The KMP algorithm efficiently finds a pattern in a text by preprocessing the pattern into a partial match table. You can implement it in TypeScript using a failure function.

The Knuth-Morris-Pratt (KMP) algorithm is a pattern-matching algorithm that improves the efficiency of finding a pattern within a text by avoiding unnecessary rechecks of characters. KMP preprocesses the pattern into a partial match table (also known as the failure function), which helps determine the next positions to check in case of a mismatch. This preprocessing ensures that when a mismatch occurs, you can skip several comparisons, reducing the overall time complexity to O(n), where n is the length of the text. In TypeScript, you can implement the KMP algorithm by first constructing the partial match table for the pattern, then using it to search for the pattern in the text. The partial match table indicates the longest proper prefix of the pattern that is also a suffix, allowing the algorithm to 'jump' to the appropriate position after a mismatch. The KMP algorithm is widely used in text search utilities, DNA sequence analysis, and search engines. By implementing KMP in TypeScript, you can efficiently solve string-matching problems in a variety of applications, ensuring optimal performance when handling large datasets or repeated searches.