\begin{code}
module Digraph(
- -- At present the only one with a "nice" external interface
- stronglyConnComp, stronglyConnCompR, SCC(..), flattenSCC, flattenSCCs,
-
- Graph, Vertex,
- graphFromEdges, graphFromEdges',
- buildG, transposeG, reverseE, outdegree, indegree,
-
- Tree(..), Forest,
- showTree, showForest,
-
- dfs, dff,
- topSort,
- components,
- scc,
- back, cross, forward,
- reachable, path,
- bcc
-
+ -- At present the only one with a "nice" external interface
+ stronglyConnComp, stronglyConnCompR, SCC(..), flattenSCC, flattenSCCs,
+
+ Graph, Vertex,
+ graphFromEdges, graphFromEdges',
+ buildG, transposeG, reverseE, outdegree, indegree,
+
+ Tree(..), Forest,
+ showTree, showForest,
+
+ dfs, dff,
+ topSort,
+ components,
+ scc,
+ back, cross, forward,
+ reachable, path,
+ bcc
) where
# include "HsVersions.h"
------------------------------------------------------------------------------
-- A version of the graph algorithms described in:
---
+--
-- ``Lazy Depth-First Search and Linear Graph Algorithms in Haskell''
-- by David King and John Launchbury
---
+--
-- Also included is some additional code for printing tree structures ...
------------------------------------------------------------------------------
-import Util ( sortLe )
+import Util ( sortLe )
import Outputable
-- Extensions
%************************************************************************
-%* *
-%* External interface
-%* *
+%* *
+%* External interface
+%* *
%************************************************************************
\begin{code}
data SCC vertex = AcyclicSCC vertex
- | CyclicSCC [vertex]
+ | CyclicSCC [vertex]
flattenSCCs :: [SCC a] -> [a]
flattenSCCs = concatMap flattenSCC
\begin{code}
stronglyConnComp
- :: Ord key
- => [(node, key, [key])] -- The graph; its ok for the
- -- out-list to contain keys which arent
- -- a vertex key, they are ignored
- -> [SCC node] -- Returned in topologically sorted order
- -- Later components depend on earlier ones, but not vice versa
+ :: Ord key
+ => [(node, key, [key])] -- The graph; its ok for the
+ -- out-list to contain keys which arent
+ -- a vertex key, they are ignored
+ -> [SCC node] -- Returned in topologically sorted order
+ -- Later components depend on earlier ones, but not vice versa
stronglyConnComp edges
= map get_node (stronglyConnCompR edges)
-- The "R" interface is used when you expect to apply SCC to
-- the (some of) the result of SCC, so you dont want to lose the dependency info
stronglyConnCompR
- :: Ord key
- => [(node, key, [key])] -- The graph; its ok for the
- -- out-list to contain keys which arent
- -- a vertex key, they are ignored
- -> [SCC (node, key, [key])] -- Topologically sorted
+ :: Ord key
+ => [(node, key, [key])] -- The graph; its ok for the
+ -- out-list to contain keys which arent
+ -- a vertex key, they are ignored
+ -> [SCC (node, key, [key])] -- Topologically sorted
stronglyConnCompR [] = [] -- added to avoid creating empty array in graphFromEdges -- SOF
stronglyConnCompR edges
= map decode forest
where
(graph, vertex_fn) = _scc_ "graphFromEdges" graphFromEdges edges
- forest = _scc_ "Digraph.scc" scc graph
+ forest = _scc_ "Digraph.scc" scc graph
decode (Node v []) | mentions_itself v = CyclicSCC [vertex_fn v]
- | otherwise = AcyclicSCC (vertex_fn v)
+ | otherwise = AcyclicSCC (vertex_fn v)
decode other = CyclicSCC (dec other [])
- where
- dec (Node v ts) vs = vertex_fn v : foldr dec vs ts
+ where
+ dec (Node v ts) vs = vertex_fn v : foldr dec vs ts
mentions_itself v = v `elem` (graph ! v)
\end{code}
%************************************************************************
-%* *
-%* Graphs
-%* *
+%* *
+%* Graphs
+%* *
%************************************************************************
edges g = [ (v, w) | v <- vertices g, w <- g!v ]
mapT :: (Vertex -> a -> b) -> Table a -> Table b
-mapT f t = array (bounds t) [ (,) v (f v (t!v)) | v <- indices t ]
+mapT f t = array (bounds t) [ (v, f v (t ! v)) | v <- indices t ]
buildG :: Bounds -> [Edge] -> Graph
buildG bounds edges = accumArray (flip (:)) [] bounds edges
\begin{code}
-graphFromEdges
- :: Ord key
- => [(node, key, [key])]
- -> (Graph, Vertex -> (node, key, [key]))
-graphFromEdges edges =
- case graphFromEdges' edges of (graph, vertex_fn, _) -> (graph, vertex_fn)
+graphFromEdges
+ :: Ord key
+ => [(node, key, [key])]
+ -> (Graph, Vertex -> (node, key, [key]))
+graphFromEdges edges =
+ case graphFromEdges' edges of (graph, vertex_fn, _) -> (graph, vertex_fn)
graphFromEdges'
- :: Ord key
- => [(node, key, [key])]
- -> (Graph, Vertex -> (node, key, [key]), key -> Maybe Vertex)
+ :: Ord key
+ => [(node, key, [key])]
+ -> (Graph, Vertex -> (node, key, [key]), key -> Maybe Vertex)
graphFromEdges' edges
= (graph, \v -> vertex_map ! v, key_vertex)
where
- max_v = length edges - 1
+ max_v = length edges - 1
bounds = (0,max_v) :: (Vertex, Vertex)
sorted_edges = let
- (_,k1,_) `le` (_,k2,_) = case k1 `compare` k2 of { GT -> False; other -> True }
- in
- sortLe le edges
- edges1 = zipWith (,) [0..] sorted_edges
+ (_,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
+ 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
-- key_vertex :: key -> Maybe Vertex
- -- returns Nothing for non-interesting vertices
- key_vertex k = find 0 max_v
- where
- find a b | a > b
- = Nothing
- find a b = case compare k (key_map ! mid) of
- LT -> find a (mid-1)
- EQ -> Just mid
- GT -> find (mid+1) b
- where
- mid = (a + b) `div` 2
+ -- returns Nothing for non-interesting vertices
+ key_vertex k = find 0 max_v
+ where
+ find a b | a > b
+ = Nothing
+ find a b = case compare k (key_map ! mid) of
+ LT -> find a (mid-1)
+ EQ -> Just mid
+ GT -> find (mid+1) b
+ where
+ mid = (a + b) `div` 2
\end{code}
%************************************************************************
-%* *
-%* Trees and forests
-%* *
+%* *
+%* Trees and forests
+%* *
%************************************************************************
\begin{code}
%************************************************************************
-%* *
-%* Depth first search
-%* *
+%* *
+%* Depth first search
+%* *
%************************************************************************
\begin{code}
%************************************************************************
-%* *
-%* Algorithms
-%* *
+%* *
+%* Algorithms
+%* *
%************************************************************************
------------------------------------------------------------
projects / ghc-hetmet.git / commitdiff