-module BellmanFord {-(spTree)-} where
-import Data.Graph.Inductive.Graph
-import Data.Graph.Inductive.Internal.Queue
-import Data.Graph.Inductive.Internal.RootPath
-import Data.Array.Diff
-
-data NodeInfo b = NodeInfo {
- path :: Maybe [LNode b],
- changed :: Bool
-}
-data Graph gr => BFState gr a b = BFState {
- theGraph :: gr a b,
- nis :: DiffArray Node (NodeInfo b),
- changedQ :: Queue Node
-}
-
-nisToLRTree nis = do
- ni <- elems nis
- case path ni of
- Just lnl -> return (LP lnl)
- Nothing -> fail "Node is unreachable"
-
-offerPath :: (Graph gr, Real b) => BFState gr a b -> [LNode b] -> BFState gr a b
-offerPath bfs newPath@((dest, newDist): _) =
- -- Is newPath the first path to dest, or better than the previous one?
- let adoptPath =
- case path (nis bfs ! dest) of
- Nothing -> True
- Just ((_, oldDist) : _) -> newDist < oldDist
- in
- if adoptPath then
- bfs{
- -- Update NodeInfo with the new path.
- nis = nis bfs // [(dest, NodeInfo (Just newPath) True)],
- changedQ = if changed (nis bfs ! dest)
- then changedQ bfs -- Already on the queue; leave as is.
- else queuePut dest (changedQ bfs) -- Add to queue.
- }
- else bfs -- Don't update anything.
-
-processEdge :: (Graph gr, Real b) => [LNode b] -> LEdge b -> BFState gr a b -> BFState gr a b
-processEdge srcPath@((_, srcDist) : _) (_, dest, edgeLen) bfs =
- let newPath = (dest, srcDist + edgeLen) : srcPath in
- offerPath bfs newPath
-
-search :: (Graph gr, Real b) => BFState gr a b -> LRTree b
-search bfs =
- if queueEmpty (changedQ bfs) then
- -- Finished.
- nisToLRTree (nis bfs)
- else
- -- Process a changed node from the queue.
- let (src, moreQ) = queueGet (changedQ bfs) in
- let srcNI = nis bfs ! src in
- -- Clear src's changed flag.
- let bfs1 = bfs{nis = nis bfs // [(src, srcNI{changed = False})], changedQ = moreQ} in
- let Just srcPath = path srcNI in
- let outEdges = out (theGraph bfs) src in
- let newBFS = foldr (processEdge srcPath) bfs1 outEdges in
- search newBFS
-
-spTree :: (Graph gr, Real b) => Node -> gr a b -> LRTree b
-spTree source theGraph = let theNodes = range (nodeRange theGraph) in
- let emptyBFS = BFState theGraph
- (array (nodeRange theGraph) (map (\n -> (n, NodeInfo Nothing False)) theNodes))
- mkQueue in
- -- Start with a zero-length path to the source.
- let initBFS = offerPath emptyBFS [(source, 0)] in
- search initBFS