Algorithms Lecture 8: Pattern Algorithms

Analysis and Design of Algorithms
Patterns Algorithms

Pattern searching
Naive Pattern Searching
Regular Expression

Pattern searching is an important problem in
computer science. When we do search for a string in
notepad/word file or browser or database, pattern
searching algorithms are used to show the search
results.

Naive Pattern Searching

Slide the pattern over text one by one and
check for a match. If a match is found, then
slides by 1 again to check for subsequent
matches.

Example 1:
Input: txt[] = "THIS IS A TEST TEXT"
pat[] = "TEST"
Output: Pattern found at index 10

Example 2:
Input: txt[] = "AABAACAADAABAABA"
pat[] = "AABA"
Pattern found at index 9

 Compare
A A B A A C A A D A A B A A B A
A A B A

j
i

 Compare
A A B A

j
i i+j

 Pattern found at index 0
A A B A
i

 Compare
A A B A
i

A A B A
i

 Compare
A A B
i

 Compare
A A
i

Input: txt[] = "AABAACAADAABAABA"
pat[] = "AABA"

 Python Code:

What is the best case?
The best case occurs when the first character of the pattern
is not present in text at all.
txt[] = "AABCCAADDEE"
pat[] = "FAA"

What is the worst case ?
1) When all characters of the text and pattern are same.
txt[] = "AAAAAAAAAAAAAAAAAA"
pat[] = "AAAAA"

2) Worst case also occurs when only the last character is
different.
txt[] = "AAAAAAAAAAAAAAAAAB"
pat[] = "AAAAB"

The worst case is O(m*(n-m+1))

Regular Expression

Regular expressions are a
powerful language for matching
text patterns.

re.match() checks for a match only at the beginning of
the string.
re.search() checks for a match anywhere in the string.

Import Regular Expression (Python)

In Python a regular expression search is
typically written as:
 match = re.search(pat, str)

Simple match

w (lowercase w): matches a "word" character:
a letter or digit or underbar [a-z A-Z 0-9 _].

W (upper case W): matches any non-word
character.

d (lowercase d): decimal digit [0-9]

s (lowercase s): matches a single whitespace
character -- space, newline, return, tab, form [
nrtf].

 . (dot) : matches any single character except
newline 'n'

 ^ = start : match the start
Match is empty

 $ = end : match the end of the string
Match is empty

 [ ] : a range of characters can be
indicated by giving two characters and
separating them by a “-”.

 [ ]

 [^ ] : will match any character except this.

 {n} : match exactly with any number of n.

 {n,m} : match exactly with any number of n to m.

Syntax Description Equivalent
d Matches any decimal digit [0-9]
D Matches any non-digit character [^0-9]
s Matches any whitespace character [ tnrfv]
S Matches any non-whitespace character [^ tnrfv]
w Matches any alphanumeric character [a-zA-Z0-9_]
W Matches any non-alphanumeric character [^a-zA-Z0-9_]

+ : 1 or more occurrences of the pattern

* : 0 or more occurrences of the pattern

? : match 0 or 1 occurrences of the pattern

 Emails:

 Emails:
 Square brackets can be used to indicate a set of chars, so [abc]
matches 'a' or 'b' or 'c'.

 Emails:
 findall() finds all the matches and returns them as a list of strings.

( ): match group of pattern

Operators Description
. Matches with any single character except newline ‘n’
? Match 0 or 1 occurrence of the pattern to its left
+ Match 1 or more occurrences of the pattern to its left
* Match 0 or more occurrences of the pattern to its left
w Matches with a alphanumeric character
W Matches non alphanumeric character
d Matches with digits [0-9]
D Matches with non-digits

s Matches with a single white space character (space, newline, tab)
S Matches any non-white space character
[..] Matches any single character in a square bracket
[^..] Matches any single character not in square bracket
It is used for special meaning characters
^ and $ ^ and $ match the start or end of the string respectively
{n,m} Matches at least n and at most m occurrences of expression
a| b Matches either a or b

( ) Groups regular expressions and returns matched text
t, n, r Matches tab, newline, return

Validate a phone number (phone number must be of
10 digits and starts with 8 or 9)

 Solution

Return date from given string
str= Amit 34-3456 12-05-2007, XYZ 56-4532 11-
11-2011

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Algorithms Lecture 8: Pattern Algorithms

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Algorithms Lecture 8: Pattern Algorithms