mirror of
https://github.com/gonum/gonum.git
synced 2025-10-07 08:01:20 +08:00
46d85b5bdf
With the approach to graph node mutation on edge setting the previously existed there was an issue that the edge last used connect a pair of nodes could result in a difference in the nodes being returned by a node query compared to the same node associated with edges returned from an edge query. This change avoids dealing with that by making it implementation dependent and stating this, and by making all the node-storing graphs we provide mutate the nodes when edges are set.
503 lines
13 KiB
Go
503 lines
13 KiB
Go
// Copyright ©2014 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package dynamic
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import (
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"container/heap"
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"fmt"
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"math"
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"gonum.org/v1/gonum/graph"
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"gonum.org/v1/gonum/graph/path"
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"gonum.org/v1/gonum/graph/simple"
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)
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// DStarLite implements the D* Lite dynamic re-planning path search algorithm.
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//
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// doi:10.1109/tro.2004.838026 and ISBN:0-262-51129-0 pp476-483
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//
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type DStarLite struct {
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s, t *dStarLiteNode
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last *dStarLiteNode
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model WorldModel
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queue dStarLiteQueue
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keyModifier float64
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weight path.Weighting
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heuristic path.Heuristic
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}
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// WorldModel is a mutable weighted directed graph that returns nodes identified
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// by id number.
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type WorldModel interface {
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graph.WeightedBuilder
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graph.WeightedDirected
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}
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// NewDStarLite returns a new DStarLite planner for the path from s to t in g using the
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// heuristic h. The world model, m, is used to store shortest path information during path
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// planning. The world model must be an empty graph when NewDStarLite is called.
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//
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// If h is nil, the DStarLite will use the g.HeuristicCost method if g implements
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// path.HeuristicCoster, falling back to path.NullHeuristic otherwise. If the graph does not
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// implement graph.Weighter, path.UniformCost is used. NewDStarLite will panic if g has
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// a negative edge weight.
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func NewDStarLite(s, t graph.Node, g graph.Graph, h path.Heuristic, m WorldModel) *DStarLite {
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/*
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procedure Initialize()
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{02”} U = ∅;
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{03”} k_m = 0;
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{04”} for all s ∈ S rhs(s) = g(s) = ∞;
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{05”} rhs(s_goal) = 0;
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{06”} U.Insert(s_goal, [h(s_start, s_goal); 0]);
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*/
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d := &DStarLite{
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s: newDStarLiteNode(s),
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t: newDStarLiteNode(t), // badKey is overwritten below.
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model: m,
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heuristic: h,
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}
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d.t.rhs = 0
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/*
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procedure Main()
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{29”} s_last = s_start;
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{30”} Initialize();
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*/
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d.last = d.s
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if wg, ok := g.(graph.Weighted); ok {
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d.weight = wg.Weight
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} else {
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d.weight = path.UniformCost(g)
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}
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if d.heuristic == nil {
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if g, ok := g.(path.HeuristicCoster); ok {
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d.heuristic = g.HeuristicCost
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} else {
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d.heuristic = path.NullHeuristic
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}
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}
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d.queue.insert(d.t, key{d.heuristic(s, t), 0})
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for _, n := range graph.NodesOf(g.Nodes()) {
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switch n.ID() {
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case d.s.ID():
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d.model.AddNode(d.s)
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case d.t.ID():
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d.model.AddNode(d.t)
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default:
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d.model.AddNode(newDStarLiteNode(n))
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}
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}
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for _, u := range graph.NodesOf(d.model.Nodes()) {
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uid := u.ID()
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for _, v := range graph.NodesOf(g.From(uid)) {
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vid := v.ID()
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w := edgeWeight(d.weight, uid, vid)
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if w < 0 {
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panic("D* Lite: negative edge weight")
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}
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d.model.SetWeightedEdge(simple.WeightedEdge{F: u, T: d.model.Node(vid), W: w})
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}
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}
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/*
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procedure Main()
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{31”} ComputeShortestPath();
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*/
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d.findShortestPath()
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return d
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}
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// edgeWeight is a helper function that returns the weight of the edge between
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// two connected nodes, u and v, using the provided weight function. It panics
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// if there is no edge between u and v.
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func edgeWeight(weight path.Weighting, uid, vid int64) float64 {
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w, ok := weight(uid, vid)
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if !ok {
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panic("D* Lite: unexpected invalid weight")
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}
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return w
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}
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// keyFor is the CalculateKey procedure in the D* Lite papers.
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func (d *DStarLite) keyFor(s *dStarLiteNode) key {
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/*
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procedure CalculateKey(s)
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{01”} return [min(g(s), rhs(s)) + h(s_start, s) + k_m; min(g(s), rhs(s))];
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*/
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k := key{1: math.Min(s.g, s.rhs)}
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k[0] = k[1] + d.heuristic(d.s.Node, s.Node) + d.keyModifier
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return k
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}
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// update is the UpdateVertex procedure in the D* Lite papers.
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func (d *DStarLite) update(u *dStarLiteNode) {
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/*
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procedure UpdateVertex(u)
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{07”} if (g(u) != rhs(u) AND u ∈ U) U.Update(u,CalculateKey(u));
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{08”} else if (g(u) != rhs(u) AND u /∈ U) U.Insert(u,CalculateKey(u));
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{09”} else if (g(u) = rhs(u) AND u ∈ U) U.Remove(u);
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*/
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inQueue := u.inQueue()
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switch {
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case inQueue && u.g != u.rhs:
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d.queue.update(u, d.keyFor(u))
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case !inQueue && u.g != u.rhs:
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d.queue.insert(u, d.keyFor(u))
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case inQueue && u.g == u.rhs:
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d.queue.remove(u)
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}
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}
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// findShortestPath is the ComputeShortestPath procedure in the D* Lite papers.
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func (d *DStarLite) findShortestPath() {
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/*
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procedure ComputeShortestPath()
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{10”} while (U.TopKey() < CalculateKey(s_start) OR rhs(s_start) > g(s_start))
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{11”} u = U.Top();
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{12”} k_old = U.TopKey();
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{13”} k_new = CalculateKey(u);
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{14”} if(k_old < k_new)
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{15”} U.Update(u, k_new);
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{16”} else if (g(u) > rhs(u))
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{17”} g(u) = rhs(u);
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{18”} U.Remove(u);
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{19”} for all s ∈ Pred(u)
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{20”} if (s != s_goal) rhs(s) = min(rhs(s), c(s, u) + g(u));
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{21”} UpdateVertex(s);
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{22”} else
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{23”} g_old = g(u);
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{24”} g(u) = ∞;
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{25”} for all s ∈ Pred(u) ∪ {u}
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{26”} if (rhs(s) = c(s, u) + g_old)
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{27”} if (s != s_goal) rhs(s) = min s'∈Succ(s)(c(s, s') + g(s'));
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{28”} UpdateVertex(s);
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*/
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for d.queue.Len() != 0 { // We use d.queue.Len since d.queue does not return an infinite key when empty.
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u := d.queue.top()
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if !u.key.less(d.keyFor(d.s)) && d.s.rhs <= d.s.g {
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break
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}
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uid := u.ID()
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switch kNew := d.keyFor(u); {
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case u.key.less(kNew):
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d.queue.update(u, kNew)
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case u.g > u.rhs:
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u.g = u.rhs
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d.queue.remove(u)
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for _, _s := range graph.NodesOf(d.model.To(uid)) {
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s := _s.(*dStarLiteNode)
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sid := s.ID()
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if sid != d.t.ID() {
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s.rhs = math.Min(s.rhs, edgeWeight(d.model.Weight, sid, uid)+u.g)
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}
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d.update(s)
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}
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default:
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gOld := u.g
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u.g = math.Inf(1)
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for _, _s := range append(graph.NodesOf(d.model.To(uid)), u) {
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s := _s.(*dStarLiteNode)
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sid := s.ID()
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if s.rhs == edgeWeight(d.model.Weight, sid, uid)+gOld {
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if s.ID() != d.t.ID() {
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s.rhs = math.Inf(1)
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for _, t := range graph.NodesOf(d.model.From(sid)) {
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tid := t.ID()
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s.rhs = math.Min(s.rhs, edgeWeight(d.model.Weight, sid, tid)+t.(*dStarLiteNode).g)
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}
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}
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}
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d.update(s)
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}
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}
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}
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}
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// Step performs one movement step along the best path towards the goal.
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// It returns false if no further progression toward the goal can be
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// achieved, either because the goal has been reached or because there
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// is no path.
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func (d *DStarLite) Step() bool {
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/*
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procedure Main()
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{32”} while (s_start != s_goal)
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{33”} // if (rhs(s_start) = ∞) then there is no known path
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{34”} s_start = argmin s'∈Succ(s_start)(c(s_start, s') + g(s'));
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*/
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if d.s.ID() == d.t.ID() {
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return false
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}
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if math.IsInf(d.s.rhs, 1) {
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return false
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}
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// We use rhs comparison to break ties
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// between coequally weighted nodes.
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rhs := math.Inf(1)
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min := math.Inf(1)
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var next *dStarLiteNode
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dsid := d.s.ID()
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for _, _s := range graph.NodesOf(d.model.From(dsid)) {
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s := _s.(*dStarLiteNode)
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w := edgeWeight(d.model.Weight, dsid, s.ID()) + s.g
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if w < min || (w == min && s.rhs < rhs) {
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next = s
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min = w
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rhs = s.rhs
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}
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}
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d.s = next
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/*
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procedure Main()
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{35”} Move to s_start;
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*/
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return true
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}
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// MoveTo moves to n in the world graph.
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func (d *DStarLite) MoveTo(n graph.Node) {
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d.last = d.s
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d.s = d.model.Node(n.ID()).(*dStarLiteNode)
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d.keyModifier += d.heuristic(d.last, d.s)
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}
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// UpdateWorld updates or adds edges in the world graph. UpdateWorld will
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// panic if changes include a negative edge weight.
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func (d *DStarLite) UpdateWorld(changes []graph.Edge) {
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/*
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procedure Main()
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{36”} Scan graph for changed edge costs;
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{37”} if any edge costs changed
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{38”} k_m = k_m + h(s_last, s_start);
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{39”} s_last = s_start;
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{40”} for all directed edges (u, v) with changed edge costs
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{41”} c_old = c(u, v);
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{42”} Update the edge cost c(u, v);
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{43”} if (c_old > c(u, v))
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{44”} if (u != s_goal) rhs(u) = min(rhs(u), c(u, v) + g(v));
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{45”} else if (rhs(u) = c_old + g(v))
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{46”} if (u != s_goal) rhs(u) = min s'∈Succ(u)(c(u, s') + g(s'));
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{47”} UpdateVertex(u);
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{48”} ComputeShortestPath()
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*/
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if len(changes) == 0 {
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return
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}
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d.keyModifier += d.heuristic(d.last, d.s)
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d.last = d.s
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for _, e := range changes {
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from := e.From()
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fid := from.ID()
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to := e.To()
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tid := to.ID()
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c, _ := d.weight(fid, tid)
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if c < 0 {
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panic("D* Lite: negative edge weight")
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}
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cOld, _ := d.model.Weight(fid, tid)
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u := d.worldNodeFor(from)
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v := d.worldNodeFor(to)
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d.model.SetWeightedEdge(simple.WeightedEdge{F: u, T: v, W: c})
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uid := u.ID()
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if cOld > c {
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if uid != d.t.ID() {
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u.rhs = math.Min(u.rhs, c+v.g)
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}
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} else if u.rhs == cOld+v.g {
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if uid != d.t.ID() {
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u.rhs = math.Inf(1)
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for _, t := range graph.NodesOf(d.model.From(uid)) {
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u.rhs = math.Min(u.rhs, edgeWeight(d.model.Weight, uid, t.ID())+t.(*dStarLiteNode).g)
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}
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}
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}
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d.update(u)
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}
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d.findShortestPath()
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}
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func (d *DStarLite) worldNodeFor(n graph.Node) *dStarLiteNode {
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switch w := d.model.Node(n.ID()).(type) {
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case *dStarLiteNode:
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return w
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case graph.Node:
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panic(fmt.Sprintf("D* Lite: illegal world model node type: %T", w))
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default:
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return newDStarLiteNode(n)
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}
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}
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// Here returns the current location.
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func (d *DStarLite) Here() graph.Node {
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return d.s.Node
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}
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// Path returns the path from the current location to the goal and the
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// weight of the path.
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func (d *DStarLite) Path() (p []graph.Node, weight float64) {
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u := d.s
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p = []graph.Node{u.Node}
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for u.ID() != d.t.ID() {
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if math.IsInf(u.rhs, 1) {
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return nil, math.Inf(1)
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}
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// We use stored rhs comparison to break
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// ties between calculated rhs-coequal nodes.
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rhsMin := math.Inf(1)
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min := math.Inf(1)
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var (
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next *dStarLiteNode
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cost float64
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)
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uid := u.ID()
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for _, _v := range graph.NodesOf(d.model.From(uid)) {
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v := _v.(*dStarLiteNode)
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vid := v.ID()
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w := edgeWeight(d.model.Weight, uid, vid)
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if rhs := w + v.g; rhs < min || (rhs == min && v.rhs < rhsMin) {
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next = v
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min = rhs
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rhsMin = v.rhs
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cost = w
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}
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}
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if next == nil {
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return nil, math.NaN()
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}
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u = next
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weight += cost
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p = append(p, u.Node)
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}
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return p, weight
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}
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/*
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The pseudocode uses the following functions to manage the priority
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queue:
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* U.Top() returns a vertex with the smallest priority of all
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vertices in priority queue U.
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* U.TopKey() returns the smallest priority of all vertices in
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priority queue U. (If is empty, then U.TopKey() returns [∞;∞].)
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* U.Pop() deletes the vertex with the smallest priority in
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priority queue U and returns the vertex.
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* U.Insert(s, k) inserts vertex s into priority queue with
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priority k.
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* U.Update(s, k) changes the priority of vertex s in priority
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queue U to k. (It does nothing if the current priority of vertex
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s already equals k.)
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* Finally, U.Remove(s) removes vertex s from priority queue U.
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*/
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// key is a D* Lite priority queue key.
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type key [2]float64
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var badKey = key{math.NaN(), math.NaN()}
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// less returns whether k is less than other. From ISBN:0-262-51129-0 pp476-483:
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//
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// k ≤ k' iff k₁ < k'₁ OR (k₁ == k'₁ AND k₂ ≤ k'₂)
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//
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func (k key) less(other key) bool {
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if k != k || other != other {
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panic("D* Lite: poisoned key")
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}
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return k[0] < other[0] || (k[0] == other[0] && k[1] < other[1])
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}
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// dStarLiteNode adds D* Lite accounting to a graph.Node.
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type dStarLiteNode struct {
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graph.Node
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key key
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idx int
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rhs float64
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g float64
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}
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// newDStarLiteNode returns a dStarLite node that is in a legal state
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// for existence outside the DStarLite priority queue.
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func newDStarLiteNode(n graph.Node) *dStarLiteNode {
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return &dStarLiteNode{
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Node: n,
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rhs: math.Inf(1),
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g: math.Inf(1),
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key: badKey,
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idx: -1,
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}
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}
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// inQueue returns whether the node is in the queue.
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func (q *dStarLiteNode) inQueue() bool {
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return q.idx >= 0
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}
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// dStarLiteQueue is a D* Lite priority queue.
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type dStarLiteQueue []*dStarLiteNode
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func (q dStarLiteQueue) Less(i, j int) bool {
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return q[i].key.less(q[j].key)
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}
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func (q dStarLiteQueue) Swap(i, j int) {
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q[i], q[j] = q[j], q[i]
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q[i].idx = i
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q[j].idx = j
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}
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func (q dStarLiteQueue) Len() int {
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return len(q)
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}
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func (q *dStarLiteQueue) Push(x interface{}) {
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n := x.(*dStarLiteNode)
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n.idx = len(*q)
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*q = append(*q, n)
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}
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func (q *dStarLiteQueue) Pop() interface{} {
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n := (*q)[len(*q)-1]
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n.idx = -1
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*q = (*q)[:len(*q)-1]
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return n
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}
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// top returns the top node in the queue. Note that instead of
|
||
// returning a key [∞;∞] when q is empty, the caller checks for
|
||
// an empty queue by calling q.Len.
|
||
func (q dStarLiteQueue) top() *dStarLiteNode {
|
||
return q[0]
|
||
}
|
||
|
||
// insert puts the node u into the queue with the key k.
|
||
func (q *dStarLiteQueue) insert(u *dStarLiteNode, k key) {
|
||
u.key = k
|
||
heap.Push(q, u)
|
||
}
|
||
|
||
// update updates the node in the queue identified by id with the key k.
|
||
func (q *dStarLiteQueue) update(n *dStarLiteNode, k key) {
|
||
n.key = k
|
||
heap.Fix(q, n.idx)
|
||
}
|
||
|
||
// remove removes the node identified by id from the queue.
|
||
func (q *dStarLiteQueue) remove(n *dStarLiteNode) {
|
||
heap.Remove(q, n.idx)
|
||
n.key = badKey
|
||
n.idx = -1
|
||
}
|