KMP Algorithm for Longest Prefix Suffix problem
The Longest Prefix Suffix (LPS) problem is central to the Knuth-Morris-Pratt (KMP) algorithm for pattern matching. Here's a detailed explanation: Problem: Longest Prefix Suffix (LPS) For a given string s , the LPS array (or prefix table) at position i stores the length of the longest prefix of s[0:i] that is also a suffix of s[0:i] , excluding the entire string itself. Example For the string s = "abab" , the LPS array is [0, 0, 1, 2] : LPS[0] = 0 because "a" has no prefix that is also a suffix. LPS[1] = 0 because "ab" has no prefix that matches a suffix. LPS[2] = 1 because "a" is the longest prefix of "aba" that is also a suffix. LPS[3] = 2 because "ab" is the longest prefix of "abab" that is also a suffix. Importance in the KMP Algorithm The KMP algorithm uses the LPS array to avoid redundant comparisons when a mismatch occurs during pattern matching. Specifically: If a mismatch occurs after j matches...