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Move Minimum Spanning Tree Algorithm to its own module (#624)
* refact: move minimum spanning tree algo to its own module * refact: move min_spanning_tree benches to a different test file
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,60 @@ | ||
| #![feature(test)] | ||
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| extern crate petgraph; | ||
| extern crate test; | ||
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| use test::Bencher; | ||
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| #[allow(dead_code)] | ||
| mod common; | ||
| use common::{digraph, ungraph}; | ||
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| use petgraph::algo::min_spanning_tree; | ||
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| #[bench] | ||
| fn min_spanning_tree_praust_undir_bench(bench: &mut Bencher) { | ||
| let a = ungraph().praust_a(); | ||
| let b = ungraph().praust_b(); | ||
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| bench.iter(|| (min_spanning_tree(&a), min_spanning_tree(&b))); | ||
| } | ||
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| #[bench] | ||
| fn min_spanning_tree_praust_dir_bench(bench: &mut Bencher) { | ||
| let a = digraph().praust_a(); | ||
| let b = digraph().praust_b(); | ||
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| bench.iter(|| (min_spanning_tree(&a), min_spanning_tree(&b))); | ||
| } | ||
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| #[bench] | ||
| fn min_spanning_tree_full_undir_bench(bench: &mut Bencher) { | ||
| let a = ungraph().full_a(); | ||
| let b = ungraph().full_b(); | ||
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| bench.iter(|| (min_spanning_tree(&a), min_spanning_tree(&b))); | ||
| } | ||
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| #[bench] | ||
| fn min_spanning_tree_full_dir_bench(bench: &mut Bencher) { | ||
| let a = digraph().full_a(); | ||
| let b = digraph().full_b(); | ||
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| bench.iter(|| (min_spanning_tree(&a), min_spanning_tree(&b))); | ||
| } | ||
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| #[bench] | ||
| fn min_spanning_tree_petersen_undir_bench(bench: &mut Bencher) { | ||
| let a = ungraph().petersen_a(); | ||
| let b = ungraph().petersen_b(); | ||
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| bench.iter(|| (min_spanning_tree(&a), min_spanning_tree(&b))); | ||
| } | ||
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| #[bench] | ||
| fn min_spanning_tree_petersen_dir_bench(bench: &mut Bencher) { | ||
| let a = digraph().petersen_a(); | ||
| let b = digraph().petersen_b(); | ||
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| bench.iter(|| (min_spanning_tree(&a), min_spanning_tree(&b))); | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,117 @@ | ||
| //! Minimum Spanning Tree algorithms. | ||
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| use std::collections::{BinaryHeap, HashMap}; | ||
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| use crate::prelude::*; | ||
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| use crate::data::Element; | ||
| use crate::scored::MinScored; | ||
| use crate::unionfind::UnionFind; | ||
| use crate::visit::{Data, IntoNodeReferences, NodeRef}; | ||
| use crate::visit::{IntoEdgeReferences, NodeIndexable}; | ||
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| /// \[Generic\] 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()); | ||
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| 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()), | ||
| )); | ||
| } | ||
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| MinSpanningTree { | ||
| graph: g, | ||
| node_ids: Some(g.node_references()), | ||
| subgraphs, | ||
| sort_edges, | ||
| node_map: HashMap::new(), | ||
| node_count: 0, | ||
| } | ||
| } | ||
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| /// 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, | ||
| } | ||
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| impl<G> Iterator for MinSpanningTree<G> | ||
| where | ||
| G: IntoNodeReferences + NodeIndexable, | ||
| G::NodeWeight: Clone, | ||
| G::EdgeWeight: PartialOrd, | ||
| { | ||
| type Item = Element<G::NodeWeight, G::EdgeWeight>; | ||
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| 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; | ||
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| // 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 | ||
| } | ||
| } |
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