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dijkstra.go
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dijkstra.go
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package graph
import "github.com/ailidani/graph/heap"
// DijkstraFrom returns a shortest-path tree for a shortest path from u to all nodes in
// the graph g. If the graph does not implement Weighted, UniformCost is used.
// DijkstraFrom will panic if g has a u-reachable negative edge weight.
//
// If g is a graph.Graph, all nodes of the graph will be stored in the shortest-path
// tree, otherwise only nodes reachable from u will be stored.
//
// The time complexity of DijkstraFrom is O(|E|.log|V|).
func DijkstraFrom[K comparable](g Graph[K], u Node[K]) Shortest[K] {
var path Shortest[K]
if g.From(u.ID()) == nil {
return Shortest[K]{from: u}
}
path = newShortest(u, g.Nodes().Slice())
var weight Weighting[K]
if wg, ok := g.(WeightedGraph[K]); ok {
weight = wg.Weight
} else {
weight = UniformCost(g)
}
// Dijkstra's algorithm here is implemented essentially as
// described in Function B.2 in figure 6 of UTCS Technical
// Report TR-07-54.
//
// This implementation deviates from the report as follows:
// - the value of path.dist for the start vertex u is initialized to 0;
// - outdated elements from the priority queue (i.e. with respect to the dist value)
// are skipped.
//
// http://www.cs.utexas.edu/ftp/techreports/tr07-54.pdf
Q := heap.New(func(i, j distanceNode[K]) bool {
return i.dist < j.dist
})
Q.Push(distanceNode[K]{node: u, dist: 0})
for Q.Size() > 0 {
mid, ok := Q.Pop()
if !ok {
panic("dijkstra: unexpected empty priority queue")
}
k := path.index[mid.node.ID()]
if mid.dist > path.dist[k] {
continue
}
mnid := mid.node.ID()
to := g.From(mnid)
for _, v := range to {
vid := v.ID()
j, ok := path.index[vid]
if !ok {
j = path.add(v)
}
w, ok := weight(mnid, vid)
if !ok {
panic("dijkstra: unexpected invalid weight")
}
if w < 0 {
panic("dijkstra: negative edge weight")
}
joint := path.dist[k] + w
if joint < path.dist[j] {
Q.Push(distanceNode[K]{node: v, dist: joint})
path.set(j, joint, k)
}
}
}
return path
}
type distanceNode[K comparable] struct {
node Node[K]
dist float64
}