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//! Separate nodes of a directed graph into [strongly connected
//! components](https://en.wikipedia.org/wiki/Strongly_connected_component).
//!
//! A [path-based strong component
//! algorithm](https://en.wikipedia.org/wiki/Path-based_strong_component_algorithm)
//! is used.
use std::collections::{HashMap, HashSet};
use std::hash::Hash;
struct Params<N, FN>
where
N: Hash + Eq,
{
preorders: HashMap<N, Option<usize>>,
c: usize,
successors: FN,
p: Vec<N>,
s: Vec<N>,
scc: Vec<Vec<N>>,
scca: HashSet<N>,
}
impl<N, FN, IN> Params<N, FN>
where
N: Clone + Hash + Eq,
FN: FnMut(&N) -> IN,
IN: IntoIterator<Item = N>,
{
fn new(nodes: &[N], successors: FN) -> Self {
Self {
preorders: nodes
.iter()
.map(|n| (n.clone(), None))
.collect::<HashMap<N, Option<usize>>>(),
c: 0,
successors,
p: Vec::new(),
s: Vec::new(),
scc: Vec::new(),
scca: HashSet::new(),
}
}
}
fn recurse_onto<N, FN, IN>(v: &N, params: &mut Params<N, FN>)
where
N: Clone + Hash + Eq,
FN: FnMut(&N) -> IN,
IN: IntoIterator<Item = N>,
{
params.preorders.insert(v.clone(), Some(params.c));
params.c += 1;
params.s.push(v.clone());
params.p.push(v.clone());
for w in (params.successors)(v) {
if !params.scca.contains(&w) {
if let Some(pw) = params.preorders.get(&w).and_then(|w| *w) {
while params.preorders[¶ms.p[params.p.len() - 1]].unwrap() > pw {
params.p.pop();
}
} else {
recurse_onto(&w, params);
}
}
}
if params.p[params.p.len() - 1] == *v {
params.p.pop();
let mut component = Vec::new();
while let Some(node) = params.s.pop() {
component.push(node.clone());
params.scca.insert(node.clone());
params.preorders.remove(&node);
if node == *v {
break;
}
}
params.scc.push(component);
}
}
/// Partition nodes reachable from a starting point into strongly connected components.
///
/// - `start` is the node we want to explore the graph from.
/// - `successors` returns a list of successors for a given node.
///
/// The function returns a list of strongly connected components sets. It will contain
/// at least one component (the one containing the `start` node).
pub fn strongly_connected_components_from<N, FN, IN>(start: &N, successors: FN) -> Vec<Vec<N>>
where
N: Clone + Hash + Eq,
FN: FnMut(&N) -> IN,
IN: IntoIterator<Item = N>,
{
let mut params = Params::new(&[], successors);
recurse_onto(start, &mut params);
params.scc
}
/// Compute the strongly connected component containing a given node.
///
/// - `node` is the node we want the strongly connected component for.
/// - `successors` returns a list of successors for a given node.
///
/// The function returns the strongly connected component containing the node,
/// which is guaranteed to contain at least `node`.
#[allow(clippy::missing_panics_doc)]
pub fn strongly_connected_component<N, FN, IN>(node: &N, successors: FN) -> Vec<N>
where
N: Clone + Hash + Eq,
FN: FnMut(&N) -> IN,
IN: IntoIterator<Item = N>,
{
// The unwrap() cannot fail as there will always be at least one group.
strongly_connected_components_from(node, successors)
.pop()
.unwrap()
}
/// Partition all strongly connected components in a graph.
///
/// - `nodes` is a collection of nodes.
/// - `successors` returns a list of successors for a given node.
///
/// The function returns a list of strongly connected components sets.
pub fn strongly_connected_components<N, FN, IN>(nodes: &[N], successors: FN) -> Vec<Vec<N>>
where
N: Clone + Hash + Eq,
FN: FnMut(&N) -> IN,
IN: IntoIterator<Item = N>,
{
let mut params = Params::new(nodes, successors);
while let Some(node) = params.preorders.keys().find(|_| true).cloned() {
recurse_onto(&node, &mut params);
}
params.scc
}