”
– X=“ABEC”
– Longest common substring=AB
– Longest Common subsequence = ABC or ABE
Md Nakib Rahaman,Student,CSE,BRACU
2

3. 0 1(A) 2(B) 3(C) 4(E)
0
1(A)
2(B)
3(E)
4(C)
3
Md Nakib Rahaman,Student,CSE,BRACU
“ABCE” and “ABEC”

4. 4
Md Nakib Rahaman,Student,CSE,BRACU
Rules:-(Matching The Characters)
1. First of all, put “0” in both first column and first row.(default)
2. Then there will be two cases (i) Same Characters (ii) Different Characters [This
rule is describe below with smart art]
Rule 2
Same
Characters
Add 1 with diagonal
value and put value
and
Different
Characters
Compare Up ↑ & Left←
value
Up ↑ = Left←
Choose either Left or Up and
put the value and also put the
sign. But that should be
continued in similar cases
throughout the Table.
Up↑≠Left←
Choose the greater value and put
value and also sign .

5. 5
Md Nakib Rahaman,Student,CSE,BRACU
1. Go to the last row and last column element.(Backtracking starts from
here.)
2. Follow the arrow (←, ↑, ) and finished the tracking until reach “0”
3. Draw the Path from the backtracking point to “0” & write( )
corresponding characters from backward

6. 6 “ABCE” and “ABEC”
Md Nakib Rahaman,Student,CSE,BRACU
0 1(A) 2(B) 3(C) 4(E)
0 0 0 0 0 0
1(A) 0
2(B) 0
3(E) 0
4(C) 0
1
2
3
3 3↑
1← 1← 1←
1↑
1↑
1↑
2↑
2↑
2← 2←
2↑

7. 7
Md Nakib Rahaman,Student,CSE,BRACU
“CAKE” and “CRANE”
Practice
0 1(C) 2(R) 3(A) 4(N) 5(E)
0 0 0 0 0 0 0
1(C) 0 1 1 1 1 1
2(A) 0 1↑ 1↑ 2 2 2
3(K) 0 1↑ 1↑ 2↑ 2↑ 2↑
4(E) 0 1↑ 1↑ 2↑ 2↑ 3

8. MS OFFICE
2013
Md Nakib Rahaman,Student,CSE,BRACU
8
https://www.youtube.com/nakibakash