What Is KMP in Data Structure?

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Scott Campbell

What Is KMP in Data Structure?

The Knuth-Morris-Pratt (KMP) algorithm is a string searching algorithm that efficiently finds occurrences of a pattern within a larger text. It was developed by Donald Knuth, Vaughan Pratt, and James Morris in 1977.

Understanding the Problem

When dealing with string searching problems, we often encounter situations where we need to find occurrences of a smaller sequence of characters (known as the pattern) within a larger sequence (known as the text). Traditional string searching algorithms like the Naive algorithm have a time complexity of O(n*m), where n is the length of the text and m is the length of the pattern.

The KMP algorithm improves upon this by taking advantage of certain properties of patterns to reduce time complexity. It achieves this by using preprocessed information about previous matches to determine where to resume searching after a mismatch occurs.

Key Concepts

To understand how the KMP algorithm works, we need to familiarize ourselves with two important concepts:

  • Prefix Function: The prefix function for a string is a mapping that takes each position in the string and returns the length of the longest proper prefix that is also a suffix ending at that position.
  • Failure Function: The failure function for a pattern is similar to the prefix function, but it uses information from previously matched characters to determine where to resume searching after a mismatch.

The KMP Algorithm Steps

The KMP algorithm can be summarized in the following steps:

  1. Preprocessing:
    • Create and populate the failure function for the pattern.
  2. Searching:
    • Initialize two pointers, one for the text and one for the pattern.
    • While the text pointer is within bounds:
      • If the characters at the current positions match, move both pointers forward.
      • If the pattern pointer reaches the end, a match is found. Record the position and continue searching.
      • If there is a mismatch, use information from the failure function to determine where to resume searching in the pattern.

Benefits of KMP Algorithm

The KMP algorithm has several advantages over traditional string searching algorithms:

  • Time Complexity: The time complexity of the KMP algorithm is O(n+m), where n is the length of the text and m is the length of the pattern. This makes it more efficient than traditional algorithms for large inputs.
  • Preprocessing Overhead: The preprocessing step of creating the failure function has a time complexity of O(m), but it only needs to be done once for each pattern.

    Subsequent searches with different texts can reuse this information, resulting in better overall performance.

  • Efficient Backtracking: The use of the failure function allows for efficient backtracking after a mismatch occurs. This reduces unnecessary comparisons and improves search speed.

Conclusion

The Knuth-Morris-Pratt algorithm is a powerful string searching algorithm that efficiently finds occurrences of a pattern within a larger text. By utilizing preprocessed information about previous matches, it reduces time complexity and improves overall performance. Understanding its key concepts and steps can greatly enhance your ability to solve string searching problems effectively.

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