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//! Minimum Spanning Tree algorithms.
use std::collections::{BinaryHeap, HashMap};
use crate::prelude::*;
use crate::data::Element;
use crate::scored::MinScored;
use crate::unionfind::UnionFind;
use crate::visit::{Data, IntoNodeReferences, NodeRef};
use crate::visit::{IntoEdgeReferences, NodeIndexable};
/// \[Generic\] Compute a *minimum spanning tree* of a graph.
///
/// The input graph is treated as if undirected.
///
/// Using Kruskal's algorithm with runtime **O(|E| log |E|)**. We actually
/// return a minimum spanning forest, i.e. a minimum spanning tree for each connected
/// component of the graph.
///
/// The resulting graph has all the vertices of the input graph (with identical node indices),
/// and **|V| - c** edges, where **c** is the number of connected components in `g`.
///
/// Use `from_elements` to create a graph from the resulting iterator.
pub fn min_spanning_tree<G>(g: G) -> MinSpanningTree<G>
where
G::NodeWeight: Clone,
G::EdgeWeight: Clone + PartialOrd,
G: IntoNodeReferences + IntoEdgeReferences + NodeIndexable,
{
// Initially each vertex is its own disjoint subgraph, track the connectedness
// of the pre-MST with a union & find datastructure.
let subgraphs = UnionFind::new(g.node_bound());
let edges = g.edge_references();
let mut sort_edges = BinaryHeap::with_capacity(edges.size_hint().0);
for edge in edges {
sort_edges.push(MinScored(
edge.weight().clone(),
(edge.source(), edge.target()),
));
}
MinSpanningTree {
graph: g,
node_ids: Some(g.node_references()),
subgraphs,
sort_edges,
node_map: HashMap::new(),
node_count: 0,
}
}
/// An iterator producing a minimum spanning forest of a graph.
#[derive(Debug, Clone)]
pub struct MinSpanningTree<G>
where
G: Data + IntoNodeReferences,
{
graph: G,
node_ids: Option<G::NodeReferences>,
subgraphs: UnionFind<usize>,
#[allow(clippy::type_complexity)]
sort_edges: BinaryHeap<MinScored<G::EdgeWeight, (G::NodeId, G::NodeId)>>,
node_map: HashMap<usize, usize>,
node_count: usize,
}
impl<G> Iterator for MinSpanningTree<G>
where
G: IntoNodeReferences + NodeIndexable,
G::NodeWeight: Clone,
G::EdgeWeight: PartialOrd,
{
type Item = Element<G::NodeWeight, G::EdgeWeight>;
fn next(&mut self) -> Option<Self::Item> {
let g = self.graph;
if let Some(ref mut iter) = self.node_ids {
if let Some(node) = iter.next() {
self.node_map.insert(g.to_index(node.id()), self.node_count);
self.node_count += 1;
return Some(Element::Node {
weight: node.weight().clone(),
});
}
}
self.node_ids = None;
// Kruskal's algorithm.
// Algorithm is this:
//
// 1. Create a pre-MST with all the vertices and no edges.
// 2. Repeat:
//
// a. Remove the shortest edge from the original graph.
// b. If the edge connects two disjoint trees in the pre-MST,
// add the edge.
while let Some(MinScored(score, (a, b))) = self.sort_edges.pop() {
// check if the edge would connect two disjoint parts
let (a_index, b_index) = (g.to_index(a), g.to_index(b));
if self.subgraphs.union(a_index, b_index) {
let (&a_order, &b_order) =
match (self.node_map.get(&a_index), self.node_map.get(&b_index)) {
(Some(a_id), Some(b_id)) => (a_id, b_id),
_ => panic!("Edge references unknown node"),
};
return Some(Element::Edge {
source: a_order,
target: b_order,
weight: score,
});
}
}
None
}
}