FAST PATTERN
MATCHING IN STRINGS
Dr. DONALD E. KNUTH, Dr. JAMES H. MORRIS JR., VAUGHAN R.
PRATT
Presented by: Mangesh Sakordekar
OVERVIEW
• Goal
• Intuition
• Algorithm & Implementation
• Run Time Analysis
• Conclusion
GOAL
• Improve run time of pattern
matching algorithm to find a
pattern(M) in a given text(N)
• Naive approach run time : O(N*M)
INTUITION
• Process each character only once.
text =
A
A
A
X
pattern =
A
A
A
A
• Intelligently move the pattern across
the string.
A
ALGORITHM & IMPLEMENTATION
PART 1: LONGEST PREFIX SUFFIX (LPS) TABLE
The LPS table stores the length of the longest matching
suffix and prefix formed by the substrings of the pattern.
Code:
pattern = "aaaba"
lps = [0] * len(pattern)
prevLPS, i = 0, 1
while i < len(pattern):
if needle[i] == needle[prevLPS]:
lps[i] = prevLPS + 1
prevLPS += 1
i += 1
elif prevLPS == 0:
lps[i] = 0
i += 1
else:
prevLPS = lps[prevLPS - 1]
pattern =
LPS
=
A
A
A
B
A
0
1
2
0
1
ALGORITHM & IMPLEMENTATION
PART 2: KMP ALGORITHM
Unlike the naive algorithm, we can now use the LPS table to
intelligently match the strings instead of searching for the
pattern from each index.
Code:
i = 0 # ptr for text
j = 0 # ptr for pattern
while i < len(text):
if text[i] == pattern[j]:
i, j = i + 1, j + 1
else:
if j == 0:
i += 1
else:
j = lps[j - 1]
if j == len(pattern):
print(“Pattern found at :” + str(i - len(pattern)))
j = lps[j - 1]
text =
A
A
A
B
A
A
A
B
pattern =
A
A
A
B
A
LPS =
0
1
2
0
1
A
RUNTIME ANALYSIS
• Consider length of the text as N and length of the pattern as M.
• Time complexity of generating LPS Table = O(M)
• Time complexity of pattern matching = O(N)
• Total Time Complexity = O(M+N)
• Total Space Complexity = O(M)
CONCLUSION
a time complexity of O(M+N)
•
Achieved
•
Successfully beat Boyer-Moore algorithm.
REFERENCES
1.
K n u t h , D . E . , M o r r i s , J . H . , J R , & P r a t t , V. R . ( 1 9 7 7 ) . F a s t P a t t e r n M a t c h i n g
i n S t r i n g s . S I A M J o u r n a l o n C o m p u t i n g . h t t p s : / / d o i . o r g / 1 0 . 11 3 7 / 0 2 0 6 0 2 4
2.
NeetCode. “Knuth–Morris–Pratt KMP - Implement Strstr() - Leetcode 28 - Python.”
YouTube, YouTube, 14 Nov. 2021,
https://www.youtube.com/watch?v=JoF0Z7nVSrA&ab_channel=NeetCode.
3.
“KMP Algorithm for Pattern Searching.” GeeksforGeeks, 30 Sept. 2022,
h t t p s : / / w w w. g e e k s f o r g e e k s . o r g / k m p - a l g o r i t h m - f o r - p a t t e r n - s e a r c h i n g / .
THANK YOU
QUESTIONS ?