forked from openshift/origin
-
Notifications
You must be signed in to change notification settings - Fork 0
/
johnson_apsp.go
137 lines (114 loc) · 2.94 KB
/
johnson_apsp.go
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
// Copyright ©2015 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 (
"math"
"math/rand"
"github.com/gonum/graph"
"github.com/gonum/graph/concrete"
)
// JohnsonAllPaths returns a shortest-path tree for shortest paths in the graph g.
// If the graph does not implement graph.Weighter, graph.UniformCost is used.
//
// The time complexity of JohnsonAllPaths is O(|V|.|E|+|V|^2.log|V|).
func JohnsonAllPaths(g graph.Graph) (paths AllShortest, ok bool) {
jg := johnsonWeightAdjuster{
g: g,
from: g.From,
edgeTo: g.Edge,
}
if g, ok := g.(graph.Weighter); ok {
jg.weight = g.Weight
} else {
jg.weight = graph.UniformCost
}
paths = newAllShortest(g.Nodes(), false)
sign := -1
for {
// Choose a random node ID until we find
// one that is not in g.
jg.q = sign * rand.Int()
if _, exists := paths.indexOf[jg.q]; !exists {
break
}
sign *= -1
}
jg.bellmanFord = true
jg.adjustBy, ok = BellmanFordFrom(johnsonGraphNode(jg.q), jg)
if !ok {
return paths, false
}
jg.bellmanFord = false
dijkstraAllPaths(jg, paths)
for i, u := range paths.nodes {
hu := jg.adjustBy.WeightTo(u)
for j, v := range paths.nodes {
if i == j {
continue
}
hv := jg.adjustBy.WeightTo(v)
paths.dist.Set(i, j, paths.dist.At(i, j)-hu+hv)
}
}
return paths, ok
}
type johnsonWeightAdjuster struct {
q int
g graph.Graph
from func(graph.Node) []graph.Node
edgeTo func(graph.Node, graph.Node) graph.Edge
weight graph.WeightFunc
bellmanFord bool
adjustBy Shortest
}
var (
// johnsonWeightAdjuster has the behaviour
// of a directed graph, but we don't need
// to be explicit with the type since it
// is not exported.
_ graph.Graph = johnsonWeightAdjuster{}
_ graph.Weighter = johnsonWeightAdjuster{}
)
func (g johnsonWeightAdjuster) Has(n graph.Node) bool {
if g.bellmanFord && n.ID() == g.q {
return true
}
return g.g.Has(n)
}
func (g johnsonWeightAdjuster) Nodes() []graph.Node {
if g.bellmanFord {
return append(g.g.Nodes(), johnsonGraphNode(g.q))
}
return g.g.Nodes()
}
func (g johnsonWeightAdjuster) From(n graph.Node) []graph.Node {
if g.bellmanFord && n.ID() == g.q {
return g.g.Nodes()
}
return g.from(n)
}
func (g johnsonWeightAdjuster) Edge(u, v graph.Node) graph.Edge {
if g.bellmanFord && u.ID() == g.q && g.g.Has(v) {
return concrete.Edge{johnsonGraphNode(g.q), v}
}
return g.edgeTo(u, v)
}
func (g johnsonWeightAdjuster) Weight(e graph.Edge) float64 {
if g.bellmanFord {
switch g.q {
case e.From().ID():
return 0
case e.To().ID():
return math.Inf(1)
default:
return g.weight(e)
}
}
return g.weight(e) + g.adjustBy.WeightTo(e.From()) - g.adjustBy.WeightTo(e.To())
}
func (johnsonWeightAdjuster) HasEdge(_, _ graph.Node) bool {
panic("search: unintended use of johnsonWeightAdjuster")
}
type johnsonGraphNode int
func (n johnsonGraphNode) ID() int { return int(n) }