func Kruskal(g Graph) (map[Edge]struct{}, error) {

	// A = ∅
	A := make(map[Edge]struct{})

	// disjointSet maps a member Node to a represent.
	// (https://en.wikipedia.org/wiki/Disjoint-set_data_structure)
	forests := NewForests()

	// for each vertex v in G:
	for _, nd := range g.GetNodes() {
		// MakeDisjointSet(v)
		MakeDisjointSet(forests, nd.String())
	}

	// edges = get all edges
	edges := []Edge{}
	foundEdge := make(map[string]struct{})
	for id1, nd1 := range g.GetNodes() {
		tm, err := g.GetTargets(id1)
		if err != nil {
			return nil, err
		}
		for id2, nd2 := range tm {
			weight, err := g.GetWeight(id1, id2)
			if err != nil {
				return nil, err
			}
			edge := NewEdge(nd1, nd2, weight)
			if _, ok := foundEdge[edge.String()]; !ok {
				edges = append(edges, edge)
				foundEdge[edge.String()] = struct{}{}
			}
		}

		sm, err := g.GetSources(id1)
		if err != nil {
			return nil, err
		}
		for id3, nd3 := range sm {
			weight, err := g.GetWeight(id3, id1)
			if err != nil {
				return nil, err
			}
			edge := NewEdge(nd3, nd1, weight)
			if _, ok := foundEdge[edge.String()]; !ok {
				edges = append(edges, edge)
				foundEdge[edge.String()] = struct{}{}
			}
		}
	}

	// sort edges in ascending order of weight
	sort.Sort(EdgeSlice(edges))

	// for each edge (u, v) in edges:
	for _, edge := range edges {
		// if FindSet(u) ≠ FindSet(v):
		if FindSet(forests, edge.Source().String()).represent != FindSet(forests, edge.Target().String()).represent {

			// A = A ∪ {(u, v)}
			A[edge] = struct{}{}

			// Union(u, v)
			// overwrite v's represent with u's represent
			Union(forests, FindSet(forests, edge.Source().String()), FindSet(forests, edge.Target().String()))
		}
	}

	return A, nil
}
func Kruskal(g Graph) (map[Edge]struct{}, error) {

	// A = ∅
	A := make(map[Edge]struct{})

	// disjointSet maps a member Node to a represent.
	// (https://en.wikipedia.org/wiki/Disjoint-set_data_structure)
	forests := NewForests()

	// for each vertex v in G:
	for _, nd := range g.GetNodes() {
		// MakeDisjointSet(v)
		MakeDisjointSet(forests, nd.String())
	}

	// edges = get all edges
	edges := []Edge{}
	foundEdge := make(map[string]struct{})
	for id1, nd1 := range g.GetNodes() {
		tm, err := g.GetTargets(id1)
		if err != nil {
			return nil, err
		}
		for id2, nd2 := range tm {
			weight, err := g.GetWeight(id1, id2)
			if err != nil {
				return nil, err
			}
			edge := NewEdge(nd1, nd2, weight)
			if _, ok := foundEdge[edge.String()]; !ok {
				edges = append(edges, edge)
				foundEdge[edge.String()] = struct{}{}
			}
		}

		sm, err := g.GetSources(id1)
		if err != nil {
			return nil, err
		}
		for id3, nd3 := range sm {
			weight, err := g.GetWeight(id3, id1)
			if err != nil {
				return nil, err
			}
			edge := NewEdge(nd3, nd1, weight)
			if _, ok := foundEdge[edge.String()]; !ok {
				edges = append(edges, edge)
				foundEdge[edge.String()] = struct{}{}
			}
		}
	}

	// sort edges in ascending order of weight
	sort.Sort(EdgeSlice(edges))

	// for each edge (u, v) in edges:
	for _, edge := range edges {
		// if FindSet(u) ≠ FindSet(v):
		if FindSet(forests, edge.Source().String()).represent != FindSet(forests, edge.Target().String()).represent {

			// A = A ∪ {(u, v)}
			A[edge] = struct{}{}

			// Union(u, v)
			// overwrite v's represent with u's represent
			Union(forests, FindSet(forests, edge.Source().String()), FindSet(forests, edge.Target().String()))
		}
	}

	return A, nil
}
// Kruskal finds the minimum spanning tree with disjoint-set data structure.
// (http://en.wikipedia.org/wiki/Kruskal%27s_algorithm)
//
//	 0. Kruskal(G)
//	 1.
//	 2. 	A = ∅
//	 3.
//	 4. 	for each vertex v in G:
//	 5. 		MakeDisjointSet(v)
//	 6.
//	 7. 	edges = get all edges
//	 8. 	sort edges in ascending order of weight
//	 9.
//	10. 	for each edge (u, v) in edges:
//	11. 		if FindSet(u) ≠ FindSet(v):
//	12. 			A = A ∪ {(u, v)}
//	13. 			Union(u, v)
//	14.
//	15. 	return A
//