CCGraph
A collections of algorithms on (mostly read-only) graph structures. The user provides her own graph structure as a ('v, 'e) CCGraph.t
, where 'v
is the type of vertices and 'e
the type of edges (for instance, 'e = ('v * 'v)
is perfectly fine in many cases).
Such a ('v, 'e) CCGraph.t
structure is a record containing three functions: two relate edges to their origin and destination, and one maps vertices to their outgoing edges. This abstract notion of graph makes it possible to run the algorithms on any user-specific type that happens to have a graph structure.
Many graph algorithms here take an iterator of vertices as input. The helper module Iter
contains basic functions for that, as does the iter
library on opam. If the user only has a single vertex (e.g., for a topological sort from a given vertex), they can use Iter.return x
to build a iter of one element.
status: unstable
type 'a iter_once = 'a iter
Iter that should be used only once
module Iter : sig ... end
This interface is designed for oriented graphs with labels on edges
type ('v, 'e) t = 'v -> ('e * 'v) iter
Directed graph with vertices of type 'v
and edges labeled with e'
type ('v, 'e) graph = ('v, 'e) t
Tags
Mutable tags from values of type 'v
to tags of type bool
type ('k, 'a) table = {
mem : 'k -> bool; | |
find : 'k -> 'a; | (**) |
add : 'k -> 'a -> unit; | (* Erases previous binding *) |
}
Table
Mutable table with keys 'k
and values 'a
type 'a set = ('a, unit) table
Mutable set
val mk_table : eq:('k -> 'k -> bool) -> ?hash:('k -> int) -> int -> ('k, 'a) table
Default implementation for Table: a Hashtbl
.t.
val mk_map : cmp:('k -> 'k -> int) -> unit -> ('k, 'a) table
Use a Map
.S underneath.
type 'a bag = {
push : 'a -> unit; | |
is_empty : unit -> bool; | |
pop : unit -> 'a; | (* raises some exception is empty *) |
}
Bag of elements of type 'a
val mk_queue : unit -> 'a bag
val mk_stack : unit -> 'a bag
val mk_heap : leq:('a -> 'a -> bool) -> 'a bag
mk_heap ~leq
makes a priority queue where leq x y = true
means that x
is smaller than y
and should be prioritary.
module Traverse : sig ... end
is_dag ~graph vs
returns true
if the subset of graph
reachable from vs
is acyclic.
val topo_sort : eq:('v -> 'v -> bool) -> ?rev:bool -> tbl:'v set -> graph:('v, 'e) t ->
'v iter -> 'v list
topo_sort ~graph seq
returns a list of vertices l
where each element of l
is reachable from seq
. The list is sorted in a way such that if v -> v'
in the graph, then v
comes before v'
in the list (i.e. has a smaller index). Basically v -> v'
means that v
is smaller than v'
. See wikipedia.
val topo_sort_tag : eq:('v -> 'v -> bool) -> ?rev:bool -> tags:'v tag_set -> graph:('v, 'e) t ->
'v iter -> 'v list
Same as topo_sort
but uses an explicit tag set.
module Lazy_tree : sig ... end
val spanning_tree : tbl:'v set -> graph:('v, 'e) t -> 'v -> ('v, 'e) Lazy_tree.t
spanning_tree ~graph v
computes a lazy spanning tree that has v
as a root. The table tbl
is used for the memoization part.
val spanning_tree_tag : tags:'v tag_set -> graph:('v, 'e) t -> 'v -> ('v, 'e) Lazy_tree.t
Hidden state for scc
.
Strongly connected components reachable from the given vertices. Each component is a list of vertices that are all mutually reachable in the graph. The components are explored in a topological order (if C1 and C2 are components, and C1 points to C2, then C2 will be yielded before C1). Uses Tarjan's algorithm.
Example (print divisors from 42
):
let open CCGraph in
let open Dot in
with_out "/tmp/truc.dot"
(fun out ->
pp ~attrs_v:(fun i -> [`Label (string_of_int i)]) ~graph:divisors_graph out 42
)
module Dot : sig ... end
type ('v, 'e) mut_graph = {
graph : ('v, 'e) t; |
add_edge : 'v -> 'e -> 'v -> unit; |
remove : 'v -> unit; |
}
val mk_mut_tbl : eq:('v -> 'v -> bool) -> ?hash:('v -> int) -> int -> ('v, 'a) mut_graph
Make a new mutable graph from a Hashtbl. Edges are labelled with type 'a
.
A classic implementation of a graph structure on totally ordered vertices, with unlabelled edges. The graph allows to add and remove edges and vertices, and to iterate on edges and vertices.
module type MAP = sig ... end
val of_list : eq:('v -> 'v -> bool) -> ('v * 'v) list -> ('v, unit) t
of_list l
makes a graph from a list of pairs of vertices. Each pair (a,b)
is an edge from a
to b
.
val of_hashtbl : ('v, 'v list) Stdlib.Hashtbl.t -> ('v, unit) t
of_hashtbl tbl
makes a graph from a hashtable that maps vertices to lists of children.
val of_fun : ('v -> 'v list) -> ('v, unit) t
of_fun f
makes a graph out of a function that maps a vertex to the list of its children. The function is assumed to be deterministic.
val divisors_graph : (int, unit) t
n
points to all its strict divisors.