// 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
}
// DijkstraFrom returns a shortest-path tree for a shortest path from u to all nodes in
// the graph g. If the graph does not implement graph.Weighter, UniformCost is used.
// DijkstraFrom will panic if g has a u-reachable negative edge weight.
//
// The time complexity of DijkstrFrom is O(|E|+|V|.log|V|).
func DijkstraFrom(u graph.Node, g graph.Graph) Shortest {
if !g.Has(u) {
return Shortest{from: u}
}
var weight Weighting
if wg, ok := g.(graph.Weighter); ok {
weight = wg.Weight
} else {
weight = UniformCost(g)
}
nodes := g.Nodes()
path := newShortestFrom(u, nodes)
// Dijkstra's algorithm here is implemented essentially as
// described in Function B.2 in figure 6 of UTCS Technical
// Report TR-07-54.
//
// http://www.cs.utexas.edu/ftp/techreports/tr07-54.pdf
Q := priorityQueue{{node: u, dist: 0}}
for Q.Len() != 0 {
mid := heap.Pop(&Q).(distanceNode)
k := path.indexOf[mid.node.ID()]
if mid.dist < path.dist[k] {
path.dist[k] = mid.dist
}
for _, v := range g.From(mid.node) {
j := path.indexOf[v.ID()]
w, ok := weight(mid.node, v)
if !ok {
panic("dijkstra: unexpected invalid weight")
}
if w < 0 {
panic("dijkstra: negative edge weight")
}
joint := path.dist[k] + w
if joint < path.dist[j] {
heap.Push(&Q, distanceNode{node: v, dist: joint})
path.set(j, joint, k)
}
}
}
return path
}
// IsPathIn returns whether path is a path in g.
//
// As special cases, IsPathIn returns true for a zero length path or for
// a path of length 1 when the node in path exists in the graph.
func IsPathIn(g graph.Graph, path []graph.Node) bool {
switch len(path) {
case 0:
return true
case 1:
return g.Has(path[0])
default:
var canReach func(u, v graph.Node) bool
switch g := g.(type) {
case graph.Directed:
canReach = g.HasEdgeFromTo
default:
canReach = g.HasEdgeBetween
}
for i, u := range path[:len(path)-1] {
if !canReach(u, path[i+1]) {
return false
}
}
return true
}
}
// BellmanFordFrom returns a shortest-path tree for a shortest path from u to all nodes in
// the graph g, or false indicating that a negative cycle exists in the graph. If the graph
// does not implement graph.Weighter, UniformCost is used.
//
// The time complexity of BellmanFordFrom is O(|V|.|E|).
func BellmanFordFrom(u graph.Node, g graph.Graph) (path Shortest, ok bool) {
if !g.Has(u) {
return Shortest{from: u}, true
}
var weight Weighting
if wg, ok := g.(graph.Weighter); ok {
weight = wg.Weight
} else {
weight = UniformCost(g)
}
nodes := g.Nodes()
path = newShortestFrom(u, nodes)
path.dist[path.indexOf[u.ID()]] = 0
// TODO(kortschak): Consider adding further optimisations
// from http://arxiv.org/abs/1111.5414.
for i := 1; i < len(nodes); i++ {
changed := false
for j, u := range nodes {
for _, v := range g.From(u) {
k := path.indexOf[v.ID()]
w, ok := weight(u, v)
if !ok {
panic("bellman-ford: unexpected invalid weight")
}
joint := path.dist[j] + w
if joint < path.dist[k] {
path.set(k, joint, j)
changed = true
}
}
}
if !changed {
break
}
}
for j, u := range nodes {
for _, v := range g.From(u) {
k := path.indexOf[v.ID()]
w, ok := weight(u, v)
if !ok {
panic("bellman-ford: unexpected invalid weight")
}
if path.dist[j]+w < path.dist[k] {
return path, false
}
}
}
return path, true
}