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graph/path: indicate negative cycle weights with -Inf instead of NaN

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The paths are undefined, but the limit of the path weight is -Inf.
This commit is contained in:
Dan Kortschak
2019-02-07 20:57:33 +10:30
parent 936e3fec9e
commit ee7dd3742a
3 changed files with 14 additions and 14 deletions
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10
graph/path/floydwarshall.go
View File

@@ -13,7 +13,7 @@ import (
// FloydWarshall returns a shortest-path tree for the graph g or false indicating // FloydWarshall returns a shortest-path tree for the graph g or false indicating
// that a negative cycle exists in the graph. If a negative cycle exists in the graph // that a negative cycle exists in the graph. If a negative cycle exists in the graph
// the returned paths will be valid and edge weights on the negative cycle will be // the returned paths will be valid and edge weights on the negative cycle will be
// set to NaN. If the graph does not implement Weighted, UniformCost is used. // set to -Inf. If the graph does not implement Weighted, UniformCost is used.
// //
// The time complexity of FloydWarshall is O(|V|^3). // The time complexity of FloydWarshall is O(|V|^3).
func FloydWarshall(g graph.Graph) (paths AllShortest, ok bool) { func FloydWarshall(g graph.Graph) (paths AllShortest, ok bool) {
@@ -65,7 +65,7 @@ func FloydWarshall(g graph.Graph) (paths AllShortest, ok bool) {
if !ok { if !ok {
// If we have a negative cycle, mark all // If we have a negative cycle, mark all
// the edges in the cycles with NaN weight. // the edges in the cycles with -Inf weight.
d := paths.dist d := paths.dist
for i := range nodes { for i := range nodes {
for j := range nodes { for j := range nodes {
@@ -73,9 +73,9 @@ func FloydWarshall(g graph.Graph) (paths AllShortest, ok bool) {
if math.IsInf(d.At(i, k), 1) || math.IsInf(d.At(k, j), 1) { if math.IsInf(d.At(i, k), 1) || math.IsInf(d.At(k, j), 1) {
continue continue
} }
if d.At(k, k) < 0 || math.IsNaN(d.At(k, k)) { if d.At(k, k) < 0 {
d.Set(k, k, math.NaN()) d.Set(k, k, math.Inf(-1))
d.Set(i, j, math.NaN()) d.Set(i, j, math.Inf(-1))
} }
} }
} }

6
graph/path/negative_cycles_example_test.go
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@@ -46,7 +46,7 @@ func ExampleBellmanFordFrom_negativecycles() {
} }
for _, id := range []int64{'a', 'b', 'c', 'd', 'e', 'f'} { for _, id := range []int64{'a', 'b', 'c', 'd', 'e', 'f'} {
p, w := pt.To(id) p, w := pt.To(id)
if math.IsNaN(w) { if math.IsInf(w, -1) {
fmt.Printf("negative cycle in path to %c path:%c\n", id, p) fmt.Printf("negative cycle in path to %c path:%c\n", id, p)
} }
} }
@@ -87,7 +87,7 @@ func ExampleFloydWarshall_negativecycles() {
ids := []int64{'a', 'b', 'c', 'd', 'e', 'f'} ids := []int64{'a', 'b', 'c', 'd', 'e', 'f'}
for _, id := range ids { for _, id := range ids {
if math.IsNaN(pt.Weight(id, id)) { if math.IsInf(pt.Weight(id, id), -1) {
fmt.Printf("%c is in a negative cycle\n", id) fmt.Printf("%c is in a negative cycle\n", id)
} }
} }
@@ -95,7 +95,7 @@ func ExampleFloydWarshall_negativecycles() {
for _, uid := range ids { for _, uid := range ids {
for _, vid := range ids { for _, vid := range ids {
_, w, unique := pt.Between(uid, vid) _, w, unique := pt.Between(uid, vid)
if math.IsNaN(w) { if math.IsInf(w, -1) {
fmt.Printf("negative cycle in path from %c to %c unique=%t\n", uid, vid, unique) fmt.Printf("negative cycle in path from %c to %c unique=%t\n", uid, vid, unique)
} }
} }

12
graph/path/shortest.go
View File

@@ -119,7 +119,7 @@ func (p Shortest) WeightTo(vid int64) float64 {
// To returns a shortest path to v and the weight of the path. If the path // To returns a shortest path to v and the weight of the path. If the path
// to v includes a negative cycle, one pass through the cycle will be included // to v includes a negative cycle, one pass through the cycle will be included
// in path and weight will be returned as NaN. // in path and weight will be returned as -Inf.
func (p Shortest) To(vid int64) (path []graph.Node, weight float64) { func (p Shortest) To(vid int64) (path []graph.Node, weight float64) {
to, toOK := p.indexOf[vid] to, toOK := p.indexOf[vid]
if !toOK || math.IsInf(p.dist[to], 1) { if !toOK || math.IsInf(p.dist[to], 1) {
@@ -133,7 +133,7 @@ func (p Shortest) To(vid int64) (path []graph.Node, weight float64) {
seen.Add(from) seen.Add(from)
for to != from { for to != from {
if seen.Has(to) { if seen.Has(to) {
weight = math.NaN() weight = math.Inf(-1)
break break
} }
seen.Add(to) seen.Add(to)
@@ -253,7 +253,7 @@ func (p AllShortest) Weight(uid, vid int64) float64 {
// one shortest path exists between u and v, a randomly chosen path will be returned and // one shortest path exists between u and v, a randomly chosen path will be returned and
// unique is returned false. If a cycle with zero weight exists in the path, it will not // unique is returned false. If a cycle with zero weight exists in the path, it will not
// be included, but unique will be returned false. If a negative cycle exists on the path // be included, but unique will be returned false. If a negative cycle exists on the path
// from u to v, path will be returned nil, weight will be NaN and unique will be false. // from u to v, path will be returned nil, weight will be -Inf and unique will be false.
func (p AllShortest) Between(uid, vid int64) (path []graph.Node, weight float64, unique bool) { func (p AllShortest) Between(uid, vid int64) (path []graph.Node, weight float64, unique bool) {
from, fromOK := p.indexOf[uid] from, fromOK := p.indexOf[uid]
to, toOK := p.indexOf[vid] to, toOK := p.indexOf[vid]
@@ -265,7 +265,7 @@ func (p AllShortest) Between(uid, vid int64) (path []graph.Node, weight float64,
} }
weight = p.dist.At(from, to) weight = p.dist.At(from, to)
if math.IsNaN(weight) { if math.IsInf(weight, -1) {
return nil, weight, false return nil, weight, false
} }
@@ -314,7 +314,7 @@ func (p AllShortest) Between(uid, vid int64) (path []graph.Node, weight float64,
// AllBetween returns all shortest paths from u to v and the weight of the paths. Paths // AllBetween returns all shortest paths from u to v and the weight of the paths. Paths
// containing zero-weight cycles are not returned. If a negative cycle exists between // containing zero-weight cycles are not returned. If a negative cycle exists between
// u and v, paths is returned nil and weight is returned as NaN. // u and v, paths is returned nil and weight is returned as -Inf.
func (p AllShortest) AllBetween(uid, vid int64) (paths [][]graph.Node, weight float64) { func (p AllShortest) AllBetween(uid, vid int64) (paths [][]graph.Node, weight float64) {
from, fromOK := p.indexOf[uid] from, fromOK := p.indexOf[uid]
to, toOK := p.indexOf[vid] to, toOK := p.indexOf[vid]
@@ -326,7 +326,7 @@ func (p AllShortest) AllBetween(uid, vid int64) (paths [][]graph.Node, weight fl
} }
weight = p.dist.At(from, to) weight = p.dist.At(from, to)
if math.IsNaN(weight) { if math.IsInf(weight, -1) {
return nil, weight return nil, weight
} }