Understanding KMP Algorithm, With Examples

Have you ever wondered how search engines find results that meet your query? It turns out, all that complicated information relies on a simple string-matching algorithm. Whether you’re creating a giant database or simply setting up a data comparison feature on your website, understanding KMP algorithm as one of the basic models can help.

However, the program comes with its own set of challenges. In this article, we break down how the KMP algorithm works and what makes it so useful. We’ve even included the code you need to make it work for your own needs. So let’s get working with this string-matching algorithm that will make word searching a breeze.

Understanding KMP Algorithm: An Overview

The KMP (Knuth-Morris-Pratt) algorithm is a string-matching algorithm developed by mathematicians Donald Knuth, Vaughan Pratt, and James Morris in 1977. It was designed to help find patterns within a text. By understanding the KMP algorithm, we drastically reduce the amount of time it takes to find words or groups, allowing us to analyze large blocks of data.

Essentially, the model uses a cheat sheet to determine what parts of a text it can skip. For example, if we want to find the word “computer” in an article, the algorithm will start to look for the letter “c.” The model skips over any words that don’t match, allowing it to check only the relevant ones instead of reading each one.

How Does the KMP Algorithm Work?

Understanding KMP algorithm can prove challenging, but breaks down into three steps: Preprocessing, Searching, and Highlighting.

In the preprocessing phase, the algorithm builds a partial match table (the cheat sheet we talked about earlier). This table tells the program how much of the pattern matches as it scans each word.

Next, the KMP algorithm begins searching for the requested term. It compares each letter to the partial match table. Each time the letter doesn’t match, the algorithm moves on.

Whenever a match is found, the model makes a note of it. This is where the KMP algorithm highlights the pattern, making it easy for the user to find their requested term. From there, the algorithm restarts its search.

Code for the KMP Algorithm

Because coding the KMP algorithm includes a delicate structure, we’ve included a basic model for you to include in your programming language of choice. 

LPS ← ComputeLPS(Pattern) {build LPS table function}
i ← 0
j ← 0
n ← string length
m ← pattern length
while i < n do
    if pattern[j] = string[i] then  {if the characters are a match}
        i ← i + 1
        j ← j + 1
      if j = m then  {j pointer has reached end of pattern}
        return i - j {index of the match}
            j ← LPS[j - 1]
              
    else if i 0
            j ← LPS[j - 1]
          else
            i ← i + 1
return -1 {no match}

It’s essential to know that this code only provides the basic formula for the KMP algorithm. If you need to specialize your program, you’ll have to know what that looks like.

Applications for the KMP Algorithm

One of the most common uses for the KMP algorithm is in text search and indexing. You’ll recognize this tool used in major search engines to find your requested term. Not only does this help you find keywords and phrases within documents, but on a larger scale, can help you find related articles in a sea of information.

Other applications of the KMP algorithm include:

• Bioinformatics
• Data comparison
• Speech recognition
• Image processing

However you plan on using this formula, know that proper use allows for incredibly speedy analysis. While the algorithm can prove challenging to write, the basics come down to preprocessing, searching, and highlighting. Enjoy your time understanding KMP Algorithm.