# Implementing String Searching Algorithms

String searching algorithms are essential for finding occurrences of a pattern within a larger string. In this article, we will explore three commonly used algorithms: brute force, Knuth-Morris-Pratt, and Boyer-Moore.

## Brute Force Algorithm

The brute force algorithm, also known as the naive algorithm, is the simplest string searching method. It involves comparing the pattern to be found with all possible substrings of the input string.

The algorithm scans the input string character by character and checks if the pattern matches at each position. If a mismatch occurs, the algorithm moves to the next character in the input string and restarts the comparison. This process continues until a match is found or all positions have been checked.

Although the brute force algorithm is straightforward to implement, it has a time complexity of O(n * m), where n is the length of the input string and m is the length of the pattern. This makes it inefficient for large inputs.

## Knuth-Morris-Pratt Algorithm

The Knuth-Morris-Pratt (KMP) algorithm improves on the brute force algorithm by using information from previous comparisons to avoid unnecessary character comparisons.

The algorithm constructs a prefix table that stores the length of the longest proper prefix of the pattern that is also a suffix. This information allows the algorithm to skip characters that are guaranteed to match during the comparison process.

The KMP algorithm has a time complexity of O(n + m), where n is the length of the input string and m is the length of the pattern. This makes it more efficient than the brute force algorithm.

## Boyer-Moore Algorithm

The Boyer-Moore algorithm is another string searching algorithm that works by scanning the pattern from right to left. It utilizes two heuristic rules: the bad character rule and the good suffix rule.

The bad character rule allows the algorithm to skip comparisons by calculating the number of positions the pattern can be shifted based on the rightmost mismatched character in the input string.

The good suffix rule uses information about suffixes of the pattern to determine the next shift amount. It checks for matching suffixes and attempts to align them with suffixes of the input string.

The Boyer-Moore algorithm has a time complexity of O(n + m), making it efficient for most cases. However, in rare worst-case scenarios, it can have a time complexity of O(n * m).

## Conclusion

String searching algorithms play a crucial role in various applications where finding patterns within text is required. The brute force, Knuth-Morris-Pratt, and Boyer-Moore algorithms are three commonly used techniques, each with its own advantages and trade-offs.

While the brute force algorithm is simple to implement, it becomes inefficient for large inputs. The Knuth-Morris-Pratt algorithm improves on the brute force approach by using a prefix table to skip unnecessary comparisons. The Boyer-Moore algorithm further enhances the efficiency by utilizing heuristic rules.

Choosing the appropriate string searching algorithm depends on the specific requirements and characteristics of the problem at hand. Understanding the strengths and weaknesses of each algorithm is crucial for efficient pattern matching.