Add cycle detection for graphs

src/librustc_data_structures/graph/iterate/mod.rs

@@ -1,5 +1,5 @@
 use super::super::indexed_vec::IndexVec;
-use super::{DirectedGraph, WithNumNodes, WithSuccessors};
+use super::{DirectedGraph, WithNumNodes, WithSuccessors, WithStartNode};
 use crate::bit_set::BitSet;
 
 #[cfg(test)]
@@ -85,3 +85,205 @@ where
         Some(n)
     }
 }
+
+/// Allows searches to terminate early with a value.
+#[derive(Clone, Copy, Debug)]
+pub enum ControlFlow<T> {
+    Break(T),
+    Continue,
+}
+
+/// The status of a node in the depth-first search.
+///
+/// See the documentation of `TriColorDepthFirstSearch` to see how a node's status is updated
+/// during DFS.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum NodeStatus {
+    /// This node has been examined by the depth-first search but is not yet `Settled`.
+    ///
+    /// Also referred to as "gray" or "discovered" nodes in [CLR][].
+    ///
+    /// [CLR]: https://en.wikipedia.org/wiki/Introduction_to_Algorithms
+    Visited,
+
+    /// This node and all nodes reachable from it have been examined by the depth-first search.
+    ///
+    /// Also referred to as "black" or "finished" nodes in [CLR][].
+    ///
+    /// [CLR]: https://en.wikipedia.org/wiki/Introduction_to_Algorithms
+    Settled,
+}
+
+struct Event<N> {
+    node: N,
+    becomes: NodeStatus,
+}
+
+/// A depth-first search that also tracks when all successors of a node have been examined.
+///
+/// This is based on the DFS described in [Introduction to Algorithms (1st ed.)][CLR], hereby
+/// referred to as **CLR**. However, we use the terminology in [`NodeStatus`][] above instead of
+/// "discovered"/"finished" or "white"/"grey"/"black". Each node begins the search with no status,
+/// becomes `Visited` when it is first examined by the DFS and is `Settled` when all nodes
+/// reachable from it have been examined. This allows us to differentiate between "tree", "back"
+/// and "forward" edges (see [`TriColorVisitor::node_examined`]).
+///
+/// Unlike the pseudocode in [CLR][], this implementation is iterative and does not use timestamps.
+/// We accomplish this by storing `Event`s on the stack that result in a (possible) state change
+/// for each node. A `Visited` event signifies that we should examine this node if it has not yet
+/// been `Visited` or `Settled`. When a node is examined for the first time, we mark it as
+/// `Visited` and push a `Settled` event for it on stack followed by `Visited` events for all of
+/// its predecessors, scheduling them for examination. Multiple `Visited` events for a single node
+/// may exist on the stack simultaneously if a node has multiple predecessors, but only one
+/// `Settled` event will ever be created for each node. After all `Visited` events for a node's
+/// successors have been popped off the stack (as well as any new events triggered by visiting
+/// those successors), we will pop off that node's `Settled` event.
+///
+/// [CLR]: https://en.wikipedia.org/wiki/Introduction_to_Algorithms
+/// [`NodeStatus`]: ./enum.NodeStatus.html
+/// [`TriColorVisitor::node_examined`]: ./trait.TriColorVisitor.html#method.node_examined
+pub struct TriColorDepthFirstSearch<'graph, G>
+where
+    G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors,
+{
+    graph: &'graph G,
+    stack: Vec<Event<G::Node>>,
+    visited: BitSet<G::Node>,
+    settled: BitSet<G::Node>,
+}
+
+impl<G> TriColorDepthFirstSearch<'graph, G>
+where
+    G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors,
+{
+    pub fn new(graph: &'graph G) -> Self {
+        TriColorDepthFirstSearch {
+            graph,
+            stack: vec![],
+            visited: BitSet::new_empty(graph.num_nodes()),
+            settled: BitSet::new_empty(graph.num_nodes()),
+        }
+    }
+
+    /// Performs a depth-first search, starting from the given `root`.
+    ///
+    /// This won't visit nodes that are not reachable from `root`.
+    pub fn run_from<V>(mut self, root: G::Node, visitor: &mut V) -> Option<V::BreakVal>
+    where
+        V: TriColorVisitor<G>,
+    {
+        use NodeStatus::{Visited, Settled};
+
+        self.stack.push(Event { node: root, becomes: Visited });
+
+        loop {
+            match self.stack.pop()? {
+                Event { node, becomes: Settled } => {
+                    let not_previously_settled = self.settled.insert(node);
+                    assert!(not_previously_settled, "A node should be settled exactly once");
+                    if let ControlFlow::Break(val) = visitor.node_settled(node) {
+                        return Some(val);
+                    }
+                }
+
+                Event { node, becomes: Visited } => {
+                    let not_previously_visited = self.visited.insert(node);
+                    let prior_status = if not_previously_visited {
+                        None
+                    } else if self.settled.contains(node) {
+                        Some(Settled)
+                    } else {
+                        Some(Visited)
+                    };
+
+                    if let ControlFlow::Break(val) = visitor.node_examined(node, prior_status) {
+                        return Some(val);
+                    }
+
+                    // If this node has already been examined, we are done.
+                    if prior_status.is_some() {
+                        continue;
+                    }
+
+                    // Otherwise, push a `Settled` event for this node onto the stack, then
+                    // schedule its successors for examination.
+                    self.stack.push(Event { node, becomes: Settled });
+                    for succ in self.graph.successors(node) {
+                        self.stack.push(Event { node: succ, becomes: Visited });
+                    }
+                }
+            }
+        }
+    }
+}
+
+impl<G> TriColorDepthFirstSearch<'graph, G>
+where
+    G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors + WithStartNode,
+{
+    /// Performs a depth-first search, starting from `G::start_node()`.
+    ///
+    /// This won't visit nodes that are not reachable from the start node.
+    pub fn run_from_start<V>(self, visitor: &mut V) -> Option<V::BreakVal>
+    where
+        V: TriColorVisitor<G>,
+    {
+        let root = self.graph.start_node();
+        self.run_from(root, visitor)
+    }
+}
+
+/// What to do when a node is examined or becomes `Settled` during DFS.
+pub trait TriColorVisitor<G>
+where
+    G: ?Sized + DirectedGraph,
+{
+    /// The value returned by this search.
+    type BreakVal;
+
+    /// Called when a node is examined by the depth-first search.
+    ///
+    /// By checking the value of `prior_status`, this visitor can determine whether the edge
+    /// leading to this node was a tree edge (`None`), forward edge (`Some(Settled)`) or back edge
+    /// (`Some(Visited)`). For a full explanation of each edge type, see the "Depth-first Search"
+    /// chapter in [CLR][] or [wikipedia][].
+    ///
+    /// If you want to know *both* nodes linked by each edge, you'll need to modify
+    /// `TriColorDepthFirstSearch` to store a `source` node for each `Visited` event.
+    ///
+    /// [wikipedia]: https://en.wikipedia.org/wiki/Depth-first_search#Output_of_a_depth-first_search
+    /// [CLR]: https://en.wikipedia.org/wiki/Introduction_to_Algorithms
+    fn node_examined(
+        &mut self,
+        _target: G::Node,
+        _prior_status: Option<NodeStatus>,
+    ) -> ControlFlow<Self::BreakVal> {
+        ControlFlow::Continue
+    }
+
+    /// Called after all nodes reachable from this one have been examined.
+    fn node_settled(&mut self, _target: G::Node) -> ControlFlow<Self::BreakVal> {
+        ControlFlow::Continue
+    }
+}
+
+/// This `TriColorVisitor` looks for back edges in a graph, which indicate that a cycle exists.
+pub struct CycleDetector;
+
+impl<G> TriColorVisitor<G> for CycleDetector
+where
+    G: ?Sized + DirectedGraph,
+{
+    type BreakVal = ();
+
+    fn node_examined(
+        &mut self,
+        _node: G::Node,
+        prior_status: Option<NodeStatus>,
+    ) -> ControlFlow<Self::BreakVal> {
+        match prior_status {
+            Some(NodeStatus::Visited) => ControlFlow::Break(()),
+            _ => ControlFlow::Continue,
+        }
+    }
+}

src/librustc_data_structures/graph/iterate/tests.rs

@@ -9,3 +9,14 @@ fn diamond_post_order() {
     let result = post_order_from(&graph, 0);
     assert_eq!(result, vec![3, 1, 2, 0]);
 }
+
+#[test]
+fn is_cyclic() {
+    use super::super::is_cyclic;
+
+    let diamond_acyclic = TestGraph::new(0, &[(0, 1), (0, 2), (1, 3), (2, 3)]);
+    let diamond_cyclic = TestGraph::new(0, &[(0, 1), (1, 2), (2, 3), (3, 0)]);
+
+    assert!(!is_cyclic(&diamond_acyclic));
+    assert!(is_cyclic(&diamond_cyclic));
+}

src/librustc_data_structures/graph/mod.rs

@@ -81,3 +81,13 @@ where
         + WithNumNodes,
 {
 }
+
+/// Returns `true` if the graph has a cycle that is reachable from the start node.
+pub fn is_cyclic<G>(graph: &G) -> bool
+where
+    G: ?Sized + DirectedGraph + WithStartNode + WithSuccessors + WithNumNodes,
+{
+    iterate::TriColorDepthFirstSearch::new(graph)
+        .run_from_start(&mut iterate::CycleDetector)
+        .is_some()
+}