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// 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 path
import (
"container/heap"
"gonum.org/v1/gonum/graph"
"gonum.org/v1/gonum/graph/internal/set"
"gonum.org/v1/gonum/graph/traverse"
)
// AStar finds the A*-shortest path from s to t in g using the heuristic h. The path and
// its cost are returned in a Shortest along with paths and costs to all nodes explored
// during the search. The number of expanded nodes is also returned. This value may help
// with heuristic tuning.
//
// The path will be the shortest path if the heuristic is admissible. A heuristic is
// admissible if for any node, n, in the graph, the heuristic estimate of the cost of
// the path from n to t is less than or equal to the true cost of that path.
//
// If h is nil, AStar will use the g.HeuristicCost method if g implements HeuristicCoster,
// falling back to NullHeuristic otherwise. If the graph does not implement Weighted,
// UniformCost is used. AStar will panic if g has an A*-reachable negative edge weight.
func AStar(s, t graph.Node, g traverse.Graph, h Heuristic) (path Shortest, expanded int) {
if g, ok := g.(graph.Graph); ok {
if g.Node(s.ID()) == nil || g.Node(t.ID()) == nil {
return Shortest{from: s}, 0
}
}
var weight Weighting
if wg, ok := g.(Weighted); ok {
weight = wg.Weight
} else {
weight = UniformCost(g)
}
if h == nil {
if g, ok := g.(HeuristicCoster); ok {
h = g.HeuristicCost
} else {
h = NullHeuristic
}
}
path = newShortestFrom(s, []graph.Node{s, t})
tid := t.ID()
visited := make(set.Ints[int64])
open := &aStarQueue{indexOf: make(map[int64]int)}
heap.Push(open, aStarNode{node: s, gscore: 0, fscore: h(s, t)})
for open.Len() != 0 {
u := heap.Pop(open).(aStarNode)
uid := u.node.ID()
i := path.indexOf[uid]
expanded++
if uid == tid {
break
}
visited.Add(uid)
to := g.From(u.node.ID())
for to.Next() {
v := to.Node()
vid := v.ID()
if visited.Has(vid) {
continue
}
j, ok := path.indexOf[vid]
if !ok {
j = path.add(v)
}
w, ok := weight(u.node.ID(), vid)
if !ok {
panic("path: A* unexpected invalid weight")
}
if w < 0 {
panic("path: A* negative edge weight")
}
g := u.gscore + w
if n, ok := open.node(vid); !ok {
path.set(j, g, i)
heap.Push(open, aStarNode{node: v, gscore: g, fscore: g + h(v, t)})
} else if g < n.gscore {
path.set(j, g, i)
open.update(vid, g, g+h(v, t))
}
}
}
return path, expanded
}
// NullHeuristic is an admissible, consistent heuristic that will not speed up computation.
func NullHeuristic(_, _ graph.Node) float64 {
return 0
}
// aStarNode adds A* accounting to a graph.Node.
type aStarNode struct {
node graph.Node
gscore float64
fscore float64
}
// aStarQueue is an A* priority queue.
type aStarQueue struct {
indexOf map[int64]int
nodes []aStarNode
}
func (q *aStarQueue) Less(i, j int) bool {
return q.nodes[i].fscore < q.nodes[j].fscore
}
func (q *aStarQueue) Swap(i, j int) {
q.indexOf[q.nodes[i].node.ID()] = j
q.indexOf[q.nodes[j].node.ID()] = i
q.nodes[i], q.nodes[j] = q.nodes[j], q.nodes[i]
}
func (q *aStarQueue) Len() int {
return len(q.nodes)
}
func (q *aStarQueue) Push(x interface{}) {
n := x.(aStarNode)
q.indexOf[n.node.ID()] = len(q.nodes)
q.nodes = append(q.nodes, n)
}
func (q *aStarQueue) Pop() interface{} {
n := q.nodes[len(q.nodes)-1]
q.nodes = q.nodes[:len(q.nodes)-1]
delete(q.indexOf, n.node.ID())
return n
}
func (q *aStarQueue) update(id int64, g, f float64) {
i, ok := q.indexOf[id]
if !ok {
return
}
q.nodes[i].gscore = g
q.nodes[i].fscore = f
heap.Fix(q, i)
}
func (q *aStarQueue) node(id int64) (aStarNode, bool) {
loc, ok := q.indexOf[id]
if ok {
return q.nodes[loc], true
}
return aStarNode{}, false
}
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