1. The Longest Common Subsequence Problem
CSE 373
Data Structures

2. CSE 373 AU 04 -- Longest Common Subsequences
Reading
Goodrich and Tamassia, 3rd ed, Chapter 12, section 11.5, pp
12/31/2018
CSE 373 AU Longest Common Subsequences

3. CSE 373 AU 04 -- Longest Common Subsequences
Motivation
Two Problems and Methods for String Comparison:
The substring problem
The longest common subsequence problem.
In both cases, good algorithms do substantially better than the brute force methods.
12/31/2018
CSE 373 AU Longest Common Subsequences

4. String Matching Problem
Given two strings TEXT and PATTERN, find the first occurrence of PATTERN in TEXT.
Useful in text editing, document analysis, genome analysis, etc.
12/31/2018
CSE 373 AU Longest Common Subsequences

5. String Matching Problem: Brute-Force Algorithm
For i = 0 to n – m {
For j = 0 to m – 1 {
If TEXT[j]  PATTERN[i] then break
If j = m – 1 then return i }
return -1;
Suppose
TEXT =
PATTERN =
This type of problem has (n2) behavior.
A more efficient algorithm is the Boyer-Moore algorithm. (We will not be covering it in this course.)
12/31/2018
CSE 373 AU Longest Common Subsequences

6. Longest Common Subsequence Problem
A Longest Common Subsequence LCS of two strings S1 and S2 is a longest string the can be obtained from S1 and from S2 by deleting elements.
For example, S1 = “thoughtful” and S2 = “shuffle” have an LCS: “hufl”.
Useful in spelling correction, document comparison, etc.
12/31/2018
CSE 373 AU Longest Common Subsequences

7. CSE 373 AU 04 -- Longest Common Subsequences
Dynamic Programming
Analyze the problem in terms of a number of smaller subproblems.
Solve the subproblems and keep their answers in a table.
Each subproblem’s answer is easily computed from the answers to its own subproblems.
12/31/2018
CSE 373 AU Longest Common Subsequences

8. Longest Common Subsequence: Algorithm using Dynamic Programming
For every prefix of S1 and prefix of S2 we’ll compute the length L of an LCS.
In the end, we’ll get the length of an LCS for S1 and S2 themselves.
The subsequence can be recovered from the matrix of L values.
(see demonstration)
12/31/2018
CSE 373 AU Longest Common Subsequences