NFA complexity of worst case is O(N*M) or O(N*M^2)?

Question

N is the length of string
M is the length of Regular expression.

In the worst case, a digraph G(V,E) may have |V|^2 edges

since DFS complexity is O(|V|+|E|), here will be O(|V|^2)

So in worst case, the the NFA complexity should be O(N*M^2)?

Am I understanding correct?

Thanks.

Answer 1

在NFA的Algorithms 4th结构中，边的数量最多为3M，因此得到的是O（NM）而不是O（NM ^ 2）。