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// SPDX-License-Identifier: Apache-2.0
// Copyright 2024-2026 Dragonscale Team
//! Minimum Spanning Tree (MST) Algorithm.
//!
//! Uses Kruskal's algorithm to find the Minimum Spanning Tree of a weighted graph.
//! Treating graph as undirected (if include_reverse is true, we dedup edges; if not, we treat directed as undirected structure).
//! Returns the edges in the MST and total weight.
use crate::algo::GraphProjection;
use crate::algo::algorithms::Algorithm;
use uni_common::core::id::Vid;
pub struct MinimumSpanningTree;
#[derive(Debug, Clone, Default)]
pub struct MstConfig {
// If true, treats graph as undirected by considering u->v and v->u as same edge.
// If false, treats directed edges, but MST is usually defined for undirected.
// Kruskal's works on edges.
}
pub struct MstResult {
pub edges: Vec<(Vid, Vid, f64)>, // (u, v, weight)
pub total_weight: f64,
}
impl Algorithm for MinimumSpanningTree {
type Config = MstConfig;
type Result = MstResult;
fn name() -> &'static str {
"mst"
}
fn run(graph: &GraphProjection, _config: Self::Config) -> Self::Result {
let n = graph.vertex_count();
if n == 0 {
return MstResult {
edges: Vec::new(),
total_weight: 0.0,
};
}
// Collect all edges
// If we want to treat graph as undirected, we should dedup (u, v) and (v, u).
// Standard approach: normalize (min, max).
let mut edges = Vec::new();
for u in 0..n as u32 {
for (i, &v) in graph.out_neighbors(u).iter().enumerate() {
// If treating as undirected, only add if u < v to avoid duplicates
// assuming symmetry. If not symmetric, Kruskal's on directed graph
// produces Minimum Spanning Forest (Arborescence is different).
// Let's assume undirected MST on the underlying graph structure.
if u < v {
let weight = if graph.has_weights() {
graph.out_weight(u, i)
} else {
1.0
};
edges.push((u, v, weight));
}
}
}
// Sort by weight
edges.sort_by(|a, b| a.2.partial_cmp(&b.2).unwrap());
// Union-Find
let mut parent: Vec<u32> = (0..n as u32).collect();
let mut rank: Vec<u8> = vec![0; n];
fn find(parent: &mut [u32], mut x: u32) -> u32 {
while parent[x as usize] != x {
parent[x as usize] = parent[parent[x as usize] as usize];
x = parent[x as usize];
}
x
}
fn union(parent: &mut [u32], rank: &mut [u8], x: u32, y: u32) -> bool {
let px = find(parent, x);
let py = find(parent, y);
if px == py {
return false;
}
match rank[px as usize].cmp(&rank[py as usize]) {
std::cmp::Ordering::Less => parent[px as usize] = py,
std::cmp::Ordering::Greater => parent[py as usize] = px,
std::cmp::Ordering::Equal => {
parent[py as usize] = px;
rank[px as usize] += 1;
}
}
true
}
let mut mst_edges = Vec::new();
let mut total_weight = 0.0;
for (u, v, w) in edges {
if union(&mut parent, &mut rank, u, v) {
mst_edges.push((graph.to_vid(u), graph.to_vid(v), w));
total_weight += w;
}
}
MstResult {
edges: mst_edges,
total_weight,
}
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::algo::test_utils::build_test_graph;
#[test]
fn test_mst_simple() {
// 0-1 (1.0), 1-2 (2.0), 0-2 (10.0)
// MST should be (0,1) and (1,2) => weight 3.0
let vids = vec![Vid::from(0), Vid::from(1), Vid::from(2)];
let edges = vec![
(Vid::from(0), Vid::from(1)),
(Vid::from(1), Vid::from(2)),
(Vid::from(0), Vid::from(2)),
];
// build_test_graph does not support weights yet.
// I need to update build_test_graph or create a new helper.
// Or I can modify GraphProjection field directly since it's pub(crate) and I'm in same crate.
let mut graph = build_test_graph(vids, edges);
// Inject weights manually
// Edges in build_test_graph are added in order of iteration over `edges`.
// Order: (0,1), (1,2), (0,2).
// Node 0: out_neighbors [1, 2]
// Node 1: out_neighbors [2]
// Node 2: []
// We need to match this structure.
// 0->1 (idx 0 for node 0) -> weight 1.0
// 0->2 (idx 1 for node 0) -> weight 10.0
// 1->2 (idx 0 for node 1) -> weight 2.0
// Flattened weights vector for GraphProjection:
// Node 0 edges, then Node 1 edges, etc.
// Node 0: [1.0, 10.0]
// Node 1: [2.0]
// Node 2: []
graph.out_weights = Some(vec![1.0, 10.0, 2.0]);
let result = MinimumSpanningTree::run(&graph, MstConfig::default());
assert_eq!(result.total_weight, 3.0);
assert_eq!(result.edges.len(), 2);
}
}