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* 20 convert edge type into a tuple struct (#23) * Changed Edge (tuple type) to Edge (tuple struct) and made related changes * Added Edge changes to sync_digraph, ungraph and sync_ungraph * Changed Path<K, N, E> types iterator to use Edge<K, N, E> instead of (u, v, e) * Corrected kojarasu examples to be stable for assertion tests * Readme updated to reflect changes in pr * Correct incorrect catgory slug in Cargo.toml https://crates.io/category_slugs * 22 add minimum spanning tree to examples (#24) * #22 Add prim's algorithm example * #22 Fix example to work with Edge() tuple struct * #22 Fix exec method in ungraph to work with Edge * Add documentation to prim example, refactor * Improve package description * More descriptive names for examples * Make ungraph methods FnMut, simplify prim's example, add for_each to ungraph * Change map to for_each and remove filter_map from methods * Improve documentation * Corret memory leak. Adjacency lists need to store WeakNode references to avoid circular reference * Improve build.yml to check for leaks on examples with valgrind * Changed branch in build.yml for testing * Remove size test for now * Correct size tests * Restructure node module in ungraph and digraph, chaneg ungraph to use std's BinaryHeap * Copy new implementation to sync versions * Correct documentation * If node that an edge is pointing to has been dropped, panic * Change build.yml to point to master branch Co-authored-by: Satu Koskinen <[email protected]>
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,115 @@ | ||
| // Prim's algorithm | ||
| // | ||
| // Prim's algorithm (also known as Jarník's algorithm) is a greedy algorithm | ||
| // that finds a minimum spanning tree for a weighted undirected graph. This | ||
| // means it finds a subset of the edges that forms a tree that includes every | ||
| // vertex, where the total weight of all the edges in the tree is minimized. | ||
| // The algorithm operates by building this tree one vertex at a time, | ||
| // from an arbitrary starting vertex, at each step adding the cheapest possible | ||
| // connection from the tree to another vertex. | ||
| // | ||
| // https://en.wikipedia.org/wiki/Prim%27s_algorithm | ||
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| use gdsl::ungraph::*; | ||
| use gdsl::*; | ||
| use std::collections::{BinaryHeap, HashSet}; | ||
| use std::cmp::Reverse; | ||
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| type N = Node<usize, (), u64>; | ||
| type E = Edge<usize, (), u64>; | ||
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| // Standard library's BinaryHeap is a max-heap, so we need to reverse the | ||
| // ordering of the edge weights to get a min-heap using the Reverse wrapper. | ||
| type Heap = BinaryHeap<Reverse<E>>; | ||
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| fn prim_minimum_spanning_tree(s: &N) -> Vec<E> { | ||
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| // We collect the resulting MST edges in to a vector. | ||
| let mut mst: Vec<E> = vec![]; | ||
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| // We use a HashSet to keep track of the nodes that are in the MST. | ||
| let mut in_mst: HashSet<usize> = HashSet::new(); | ||
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| // We use a BinaryHeap to keep track of all edges sorted by weight. | ||
| let mut heap = Heap::new(); | ||
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| in_mst.insert(*s.key()); | ||
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| // Collect all edges reachable from `s` to a Min Heap. | ||
| s.bfs().for_each(&mut |edge| { | ||
| heap.push(Reverse(edge.clone())); | ||
| }).search(); | ||
|
|
||
| // When we pop from the min heap, we know that the edge is the cheapest | ||
| // edge to add to the MST, but we need to make sure that the edge | ||
| // connecting to a node that is not already in the MST, otherwise we | ||
| // we store the edge and continue to the next iteration. When we find | ||
| // an edge that connects to a node that is not in the MST, we add the | ||
| // stored edges back to the heap. | ||
| let mut tmp: Vec<E> = vec![]; | ||
|
|
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| // While the heap is not empty, search for the next edge | ||
| // that connects a node in the tree to a node not in the tree. | ||
| while let Some(Reverse(edge)) = heap.pop() { | ||
| let Edge(u, v, _) = edge.clone(); | ||
|
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| // If the edge's source node `u` is in the MST... | ||
| if in_mst.contains(u.key()) { | ||
|
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| // ...and the edge's destination node `v` is not in the MST, | ||
| // then we add the edge to the MST and add all edges | ||
| // in `tmp` back to the heap. | ||
| if in_mst.contains(v.key()) == false { | ||
| in_mst.insert(*v.key()); | ||
| mst.push(edge.clone()); | ||
| for tmp_edge in &tmp { | ||
| heap.push(Reverse(tmp_edge.clone())); | ||
| } | ||
| } | ||
| } else { | ||
|
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| // The edge is the cheapest edge to add to the MST, but | ||
| // it's source node `u` nor it's destination node `v` are | ||
| // in the MST, so we store the edge and continue to the next | ||
| // iteration. | ||
| if in_mst.contains(v.key()) == false { | ||
| tmp.push(edge); | ||
| } | ||
| } | ||
|
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| // If neither condition is met, then the edge's destination node | ||
| // `v` is already in the MST, so we continue to the next iteration. | ||
| } | ||
| mst | ||
| } | ||
|
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| fn main() { | ||
| // Example g1 from Wikipedia | ||
| let g1 = ungraph![ | ||
| (usize) => [u64] | ||
| (0) => [ (1, 1), (3, 4), (4, 3)] | ||
| (1) => [ (3, 4), (4, 2)] | ||
| (2) => [ (4, 4), (5, 5)] | ||
| (3) => [ (4, 4)] | ||
| (4) => [ (5, 7)] | ||
| (5) => [] | ||
| ]; | ||
| let forest = prim_minimum_spanning_tree(&g1[0]); | ||
| let sum = forest.iter().fold(0, |acc, e| acc + e.2); | ||
| assert!(sum == 16); | ||
|
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| // Example g2 from Figure 7.1 in https://jeffe.cs.illinois.edu/teaching/algorithms/book/07-mst.pdf | ||
| let g2 = ungraph![ | ||
| (usize) => [u64] | ||
| (0) => [ (1, 8), (2, 5)] | ||
| (1) => [ (2, 10), (3, 2), (4, 18)] | ||
| (2) => [ (3, 3), (5, 16)] | ||
| (3) => [ (4, 12), (5, 30)] | ||
| (4) => [ (6, 4)] | ||
| (5) => [ (6, 26)] | ||
| (6) => [] | ||
| ]; | ||
| let forest = prim_minimum_spanning_tree(&g2[0]); | ||
| let sum = forest.iter().fold(0, |acc, e| acc + e.2); | ||
| assert!(sum == 42); | ||
| } |
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