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Better hasEdge for Algrebra.Graph #88

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merged 10 commits into from
Jul 19, 2018
Merged

Better hasEdge for Algrebra.Graph #88

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54100e4
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nobrakal Jul 2, 2018
0eeebc5
Working amelioration
nobrakal Jul 2, 2018
3b791bb
Remove TODO comment
nobrakal Jul 2, 2018
3050195
Remove bang
nobrakal Jul 2, 2018
0a21b21
Add optimization for NonEmptyGraph
nobrakal Jul 4, 2018
9111701
Even better hasEdge, testing for loop
nobrakal Jul 4, 2018
922126e
Add optimizations for NonEmptyGraph
nobrakal Jul 5, 2018
ca3fc07
merge master
nobrakal Jul 18, 2018
216ea8b
Merge branch 'master' of https://github.com/snowleopard/alga into has…
nobrakal Jul 19, 2018
c20977c
Better hasEdge for Fold
nobrakal Jul 19, 2018
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26 changes: 22 additions & 4 deletions src/Algebra/Graph.hs
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Original file line number Diff line number Diff line change
Expand Up @@ -446,8 +446,6 @@ size = foldg 1 (const 1) (+) (+)
hasVertex :: Eq a => a -> Graph a -> Bool
hasVertex x = foldg False (==x) (||) (||)

-- TODO: Benchmark to see if this implementation is faster than the default
-- implementation provided by the ToGraph type class.
-- | Check if a graph contains a given edge.
-- Complexity: /O(s)/ time.
--
Expand All @@ -459,8 +457,28 @@ hasVertex x = foldg False (==x) (||) (||)
-- hasEdge x y == 'elem' (x,y) . 'edgeList'
-- @
{-# SPECIALISE hasEdge :: Int -> Int -> Graph Int -> Bool #-}
hasEdge :: Ord a => a -> a -> Graph a -> Bool
hasEdge u v = (edge u v `isSubgraphOf`) . induce (`elem` [u, v])
hasEdge :: Eq a => a -> a -> Graph a -> Bool
hasEdge s t = if s == t -- We test if we search for a loop
then hasSelfLoop s
else hasEdge' . induce' -- if not, we convert the supplied @Graph a@ to a @Graph Bool@
-- where @s@ is @Vertex True@, @v@ is @Vertex False@ and other
-- vertices are removed.
-- Then we check if there is an edge from @True@ to @False@
where
hasEdge' g = case foldg e v o c g of (_, _, r) -> r
where
e = (False , False , False )
v x = (x , not x , False )
o (xs, xt, xst) (ys, yt, yst) = (xs || ys, xt || yt, xst || yst)
c (xs, xt, xst) (ys, yt, yst) = (xs || ys, xt || yt, xs && yt || xst || yst)
induce' = foldg Empty
(\x -> if x == s then Vertex True else if x == t then Vertex False else Empty)
(k Overlay)
(k Connect)
where
k _ x Empty = x -- Constant folding to get rid of Empty leaves
k _ Empty y = y
k f x y = f x y

-- | Check if a graph contains a given loop.
-- Complexity: /O(s)/ time.
Expand Down
41 changes: 39 additions & 2 deletions src/Algebra/Graph/Fold.hs
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Expand Up @@ -191,6 +191,8 @@ instance Traversable Fold where
instance ToGraph (Fold a) where
type ToVertex (Fold a) = a
foldg = foldg
hasEdge = hasEdge
hasSelfLoop = hasSelfLoop

-- | Construct the /empty graph/.
-- Complexity: /O(1)/ time, memory and size.
Expand Down Expand Up @@ -408,7 +410,27 @@ hasVertex = T.hasVertex
-- hasEdge x y == 'elem' (x,y) . 'edgeList'
-- @
hasEdge :: Eq a => a -> a -> Fold a -> Bool
hasEdge = T.hasEdge
hasEdge s t = if s == t -- We test if we search for a loop
then hasSelfLoop s
else maybe False hasEdge' . induce' -- if not, we convert the supplied @Graph a@ to a @Graph Bool@
-- where @s@ is @Vertex True@, @v@ is @Vertex False@ and other
-- vertices are removed.
-- Then we check if there is an edge from @True@ to @False@
where
hasEdge' g = case foldg e v o c g of (_, _, r) -> r
where
e = (False , False , False )
v x = (x , not x , False )
o (xs, xt, xst) (ys, yt, yst) = (xs || ys, xt || yt, xst || yst)
c (xs, xt, xst) (ys, yt, yst) = (xs || ys, xt || yt, xs && yt || xst || yst)
induce' = foldg Nothing
(\x -> if x == s then Just (vertex True) else if x == t then Just (vertex False) else Nothing)
(k overlay)
(k connect)
where
k _ x Nothing = x -- Constant folding to get rid of Empty leaves
k _ Nothing y = y
k f (Just x) (Just y) = Just $ f x y

-- | Check if a graph contains a given loop.
-- Complexity: /O(s)/ time.
Expand All @@ -422,7 +444,22 @@ hasEdge = T.hasEdge
-- hasSelfLoop x == 'elem' (x,x) . 'edgeList'
-- @
hasSelfLoop :: Eq a => a -> Fold a -> Bool
hasSelfLoop = T.hasSelfLoop
hasSelfLoop t = maybe False hasEdge' . induce'
where
hasEdge' g = case foldg e v o c g of (_, _, r) -> r
where
e = (False , False , False )
v x = (x , x , False )
o (xs, xt, xst) (ys, yt, yst) = (xs || ys, xt || yt, xst || yst)
c (xs, xt, xst) (ys, yt, yst) = (xs || ys, xt || yt, xs && yt || xst || yst)
induce' = foldg Nothing
(\x -> if x==t then Just (vertex True) else Nothing)
(k overlay)
(k connect)
where
k _ x Nothing = x -- Constant folding to get rid of Empty leaves
k _ Nothing y = y
k f (Just x) (Just y) = Just $ f x y

-- | The number of vertices in a graph.
-- Complexity: /O(s * log(n))/ time.
Expand Down