use std::collections::BinaryHeap;
use std::borrow::{Borrow};
use std::cmp::min;
use super::{
Graph,
Undirected,
EdgeDirection,
EdgeType,
Outgoing,
Incoming,
Dfs,
};
use scored::MinScored;
use super::visit::{
Visitable,
VisitMap,
IntoNeighbors,
IntoNeighborsDirected,
IntoNodeIdentifiers,
IntoExternals,
NodeIndexable,
NodeCompactIndexable,
IntoEdgeReferences,
EdgeRef,
};
use super::unionfind::UnionFind;
use super::graph::{
IndexType,
NodeIndex,
};
pub use super::isomorphism::{
is_isomorphic,
is_isomorphic_matching,
};
pub use super::dijkstra::dijkstra;
pub fn connected_components<G>(g: G) -> usize
where G: NodeCompactIndexable + IntoEdgeReferences,
{
let mut vertex_sets = UnionFind::new(g.node_bound());
for edge in g.edge_references() {
let (a, b) = (edge.source(), edge.target());
vertex_sets.union(G::to_index(a), G::to_index(b));
}
let mut labels = vertex_sets.into_labeling();
labels.sort();
labels.dedup();
labels.len()
}
pub fn is_cyclic_undirected<G>(g: G) -> bool
where G: NodeIndexable + IntoEdgeReferences
{
let mut edge_sets = UnionFind::new(g.node_bound());
for edge in g.edge_references() {
let (a, b) = (edge.source(), edge.target());
if !edge_sets.union(G::to_index(a), G::to_index(b)) {
return true
}
}
false
}
#[inline]
fn toposort_generic<G, F>(g: G, mut visit: F)
where G: IntoNeighborsDirected + IntoExternals + Visitable,
F: FnMut(G, G::NodeId),
{
let mut ordered = g.borrow().visit_map();
let mut tovisit = Vec::new();
tovisit.extend(g.externals(Incoming));
while let Some(nix) = tovisit.pop() {
if ordered.is_visited(&nix) {
continue;
}
visit(g, nix.clone());
ordered.visit(nix.clone());
for neigh in g.neighbors_directed(nix, Outgoing) {
if g.neighbors_directed(neigh.clone(), Incoming)
.all(|b| ordered.is_visited(&b)) {
tovisit.push(neigh);
}
}
}
}
pub fn is_cyclic_directed<G>(g: G) -> bool
where G: IntoNodeIdentifiers + IntoNeighborsDirected + IntoExternals + Visitable,
{
let mut n_ordered = 0;
toposort_generic(g, |_, _| n_ordered += 1);
n_ordered != g.node_count()
}
pub fn toposort<G>(g: G) -> Vec<G::NodeId>
where G: IntoNodeIdentifiers + IntoNeighborsDirected + IntoExternals + Visitable,
{
let mut order = Vec::with_capacity(g.node_count());
toposort_generic(g, |_, ix| order.push(ix));
order
}
pub fn scc<G>(g: G) -> Vec<Vec<G::NodeId>>
where G: IntoNeighborsDirected + Visitable + IntoNodeIdentifiers,
{
let mut dfs = Dfs::empty(&g);
let mut finished = g.visit_map();
let mut finish_order = Vec::new();
for i in g.node_identifiers() {
if dfs.discovered.is_visited(&i) {
continue
}
dfs.stack.push(i);
while let Some(&nx) = dfs.stack.last() {
if dfs.discovered.visit(nx) {
for succ in g.neighbors_directed(nx, EdgeDirection::Incoming) {
if !dfs.discovered.is_visited(&succ) {
dfs.stack.push(succ);
}
}
} else {
dfs.stack.pop();
if finished.visit(nx) {
finish_order.push(nx);
}
}
}
}
g.reset_map(&mut dfs.discovered);
let mut sccs = Vec::new();
for i in finish_order.into_iter().rev() {
if dfs.discovered.is_visited(&i) {
continue;
}
dfs.move_to(i);
let mut scc = Vec::new();
while let Some(nx) = dfs.next(g) {
scc.push(nx);
}
sccs.push(scc);
}
sccs
}
pub fn tarjan_scc<G>(g: G) -> Vec<Vec<G::NodeId>>
where G: IntoNodeIdentifiers + IntoNeighbors + NodeIndexable
{
#[derive(Copy, Clone)]
#[derive(Debug)]
struct NodeData {
index: Option<usize>,
lowlink: usize,
on_stack: bool,
}
#[derive(Debug)]
struct Data<'a, G>
where G: NodeIndexable,
G::NodeId: 'a
{
index: usize,
nodes: Vec<NodeData>,
stack: Vec<G::NodeId>,
sccs: &'a mut Vec<Vec<G::NodeId>>,
}
fn scc_visit<G>(v: G::NodeId, g: G, data: &mut Data<G>)
where G: IntoNeighbors + NodeIndexable
{
macro_rules! node {
($node:expr) => (data.nodes[G::to_index($node)])
}
if node![v].index.is_some() {
return;
}
let v_index = data.index;
node![v].index = Some(v_index);
node![v].lowlink = v_index;
node![v].on_stack = true;
data.stack.push(v);
data.index += 1;
for w in g.neighbors(v) {
match node![w].index {
None => {
scc_visit(w, g, data);
node![v].lowlink = min(node![v].lowlink, node![w].lowlink);
}
Some(w_index) => {
if node![w].on_stack {
let v_lowlink = &mut node![v].lowlink;
*v_lowlink = min(*v_lowlink, w_index);
}
}
}
}
if let Some(v_index) = node![v].index {
if node![v].lowlink == v_index {
let mut cur_scc = Vec::new();
loop {
let w = data.stack.pop().unwrap();
node![w].on_stack = false;
cur_scc.push(w);
if G::to_index(w) == G::to_index(v) { break; }
}
data.sccs.push(cur_scc);
}
}
}
let mut sccs = Vec::new();
{
let map = (0..g.node_bound()).map(|_| {
NodeData { index: None, lowlink: !0, on_stack: false }
}).collect();
let mut data = Data {
index: 0,
nodes: map,
stack: Vec::new(),
sccs: &mut sccs,
};
for n in g.node_identifiers() {
scc_visit(n, g, &mut data);
}
}
sccs
}
pub fn condensation<N, E, Ty, Ix>(g: Graph<N, E, Ty, Ix>, make_acyclic: bool) -> Graph<Vec<N>, E, Ty, Ix>
where Ty: EdgeType,
Ix: IndexType,
{
let sccs = scc(&g);
let mut condensed: Graph<Vec<N>, E, Ty, Ix> = Graph::with_capacity(sccs.len(), g.edge_count());
let mut node_map = vec![NodeIndex::end(); g.node_count()];
for comp in sccs {
let new_nix = condensed.add_node(Vec::new());
for nix in comp {
node_map[nix.index()] = new_nix;
}
}
let (nodes, edges) = g.into_nodes_edges();
for (nix, node) in nodes.into_iter().enumerate() {
condensed[node_map[nix]].push(node.weight);
}
for edge in edges {
let source = node_map[edge.source().index()];
let target = node_map[edge.target().index()];
if make_acyclic {
if source != target {
condensed.update_edge(source, target, edge.weight);
}
} else {
condensed.add_edge(source, target, edge.weight);
}
}
condensed
}
pub fn min_spanning_tree<N, E, Ty, Ix>(g: &Graph<N, E, Ty, Ix>)
-> Graph<N, E, Undirected, Ix>
where N: Clone,
E: Clone + PartialOrd,
Ty: EdgeType,
Ix: IndexType,
{
if g.node_count() == 0 {
return Graph::with_capacity(0, 0)
}
let mut mst = Graph::with_capacity(g.node_count(), g.node_count() - 1);
for node in g.raw_nodes() {
mst.add_node(node.weight.clone());
}
let mut subgraphs = UnionFind::new(g.node_count());
let mut sort_edges = BinaryHeap::with_capacity(g.edge_count());
for edge in g.edge_references() {
sort_edges.push(MinScored(edge.weight().clone(), (edge.source(), edge.target())));
}
while let Some(MinScored(score, (a, b))) = sort_edges.pop() {
if subgraphs.union(a.index(), b.index()) {
mst.add_edge(a, b, score);
}
}
debug_assert!(mst.node_count() == g.node_count());
debug_assert!(mst.edge_count() < g.node_count());
mst
}