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```
use super::{DirectedGraph, WithNumNodes, WithStartNode, WithSuccessors};
use rustc_index::bit_set::BitSet;
use rustc_index::{IndexSlice, IndexVec};
use std::ops::ControlFlow;
#[cfg(test)]
mod tests;
pub fn post_order_from<G: DirectedGraph + WithSuccessors + WithNumNodes>(
graph: &G,
start_node: G::Node,
) -> Vec<G::Node> {
post_order_from_to(graph, start_node, None)
}
pub fn post_order_from_to<G: DirectedGraph + WithSuccessors + WithNumNodes>(
graph: &G,
start_node: G::Node,
end_node: Option<G::Node>,
) -> Vec<G::Node> {
let mut visited: IndexVec<G::Node, bool> = IndexVec::from_elem_n(false, graph.num_nodes());
let mut result: Vec<G::Node> = Vec::with_capacity(graph.num_nodes());
if let Some(end_node) = end_node {
visited[end_node] = true;
}
post_order_walk(graph, start_node, &mut result, &mut visited);
result
}
fn post_order_walk<G: DirectedGraph + WithSuccessors + WithNumNodes>(
graph: &G,
node: G::Node,
result: &mut Vec<G::Node>,
visited: &mut IndexSlice<G::Node, bool>,
) {
struct PostOrderFrame<Node, Iter> {
node: Node,
iter: Iter,
}
if visited[node] {
return;
}
let mut stack = vec![PostOrderFrame { node, iter: graph.successors(node) }];
'recurse: while let Some(frame) = stack.last_mut() {
let node = frame.node;
visited[node] = true;
while let Some(successor) = frame.iter.next() {
if !visited[successor] {
stack.push(PostOrderFrame { node: successor, iter: graph.successors(successor) });
continue 'recurse;
}
}
let _ = stack.pop();
result.push(node);
}
}
pub fn reverse_post_order<G: DirectedGraph + WithSuccessors + WithNumNodes>(
graph: &G,
start_node: G::Node,
) -> Vec<G::Node> {
let mut vec = post_order_from(graph, start_node);
vec.reverse();
vec
}
/// A "depth-first search" iterator for a directed graph.
pub struct DepthFirstSearch<'graph, G>
where
G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors,
{
graph: &'graph G,
stack: Vec<G::Node>,
visited: BitSet<G::Node>,
}
impl<'graph, G> DepthFirstSearch<'graph, G>
where
G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors,
{
pub fn new(graph: &'graph G) -> Self {
Self { graph, stack: vec![], visited: BitSet::new_empty(graph.num_nodes()) }
}
/// Version of `push_start_node` that is convenient for chained
/// use.
pub fn with_start_node(mut self, start_node: G::Node) -> Self {
self.push_start_node(start_node);
self
}
/// Pushes another start node onto the stack. If the node
/// has not already been visited, then you will be able to
/// walk its successors (and so forth) after the current
/// contents of the stack are drained. If multiple start nodes
/// are added into the walk, then their mutual successors
/// will all be walked. You can use this method once the
/// iterator has been completely drained to add additional
/// start nodes.
pub fn push_start_node(&mut self, start_node: G::Node) {
if self.visited.insert(start_node) {
self.stack.push(start_node);
}
}
/// Searches all nodes reachable from the current start nodes.
/// This is equivalent to just invoke `next` repeatedly until
/// you get a `None` result.
pub fn complete_search(&mut self) {
while let Some(_) = self.next() {}
}
/// Returns true if node has been visited thus far.
/// A node is considered "visited" once it is pushed
/// onto the internal stack; it may not yet have been yielded
/// from the iterator. This method is best used after
/// the iterator is completely drained.
pub fn visited(&self, node: G::Node) -> bool {
self.visited.contains(node)
}
}
impl<G> std::fmt::Debug for DepthFirstSearch<'_, G>
where
G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors,
{
fn fmt(&self, fmt: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
let mut f = fmt.debug_set();
for n in self.visited.iter() {
f.entry(&n);
}
f.finish()
}
}
impl<G> Iterator for DepthFirstSearch<'_, G>
where
G: ?Sized + DirectedGraph + WithNumNodes + WithSuccessors,
{
type Item = G::Node;
fn next(&mut self) -> Option<G::Node> {
let DepthFirstSearch { stack, visited, graph } = self;
let n = stack.pop()?;
stack.extend(graph.successors(n).filter(|&m| visited.insert(m)));
Some(n)
}
}
/// 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
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<'graph, 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::{Settled, Visited};
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) {
if !visitor.ignore_edge(node, succ) {
self.stack.push(Event { node: succ, becomes: Visited });
}
}
}
}
}
}
}
impl<G> TriColorDepthFirstSearch<'_, 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,
_node: 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, _node: G::Node) -> ControlFlow<Self::BreakVal> {
ControlFlow::Continue(())
}
/// Behave as if no edges exist from `source` to `target`.
fn ignore_edge(&mut self, _source: G::Node, _target: G::Node) -> bool {
false
}
}
/// 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(()),
}
}
}
```