String matching algorithm

 

String Matching Algorithms: A Friendly Guide

String matching is the backbone of search engines, plagiarism checkers, and even DNA sequencing. The goal? Find a pattern (substring) within a text (larger string). 

Here’s a breakdown of key algorithms, from brute force to genius-level optimizations.

1. Brute-Force (Naive) Algorithm

How it works:

  • Slide the pattern over the text one character at a time.

  • At each position, check if the pattern matches the current text window.

Example:
Text: "AABAACAADAABAABA"
Pattern: "AABA"

  • Checks AABA at position 0 (match!), then shifts right by 1.

Time Complexity:

  • Worst case: O(n×m) (if no matches exist).

Pros:

  • Simple to implement.
    Cons:

  • Slow for large texts.

2. Rabin-Karp Algorithm

How it works:

  • Uses hashing to compare the pattern with text windows.

  • Computes hash values for the pattern and each text window.

  • Only checks character-by-character if hashes match (to avoid false positives).

Example:
Text: "GEEKSFORGEEKS"
Pattern: "GEEK"

  • Hash("GEEK") = some value.

  • Compare hash with every 4-letter window in the text.

Time Complexity:

  • Average case: O(n + m).

  • Worst case: O(n×m) (if all hashes collide).

Pros:

  • Efficient for multiple pattern searches (like plagiarism checks).
    Cons:

  • Hash collisions can slow it down.

3. Knuth-Morris-Pratt (KMP) Algorithm

How it works:

  • Preprocesses the pattern to create a prefix table (LPS array).

  • Uses this table to skip unnecessary comparisons.

Key Idea:

  • If a mismatch occurs, KMP knows how much to shift the pattern without rechecking.

Example:
Text: "ABABDABACDABABCABAB"
Pattern: "ABABCABAB"

  • LPS table helps skip redundant checks.

Time Complexity:

  • O(n + m) (linear time!).

Pros:

  • No backtracking in text.

  • Great for long patterns.
    Cons:

  • Slightly complex to implement.

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