gonum/graph/implicit_example_test.go

// Copyright ©2014 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package graph_test

import (
	"fmt"

	"gonum.org/v1/gonum/graph"
	"gonum.org/v1/gonum/graph/iterator"
	"gonum.org/v1/gonum/graph/simple"
	"gonum.org/v1/gonum/graph/topo"
)

// GraphNode is a node in an implicit graph.
type GraphNode struct {
	id        int64
	neighbors []graph.Node
	roots     []*GraphNode

	name string
}

// NewGraphNode returns a new GraphNode.
func NewGraphNode(id int64, name string) *GraphNode {
	return &GraphNode{name: name, id: id}
}

// String returns the node's name.
func (g *GraphNode) String() string {
	return g.name
}

// Node allows GraphNode to satisfy the graph.Graph interface.
func (g *GraphNode) Node(id int64) graph.Node {
	if id == g.id {
		return g
	}

	seen := map[int64]struct{}{g.id: {}}
	for _, root := range g.roots {
		if root.ID() == id || root.has(seen, id) {
			return root
		}
	}

	for _, n := range g.neighbors {
		if n.ID() == id {
			return n
		}

		if gn, ok := n.(*GraphNode); ok {
			if gn.has(seen, id) {
				return gn
			}
		}
	}

	return nil
}

func (g *GraphNode) has(seen map[int64]struct{}, id int64) bool {
	for _, root := range g.roots {
		if _, ok := seen[root.ID()]; ok {
			continue
		}
		seen[root.ID()] = struct{}{}

		if root.ID() == id || root.has(seen, id) {
			return true
		}
	}

	for _, n := range g.neighbors {
		if _, ok := seen[n.ID()]; ok {
			continue
		}
		seen[n.ID()] = struct{}{}

		if n.ID() == id {
			return true
		}
		if gn, ok := n.(*GraphNode); ok {
			if gn.has(seen, id) {
				return true
			}
		}
	}

	return false
}

// Nodes allows GraphNode to satisfy the graph.Graph interface.
func (g *GraphNode) Nodes() graph.Nodes {
	nodes := []graph.Node{g}
	seen := map[int64]struct{}{g.id: {}}

	for _, root := range g.roots {
		seen[root.ID()] = struct{}{}
		nodes = root.nodes(append(nodes, root), seen)
	}

	for _, n := range g.neighbors {
		seen[n.ID()] = struct{}{}

		nodes = append(nodes, n)
		if gn, ok := n.(*GraphNode); ok {
			nodes = gn.nodes(nodes, seen)
		}
	}

	return iterator.NewOrderedNodes(nodes)
}

func (g *GraphNode) nodes(dst []graph.Node, seen map[int64]struct{}) []graph.Node {
	for _, root := range g.roots {
		if _, ok := seen[root.ID()]; ok {
			continue
		}
		seen[root.ID()] = struct{}{}

		dst = root.nodes(append(dst, graph.Node(root)), seen)
	}

	for _, n := range g.neighbors {
		if _, ok := seen[n.ID()]; ok {
			continue
		}
		seen[n.ID()] = struct{}{}

		dst = append(dst, n)
		if gn, ok := n.(*GraphNode); ok {
			dst = gn.nodes(dst, seen)
		}
	}

	return dst
}

// From allows GraphNode to satisfy the graph.Graph interface.
func (g *GraphNode) From(id int64) graph.Nodes {
	if id == g.ID() {
		return iterator.NewOrderedNodes(g.neighbors)
	}

	seen := map[int64]struct{}{g.id: {}}
	for _, root := range g.roots {
		seen[root.ID()] = struct{}{}

		if result := root.findNeighbors(id, seen); result != nil {
			return iterator.NewOrderedNodes(result)
		}
	}

	for _, n := range g.neighbors {
		seen[n.ID()] = struct{}{}

		if gn, ok := n.(*GraphNode); ok {
			if result := gn.findNeighbors(id, seen); result != nil {
				return iterator.NewOrderedNodes(result)
			}
		}
	}

	return graph.Empty
}

func (g *GraphNode) findNeighbors(id int64, seen map[int64]struct{}) []graph.Node {
	if id == g.ID() {
		return g.neighbors
	}

	for _, root := range g.roots {
		if _, ok := seen[root.ID()]; ok {
			continue
		}
		seen[root.ID()] = struct{}{}

		if result := root.findNeighbors(id, seen); result != nil {
			return result
		}
	}

	for _, n := range g.neighbors {
		if _, ok := seen[n.ID()]; ok {
			continue
		}
		seen[n.ID()] = struct{}{}

		if gn, ok := n.(*GraphNode); ok {
			if result := gn.findNeighbors(id, seen); result != nil {
				return result
			}
		}
	}

	return nil
}

// HasEdgeBetween allows GraphNode to satisfy the graph.Graph interface.
func (g *GraphNode) HasEdgeBetween(uid, vid int64) bool {
	return g.EdgeBetween(uid, vid) != nil
}

// Edge allows GraphNode to satisfy the graph.Graph interface.
func (g *GraphNode) Edge(uid, vid int64) graph.Edge {
	return g.EdgeBetween(uid, vid)
}

// EdgeBetween allows GraphNode to satisfy the graph.Graph interface.
func (g *GraphNode) EdgeBetween(uid, vid int64) graph.Edge {
	if uid == g.id || vid == g.id {
		for _, n := range g.neighbors {
			if n.ID() == uid || n.ID() == vid {
				return simple.Edge{F: g, T: n}
			}
		}
		return nil
	}

	seen := map[int64]struct{}{g.id: {}}
	for _, root := range g.roots {
		seen[root.ID()] = struct{}{}
		if result := root.edgeBetween(uid, vid, seen); result != nil {
			return result
		}
	}

	for _, n := range g.neighbors {
		seen[n.ID()] = struct{}{}
		if gn, ok := n.(*GraphNode); ok {
			if result := gn.edgeBetween(uid, vid, seen); result != nil {
				return result
			}
		}
	}

	return nil
}

func (g *GraphNode) edgeBetween(uid, vid int64, seen map[int64]struct{}) graph.Edge {
	if uid == g.id || vid == g.id {
		for _, n := range g.neighbors {
			if n.ID() == uid || n.ID() == vid {
				return simple.Edge{F: g, T: n}
			}
		}
		return nil
	}

	for _, root := range g.roots {
		if _, ok := seen[root.ID()]; ok {
			continue
		}
		seen[root.ID()] = struct{}{}

		if result := root.edgeBetween(uid, vid, seen); result != nil {
			return result
		}
	}

	for _, n := range g.neighbors {
		if _, ok := seen[n.ID()]; ok {
			continue
		}
		seen[n.ID()] = struct{}{}

		if gn, ok := n.(*GraphNode); ok {
			if result := gn.edgeBetween(uid, vid, seen); result != nil {
				return result
			}
		}
	}

	return nil
}

// ID allows GraphNode to satisfy the graph.Node interface.
func (g *GraphNode) ID() int64 {
	return g.id
}

// AddMeighbor adds an edge between g and n.
func (g *GraphNode) AddNeighbor(n *GraphNode) {
	g.neighbors = append(g.neighbors, graph.Node(n))
}

// AddRoot adds provides an entrance into the graph g from n.
func (g *GraphNode) AddRoot(n *GraphNode) {
	g.roots = append(g.roots, n)
}

func Example_implicit() {
	// This example shows the construction of the following graph
	// using the implicit graph type above.
	//
	// The visual representation of the graph can be seen at
	// https://graphviz.gitlab.io/_pages/Gallery/undirected/fdpclust.html
	//
	// graph G {
	// 	e
	// 	subgraph clusterA {
	// 		a -- b
	// 		subgraph clusterC {
	// 			C -- D
	// 		}
	// 	}
	// 	subgraph clusterB {
	// 		d -- f
	// 	}
	// 	d -- D
	// 	e -- clusterB
	// 	clusterC -- clusterB
	// }

	// graph G {
	G := NewGraphNode(0, "G")
	// 	e
	e := NewGraphNode(1, "e")

	// 	subgraph clusterA {
	clusterA := NewGraphNode(2, "clusterA")
	// 		a -- b
	a := NewGraphNode(3, "a")
	b := NewGraphNode(4, "b")
	a.AddNeighbor(b)
	b.AddNeighbor(a)
	clusterA.AddRoot(a)
	clusterA.AddRoot(b)

	// 		subgraph clusterC {
	clusterC := NewGraphNode(5, "clusterC")
	// 			C -- D
	C := NewGraphNode(6, "C")
	D := NewGraphNode(7, "D")
	C.AddNeighbor(D)
	D.AddNeighbor(C)

	clusterC.AddRoot(C)
	clusterC.AddRoot(D)
	// 		}
	clusterA.AddRoot(clusterC)
	// 	}

	// 	subgraph clusterB {
	clusterB := NewGraphNode(8, "clusterB")
	// 		d -- f
	d := NewGraphNode(9, "d")
	f := NewGraphNode(10, "f")
	d.AddNeighbor(f)
	f.AddNeighbor(d)
	clusterB.AddRoot(d)
	clusterB.AddRoot(f)
	// 	}

	// 	d -- D
	d.AddNeighbor(D)
	D.AddNeighbor(d)

	// 	e -- clusterB
	e.AddNeighbor(clusterB)
	clusterB.AddNeighbor(e)

	// 	clusterC -- clusterB
	clusterC.AddNeighbor(clusterB)
	clusterB.AddNeighbor(clusterC)

	G.AddRoot(e)
	G.AddRoot(clusterA)
	G.AddRoot(clusterB)
	// }

	if topo.IsPathIn(G, []graph.Node{C, D, d, f}) {
		fmt.Println("C--D--d--f is a path in G.")
	}

	fmt.Println("\nConnected components:")
	for _, c := range topo.ConnectedComponents(G) {
		fmt.Printf(" %s\n", c)
	}

	// Output:
	//
	// C--D--d--f is a path in G.
	//
	// Connected components:
	//  [G]
	//  [e clusterB clusterC]
	//  [d D C f]
	//  [clusterA]
	//  [a b]
}