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bellman_ford_moore.go
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bellman_ford_moore.go
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// 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 "gonum.org/v1/gonum/graph"
// 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 Weighted, 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.ID()) {
return Shortest{from: u}, true
}
var weight Weighting
if wg, ok := g.(Weighted); 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 {
uid := u.ID()
for _, v := range g.From(uid) {
vid := v.ID()
k := path.indexOf[vid]
w, ok := weight(uid, vid)
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 {
uid := u.ID()
for _, v := range g.From(uid) {
vid := v.ID()
k := path.indexOf[vid]
w, ok := weight(uid, vid)
if !ok {
panic("bellman-ford: unexpected invalid weight")
}
if path.dist[j]+w < path.dist[k] {
path.hasNegativeCycle = true
return path, false
}
}
}
return path, true
}