Commit c439af5f authored by Edward Z. Yang's avatar Edward Z. Yang
Browse files

Refactor Digraph to use Data.Graph when possible



Summary: This just rewrites the IntGraph data type.
Signed-off-by: default avatarEdward Z. Yang <ezyang@cs.stanford.edu>

Test Plan: validate

Reviewers: austin

Subscribers: thomie

Differential Revision: https://phabricator.haskell.org/D708
parent 2aef3205
......@@ -17,13 +17,6 @@ module Digraph(
-- For backwards compatability with the simpler version of Digraph
stronglyConnCompFromEdgedVertices, stronglyConnCompFromEdgedVerticesR,
-- No friendly interface yet, not used but exported to avoid warnings
tabulate, preArr,
components, undirected,
back, cross, forward,
path,
bcc, do_label, bicomps, collect
) where
#include "HsVersions.h"
......@@ -35,6 +28,11 @@ module Digraph(
-- by David King and John Launchbury
--
-- Also included is some additional code for printing tree structures ...
--
-- If you ever find yourself in need of algorithms for classifying edges,
-- or finding connected/biconnected components, consult the history; Sigbjorn
-- Finne contributed some implementations in 1997, although we've since
-- removed them since they were not used anywhere in GHC.
------------------------------------------------------------------------------
......@@ -56,6 +54,10 @@ import Data.Array.ST
import qualified Data.Map as Map
import qualified Data.Set as Set
import qualified Data.Graph as G
import Data.Graph hiding (Graph, Edge, transposeG, reachable)
import Data.Tree
{-
************************************************************************
* *
......@@ -206,32 +208,6 @@ findCycle graph
new_work :: [key] -> [payload] -> [WorkItem key payload]
new_work deps path = [ (n, path) | Just n <- map (`Map.lookup` env) deps ]
{-
************************************************************************
* *
* SCC
* *
************************************************************************
-}
data SCC vertex = AcyclicSCC vertex
| CyclicSCC [vertex]
instance Functor SCC where
fmap f (AcyclicSCC v) = AcyclicSCC (f v)
fmap f (CyclicSCC vs) = CyclicSCC (fmap f vs)
flattenSCCs :: [SCC a] -> [a]
flattenSCCs = concatMap flattenSCC
flattenSCC :: SCC a -> [a]
flattenSCC (AcyclicSCC v) = [v]
flattenSCC (CyclicSCC vs) = vs
instance Outputable a => Outputable (SCC a) where
ppr (AcyclicSCC v) = text "NONREC" $$ (nest 3 (ppr v))
ppr (CyclicSCC vs) = text "REC" $$ (nest 3 (vcat (map ppr vs)))
{-
************************************************************************
* *
......@@ -290,7 +266,7 @@ topologicalSortG graph = map (gr_vertex_to_node graph) result
dfsTopSortG :: Graph node -> [[node]]
dfsTopSortG graph =
map (map (gr_vertex_to_node graph) . flattenTree) $ dfs g (topSort g)
map (map (gr_vertex_to_node graph) . flatten) $ dfs g (topSort g)
where
g = gr_int_graph graph
......@@ -316,7 +292,9 @@ edgesG graph = map (\(v1, v2) -> Edge (v2n v1) (v2n v2)) $ edges (gr_int_graph g
where v2n = gr_vertex_to_node graph
transposeG :: Graph node -> Graph node
transposeG graph = Graph (transpose (gr_int_graph graph)) (gr_vertex_to_node graph) (gr_node_to_vertex graph)
transposeG graph = Graph (G.transposeG (gr_int_graph graph))
(gr_vertex_to_node graph)
(gr_node_to_vertex graph)
outdegreeG :: Graph node -> node -> Maybe Int
outdegreeG = degreeG outdegree
......@@ -324,7 +302,7 @@ outdegreeG = degreeG outdegree
indegreeG :: Graph node -> node -> Maybe Int
indegreeG = degreeG indegree
degreeG :: (IntGraph -> Table Int) -> Graph node -> node -> Maybe Int
degreeG :: (G.Graph -> Table Int) -> Graph node -> node -> Maybe Int
degreeG degree graph node = let table = degree (gr_int_graph graph)
in fmap ((!) table) $ gr_node_to_vertex graph node
......@@ -336,7 +314,8 @@ emptyG :: Graph node -> Bool
emptyG g = graphEmpty (gr_int_graph g)
componentsG :: Graph node -> [[node]]
componentsG graph = map (map (gr_vertex_to_node graph) . flattenTree) $ components (gr_int_graph graph)
componentsG graph = map (map (gr_vertex_to_node graph) . flatten)
$ components (gr_int_graph graph)
{-
************************************************************************
......@@ -355,261 +334,43 @@ instance Outputable node => Outputable (Graph node) where
instance Outputable node => Outputable (Edge node) where
ppr (Edge from to) = ppr from <+> text "->" <+> ppr to
{-
************************************************************************
* *
* IntGraphs
* *
************************************************************************
-}
type Vertex = Int
type Table a = Array Vertex a
type IntGraph = Table [Vertex]
type Bounds = (Vertex, Vertex)
type IntEdge = (Vertex, Vertex)
vertices :: IntGraph -> [Vertex]
vertices = indices
edges :: IntGraph -> [IntEdge]
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 ]
buildG :: Bounds -> [IntEdge] -> IntGraph
buildG bounds edges = accumArray (flip (:)) [] bounds edges
transpose :: IntGraph -> IntGraph
transpose g = buildG (bounds g) (reverseE g)
reverseE :: IntGraph -> [IntEdge]
reverseE g = [ (w, v) | (v, w) <- edges g ]
outdegree :: IntGraph -> Table Int
outdegree = mapT numEdges
where numEdges _ ws = length ws
indegree :: IntGraph -> Table Int
indegree = outdegree . transpose
graphEmpty :: IntGraph -> Bool
graphEmpty :: G.Graph -> Bool
graphEmpty g = lo > hi
where (lo, hi) = bounds g
{-
************************************************************************
* *
* Trees and forests
* IntGraphs
* *
************************************************************************
-}
data Tree a = Node a (Forest a)
type Forest a = [Tree a]
mapTree :: (a -> b) -> (Tree a -> Tree b)
mapTree f (Node x ts) = Node (f x) (map (mapTree f) ts)
flattenTree :: Tree a -> [a]
flattenTree (Node x ts) = x : concatMap flattenTree ts
instance Show a => Show (Tree a) where
showsPrec _ t s = showTree t ++ s
showTree :: Show a => Tree a -> String
showTree = drawTree . mapTree show
drawTree :: Tree String -> String
drawTree = unlines . draw
draw :: Tree String -> [String]
draw (Node x ts) = grp this (space (length this)) (stLoop ts)
where this = s1 ++ x ++ " "
space n = replicate n ' '
stLoop [] = [""]
stLoop [t] = grp s2 " " (draw t)
stLoop (t:ts) = grp s3 s4 (draw t) ++ [s4] ++ rsLoop ts
rsLoop [] = []
rsLoop [t] = grp s5 " " (draw t)
rsLoop (t:ts) = grp s6 s4 (draw t) ++ [s4] ++ rsLoop ts
grp fst rst = zipWith (++) (fst:repeat rst)
[s1,s2,s3,s4,s5,s6] = ["- ", "--", "-+", " |", " `", " +"]
type IntGraph = G.Graph
{-
************************************************************************
* *
* Depth first search
* *
************************************************************************
-}
type Set s = STArray s Vertex Bool
mkEmpty :: Bounds -> ST s (Set s)
mkEmpty bnds = newArray bnds False
contains :: Set s -> Vertex -> ST s Bool
contains m v = readArray m v
include :: Set s -> Vertex -> ST s ()
include m v = writeArray m v True
dff :: IntGraph -> Forest Vertex
dff g = dfs g (vertices g)
dfs :: IntGraph -> [Vertex] -> Forest Vertex
dfs g vs = prune (bounds g) (map (generate g) vs)
generate :: IntGraph -> Vertex -> Tree Vertex
generate g v = Node v (map (generate g) (g!v))
prune :: Bounds -> Forest Vertex -> Forest Vertex
prune bnds ts = runST (mkEmpty bnds >>= \m ->
chop m ts)
chop :: Set s -> Forest Vertex -> ST s (Forest Vertex)
chop _ [] = return []
chop m (Node v ts : us)
= contains m v >>= \visited ->
if visited then
chop m us
else
include m v >>= \_ ->
chop m ts >>= \as ->
chop m us >>= \bs ->
return (Node v as : bs)
{-
************************************************************************
* *
* Algorithms
* *
************************************************************************
------------------------------------------------------------
-- Algorithm 1: depth first search numbering
-- Depth first search numbering
------------------------------------------------------------
-}
preorder :: Tree a -> [a]
preorder (Node a ts) = a : preorderF ts
-- Data.Tree has flatten for Tree, but nothing for Forest
preorderF :: Forest a -> [a]
preorderF ts = concat (map preorder ts)
tabulate :: Bounds -> [Vertex] -> Table Int
tabulate bnds vs = array bnds (zip vs [1..])
preArr :: Bounds -> Forest Vertex -> Table Int
preArr bnds = tabulate bnds . preorderF
{-
------------------------------------------------------------
-- Algorithm 2: topological sorting
------------------------------------------------------------
-}
postorder :: Tree a -> [a] -> [a]
postorder (Node a ts) = postorderF ts . (a :)
postorderF :: Forest a -> [a] -> [a]
postorderF ts = foldr (.) id $ map postorder ts
postOrd :: IntGraph -> [Vertex]
postOrd g = postorderF (dff g) []
topSort :: IntGraph -> [Vertex]
topSort = reverse . postOrd
{-
------------------------------------------------------------
-- Algorithm 3: connected components
------------------------------------------------------------
-}
components :: IntGraph -> Forest Vertex
components = dff . undirected
undirected :: IntGraph -> IntGraph
undirected g = buildG (bounds g) (edges g ++ reverseE g)
preorderF ts = concat (map flatten ts)
{-
------------------------------------------------------------
-- Algorithm 4: strongly connected components
------------------------------------------------------------
-}
scc :: IntGraph -> Forest Vertex
scc g = dfs g (reverse (postOrd (transpose g)))
{-
------------------------------------------------------------
-- Algorithm 5: Classifying edges
------------------------------------------------------------
-}
back :: IntGraph -> Table Int -> IntGraph
back g post = mapT select g
where select v ws = [ w | w <- ws, post!v < post!w ]
cross :: IntGraph -> Table Int -> Table Int -> IntGraph
cross g pre post = mapT select g
where select v ws = [ w | w <- ws, post!v > post!w, pre!v > pre!w ]
forward :: IntGraph -> IntGraph -> Table Int -> IntGraph
forward g tree pre = mapT select g
where select v ws = [ w | w <- ws, pre!v < pre!w ] \\ tree!v
{-
------------------------------------------------------------
-- Algorithm 6: Finding reachable vertices
-- Finding reachable vertices
------------------------------------------------------------
-}
-- This generalizes reachable which was found in Data.Graph
reachable :: IntGraph -> [Vertex] -> [Vertex]
reachable g vs = preorderF (dfs g vs)
path :: IntGraph -> Vertex -> Vertex -> Bool
path g v w = w `elem` (reachable g [v])
{-
------------------------------------------------------------
-- Algorithm 7: Biconnected components
------------------------------------------------------------
-}
bcc :: IntGraph -> Forest [Vertex]
bcc g = (concat . map bicomps . map (do_label g dnum)) forest
where forest = dff g
dnum = preArr (bounds g) forest
do_label :: IntGraph -> Table Int -> Tree Vertex -> Tree (Vertex,Int,Int)
do_label g dnum (Node v ts) = Node (v,dnum!v,lv) us
where us = map (do_label g dnum) ts
lv = minimum ([dnum!v] ++ [dnum!w | w <- g!v]
++ [lu | Node (_,_,lu) _ <- us])
bicomps :: Tree (Vertex, Int, Int) -> Forest [Vertex]
bicomps (Node (v,_,_) ts)
= [ Node (v:vs) us | (_,Node vs us) <- map collect ts]
collect :: Tree (Vertex, Int, Int) -> (Int, Tree [Vertex])
collect (Node (v,dv,lv) ts) = (lv, Node (v:vs) cs)
where collected = map collect ts
vs = concat [ ws | (lw, Node ws _) <- collected, lw<dv]
cs = concat [ if lw<dv then us else [Node (v:ws) us]
| (lw, Node ws us) <- collected ]
{-
------------------------------------------------------------
-- Algorithm 8: Total ordering on groups of vertices
-- Total ordering on groups of vertices
------------------------------------------------------------
The plan here is to extract a list of groups of elements of the graph
......@@ -625,6 +386,17 @@ and their associated edges from the graph.
This probably isn't very efficient and certainly isn't very clever.
-}
type Set s = STArray s Vertex Bool
mkEmpty :: Bounds -> ST s (Set s)
mkEmpty bnds = newArray bnds False
contains :: Set s -> Vertex -> ST s Bool
contains m v = readArray m v
include :: Set s -> Vertex -> ST s ()
include m v = writeArray m v True
vertexGroups :: IntGraph -> [[Vertex]]
vertexGroups g = runST (mkEmpty (bounds g) >>= \provided -> vertexGroupsS provided g next_vertices)
where next_vertices = noOutEdges g
......
......@@ -105,6 +105,7 @@ import Data.Word
import System.IO ( Handle )
import System.FilePath
import Text.Printf
import Data.Graph (SCC(..))
import GHC.Fingerprint
import GHC.Show ( showMultiLineString )
......@@ -769,6 +770,10 @@ instance (Outputable elt) => Outputable (IM.IntMap elt) where
instance Outputable Fingerprint where
ppr (Fingerprint w1 w2) = text (printf "%016x%016x" w1 w2)
instance Outputable a => Outputable (SCC a) where
ppr (AcyclicSCC v) = text "NONREC" $$ (nest 3 (ppr v))
ppr (CyclicSCC vs) = text "REC" $$ (nest 3 (vcat (map ppr vs)))
{-
************************************************************************
* *
......
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