What is the Knuth-Morris-Pratt (KMP) Algorithm?

When you are working with strings in programming, one of the most frequently encountered tasks is to search for a pattern within a larger text. The KMP algorithm, which is also known as the Knuth-Morris-Pratt algorithm, is one of the most efficient ways to solve this issue. In this blog, you will understand the Knuth-Morris-Pratt algorithm, its working and logic, and time complexity, along with a simple example for better understanding.

Table of Contents:

• What is the KMP Algorithm and String Matching?
• Why is the KMP Algorithm Important for Pattern Searching?
• Components of the KMP Algorithm
• How the KMP Algorithm Works
• Complexity Analysis of the KMP Algorithm
  1. Time Complexity of the KMP Algorithm
  2. Space Complexity of the KMP Algorithm
• Advantages and Disadvantages of the KMP Algorithm
• Common Mistakes While Implementing KMP
• Best Practices for the KMP Algorithm
• Real-World Applications of the KMP Algorithm
• Conclusion

What is the KMP Algorithm and String Matching?

The Knuth-Morris-Pratt algorithm is a very efficient technique that is used for searching a specific pattern within a larger body of text. Unlike simple string searching algorithms that restart the comparisons after each mismatch, this algorithm uses a smarter approach. It pre-processes the pattern to construct an LPS (Longest Prefix Suffix) array, which helps the algorithm in calculating the already matched characters that need not be rechecked again. This process helps to reduce the number of unnecessary comparisons, which makes the searching process of the algorithm much faster and more accurate.

The KMP string matching algorithm is one of the most popular algorithms for pattern matching problems. It is useful when you need to find multiple occurrences of a pattern inside a long string, like for a word in a document or matching DNA sequences in bioinformatics. By using the Knuth-Morris-Pratt algorithm, you can get efficient results even for large datasets. This is because it uses linear time, which means that if the text becomes twice as long, the algorithm will take roughly twice as much time to finish. This makes it a very important concept in computer science and an important tool for anyone who is dealing with text processing or data analysis.

Unlock Python: Power Up Your Programming Skills!

Dive into real-world coding projects and become confident in writing clean, efficient Python code.

Explore Program

Why is the KMP Algorithm Important for Pattern Searching?

1. The Knuth-Morris-Pratt algorithm helps you to find a specific sequence of characters in a text in a quick and effective way.
2. Unlike other naive search methods, it avoids restarting the comparison from the beginning after each mismatch. This helps to save a lot of time.
3. It also uses an LPS (Longest Prefix Suffix) table to remember certain parts of the pattern that have already matched. Therefore, it knows where you should continue after a mismatch.
4. This algorithm works very efficiently even for very long texts or patterns. This makes it a suitable choice for large datasets.
5. It is used widely in real-world applications like search engines, text editors, and DNA sequence analysis.
6. By reducing unnecessary comparisons, the Knuth-Morris-Pratt algorithm ensures that you get a faster, accurate, and more reliable searching pattern.
7. The efficiency and speed of the algorithm make it a very important tool in computer science for string processing and text analysis.

Components of the KMP Algorithm

In this section, we are going to discuss the various components of the Knuth-Morris-Pratt algorithm:

1. Prefix in KMP

In this algorithm, there are two terms that you need to know. They are proper prefixes and suffixes. A proper prefix of a pattern is basically a part of the pattern that starts from the beginning but does not include the last character. To make a proper prefix, you can take as many characters as you want, excluding the entire string. If you add the last character in the proper prefix, it becomes the whole pattern, and a proper prefix should always be smaller than the full pattern. For example, if your pattern is “ABABC”, the proper prefixes are:

• “A”
• “AB”
• “ABA”
• “ABAB”

As you can see above, the “ABABC” is not included, because it will complete the whole pattern. It is important to understand proper prefixes in the Knuth-Morris-Pratt algorithm because it will help build the LPS array. This LPS array is used to skip unnecessary comparisons while searching for the pattern.

2. Suffix in KMP

In this algorithm, a proper suffix of a pattern is a part of the pattern that comes from the end but does not include the entire pattern. It can include any number of characters from the end toward the start, as long as it does not form the complete pattern.

For example, if the pattern is “abcd”, then the proper suffixes would be:

• “d”
• “cd”
• “bcd”
• “abcd” is not included as it is the full pattern.

3. Patterns in KMP

In the Knuth-Morris-Pratt algorithm, a pattern is basically the smaller string that you want to search for inside a larger text. It is the target sequence that the algorithm tries to find within the given text using an efficient searching method. Patterns play a very important role in how the algorithm works. This is because all the processing and comparisons are based on it. 

For example, if your text is “ABABDABACDABABCABAB” and your pattern is “ABABCABAB”, then the Algorithm will try to find where this pattern occurs inside the text. The algorithm uses the pattern to build the LPS (Longest Prefix Suffix) array. This helps it to skip the unnecessary checks when a mismatch occurs.

How the KMP Algorithm Works

The working of the Knuth-Morris-Pratt algorithm involves finding a pattern inside a text in an efficient way. Instead of checking every character repeatedly like simple methods, the algorithm uses information from the pattern to skip any unwanted comparisons. It does this through two main steps: preprocessing and searching.

Now, let’s understand the working process of this algorithm with a practical example. The above image shows what happens when a mismatch occurs and how the algorithm shifts the pattern to continue matching without restarting from the beginning.

In the first part of the image, the pattern “AAABC” is matched with the text “AAAABCAABA”. The first few characters of the pattern match exactly, but the mismatch occurs when the character “A” in the text is compared with the character “B” in the pattern. In a normal string matching method, you have to move the pattern one step forward and start checking from the very first character. But the same thing is done by the KMP algorithm in a smarter way.

In the second part of the image, the Knuth-Morris-Pratt algorithm is used to shift the pattern based on the LPS (Longest Prefix Suffix) values. Instead of starting from the start, it uses the information about how the patterns repeat themselves to move ahead. In this way, the algorithm avoids rechecking the characters that have already matched. After the shift is done, the pattern “AAABC” now aligns perfectly with a part of the text where the full match occurs.

The above example clearly shows that the Algorithm helps to save time by skipping unwanted comparisons. It uses the LPS array to decide how far the pattern has to be moved after a mismatch. This makes the process of searching faster and more efficient than simple methods.

Complexity Analysis of the KMP Algorithm

Now, in this section, we are going to discuss the Time and Space Complexity of the KMP algorithm.

1. Time Complexity of the KMP Algorithm

The Knuth-Morris-Pratt algorithm’s time complexity is very efficient compared to naive string matching. It consists of two main steps: building the LPS (Longest Prefix Suffix) array in O(m) and searching the pattern in O(n) time, where m is the length of the pattern and n is the length of the text. Hence, the overall time complexity of this algorithm is O(n + m). This makes it ideal for handling large datasets.

2. Space Complexity of the KMP Algorithm

The space complexity of the Knuth-Morris-Pratt algorithm is O(m). This is because it only requires extra memory to store the LPS array, where m is the length of the pattern. Other than that, it uses only a few constant variables. This makes it lightweight and does not consume a lot of space for pattern searching.

Advantages and Disadvantages of the KMP Algorithm

Now, let’s discuss the advantages and disadvantages of the Knuth-Morris-Pratt algorithm:

Advantages

1. This algorithm avoids rechecking characters. This helps to make the pattern searching process much faster.

2. It works efficiently even for long texts or patterns.

3. The time complexity of the KMP algorithm is O(n + m). This means that it grows steadily with the size of the input.

4. This algorithm uses the LPS array to skip any unnecessary checks during mismatches.

5. It is also used widely in real-world tasks like search engines, text editors, and DNA sequence matching.

Disadvantages

1. This algorithm makes the logic of building and using the LPS array hard for beginners to understand.

2. It requires additional space for you to store the LPS array. This slightly increases the memory usage.

3. For short patterns or texts, simpler algorithms might perform the same way with less effort.

4. The KMP algorithm works well for exact pattern matching and not for partial or fuzzy matches.

5. Writing this algorithm correctly needs more attention and understanding compared to basic string search methods. This is due to complex logic and the need to handle the LPS array properly.

Common Mistakes While Implementing KMP

Some common mistakes while implementing KMP are given below:

1. If you build the LPS array incorrectly, it makes the pattern search fail.

2. Mixing text and indices of patterns can result in infinite loops or missed matches.

3. Not handling empty strings or single-character patterns can break the KMP algorithm.

4. Many beginners nowadays confuse the LPS array with direct matching, but it only helps skip unnecessary comparisons.

5. Forgetting to reset index variables after each match can lead to incorrect or repeated outputs.

Best Practices for the KMP Algorithm

1. You should always build the LPS array correctly and carefully. This is because it decides how efficiently the matches are handled.

2. The KMP algorithm works best when there is a need to search the same pattern in large or multiple texts.

3. You should always look for empty strings or very short patterns to avoid unexpected errors during execution.

4. You should always try to keep the LPS array size just enough for your pattern so that you can save extra memory.

5. Always test the Knuth-Morris-Pratt algorithm with various examples to ensure it handles all kinds of inputs correctly.

Real-World Applications of the KMP Algorithm

1. The Knuth-Morris-Pratt algorithm allows you to quickly find a word or phrase in large documents.

2. It is also used to find specific gene patterns in long DNA sequences in an efficient manner.

3. It is also used to scan emails to detect spam keywords.

4. This algorithm also helps to compare documents to identify copied content quickly.

5. Web browsers use this algorithm to highlight words on a webpage.

Start Coding in Python for Free: No Experience Needed!

Begin writing real Python code through interactive, beginner-friendly modules completely for free.

Explore Program

Conclusion

The Knuth-Morris-Pratt algorithm is one of the most efficient ways to search for a pattern within a text by avoiding unnecessary comparisons. It is widely used in areas like text processing, DNA sequence analysis, and search engines because of its smart use of the LPS array. When you study any KMP algorithm example, you can clearly see how it saves time compared to simple brute-force methods. Overall, learning and understanding this algorithm helps you write faster and more optimized programs for pattern-matching tasks.

Upskill today by enrolling in our Python Course, and also prepare for your next interview with Python Interview Questions prepared by the industry experts.

What is the Knuth-Morris-Pratt (KMP) Algorithm? – FAQs