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[smlnj] View of /sml/branches/FLINT/src/comp-lib/scc.sml
 [smlnj] / sml / branches / FLINT / src / comp-lib / scc.sml

# View of /sml/branches/FLINT/src/comp-lib/scc.sml

Revision 113 - (download) (annotate)
Fri Jun 5 19:41:21 1998 UTC (21 years, 11 months ago) by monnier
File size: 3674 byte(s)
```110.7
```
```(* scc.sml
*
* COPYRIGHT (c) 1996 Bell Laboratories.
*
* Calculate strongly-connected components of directed graph.
* The graph can have nodes with self-loops.
*
* author: Matthias Blume
*
*)

signature SCCNODE = sig
type node
val eq: node * node -> bool
val lt: node * node -> bool
end

signature SCC = sig

structure Node: SCCNODE

datatype component =
SIMPLE of Node.node		(* singleton, no self-loop *)
| RECURSIVE of Node.node list

(* take root node and follow function and return
* list of topologically sorted strongly-connected components;
* root component goes first *)
val topOrder:
{ root: Node.node, follow: Node.node -> Node.node list } ->
component list
end

functor SCCUtilFun (structure Node: SCCNODE): SCC = struct

exception SccBug

structure Node = Node

structure NodeOrdSet = struct
type elem = Node.node
val (op <) = Node.lt
end

structure Map = MapF (NodeOrdSet)

type node = Node.node

datatype component =
SIMPLE of node
| RECURSIVE of node list

fun topOrder { root, follow } = let

fun getNode (n, nm as (npre, m)) =
(nm, (Map.lookup m n))
handle Map.MapF => let
val r = { pre = npre, low = ref npre }
val m' = Map.add (m, n, r)
in
((npre + 1, m'), r)
end

fun theNode x y = Node.eq (x, y)

fun component (x, []) =
if List.exists (theNode x) (follow x) then
RECURSIVE [x]
else
SIMPLE x
| component (x, xl) = RECURSIVE (x :: xl)

(* depth-first search in continuation-passing, state-passing style *)
fun dfs args = let

(* the nodemap represents the mapping from nodes to
* pre-order numbers and low-numbers. The latter are ref-cells.
* nodemap also remembers the next available pre-order number. *)
val { node, node_pre, node_low, parent_low, nodemap,
stack, sccl, cont } = args

(* loop over the follow-set of a node *)
fun loop [] (nodemap, stack, sccl) =
let
val nl = !node_low
in
if nl = node_pre then
let
fun grab (top :: stack, scc) =
if Node.eq (top, node) then
cont (nodemap, stack,
component (top, scc) :: sccl)
else
grab (stack, top :: scc)
| grab _ = raise SccBug
in
grab (stack, [])
end
else let
val _ =
(* propagate node_low up *)
if nl < (!parent_low) then parent_low := nl else ()
in
(* `return' *)
cont (nodemap, stack, sccl)
end
end
| loop (tn :: tnl) (nodemap as (npre, theMap), stack, sccl) = let
val { pre = tn_pre, low = tn_low } = Map.lookup theMap tn
(* the lookup succeeded -> we have seen tn before *)
val tl = !tn_low
in
if tl < (!node_low) andalso
List.exists (theNode tn) stack then
node_low := tl
else ();
loop tnl (nodemap, stack, sccl)
end handle Map.MapF => let
(* lookup failed -> tn is a new node *)
val tn_pre = npre
val tn_low = ref npre
val npre = npre + 1
val theMap = Map.add (theMap, tn,
{ pre = tn_pre, low = tn_low })
val nodemap = (npre, theMap)
in
dfs { node = tn, node_pre = tn_pre, node_low = tn_low,
parent_low = node_low,
nodemap = nodemap,
stack = tn :: stack,
sccl = sccl,
cont = loop tnl }
end
in
loop (follow node) (nodemap, stack, sccl)
end

val root_low = ref 0
in
dfs { node = root, node_pre = 0, node_low = root_low,
parent_low = ref 0,	(* dummy *)
nodemap = (1, Map.singleton (root, { pre = 0, low = root_low })),
stack = [root],
sccl = [],
cont = fn (_, _, sccl) => sccl }
end
end

(*
* \$Log\$
*)
```

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