### SUBSTRING SEARCH STUDY GUIDE

Terminology and Basics

• Substring search problem: Find an instance (or all instances) of a query substring of length M in a text string of length N.
• Sustring must be precisely defined (no regular expressions).
• You should be able to manually use a KMP DFA, and you should be able to manually carry out Boyers-Moore and Rabin Karp.
KMP
• How do you construct the DFA?
• How much time does it take if you re-simulate every time you have a mismatch? It's ok if you don't fully understand the linear time construction process.
• What is the best-case running time for DFA construction and DFA simulation? The worst-case running time?
Boyer-Moore
• What is the mismatched character heuristic? Why do we use the rightmost character?
• Why is the mismatched character heuristic strictly suboptimal? Why do we use it then -- because the basic idea is very similar to KMP and you'll learn it if you ever really need to.
• What is the best-case running time? The worst-case running time?
• Which inputs result in best and worst case performance?
Rabin Karp
• If we know mod(ABCDEFG, R), how do we compute mod(BCDEFGH, R) in constant time (where A through H are arbitrary digits of a number from some alphabet of radix R)?
• What are the Las Vegas and Monte Carlo versions of Rabin-Karp?
• How would we extend Rabin-Karp to efficiently search for any one of P possible patterns in a text of length N? How would this technique compare to using KMP or Boyer-Moore for the same task?

### Recommended Problems

#### C level

1. Spring 2008 Final, #6
2. Fall 2009 Final, #6
3. Fall 2012 Final, #10

#### B level

1. Fall 2009 Final, #5
2. Fall 2009 Final, #10 [great problem!]
3. Fall 2010 Final, #10
4. Fall 2011 Final, #6
5. Spring 2012 Final, #7
6. Fall 2012 Final, #9
7. Give an example of when you might want to use KMP? Boyer Moore? Rabin Karp?

#### A level

1. Fall 2010 Final, #10
2. Fall 2012 Final, #14
3. Give an example of when you might prefer to use the Monte Carlo version of Rabin Karp over the Las Vegas version.
4. Textbook: 5.3.22
5. Textbook: 5.3.26