The KMP algorithm is an efficient string matching algorithm that reduces repeated matching steps through the prefix table. The prefix table is a pre-calculated array of strings that stores the length of the prefix substring for each position and its corresponding longest common prefix. During the matching process, the KMP algorithm first checks whether the current character matches a character in the prefix table. If the match is successful, it will continue to match backwards; if it does not match, it will move the prefix table forward one bit and match again. In this way, the KMP algorithm can skip the repeated matching steps without backtracking, thereby improving the efficiency of the algorithm.
In computer science, string matching is a basic and important problem.
What is KMP Algorithm?.
KMP algorithm is an efficient algorithm for string matching, proposed by Donald Knuth, Vaughan Pratt and James H. Morris in 1977.
The role of the prefix table.
The prefix table (also known as the partial match table or next array) is a key part of the KMP algorithm.
How to build a prefix table?.
The process of constructing the prefix table can be divided into the following steps:
1. # Initialization #: Create an array of the same length as the pattern string
The matching process of the KMP algorithm.
With the prefix table, we can perform string matching.
Practical application scenarios.
KMP algorithm has a wide range of application scenarios in practice, such as:
1. # Text Editor #: Find and replace functions in the text editor.
Summarize.
The KMP algorithm effectively avoids repeated matching steps by constructing a prefix table, and reduces the time complexity of string matching to O (n + m), where n is the length of the text string and m is the length of the pattern string.
An efficient algorithm is essential when we need to find a specific substring in a large text.
KMP (Knuth-Morris-Pratt) algorithm is one of the classic methods to solve this problem.
It greatly improves the matching efficiency by using the prefix table to avoid repeated matching steps.
What is KMP Algorithm?.
KMP algorithm is an efficient algorithm for string matching, proposed by Donald Knuth, Vaughan Pratt and James H. Morris in 1977. The core idea of the algorithm is: when mismatch occurs, use the information that has been partially matched to avoid matching from scratch, thereby improving the matching efficiency.
The role of the prefix table.
The prefix table (also known as the partial match table or next array) is a key part of the KMP algorithm. It records the maximum length of the same prefix and suffix of the substring before each position in the pattern string.
With this table, we can quickly skip some unnecessary comparisons when mismatches occur, thereby reducing the matching steps.
How to build a prefix table?.
The process of constructing the prefix table can be divided into the following steps:
1. # Initialization #: Create an array of the same length as the pattern string prefix, and set the first element to 0.
2. # Traverse Mode String #: Starting from the second character, calculate the prefix value of each position one by one.
3. # Update the prefix value #: If the current character matches the previous character, add 1 to the prefix value of the previous position; otherwise, backtrack based on the prefix value of the previous position until a matching position is found or the starting point is returned.
Below is an example of Python code for building a prefix table:
def build_prefix_table(pattern):
m = len(pattern)
prefix = [0] * m
j = 0 # length of previous longest prefix suffix
i = 1
while i < m:
if pattern[i] == pattern[j]:
j += 1
prefix[i] = j
i += 1
else:
if j != 0:
j = prefix[j - 1]
else:
prefix[i] = 0
i += 1
return prefix
The matching process of the KMP algorithm.
With the prefix table, we can perform string matching. The matching process is as follows:
1. # Initialize pointer #: Initialize the pointer of the text string and the pattern string respectively iSumj。
2. # Compare character by character #: Compare character by character, move both pointers at the same time if they match; if they do not match, adjust the pointer of the pattern string according to the prefix table j。
3. # Handling Mismatch #: If the pointer of the pattern string jBack to the starting point, the pointer to the text string iMove one place forward and continue the comparison.
4. # find match #: if the pointer of the pattern string jThe length of the pattern string is reached, indicating that a match has been found, the position of the match can be recorded, and then the pointer can be adjusted according to the prefix table to continue searching for the next possible match.
Below is an example of Python code for the KMP algorithm:
def kmp_search(text, pattern):
n = len(text)
m = len(pattern)
prefix = build_prefix_table(pattern)
i = 0 # index for text[]
j = 0 # index for pattern[]
matches = []
while i < n:
if pattern[j] == text[i]:
i += 1
j += 1
if j == m:
matches.append(i - j)
j = prefix[j - 1]
elif i < n and pattern[j] != text[i]:
if j != 0:
j = prefix[j - 1]
else:
i += 1
return matches
Practical application scenarios.
KMP algorithm has a wide range of application scenarios in practice, such as:
1. # Text Editor #: Find and replace functions in the text editor.
2. # Data Compression #: Used to find duplicate patterns in data compression algorithms.
3. # Bioinformatics #: Used to quickly find gene fragments in DNA sequence alignment.
4. # web search #: used in search engines to quickly find keywords.
Summarize.
The KMP algorithm effectively avoids repeated matching steps by constructing a prefix table, and reduces the time complexity of string matching to O (n + m), where n is the length of the text string and m is the length of the pattern string. This gives the KMP algorithm a significant advantage when dealing with large-scale text matching.
I hope that through this article, you can better understand the principle and application of KMP algorithm, and use this powerful tool flexibly in actual projects.
