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floydwarshall.go
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floydwarshall.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 "github.com/gonum/graph"
// FloydWarshall returns a shortest-path tree for the graph g or false indicating
// that a negative cycle exists in the graph. If the graph does not implement
// graph.Weighter, graph.UniformCost is used.
//
// The time complexity of FloydWarshall is O(|V|^3).
func FloydWarshall(g graph.Graph) (paths AllShortest, ok bool) {
var weight graph.WeightFunc
if g, ok := g.(graph.Weighter); ok {
weight = g.Weight
} else {
weight = graph.UniformCost
}
nodes := g.Nodes()
paths = newAllShortest(nodes, true)
for i, u := range nodes {
paths.dist.Set(i, i, 0)
for _, v := range g.From(u) {
j := paths.indexOf[v.ID()]
paths.set(i, j, weight(g.Edge(u, v)), j)
}
}
for k := range nodes {
for i := range nodes {
for j := range nodes {
ij := paths.dist.At(i, j)
joint := paths.dist.At(i, k) + paths.dist.At(k, j)
if ij > joint {
paths.set(i, j, joint, paths.at(i, k)...)
} else if ij-joint == 0 {
paths.add(i, j, paths.at(i, k)...)
}
}
}
}
ok = true
for i := range nodes {
if paths.dist.At(i, i) < 0 {
ok = false
break
}
}
return paths, ok
}