Final answer:
The Knuth-Morris-Pratt (KMP) pattern search algorithm increases string matching efficiency through a precomputed partial match table, allowing it to operate with O(n + m) time complexity by skipping unnecessary character comparisons.
Step-by-step explanation:
The logic behind the Knuth-Morris-Pratt (KMP) pattern search algorithm is to enhance the efficiency of string matching by using a precomputed 'partial match' table (also known as 'failure function' or 'pi table'). Instead of naively checking for a match at every step, KMP makes use of information from previous comparisons. The algorithm preprocesses the pattern to identify prefixes that are also suffixes, allowing the search to skip over these portions without re-checking, effectively avoiding unnecessary comparisons during the search process.
KMP's efficiency comes from its ability to bypass re-examination of characters that are already known to match or mismatch. As a result, the KMP algorithm operates in O(n + m) time complexity, where 'n' is the length of the text to be searched and 'm' is the length of the pattern. This is significantly more efficient than naive search algorithms, which operate in O(n*m).
Here's a simplified version of KMP pseudocode:
- Preprocess the pattern to create a partial match table.
- Iterate through the text using pointers for text and pattern positions.
- When mismatch occurs:
- If pattern pointer is at the start, move text pointer.
- Otherwise, use the partial match table to shift the pattern and adjust the pattern pointer.
- Continue until the end of text or pattern is found within the text.
The partial match table is what powers KMP's efficiency, informing how far to shift the pattern upon a mismatch, avoiding the reassessment of previously matched characters.