(* This module provides an implementation of Tarjan's algorithm for
finding the strongly connected components of a graph.
The algorithm runs when the functor is applied. Its complexity is
$O(V+E)$, where $V$ is the number of vertices in the graph $G$, and
$E$ is the number of edges. *)
module Run (G : sig
type node
(* We assume each node has a unique index. Indices must range from
$0$ to $n-1$, where $n$ is the number of nodes in the graph. *)
val n: int
val index: node -> int
(* Iterating over a node's immediate successors. *)
val successors: (node -> unit) -> node -> unit
(* Iterating over all nodes. *)
val iter: (node -> unit) -> unit
end) : sig
open G
(* This function maps each node to a representative element of its strongly connected component. *)
val representative: node -> node
(* This function maps each representative element to a list of all
members of its strongly connected component. Non-representative
elements are mapped to an empty list. *)
val scc: node -> node list
(* [iter action] allows iterating over all strongly connected
components. For each component, the [action] function is applied
to the representative element and to a (non-empty) list of all
elements. *)
val iter: (node -> node list -> unit) -> unit
end