String matching algorithm design

Question

Given a text t[1...n] and k pattern p1,p2,...pk each of length m, n=2m, from alphabet [0, Sigma-1]. Design an efficient algorithm to find all locations i in t where any of the patterns pj's match.

So I have a string t = "1 2 3 4 5 2 2 9" and the pattern p = "4 5 2 2". I know there will be m+1 locations I can find a pattern (either from "1 2 3 4", "2 3 4 5", etc...).

Then we have k characters in the pattern so the bigO comes outs to be O(k(m+1)).

My algorithm would be to search through the string checking each character with the characters in the pattern. That will run me k iterations for m+1 locations.

Hopefully, I'm explaining it correctly. I just want to know if I'm doing it right and if there are any flaws in my logic. Thank you!

Answer 1

My algorithm would be to search through the string checking each character with the characters in the pattern. That will run me k iterations for m+1 locations.

That means for each pattern, you can do it O(m+1), right?

Although there are algorithms that can achieve this performance, your brute force one isn't. You have m+1 locations, and for each location you need to check m characters, so the total complexity for each pattern is O(m(m+1)).