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use std::fmt::Debug;
use bevy_utils::{HashMap, HashSet};
use fixedbitset::FixedBitSet;
use petgraph::{algo::TarjanScc, graphmap::NodeTrait, prelude::*};
use crate::schedule::set::*;
/// Unique identifier for a system or system set stored in a [`ScheduleGraph`].
///
/// [`ScheduleGraph`]: super::ScheduleGraph
#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
pub enum NodeId {
/// Identifier for a system.
System(usize),
/// Identifier for a system set.
Set(usize),
}
impl NodeId {
/// Returns the internal integer value.
pub(crate) fn index(&self) -> usize {
match self {
NodeId::System(index) | NodeId::Set(index) => *index,
}
}
/// Returns `true` if the identified node is a system.
pub const fn is_system(&self) -> bool {
matches!(self, NodeId::System(_))
}
/// Returns `true` if the identified node is a system set.
pub const fn is_set(&self) -> bool {
matches!(self, NodeId::Set(_))
}
}
/// Specifies what kind of edge should be added to the dependency graph.
#[derive(Debug, Clone, Copy, Eq, PartialEq, PartialOrd, Ord, Hash)]
pub(crate) enum DependencyKind {
/// A node that should be preceded.
Before,
/// A node that should be succeeded.
After,
/// A node that should be preceded and will **not** automatically insert an instance of `apply_deferred` on the edge.
BeforeNoSync,
/// A node that should be succeeded and will **not** automatically insert an instance of `apply_deferred` on the edge.
AfterNoSync,
}
/// An edge to be added to the dependency graph.
#[derive(Clone)]
pub(crate) struct Dependency {
pub(crate) kind: DependencyKind,
pub(crate) set: InternedSystemSet,
}
impl Dependency {
pub fn new(kind: DependencyKind, set: InternedSystemSet) -> Self {
Self { kind, set }
}
}
/// Configures ambiguity detection for a single system.
#[derive(Clone, Debug, Default)]
pub(crate) enum Ambiguity {
#[default]
Check,
/// Ignore warnings with systems in any of these system sets. May contain duplicates.
IgnoreWithSet(Vec<InternedSystemSet>),
/// Ignore all warnings.
IgnoreAll,
}
/// Metadata about how the node fits in the schedule graph
#[derive(Clone, Default)]
pub(crate) struct GraphInfo {
/// the sets that the node belongs to (hierarchy)
pub(crate) hierarchy: Vec<InternedSystemSet>,
/// the sets that the node depends on (must run before or after)
pub(crate) dependencies: Vec<Dependency>,
pub(crate) ambiguous_with: Ambiguity,
}
/// Converts 2D row-major pair of indices into a 1D array index.
pub(crate) fn index(row: usize, col: usize, num_cols: usize) -> usize {
debug_assert!(col < num_cols);
(row * num_cols) + col
}
/// Converts a 1D array index into a 2D row-major pair of indices.
pub(crate) fn row_col(index: usize, num_cols: usize) -> (usize, usize) {
(index / num_cols, index % num_cols)
}
/// Stores the results of the graph analysis.
pub(crate) struct CheckGraphResults<V> {
/// Boolean reachability matrix for the graph.
pub(crate) reachable: FixedBitSet,
/// Pairs of nodes that have a path connecting them.
pub(crate) connected: HashSet<(V, V)>,
/// Pairs of nodes that don't have a path connecting them.
pub(crate) disconnected: Vec<(V, V)>,
/// Edges that are redundant because a longer path exists.
pub(crate) transitive_edges: Vec<(V, V)>,
/// Variant of the graph with no transitive edges.
pub(crate) transitive_reduction: DiGraphMap<V, ()>,
/// Variant of the graph with all possible transitive edges.
// TODO: this will very likely be used by "if-needed" ordering
#[allow(dead_code)]
pub(crate) transitive_closure: DiGraphMap<V, ()>,
}
impl<V: NodeTrait + Debug> Default for CheckGraphResults<V> {
fn default() -> Self {
Self {
reachable: FixedBitSet::new(),
connected: HashSet::new(),
disconnected: Vec::new(),
transitive_edges: Vec::new(),
transitive_reduction: DiGraphMap::new(),
transitive_closure: DiGraphMap::new(),
}
}
}
/// Processes a DAG and computes its:
/// - transitive reduction (along with the set of removed edges)
/// - transitive closure
/// - reachability matrix (as a bitset)
/// - pairs of nodes connected by a path
/// - pairs of nodes not connected by a path
///
/// The algorithm implemented comes from
/// ["On the calculation of transitive reduction-closure of orders"][1] by Habib, Morvan and Rampon.
///
/// [1]: https://doi.org/10.1016/0012-365X(93)90164-O
pub(crate) fn check_graph<V>(
graph: &DiGraphMap<V, ()>,
topological_order: &[V],
) -> CheckGraphResults<V>
where
V: NodeTrait + Debug,
{
if graph.node_count() == 0 {
return CheckGraphResults::default();
}
let n = graph.node_count();
// build a copy of the graph where the nodes and edges appear in topsorted order
let mut map = HashMap::with_capacity(n);
let mut topsorted = DiGraphMap::<V, ()>::new();
// iterate nodes in topological order
for (i, &node) in topological_order.iter().enumerate() {
map.insert(node, i);
topsorted.add_node(node);
// insert nodes as successors to their predecessors
for pred in graph.neighbors_directed(node, Incoming) {
topsorted.add_edge(pred, node, ());
}
}
let mut reachable = FixedBitSet::with_capacity(n * n);
let mut connected = HashSet::new();
let mut disconnected = Vec::new();
let mut transitive_edges = Vec::new();
let mut transitive_reduction = DiGraphMap::<V, ()>::new();
let mut transitive_closure = DiGraphMap::<V, ()>::new();
let mut visited = FixedBitSet::with_capacity(n);
// iterate nodes in topological order
for node in topsorted.nodes() {
transitive_reduction.add_node(node);
transitive_closure.add_node(node);
}
// iterate nodes in reverse topological order
for a in topsorted.nodes().rev() {
let index_a = *map.get(&a).unwrap();
// iterate their successors in topological order
for b in topsorted.neighbors_directed(a, Outgoing) {
let index_b = *map.get(&b).unwrap();
debug_assert!(index_a < index_b);
if !visited[index_b] {
// edge <a, b> is not redundant
transitive_reduction.add_edge(a, b, ());
transitive_closure.add_edge(a, b, ());
reachable.insert(index(index_a, index_b, n));
let successors = transitive_closure
.neighbors_directed(b, Outgoing)
.collect::<Vec<_>>();
for c in successors {
let index_c = *map.get(&c).unwrap();
debug_assert!(index_b < index_c);
if !visited[index_c] {
visited.insert(index_c);
transitive_closure.add_edge(a, c, ());
reachable.insert(index(index_a, index_c, n));
}
}
} else {
// edge <a, b> is redundant
transitive_edges.push((a, b));
}
}
visited.clear();
}
// partition pairs of nodes into "connected by path" and "not connected by path"
for i in 0..(n - 1) {
// reachable is upper triangular because the nodes were topsorted
for index in index(i, i + 1, n)..=index(i, n - 1, n) {
let (a, b) = row_col(index, n);
let pair = (topological_order[a], topological_order[b]);
if reachable[index] {
connected.insert(pair);
} else {
disconnected.push(pair);
}
}
}
// fill diagonal (nodes reach themselves)
// for i in 0..n {
// reachable.set(index(i, i, n), true);
// }
CheckGraphResults {
reachable,
connected,
disconnected,
transitive_edges,
transitive_reduction,
transitive_closure,
}
}
/// Returns the simple cycles in a strongly-connected component of a directed graph.
///
/// The algorithm implemented comes from
/// ["Finding all the elementary circuits of a directed graph"][1] by D. B. Johnson.
///
/// [1]: https://doi.org/10.1137/0204007
pub fn simple_cycles_in_component<N>(graph: &DiGraphMap<N, ()>, scc: &[N]) -> Vec<Vec<N>>
where
N: NodeTrait + Debug,
{
let mut cycles = vec![];
let mut sccs = vec![scc.to_vec()];
while let Some(mut scc) = sccs.pop() {
// only look at nodes and edges in this strongly-connected component
let mut subgraph = DiGraphMap::new();
for &node in &scc {
subgraph.add_node(node);
}
for &node in &scc {
for successor in graph.neighbors(node) {
if subgraph.contains_node(successor) {
subgraph.add_edge(node, successor, ());
}
}
}
// path of nodes that may form a cycle
let mut path = Vec::with_capacity(subgraph.node_count());
// we mark nodes as "blocked" to avoid finding permutations of the same cycles
let mut blocked = HashSet::with_capacity(subgraph.node_count());
// connects nodes along path segments that can't be part of a cycle (given current root)
// those nodes can be unblocked at the same time
let mut unblock_together: HashMap<N, HashSet<N>> =
HashMap::with_capacity(subgraph.node_count());
// stack for unblocking nodes
let mut unblock_stack = Vec::with_capacity(subgraph.node_count());
// nodes can be involved in multiple cycles
let mut maybe_in_more_cycles: HashSet<N> = HashSet::with_capacity(subgraph.node_count());
// stack for DFS
let mut stack = Vec::with_capacity(subgraph.node_count());
// we're going to look for all cycles that begin and end at this node
let root = scc.pop().unwrap();
// start a path at the root
path.clear();
path.push(root);
// mark this node as blocked
blocked.insert(root);
// DFS
stack.clear();
stack.push((root, subgraph.neighbors(root)));
while !stack.is_empty() {
let (ref node, successors) = stack.last_mut().unwrap();
if let Some(next) = successors.next() {
if next == root {
// found a cycle
maybe_in_more_cycles.extend(path.iter());
cycles.push(path.clone());
} else if !blocked.contains(&next) {
// first time seeing `next` on this path
maybe_in_more_cycles.remove(&next);
path.push(next);
blocked.insert(next);
stack.push((next, subgraph.neighbors(next)));
continue;
} else {
// not first time seeing `next` on this path
}
}
if successors.peekable().peek().is_none() {
if maybe_in_more_cycles.contains(node) {
unblock_stack.push(*node);
// unblock this node's ancestors
while let Some(n) = unblock_stack.pop() {
if blocked.remove(&n) {
let unblock_predecessors =
unblock_together.entry(n).or_insert_with(HashSet::new);
unblock_stack.extend(unblock_predecessors.iter());
unblock_predecessors.clear();
}
}
} else {
// if its descendants can be unblocked later, this node will be too
for successor in subgraph.neighbors(*node) {
unblock_together
.entry(successor)
.or_insert_with(HashSet::new)
.insert(*node);
}
}
// remove node from path and DFS stack
path.pop();
stack.pop();
}
}
// remove node from subgraph
subgraph.remove_node(root);
// divide remainder into smaller SCCs
let mut tarjan_scc = TarjanScc::new();
tarjan_scc.run(&subgraph, |scc| {
if scc.len() > 1 {
sccs.push(scc.to_vec());
}
});
}
cycles
}