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/// Implementation of Kruskal's Minimum Spanning Tree algorithm.
///
/// This module provides an implementation of Kruskal's algorithm for finding
/// the minimum spanning tree (MST) of an undirected weighted graph.
use crate::{edge::SimpleEdge, union_find::UnionFind};
use core::cmp::{Reverse, max};
use std::collections::BinaryHeap;
/// Computes the minimum spanning tree using Kruskal's algorithm.
///
/// # Arguments
///
/// * `input_edges` - A slice of `SimpleEdge`s representing the graph's edge
/// Each edge contains source and target vertices and a weight.
///
/// # Returns
///
/// Returns a tuple containing:
/// * The total cost of the minimum spanning tree
/// * A vector of edges that form the minimum spanning tree
///
/// # Example
///
/// ```
/// use toolbox_rs::edge::SimpleEdge;
/// use toolbox_rs::kruskal::kruskal;
///
/// let edges = vec![
/// SimpleEdge::new(0, 1, 7),
/// SimpleEdge::new(0, 3, 5),
/// SimpleEdge::new(1, 2, 8)
/// ];
///
/// let (cost, mst) = kruskal(&edges);
/// ```
pub fn kruskal(input_edges: &[SimpleEdge]) -> (u32, Vec<SimpleEdge>) {
// find max node id
let mut number_of_nodes = 0;
let mut heap = BinaryHeap::new();
for edge in input_edges {
number_of_nodes = max(edge.source, number_of_nodes);
number_of_nodes = max(edge.target, number_of_nodes);
heap.push((Reverse(edge.data), heap.len()));
}
let mut mst = Vec::new();
let mut uf = UnionFind::new(number_of_nodes + 1);
let mut mst_cost = 0;
while mst.len() < number_of_nodes && !heap.is_empty() {
// pop the smallest edge
// we use the index to avoid having to sort the edges
// in the heap
// this is a bit of a hack, but it works
// and is faster than sorting the edges
// in the heap
let (_, idx) = heap.pop().unwrap();
let edge = input_edges[idx];
let x = uf.find(edge.source);
let y = uf.find(edge.target);
if x == y {
continue;
}
mst.push(edge);
uf.union(x, y);
mst_cost += edge.data;
}
(mst_cost, mst)
}
#[cfg(test)]
mod tests {
use crate::{edge::SimpleEdge, kruskal::kruskal};
#[test]
fn wiki_example() {
let edges = vec![
SimpleEdge::new(0, 1, 7),
SimpleEdge::new(0, 3, 5),
SimpleEdge::new(1, 3, 9),
SimpleEdge::new(1, 2, 8),
SimpleEdge::new(1, 4, 7),
SimpleEdge::new(2, 4, 5),
SimpleEdge::new(3, 4, 15),
SimpleEdge::new(3, 5, 6),
SimpleEdge::new(5, 4, 8),
SimpleEdge::new(6, 4, 9),
SimpleEdge::new(5, 6, 11),
];
let (cost, mst) = kruskal(&edges);
assert_eq!(cost, 39);
// Verify the expected edges in the MST
let expected_edges: Vec<(usize, usize)> =
vec![(0, 3), (2, 4), (3, 5), (0, 1), (1, 4), (4, 6)];
assert_eq!(mst.len(), expected_edges.len());
for (src, tgt) in expected_edges {
assert!(
mst.iter().any(|e| (e.source == src && e.target == tgt)
|| (e.source == tgt && e.target == src))
);
}
}
#[test]
fn clr_example() {
let edges = vec![
SimpleEdge::new(0, 1, 16),
SimpleEdge::new(0, 2, 13),
SimpleEdge::new(1, 2, 10),
SimpleEdge::new(1, 3, 12),
SimpleEdge::new(2, 1, 4),
SimpleEdge::new(2, 4, 14),
SimpleEdge::new(3, 2, 9),
SimpleEdge::new(3, 5, 20),
SimpleEdge::new(4, 3, 7),
SimpleEdge::new(4, 5, 4),
];
let (cost, mst) = kruskal(&edges);
assert_eq!(cost, 37);
// Verify the expected edges in the MST
let expected_edges: Vec<(usize, usize)> = vec![(2, 1), (4, 5), (4, 3), (0, 2), (2, 3)];
// Check if the MST contains the expected edges
// Note: The order of edges in the MST may vary, so we check for presence
// rather than exact order
assert_eq!(mst.len(), expected_edges.len());
for (src, tgt) in expected_edges {
assert!(
mst.iter().any(|e| (e.source == src && e.target == tgt)
|| (e.source == tgt && e.target == src))
);
}
}
#[test]
fn empty_graph() {
let edges = vec![];
let (cost, mst) = kruskal(&edges);
assert_eq!(cost, 0);
assert!(mst.is_empty());
}
#[test]
fn single_edge() {
let edges = vec![SimpleEdge::new(0, 1, 5)];
let (cost, mst) = kruskal(&edges);
assert_eq!(cost, 5);
assert_eq!(mst.len(), 1);
assert_eq!(mst[0].data, 5);
}
#[test]
fn disconnected_graph() {
let edges = vec![
SimpleEdge::new(0, 1, 1),
SimpleEdge::new(2, 3, 2),
// No edges between components (0,1) and (2,3)
];
let (cost, mst) = kruskal(&edges);
assert_eq!(cost, 3);
assert_eq!(mst.len(), 2);
}
}