// edgeNodesFor returns the pair of nodes for the ith edge in a simple
// undirected graph. The pair is returned such that w.ID < v.ID.
func edgeNodesFor(i int) (v, w simple.Node) {
	// This is an algebraic simplification of the expressions described
	// on p3 of http://algo.uni-konstanz.de/publications/bb-eglrn-05.pdf
	v = simple.Node(0.5 + math.Sqrt(float64(1+8*i))/2)
	w = simple.Node(i) - v*(v-1)/2
	return v, w
}

// Builds a BFS tree (as a directed graph) from the given graph and start node.
func BFSTree(g graph.Graph, start graph.Node) *simple.DirectedGraph {
	if !g.Has(start) {
		panic(fmt.Sprintf("BFSTree: Start node %r not in graph %r", start, g))
	}

	ret := simple.NewDirectedGraph(0.0, math.Inf(1))
	seen := make(map[int]bool)
	q := queue.New()
	q.Add(start)
	ret.AddNode(simple.Node(start.ID()))

	for q.Length() > 0 {
		node := q.Peek().(graph.Node)
		q.Remove()
		for _, neighbor := range g.From(node) {
			if !seen[neighbor.ID()] {
				seen[neighbor.ID()] = true
				ret.AddNode(simple.Node(neighbor.ID()))
				ret.SetEdge(simple.Edge{F: simple.Node(node.ID()), T: simple.Node(neighbor.ID()), W: g.Edge(node, neighbor).Weight()})
				q.Add(neighbor)
			}
		}
	}

	return ret
}

func TestCommunityQ(t *testing.T) {
	for _, test := range communityQTests {
		g := simple.NewUndirectedGraph(0, 0)
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
			}
		}
		for _, structure := range test.structures {
			communities := make([][]graph.Node, len(structure.memberships))
			for i, c := range structure.memberships {
				for n := range c {
					communities[i] = append(communities[i], simple.Node(n))
				}
			}
			got := Q(g, communities, structure.resolution)
			if !floats.EqualWithinAbsOrRel(got, structure.want, structure.tol, structure.tol) && math.IsNaN(got) != math.IsNaN(structure.want) {
				for _, c := range communities {
					sort.Sort(ordered.ByID(c))
				}
				t.Errorf("unexpected Q value for %q %v: got: %v want: %v",
					test.name, communities, got, structure.want)
			}
		}
	}
}

func TestBetweennessWeighted(t *testing.T) {
	for i, test := range betweennessTests {
		g := simple.NewUndirectedGraph(0, math.Inf(1))
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
			}
		}

		p, ok := path.FloydWarshall(g)
		if !ok {
			t.Errorf("unexpected negative cycle in test %d", i)
			continue
		}

		got := BetweennessWeighted(g, p)
		prec := 1 - int(math.Log10(test.wantTol))
		for n := range test.g {
			gotN, gotOK := got[n]
			wantN, wantOK := test.want[n]
			if gotOK != wantOK {
				t.Errorf("unexpected betweenness existence for test %d, node %c", i, n+'A')
			}
			if !floats.EqualWithinAbsOrRel(gotN, wantN, test.wantTol, test.wantTol) {
				t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
					i, orderedFloats(got, prec), orderedFloats(test.want, prec))
				break
			}
		}
	}
}

func TestDepthFirst(t *testing.T) {
	for i, test := range depthFirstTests {
		g := simple.NewUndirectedGraph(0, math.Inf(1))
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
			}
		}
		w := DepthFirst{
			EdgeFilter: test.edge,
		}
		var got []int
		final := w.Walk(g, test.from, func(n graph.Node) bool {
			if test.until != nil && test.until(n) {
				return true
			}
			got = append(got, n.ID())
			return false
		})
		if !test.final[final] {
			t.Errorf("unexepected final node for test %d:\ngot:  %v\nwant: %v", i, final, test.final)
		}
		sort.Ints(got)
		if test.want != nil && !reflect.DeepEqual(got, test.want) {
			t.Errorf("unexepected DFS traversed nodes for test %d:\ngot:  %v\nwant: %v", i, got, test.want)
		}
	}
}

func TestHITS(t *testing.T) {
	for i, test := range hitsTests {
		g := simple.NewDirectedGraph(0, math.Inf(1))
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
			}
		}
		got := HITS(g, test.tol)
		prec := 1 - int(math.Log10(test.wantTol))
		for n := range test.g {
			if !floats.EqualWithinAbsOrRel(got[n].Hub, test.want[n].Hub, test.wantTol, test.wantTol) {
				t.Errorf("unexpected HITS result for test %d:\ngot: %v\nwant:%v",
					i, orderedHubAuth(got, prec), orderedHubAuth(test.want, prec))
				break
			}
			if !floats.EqualWithinAbsOrRel(got[n].Authority, test.want[n].Authority, test.wantTol, test.wantTol) {
				t.Errorf("unexpected HITS result for test %d:\ngot: %v\nwant:%v",
					i, orderedHubAuth(got, prec), orderedHubAuth(test.want, prec))
				break
			}
		}
	}
}

func TestSort(t *testing.T) {
	for i, test := range tarjanTests {
		g := simple.NewDirectedGraph(0, math.Inf(1))
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
			}
		}
		sorted, err := Sort(g)
		var gotSortedLen int
		for _, n := range sorted {
			if n != nil {
				gotSortedLen++
			}
		}
		if gotSortedLen != test.sortedLength {
			t.Errorf("unexpected number of sortable nodes for test %d: got:%d want:%d", i, gotSortedLen, test.sortedLength)
		}
		if err == nil != test.sortable {
			t.Errorf("unexpected sortability for test %d: got error: %v want: nil-error=%t", i, err, test.sortable)
		}
		if err != nil && len(err.(Unorderable)) != test.unorderableLength {
			t.Errorf("unexpected number of unorderable nodes for test %d: got:%d want:%d", i, len(err.(Unorderable)), test.unorderableLength)
		}
	}
}

func TestTarjanSCC(t *testing.T) {
	for i, test := range tarjanTests {
		g := simple.NewDirectedGraph(0, math.Inf(1))
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
			}
		}
		gotSCCs := TarjanSCC(g)
		// tarjan.strongconnect does range iteration over maps,
		// so sort SCC members to ensure consistent ordering.
		gotIDs := make([][]int, len(gotSCCs))
		for i, scc := range gotSCCs {
			gotIDs[i] = make([]int, len(scc))
			for j, id := range scc {
				gotIDs[i][j] = id.ID()
			}
			sort.Ints(gotIDs[i])
		}
		for _, iv := range test.ambiguousOrder {
			sort.Sort(internal.BySliceValues(test.want[iv.start:iv.end]))
			sort.Sort(internal.BySliceValues(gotIDs[iv.start:iv.end]))
		}
		if !reflect.DeepEqual(gotIDs, test.want) {
			t.Errorf("unexpected Tarjan scc result for %d:\n\tgot:%v\n\twant:%v", i, gotIDs, test.want)
		}
	}
}

func TestAStar(t *testing.T) {
	for _, test := range aStarTests {
		pt, _ := AStar(simple.Node(test.s), simple.Node(test.t), test.g, test.heuristic)

		p, cost := pt.To(simple.Node(test.t))

		if !topo.IsPathIn(test.g, p) {
			t.Error("got path that is not path in input graph for %q", test.name)
		}

		bfp, ok := BellmanFordFrom(simple.Node(test.s), test.g)
		if !ok {
			t.Fatalf("unexpected negative cycle in %q", test.name)
		}
		if want := bfp.WeightTo(simple.Node(test.t)); cost != want {
			t.Errorf("unexpected cost for %q: got:%v want:%v", test.name, cost, want)
		}

		var got = make([]int, 0, len(p))
		for _, n := range p {
			got = append(got, n.ID())
		}
		if test.wantPath != nil && !reflect.DeepEqual(got, test.wantPath) {
			t.Errorf("unexpected result for %q:\ngot: %v\nwant:%v", test.name, got, test.wantPath)
		}
	}
}

func TestBronKerbosch(t *testing.T) {
	for i, test := range bronKerboschTests {
		g := simple.NewUndirectedGraph(0, math.Inf(1))
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
			}
		}
		cliques := BronKerbosch(g)
		got := make([][]int, len(cliques))
		for j, c := range cliques {
			ids := make([]int, len(c))
			for k, n := range c {
				ids[k] = n.ID()
			}
			sort.Ints(ids)
			got[j] = ids
		}
		sort.Sort(ordered.BySliceValues(got))
		if !reflect.DeepEqual(got, test.want) {
			t.Errorf("unexpected cliques for test %d:\ngot: %v\nwant:%v", i, got, test.want)
		}
	}
}

func TestCyclesIn(t *testing.T) {
	for i, test := range cyclesInTests {
		g := simple.NewDirectedGraph(0, math.Inf(1))
		g.AddNode(simple.Node(-10)) // Make sure we test graphs with sparse IDs.
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
			}
		}
		cycles := CyclesIn(g)
		var got [][]int
		if cycles != nil {
			got = make([][]int, len(cycles))
		}
		// johnson.circuit does range iteration over maps,
		// so sort to ensure consistent ordering.
		for j, c := range cycles {
			ids := make([]int, len(c))
			for k, n := range c {
				ids[k] = n.ID()
			}
			got[j] = ids
		}
		sort.Sort(ordered.BySliceValues(got))
		if !reflect.DeepEqual(got, test.want) {
			t.Errorf("unexpected johnson result for %d:\n\tgot:%#v\n\twant:%#v", i, got, test.want)
		}
	}
}

func TestEdgeBetweenness(t *testing.T) {
	for i, test := range betweennessTests {
		g := simple.NewUndirectedGraph(0, math.Inf(1))
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				// Weight omitted to show weight-independence.
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 0})
			}
		}
		got := EdgeBetweenness(g)
		prec := 1 - int(math.Log10(test.wantTol))
	outer:
		for u := range test.g {
			for v := range test.g {
				wantQ, gotOK := got[[2]int{u, v}]
				gotQ, wantOK := test.wantEdges[[2]int{u, v}]
				if gotOK != wantOK {
					t.Errorf("unexpected betweenness result for test %d, edge (%c,%c)", i, u+'A', v+'A')
				}
				if !floats.EqualWithinAbsOrRel(gotQ, wantQ, test.wantTol, test.wantTol) {
					t.Errorf("unexpected betweenness result for test %d:\ngot: %v\nwant:%v",
						i, orderedPairFloats(got, prec), orderedPairFloats(test.wantEdges, prec))
					break outer
				}
			}
		}
	}
}

// Gnm constructs a graph in the destination, dst, of order n and size m. If src is not
// nil it is used as the random source, otherwise rand.Float64 is used. The graph is
// constructed in O(m) expected time for m ≤ (n choose 2)/2.
func Gnm(dst GraphBuilder, n, m int, src *rand.Rand) error {
	if m == 0 {
		return nil
	}

	hasEdge := dst.HasEdgeBetween
	d, isDirected := dst.(graph.Directed)
	if isDirected {
		m /= 2
		hasEdge = d.HasEdgeFromTo
	}

	nChoose2 := (n - 1) * n / 2
	if m < 0 || m > nChoose2 {
		return fmt.Errorf("gen: bad size: m=%d", m)
	}

	var rnd func(int) int
	if src == nil {
		rnd = rand.Intn
	} else {
		rnd = src.Intn
	}

	for i := 0; i < n; i++ {
		if !dst.Has(simple.Node(i)) {
			dst.AddNode(simple.Node(i))
		}
	}

	// Add forward edges for all graphs.
	for i := 0; i < m; i++ {
		for {
			v, w := edgeNodesFor(rnd(nChoose2))
			e := simple.Edge{F: w, T: v, W: 1}
			if !hasEdge(e.F, e.T) {
				dst.SetEdge(e)
				break
			}
		}
	}

	// Add backward edges for directed graphs.
	if !isDirected {
		return nil
	}
	for i := 0; i < m; i++ {
		for {
			v, w := edgeNodesFor(rnd(nChoose2))
			e := simple.Edge{F: v, T: w, W: 1}
			if !hasEdge(e.F, e.T) {
				dst.SetEdge(e)
				break
			}
		}
	}

	return nil
}

func benchmarkAStarHeuristic(b *testing.B, g graph.Undirected, h Heuristic) {
	var expanded int
	for i := 0; i < b.N; i++ {
		_, expanded = AStar(simple.Node(0), simple.Node(1), g, h)
	}
	if expanded == 0 {
		b.Fatal("unexpected number of expanded nodes")
	}
}

func undirectedEdgeAttrGraphFrom(g []set, attr map[edge][]Attribute) graph.Graph {
	dg := simple.NewUndirectedGraph(0, math.Inf(1))
	for u, e := range g {
		for v := range e {
			dg.SetEdge(attrEdge{from: simple.Node(u), to: simple.Node(v), attr: attr[edge{from: u, to: v}]})
		}
	}
	return dg
}

func undirectedGraphFrom(g []set) graph.Graph {
	dg := simple.NewUndirectedGraph(0, math.Inf(1))
	for u, e := range g {
		for v := range e {
			dg.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
		}
	}
	return dg
}

func TestReduceQConsistency(t *testing.T) {
tests:
	for _, test := range communityQTests {
		g := simple.NewUndirectedGraph(0, 0)
		for u, e := range test.g {
			// Add nodes that are not defined by an edge.
			if !g.Has(simple.Node(u)) {
				g.AddNode(simple.Node(u))
			}
			for v := range e {
				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
			}
		}

		for _, structure := range test.structures {
			if math.IsNaN(structure.want) {
				continue tests
			}

			communities := make([][]graph.Node, len(structure.memberships))
			for i, c := range structure.memberships {
				for n := range c {
					communities[i] = append(communities[i], simple.Node(n))
				}
				sort.Sort(ordered.ByID(communities[i]))
			}

			gQ := Q(g, communities, structure.resolution)
			gQnull := Q(g, nil, 1)

			cg0 := reduce(g, nil)
			cg0Qnull := Q(cg0, cg0.Structure(), 1)
			if !floats.EqualWithinAbsOrRel(gQnull, cg0Qnull, structure.tol, structure.tol) {
				t.Errorf("disgagreement between null Q from method: %v and function: %v", cg0Qnull, gQnull)
			}
			cg0Q := Q(cg0, communities, structure.resolution)
			if !floats.EqualWithinAbsOrRel(gQ, cg0Q, structure.tol, structure.tol) {
				t.Errorf("unexpected Q result after initial conversion: got: %v want :%v", gQ, cg0Q)
			}

			cg1 := reduce(cg0, communities)
			cg1Q := Q(cg1, cg1.Structure(), structure.resolution)
			if !floats.EqualWithinAbsOrRel(gQ, cg1Q, structure.tol, structure.tol) {
				t.Errorf("unexpected Q result after initial condensation: got: %v want :%v", gQ, cg1Q)
			}
		}
	}
}

// Nodes returns all the nodes in the grid.
func (l *LimitedVisionGrid) Nodes() []graph.Node {
	nodes := make([]graph.Node, 0, len(l.Grid.open))
	for id := range l.Grid.open {
		nodes = append(nodes, simple.Node(id))
	}
	return nodes
}

// Nodes returns all the open nodes in the grid if AllVisible is
// false, otherwise all nodes are returned.
func (g *Grid) Nodes() []graph.Node {
	var nodes []graph.Node
	for id, ok := range g.open {
		if ok || g.AllVisible {
			nodes = append(nodes, simple.Node(id))
		}
	}
	return nodes
}

func undirectedStructuredGraphFrom(c []edge, g ...[]set) graph.Graph {
	s := &structuredGraph{UndirectedGraph: simple.NewUndirectedGraph(0, math.Inf(1))}
	var base int
	for i, sg := range g {
		sub := simple.NewUndirectedGraph(0, math.Inf(1))
		for u, e := range sg {
			for v := range e {
				ce := simple.Edge{F: simple.Node(u + base), T: simple.Node(v + base)}
				sub.SetEdge(ce)
			}
		}
		s.sub = append(s.sub, namedGraph{id: i, Graph: sub})
		base += len(sg)
	}
	for _, e := range c {
		s.SetEdge(simple.Edge{F: simple.Node(e.from), T: simple.Node(e.to)})
	}
	return s
}