使用Ukkonen算法的时间复杂度，Knuth–Morris–Pratt（KMP）和后缀树之间的差异。

Question

Is it possible to find Longest Common Substring, Longest Palindromic Substring, Longest Repeated Substring, Searching All Patterns and Substring Check by both KMP and suffix tree using Ukkonen's algorithm? If yes then which one should I use since both algorithms have a linear-time complexity?

Answer 1

For finding the longest common substring, I would use Kadane's algorithm which has linear complexity. For the longest Palindromic Substring, the choice would be Manacher's algorithm which also has linear complexity. For repeated string and searching all patterns, yes the choice would boil down between KMP and Boyer-Moore. As to which one, Boyer-Moore's matches the last character of the pattern instead of the first one with the assumption that if there's not match at the end no need to try to match at the beginning. KMP searches for occurrences of a word W within a main text string S by employing the observation that when a mismatch occurs, thus bypassing re-examination of previously matched characters. This makes KMP slightly better optimized for small sets like ACTGT.