Correct cycle finding for graphs (#2199)

Closes #2198 .  Adds a new function `findCycle` for finding directed cycles in graphs via DFS, and updates `failOnCyclicGraph` to use it rather than SCCs for reporting cycles.

data/scenarios/Testing/_Validation/2198-prerequisite-SCC.yaml

@@ -0,0 +1,38 @@
+version: 1
+name: |
+  Prerequisite objectives: dependency cycles in a larger SCC
+author: Brent Yorgey
+description: |
+  This should be rejected by the parser due to cyclic dependencies.
+  The dependency graph is strongly connected, but not all four
+  dependencies are in a single cycle together.
+robots:
+  - name: base
+objectives:
+  - id: a
+    condition: 'true'
+    prerequisite:
+      logic:
+        and:
+          - b
+          - c
+          - d
+  - id: b
+    condition: 'true'
+    prerequisite: a
+  - id: c
+    condition: 'true'
+    prerequisite:
+      logic:
+        and:
+          - a
+          - d
+  - id: d
+    condition: 'true'
+    prerequisite:
+      logic:
+        and:
+          - a
+          - c
+world:
+  dsl: '{stone}'

src/swarm-util/Swarm/Util/Graph.hs

@@ -6,13 +6,17 @@
 -- Graph utilities shared by multiple aspects of scenarios
 module Swarm.Util.Graph (
   isAcyclicGraph,
+  findCycle,
   failOnCyclicGraph,
 ) where
 
 import Control.Monad (forM_)
-import Data.Graph (SCC (..), stronglyConnComp)
-import Data.List.NonEmpty qualified as NE
-import Data.Maybe (mapMaybe)
+import Control.Monad.ST
+import Data.Array ((!))
+import Data.Array.ST
+import Data.Graph (SCC (..), Vertex, graphFromEdges)
+import Data.IntSet (IntSet)
+import Data.IntSet qualified as IS
 import Data.Text (Text)
 import Data.Text qualified as T
 import Swarm.Util
@@ -25,13 +29,62 @@ isAcyclicGraph =
     AcyclicSCC _ -> True
     _ -> False
 
-getGraphCycles :: [SCC a] -> [[a]]
-getGraphCycles =
-  mapMaybe getCycle
+-- | Keep track of the current search path in a DFS, both as a set of
+--   vertices (for fast membership testing) and as a reversed list of
+--   vertices visited along the current path, in order.
+--
+--   Note this is different than just keeping track of which vertices
+--   have been visited at all; visited vertices remain visited when
+--   DFS backtracks, but the DFSPath gets shorter again.
+data DFSPath = DFSPath IntSet [Vertex]
+
+emptyDFSPath :: DFSPath
+emptyDFSPath = DFSPath IS.empty []
+
+appendPath :: DFSPath -> Vertex -> DFSPath
+appendPath (DFSPath s p) v = DFSPath (IS.insert v s) (v : p)
+
+-- | Find a cycle in a directed graph (if any exist) via DFS.
+--
+-- >>> findCycle [("a", 0, [0])]
+-- Just ["a"]
+-- >>> findCycle [("a", 0, [1]), ("b", 1, [])]
+-- Nothing
+-- >>> findCycle [("a", 0, [1]), ("b", 1, [0])]
+-- Just ["a","b"]
+-- >>> findCycle [("a", 0, [1]), ("b", 1, [2]), ("c", 2, [1])]
+-- Just ["b","c"]
+-- >>> findCycle [("a",3,[1]), ("b",1,[0,3]), ("c",2,[1]), ("d",0,[])]
+-- Just ["b","a"]
+-- >>> findCycle [("a",3,[]), ("b",1,[0,3]), ("c",2,[1]), ("d",0,[])]
+-- Nothing
+-- >>> findCycle [("a",3,[1]), ("b",1,[0,3]), ("c",2,[1]), ("d",0,[2])]
+-- Just ["d","c","b"]
+findCycle :: Ord key => [(a, key, [key])] -> Maybe [a]
+findCycle es = runST $ do
+  visited <- newArray (0, n - 1) False
+  (fmap . map) (fst3 . v2l) <$> dfsL visited emptyDFSPath [0 .. n - 1]
  where
-  getCycle = \case
-    AcyclicSCC _ -> Nothing
-    CyclicSCC c -> Just c
+  n = length es
+  (g, v2l, _) = graphFromEdges es
+  fst3 (a, _, _) = a
+
+  dfsL :: STUArray s Vertex Bool -> DFSPath -> [Vertex] -> ST s (Maybe [Vertex])
+  dfsL _ _ [] = pure Nothing
+  dfsL visited path (v : vs) = do
+    found <- dfs visited path v
+    case found of
+      Nothing -> dfsL visited path vs
+      Just cyc -> pure (Just cyc)
+
+  dfs :: STUArray s Vertex Bool -> DFSPath -> Vertex -> ST s (Maybe [Vertex])
+  dfs visited p@(DFSPath pathMembers path) v
+    | v `IS.member` pathMembers = pure . Just . (v :) . reverse $ takeWhile (/= v) path
+    | otherwise = do
+        vis <- readArray visited v
+        case vis of
+          True -> pure Nothing
+          False -> dfsL visited (appendPath p v) (g ! v)
 
 failOnCyclicGraph ::
   Ord key =>
@@ -40,12 +93,10 @@ failOnCyclicGraph ::
   [(a, key, [key])] ->
   Either Text ()
 failOnCyclicGraph graphType keyFunction gEdges =
-  forM_ (NE.nonEmpty $ getGraphCycles $ stronglyConnComp gEdges) $ \cycles ->
+  forM_ (findCycle gEdges) $ \cyc ->
     Left $
       T.unwords
         [ graphType
-        , "graph contains cycles:"
-        , commaList $
-            NE.toList $
-              fmap (brackets . T.intercalate " -> " . fmap keyFunction) cycles
+        , "graph contains a cycle:"
+        , brackets . T.intercalate " -> " . fmap keyFunction $ cyc
         ]