I am thinking about an effient algorithm for wildcard searching with * representing any characters with any length.

aa*c, she*he, *she*he

When I am supposed to return say the beginning index of the first matching instance.

Say the pattern is of length M and the document is of length N, and the pattern has K '*' signs. I can think of a solution that first uses AC Automation to find all occurences of each chunk in O(N + M), with bitmask.

While converting the bitmask to indexes takes O(N * K)

Then binary search for the last possible beginning positions for each chunk. This could take O (K log N)

So the overall time complexity is still O (N * K), any way to do better?