1 use super::{DirectedGraph, WithNumNodes, WithStartNode, WithSuccessors};
2 use rustc_index::bit_set::BitSet;
3 use rustc_index::vec::IndexVec;
4 use std::ops::ControlFlow;
9 pub fn post_order_from<G: DirectedGraph + WithSuccessors + WithNumNodes>(
13 post_order_from_to(graph, start_node, None)
16 pub fn post_order_from_to<G: DirectedGraph + WithSuccessors + WithNumNodes>(
19 end_node: Option<G::Node>,
21 let mut visited: IndexVec<G::Node, bool> = IndexVec::from_elem_n(false, graph.num_nodes());
22 let mut result: Vec<G::Node> = Vec::with_capacity(graph.num_nodes());
23 if let Some(end_node) = end_node {
24 visited[end_node] = true;
26 post_order_walk(graph, start_node, &mut result, &mut visited);
30 fn post_order_walk<G: DirectedGraph + WithSuccessors + WithNumNodes>(
33 result: &mut Vec<G::Node>,
34 visited: &mut IndexVec<G::Node, bool>,
36 struct PostOrderFrame<Node, Iter> {
45 let mut stack = vec![PostOrderFrame { node, iter: graph.successors(node) }];
47 'recurse: while let Some(frame) = stack.last_mut() {
48 let node = frame.node;
51 while let Some(successor) = frame.iter.next() {
52 if !visited[successor] {
53 stack.push(PostOrderFrame { node: successor, iter: graph.successors(successor) });
63 pub fn reverse_post_order<G: DirectedGraph + WithSuccessors + WithNumNodes>(
67 let mut vec = post_order_from(graph, start_node);
72 /// A "depth-first search" iterator for a directed graph.
73 pub struct DepthFirstSearch<'graph, G>
75 G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors,
79 visited: BitSet<G::Node>,
82 impl<G> DepthFirstSearch<'graph, G>
84 G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors,
86 pub fn new(graph: &'graph G, start_node: G::Node) -> Self {
87 Self { graph, stack: vec![start_node], visited: BitSet::new_empty(graph.num_nodes()) }
91 impl<G> Iterator for DepthFirstSearch<'_, G>
93 G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors,
97 fn next(&mut self) -> Option<G::Node> {
98 let DepthFirstSearch { stack, visited, graph } = self;
100 stack.extend(graph.successors(n).filter(|&m| visited.insert(m)));
105 /// The status of a node in the depth-first search.
107 /// See the documentation of `TriColorDepthFirstSearch` to see how a node's status is updated
109 #[derive(Clone, Copy, Debug, PartialEq, Eq)]
110 pub enum NodeStatus {
111 /// This node has been examined by the depth-first search but is not yet `Settled`.
113 /// Also referred to as "gray" or "discovered" nodes in [CLR].
115 /// [CLR]: https://en.wikipedia.org/wiki/Introduction_to_Algorithms
118 /// This node and all nodes reachable from it have been examined by the depth-first search.
120 /// Also referred to as "black" or "finished" nodes in [CLR].
122 /// [CLR]: https://en.wikipedia.org/wiki/Introduction_to_Algorithms
131 /// A depth-first search that also tracks when all successors of a node have been examined.
133 /// This is based on the DFS described in [Introduction to Algorithms (1st ed.)][CLR], hereby
134 /// referred to as **CLR**. However, we use the terminology in [`NodeStatus`] above instead of
135 /// "discovered"/"finished" or "white"/"grey"/"black". Each node begins the search with no status,
136 /// becomes `Visited` when it is first examined by the DFS and is `Settled` when all nodes
137 /// reachable from it have been examined. This allows us to differentiate between "tree", "back"
138 /// and "forward" edges (see [`TriColorVisitor::node_examined`]).
140 /// Unlike the pseudocode in [CLR], this implementation is iterative and does not use timestamps.
141 /// We accomplish this by storing `Event`s on the stack that result in a (possible) state change
142 /// for each node. A `Visited` event signifies that we should examine this node if it has not yet
143 /// been `Visited` or `Settled`. When a node is examined for the first time, we mark it as
144 /// `Visited` and push a `Settled` event for it on stack followed by `Visited` events for all of
145 /// its predecessors, scheduling them for examination. Multiple `Visited` events for a single node
146 /// may exist on the stack simultaneously if a node has multiple predecessors, but only one
147 /// `Settled` event will ever be created for each node. After all `Visited` events for a node's
148 /// successors have been popped off the stack (as well as any new events triggered by visiting
149 /// those successors), we will pop off that node's `Settled` event.
151 /// [CLR]: https://en.wikipedia.org/wiki/Introduction_to_Algorithms
152 pub struct TriColorDepthFirstSearch<'graph, G>
154 G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors,
157 stack: Vec<Event<G::Node>>,
158 visited: BitSet<G::Node>,
159 settled: BitSet<G::Node>,
162 impl<G> TriColorDepthFirstSearch<'graph, G>
164 G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors,
166 pub fn new(graph: &'graph G) -> Self {
167 TriColorDepthFirstSearch {
170 visited: BitSet::new_empty(graph.num_nodes()),
171 settled: BitSet::new_empty(graph.num_nodes()),
175 /// Performs a depth-first search, starting from the given `root`.
177 /// This won't visit nodes that are not reachable from `root`.
178 pub fn run_from<V>(mut self, root: G::Node, visitor: &mut V) -> Option<V::BreakVal>
180 V: TriColorVisitor<G>,
182 use NodeStatus::{Settled, Visited};
184 self.stack.push(Event { node: root, becomes: Visited });
187 match self.stack.pop()? {
188 Event { node, becomes: Settled } => {
189 let not_previously_settled = self.settled.insert(node);
190 assert!(not_previously_settled, "A node should be settled exactly once");
191 if let ControlFlow::Break(val) = visitor.node_settled(node) {
196 Event { node, becomes: Visited } => {
197 let not_previously_visited = self.visited.insert(node);
198 let prior_status = if not_previously_visited {
200 } else if self.settled.contains(node) {
206 if let ControlFlow::Break(val) = visitor.node_examined(node, prior_status) {
210 // If this node has already been examined, we are done.
211 if prior_status.is_some() {
215 // Otherwise, push a `Settled` event for this node onto the stack, then
216 // schedule its successors for examination.
217 self.stack.push(Event { node, becomes: Settled });
218 for succ in self.graph.successors(node) {
219 if !visitor.ignore_edge(node, succ) {
220 self.stack.push(Event { node: succ, becomes: Visited });
229 impl<G> TriColorDepthFirstSearch<'graph, G>
231 G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors + WithStartNode,
233 /// Performs a depth-first search, starting from `G::start_node()`.
235 /// This won't visit nodes that are not reachable from the start node.
236 pub fn run_from_start<V>(self, visitor: &mut V) -> Option<V::BreakVal>
238 V: TriColorVisitor<G>,
240 let root = self.graph.start_node();
241 self.run_from(root, visitor)
245 /// What to do when a node is examined or becomes `Settled` during DFS.
246 pub trait TriColorVisitor<G>
248 G: ?Sized + DirectedGraph,
250 /// The value returned by this search.
253 /// Called when a node is examined by the depth-first search.
255 /// By checking the value of `prior_status`, this visitor can determine whether the edge
256 /// leading to this node was a tree edge (`None`), forward edge (`Some(Settled)`) or back edge
257 /// (`Some(Visited)`). For a full explanation of each edge type, see the "Depth-first Search"
258 /// chapter in [CLR] or [wikipedia].
260 /// If you want to know *both* nodes linked by each edge, you'll need to modify
261 /// `TriColorDepthFirstSearch` to store a `source` node for each `Visited` event.
263 /// [wikipedia]: https://en.wikipedia.org/wiki/Depth-first_search#Output_of_a_depth-first_search
264 /// [CLR]: https://en.wikipedia.org/wiki/Introduction_to_Algorithms
268 _prior_status: Option<NodeStatus>,
269 ) -> ControlFlow<Self::BreakVal> {
270 ControlFlow::CONTINUE
273 /// Called after all nodes reachable from this one have been examined.
274 fn node_settled(&mut self, _node: G::Node) -> ControlFlow<Self::BreakVal> {
275 ControlFlow::CONTINUE
278 /// Behave as if no edges exist from `source` to `target`.
279 fn ignore_edge(&mut self, _source: G::Node, _target: G::Node) -> bool {
284 /// This `TriColorVisitor` looks for back edges in a graph, which indicate that a cycle exists.
285 pub struct CycleDetector;
287 impl<G> TriColorVisitor<G> for CycleDetector
289 G: ?Sized + DirectedGraph,
296 prior_status: Option<NodeStatus>,
297 ) -> ControlFlow<Self::BreakVal> {
299 Some(NodeStatus::Visited) => ControlFlow::BREAK,
300 _ => ControlFlow::CONTINUE,