------------------------------------------------------------------------------
-#define ARR_ELT (COMMA)
-
-import Util ( sortLt )
+import Util ( sortLe )
-- Extensions
import MONAD_ST
=> [(node, key, [key])] -- The graph; its ok for the
-- out-list to contain keys which arent
-- a vertex key, they are ignored
- -> [SCC node]
+ -> [SCC node] -- Returned in topologically sorted order
+ -- Later components depend on earlier ones, but not vice versa
stronglyConnComp edges
= map get_node (stronglyConnCompR edges)
stronglyConnCompR edges
= map decode forest
where
- (graph, vertex_fn) = graphFromEdges edges
- forest = scc graph
+ (graph, vertex_fn) = _scc_ "graphFromEdges" graphFromEdges edges
+ forest = _scc_ "Digraph.scc" scc graph
decode (Node v []) | mentions_itself v = CyclicSCC [vertex_fn v]
| otherwise = AcyclicSCC (vertex_fn v)
decode other = CyclicSCC (dec other [])
where
max_v = length edges - 1
bounds = (0,max_v) :: (Vertex, Vertex)
- sorted_edges = sortLt lt edges
+ sorted_edges = let
+ (_,k1,_) `le` (_,k2,_) = case k1 `compare` k2 of { GT -> False; other -> True }
+ in
+ sortLe le edges
edges1 = zipWith (,) [0..] sorted_edges
graph = array bounds [(,) v (mapMaybe key_vertex ks) | (,) v (_, _, ks) <- edges1]
key_map = array bounds [(,) v k | (,) v (_, k, _ ) <- edges1]
vertex_map = array bounds edges1
- (_,k1,_) `lt` (_,k2,_) = case k1 `compare` k2 of { LT -> True; other -> False }
-- key_vertex :: key -> Maybe Vertex
-- returns Nothing for non-interesting vertices
preorderF :: Forest a -> [a]
preorderF ts = concat (map preorder ts)
-preOrd :: Graph -> [Vertex]
-preOrd = preorderF . dff
-
tabulate :: Bounds -> [Vertex] -> Table Int
tabulate bnds vs = array bnds (zipWith (,) vs [1..])
------------------------------------------------------------
\begin{code}
-tree :: Bounds -> Forest Vertex -> Graph
-tree bnds ts = buildG bnds (concat (map flat ts))
- where
- flat (Node v rs) = [ (v, w) | Node w us <- ts ] ++
- concat (map flat ts)
-
back :: Graph -> Table Int -> Graph
back g post = mapT select g
where select v ws = [ w | w <- ws, post!v < post!w ]