Fastest way to check if prefix of small string is substring of big string Let's say we have given 2 strings $A, B$, and let's suppose that the size of $A$ is pretty small (100 characters) and the size of $B$ is pretty big (1 million).

We define prefix of string $S$ as string $Y$ that contains the first $x$ letters (size of prefix always is less than or equal to size of whole string).

And the problem is to check for all prefixes of $A$, they are not too many if they are substrings of string $B$.

It is pretty slow if for each prefix we are traversing the whole string, is it possible to do something faster, maybe using string hasing?
Why would you need to traverse the big string for each prefix? Let's say A = "Some short string". So you traverse string B, looking for the letter "S". If not found, then no prefix of A is contained in B. If found, you found the prefix "S", and start at that point searching for "So". And so on.