问题
I am reading about the KMP substring search algorithm and the examples I find online use an one-dimensional table to build the prefix information table.
I also read the Sedgewick explanation and he used a 2-D array to build the table and explicitly states that the space complexity of KMP is O(RM) where R is the alphabet size and M the pattern size while everywhere else it is stated that the space complexity is just O(M + N) i.e. the text to process and the pattern size itself.
So I am confused on the difference. Are there multiple KMP algorithmic approaches? And do they have different scope? Or what am I missing?
Why is the 2D needed if 1D can solve the substring problem too?
回答1:
I guess Sedgewick wanted to demonstrate a variant of KMP that constructs a deterministic finite automaton in the standard sense of that term. It's a weird choice that (as you observe) bloats the running time, but maybe there was a compelling pedagogical reason that I don't appreciate (then again my PhD was on algorithms, so...). I'd find another description that follows the original more closely.
来源：https://stackoverflow.com/questions/63383650/are-there-multiple-kmp-algorithmic-approaches-with-different-space-complexities