From f3517287621fd44e3a2d2c9f2525c95b1caf1ddf Mon Sep 17 00:00:00 2001
From: Mikolaj Wielgus <wielgusmikolaj@gmail.com>
Date: Thu, 19 Mar 2026 19:50:50 +0100
Subject: [PATCH] Add Kruskal's minimum spanning tree algorithm

---
 topola/Cargo.toml  |  2 ++
 topola/src/math.rs | 47 ++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 49 insertions(+)

diff --git a/topola/Cargo.toml b/topola/Cargo.toml
index d8287c0..0e26470 100644
--- a/topola/Cargo.toml
+++ b/topola/Cargo.toml
@@ -14,8 +14,10 @@ dearcut = { version = "0.3", features = ["serde", "undoredo"] }
 derive-getters.workspace = true
 derive_more.workspace = true
 i_triangle = "0.40"
+polygon_unionfind = "0.5"
 rstar = "0.12"
 serde.workspace = true
+spade = "2.15"
 specctra = { path = "../specctra" }
 stable-vec = "0.4"
 undoredo.workspace = true
diff --git a/topola/src/math.rs b/topola/src/math.rs
index 0a33ec6..d86a457 100644
--- a/topola/src/math.rs
+++ b/topola/src/math.rs
@@ -168,3 +168,50 @@ impl_polygon_centroid!(f32);
 impl_polygon_centroid!(f64);
 impl_polygon_centroid!(i32);
 impl_polygon_centroid!(i64);
+
+/// Kruskal's minimum spanning tree algorithm.
+pub fn kruskal_mst<W: Copy + Ord>(
+    vertex_count: usize,
+    edges: &[(W, [usize; 2])],
+) -> Vec<[usize; 2]> {
+    let mut sorted_edges = edges.to_vec();
+    sorted_edges.sort_by_key(|(w, _)| *w);
+
+    let mut unionfind: polygon_unionfind::UnionFind<Vec<usize>, Vec<usize>> =
+        polygon_unionfind::UnionFind::with_len(vertex_count);
+    let mut min_spanning_tree = Vec::new();
+
+    for (_, uv) in sorted_edges {
+        if unionfind.union(uv[0], uv[1]) {
+            min_spanning_tree.push(uv);
+        }
+    }
+
+    min_spanning_tree
+}
+
+#[cfg(test)]
+mod tests {
+    use super::kruskal_mst;
+
+    #[test]
+    fn kruskal_mst_on_path_graph() {
+        // Path graph. Graph edges just form a sequence without cycle.
+        let edges = [(1, [0, 1]), (2, [1, 2]), (3, [2, 3])];
+        let mst = kruskal_mst(4, &edges);
+
+        assert_eq!(mst.len(), 3);
+        assert_eq!(mst, [[0, 1], [1, 2], [2, 3]]);
+    }
+
+    #[test]
+    fn kruskal_mst_on_triangle() {
+        // Triangle graph. Graph edges form a triangle.
+        let edges = [(1, [0, 1]), (2, [1, 2]), (3, [0, 2])];
+        let mst = kruskal_mst(3, &edges);
+
+        assert_eq!(mst.len(), 2);
+        assert!(mst.contains(&[0, 1]));
+        assert!(mst.contains(&[1, 2]));
+    }
+}