Add Prim's Algorithm for Minimum Spanning Tree

[BryanCruz]

Prim's algorithm: https://en.wikipedia.org/wiki/Prim%27s_algorithm

This PR adds another algorithm to find the Minimum Spanning Tree of a graph, an alternative to Kruskal's.

1. Prim's algorithm has some limitations, such as the input graph must be undirected and it should not have disconnected components.
   I'm wondering if this can be enforced with traits, if anyone can help on this.

2. I would like to suggest adding another algorithm as well, min_spanning_forest_prim, that iterates through this algorithm to find min spanning tree for all input graph components. min_spanning_forest_kruskal would be trivial to implement, since current min_spanning_tree function, using Kruskal's algorithm, already finds a min spanning forest. Any thoughts on this?

This PR also aims to fix current min_spanning_tree benches, since they currently do not iterate through the created MinSpanningTree structure, not giving the actual bench for Kruskal algorithm.

3. I added a simple function to iterate through the generated tree elements, but I'm not very familiar with Rust ecosystem, so I would appreciate if anyone knows a better way to force the iteration:

// Current Bench:
bench.iter(|| (min_spanning_tree(&a), min_spanning_tree(&b)));

// Suggested Bench:
bench.iter(|| (iterate_mst_kruskal(&a), iterate_mst_kruskal(&b)));

// Force Tree Iteration:
fn iterate_mst_kruskal<G>(g: G) -> bool
where
    G: Data + IntoEdges + IntoNodeReferences + IntoEdgeReferences + NodeIndexable,
    G::NodeWeight: Clone,
    G::EdgeWeight: Clone + PartialOrd,
{
    let mst = min_spanning_tree(g);
    mst.into_iter().all(|_| true)
}

[ABorgna]

Thanks for the PR!

1. Kruskal's doc states
   The input graph is treated as if undirected.
   perhaps we could do the same here
2. That could be useful.
   It is a bit inconsistent that Kruscal always returns a forest, but leaving it as undefined behaviour if there is more than one component sounds OK.

[ABorgna]

Good catch. Using black_box is the best bet to avoid it getting optimised away.

Suggested change

	fn iterate_mst_kruskal<G>(g: G) -> bool
	where
	G: Data + IntoEdges + IntoNodeReferences + IntoEdgeReferences + NodeIndexable,
	G::NodeWeight: Clone,
	G::EdgeWeight: Clone + PartialOrd,
	{
	let mst = min_spanning_tree(g);
	mst.into_iter().all(|_| true)
	}
	fn iterate_mst_prim<G>(g: G) -> bool
	where
	G: Data + IntoEdges + IntoNodeReferences + IntoEdgeReferences + NodeIndexable,
	G::NodeWeight: Clone,
	G::EdgeWeight: Clone + PartialOrd,
	{
	let mst = min_spanning_tree_prim(g);
	mst.into_iter().all(|_| true)
	fn iterate_mst_kruskal<G>(g: G)
	where
	G: Data + IntoEdges + IntoNodeReferences + IntoEdgeReferences + NodeIndexable,
	G::NodeWeight: Clone,
	G::EdgeWeight: Clone + PartialOrd,
	{
	for e in min_spanning_tree(g) {
	std::hint::black_box(e);
	}
	}
	fn iterate_mst_prim<G>(g: G)
	where
	G: Data + IntoEdges + IntoNodeReferences + IntoEdgeReferences + NodeIndexable,
	G::NodeWeight: Clone,
	G::EdgeWeight: Clone + PartialOrd,
	{
	for e in min_spanning_tree_prim(g) {
	std::hint::black_box(e);
	}

[BryanCruz]

1. Kruskal's doc states
   The input graph is treated as if undirected.
   perhaps we could do the same here

Thanks for the review @ABorgna :)

I updated the docs to let more explicit what will happen if input graph is directed or has more than 1 component, and applied the suggested change for benches.

I think we would need to convert a directed graph to an undirected one in order to Prim behave correctly on it. For example, a graph where edges are: (I) A-5->B , (II) B-10->C and (III) C-15->A, the valid MST computed by Prim would be {I and II} (undirected), but in order to actually implement this behavior we would need some sort of inverse of IntoEdgeReferences, to access edges that goes to a certain node

So I don't think it's worth the complexity, since there are other algorithms specifically for directed graphs that could be implemented.

What do you think?