Knuth-Morris-Pratt Algorithm The Knuth-Morris-Pratt algorithm is a powerful and efficient technique for string matching, especially for long strings. It wor...
Knuth-Morris-Pratt Algorithm
The Knuth-Morris-Pratt algorithm is a powerful and efficient technique for string matching, especially for long strings. It works by using a hash function to create a compressed representation of the string. This representation allows the algorithm to efficiently search for occurrences of the string in a large database of strings.
How it works:
Hash Function: The algorithm starts by using a hash function, such as the MD5 hash function, to create a unique "hash value" for the string. This hash value represents the string's location in the compressed space.
Compression: The string is then compressed into a shorter "prefix" and a "suffix". The prefix is the part of the string that appears at the beginning, while the suffix is the part that appears at the end.
Matching: To find all occurrences of the string in a database of strings, the algorithm searches for the prefix in each string. If the prefix is found, the algorithm then searches for the suffix in the string at that position. This process is repeated for all positions in the string.
Time Complexity: The time complexity of the Knuth-Morris-Pratt algorithm is O(n), where n is the length of the string. This is because the algorithm iterates over the string once to create the hash value, and then iterates over the string again to find all occurrences of the string.
Example:
Suppose we have the following string:
abcxyz123abcxyz
The hash function would create the following hash value:
a5d3e6f4b8290c34a1234567890
The prefix would be "abcxyz", and the suffix would be "123abcxyz".
The algorithm would then search for the prefix in each string in the database and find all occurrences of the string