+%
+% (c) The University of Glasgow 2006
+%
+
\begin{code}
-module Digraph(
+{-# OPTIONS -w #-}
+-- The above warning supression flag is a temporary kludge.
+-- While working on this module you are encouraged to remove it and fix
+-- any warnings in the module. See
+-- http://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#Warnings
+-- for details
- -- At present the only one with a "nice" external interface
- stronglyConnComp, stronglyConnCompR, SCC(..), flattenSCC, flattenSCCs,
+module Digraph(
- Graph, Vertex,
- graphFromEdges, graphFromEdges',
- buildG, transposeG, reverseE, outdegree, indegree,
+ -- At present the only one with a "nice" external interface
+ stronglyConnComp, stronglyConnCompR, SCC(..), flattenSCC, flattenSCCs,
- Tree(..), Forest,
- showTree, showForest,
+ Graph, Vertex,
+ graphFromEdges, graphFromEdges',
+ buildG, transposeG, reverseE, outdegree, indegree,
- dfs, dff,
- topSort,
- components,
- scc,
- back, cross, forward,
- reachable, path,
- bcc
+ 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
-import MONAD_ST
+import Control.Monad.ST
-- std interfaces
-import Maybe
-import Array
-import List
-import Outputable
+import Data.Maybe
+import Data.Array
+import Data.List
#if __GLASGOW_HASKELL__ > 604
import Data.Array.ST
-#elif __GLASGOW_HASKELL__ >= 504
-import Data.Array.ST hiding ( indices, bounds )
#else
-import ST
+import Data.Array.ST hiding ( indices, bounds )
#endif
\end{code}
%************************************************************************
-%* *
-%* 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
+ (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)
+ | 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}
-#if __GLASGOW_HASKELL__ >= 504
-newSTArray :: Ix i => (i,i) -> e -> ST s (STArray s i e)
-newSTArray = newArray
-
-readSTArray :: Ix i => STArray s i e -> i -> ST s e
-readSTArray = readArray
-
-writeSTArray :: Ix i => STArray s i e -> i -> e -> ST s ()
-writeSTArray = writeArray
-#endif
-
type Set s = STArray s Vertex Bool
mkEmpty :: Bounds -> ST s (Set s)
-mkEmpty bnds = newSTArray bnds False
+mkEmpty bnds = newArray bnds False
contains :: Set s -> Vertex -> ST s Bool
-contains m v = readSTArray m v
+contains m v = readArray m v
include :: Set s -> Vertex -> ST s ()
-include m v = writeSTArray m v True
+include m v = writeArray m v True
\end{code}
\begin{code}
%************************************************************************
-%* *
-%* Algorithms
-%* *
+%* *
+%* Algorithms
+%* *
%************************************************************************
------------------------------------------------------------
------------------------------------------------------------
\begin{code}
---postorder :: Tree a -> [a]
-postorder (Node a ts) = postorderF ts ++ [a]
+postorder :: Tree a -> [a] -> [a]
+postorder (Node a ts) = postorderF ts . (a :)
-postorderF :: Forest a -> [a]
-postorderF ts = concat (map postorder ts)
+postorderF :: Forest a -> [a] -> [a]
+postorderF ts = foldr (.) id $ map postorder ts
-postOrd :: Graph -> [Vertex]
-postOrd = postorderF . dff
+postOrd :: Graph -> [Vertex]
+postOrd g = postorderF (dff g) []
-topSort :: Graph -> [Vertex]
-topSort = reverse . postOrd
+topSort :: Graph -> [Vertex]
+topSort = reverse . postOrd
\end{code}
projects / ghc-hetmet.git / blobdiff