Documentation
¶
Overview ¶
Package path provides graph path finding functions.
Index ¶
- func Kruskal(dst WeightedBuilder, g UndirectedWeightLister) float64
- func NullHeuristic(_, _ graph.Node) float64
- func Prim(dst WeightedBuilder, g graph.WeightedUndirected) float64
- type AllShortest
- type DominatorTree
- type Heuristic
- type HeuristicCoster
- type Shortest
- type UndirectedWeightLister
- type Weighted
- type WeightedBuilder
- type Weighting
Examples ¶
Constants ¶
This section is empty.
Variables ¶
This section is empty.
Functions ¶
func Kruskal ¶
func Kruskal(dst WeightedBuilder, g UndirectedWeightLister) float64
Kruskal generates a minimum spanning tree of g by greedy tree coalescence, placing the result in the destination, dst. If the edge weights of g are distinct it will be the unique minimum spanning tree of g. The destination is not cleared first. The weight of the minimum spanning tree is returned. If g is not connected, a minimum spanning forest will be constructed in dst and the sum of minimum spanning tree weights will be returned.
Nodes and Edges from g are used to construct dst, so if the Node and Edge types used in g are pointer or reference-like, then the values will be shared between the graphs.
If dst has nodes that exist in g, Kruskal will panic.
func NullHeuristic ¶
NullHeuristic is an admissible, consistent heuristic that will not speed up computation.
func Prim ¶
func Prim(dst WeightedBuilder, g graph.WeightedUndirected) float64
Prim generates a minimum spanning tree of g by greedy tree extension, placing the result in the destination, dst. If the edge weights of g are distinct it will be the unique minimum spanning tree of g. The destination is not cleared first. The weight of the minimum spanning tree is returned. If g is not connected, a minimum spanning forest will be constructed in dst and the sum of minimum spanning tree weights will be returned.
Nodes and Edges from g are used to construct dst, so if the Node and Edge types used in g are pointer or reference-like, then the values will be shared between the graphs.
If dst has nodes that exist in g, Prim will panic.
Types ¶
type AllShortest ¶
type AllShortest struct {
// contains filtered or unexported fields
}
AllShortest is a shortest-path tree created by the DijkstraAllPaths, FloydWarshall or JohnsonAllPaths all-pairs shortest paths functions.
func DijkstraAllPaths ¶
func DijkstraAllPaths(g graph.Graph) (paths AllShortest)
DijkstraAllPaths returns a shortest-path tree for shortest paths in the graph g. If the graph does not implement graph.Weighter, UniformCost is used. DijkstraAllPaths will panic if g has a negative edge weight.
The time complexity of DijkstrAllPaths is O(|V|.|E|+|V|^2.log|V|).
func FloydWarshall ¶
func FloydWarshall(g graph.Graph) (paths AllShortest, ok bool)
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 Weighted, UniformCost is used.
The time complexity of FloydWarshall is O(|V|^3).
func JohnsonAllPaths ¶
func JohnsonAllPaths(g graph.Graph) (paths AllShortest, ok bool)
JohnsonAllPaths returns a shortest-path tree for shortest paths in the graph g. If the graph does not implement Weighted, UniformCost is used.
The time complexity of JohnsonAllPaths is O(|V|.|E|+|V|^2.log|V|).
func (AllShortest) AllBetween ¶
func (p AllShortest) AllBetween(uid, vid int64) (paths [][]graph.Node, weight float64)
AllBetween returns all shortest paths from u to v and the weight of the paths. Paths containing zero-weight cycles are not returned.
func (AllShortest) Between ¶
Between returns a shortest path from u to v and the weight of the path. If more than 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 be included, but unique will be returned false.
func (AllShortest) Weight ¶
func (p AllShortest) Weight(uid, vid int64) float64
Weight returns the weight of the minimum path between u and v.
type DominatorTree ¶
type DominatorTree struct {
// contains filtered or unexported fields
}
DominatorTree is a flow graph dominator tree.
func Dominators ¶
func Dominators(root graph.Node, g graph.Directed) DominatorTree
Dominators returns a dominator tree for all nodes in the flow graph g starting from the given root node.
func DominatorsSLT ¶
func DominatorsSLT(root graph.Node, g graph.Directed) DominatorTree
DominatorsSLT returns a dominator tree for all nodes in the flow graph g starting from the given root node using the sophisticated version of the Lengauer-Tarjan algorithm. The SLT algorithm may outperform the simple LT algorithm for very large dense graphs.
func (DominatorTree) DominatedBy ¶
func (d DominatorTree) DominatedBy(n graph.Node) []graph.Node
DominatedBy returns a slice of all nodes immediately dominated by n. Elements of the slice are retained by the DominatorTree.
func (DominatorTree) DominatorOf ¶
func (d DominatorTree) DominatorOf(n graph.Node) graph.Node
DominatorOf returns the immediate dominator of n.
func (DominatorTree) Root ¶
func (d DominatorTree) Root() graph.Node
Root returns the root of the tree.
type HeuristicCoster ¶
HeuristicCoster wraps the HeuristicCost method. A graph implementing the interface provides a heuristic between any two given nodes.
type Shortest ¶
type Shortest struct {
// contains filtered or unexported fields
}
Shortest is a shortest-path tree created by the BellmanFordFrom or DijkstraFrom single-source shortest path functions.
func AStar ¶
AStar finds the A*-shortest path from s to t in g using the heuristic h. The path and its cost are returned in a Shortest along with paths and costs to all nodes explored during the search. The number of expanded nodes is also returned. This value may help with heuristic tuning.
The path will be the shortest path if the heuristic is admissible. A heuristic is admissible if for any node, n, in the graph, the heuristic estimate of the cost of the path from n to t is less than or equal to the true cost of that path.
If h is nil, AStar will use the g.HeuristicCost method if g implements HeuristicCoster, falling back to NullHeuristic otherwise. If the graph does not implement Weighted, UniformCost is used. AStar will panic if g has an A*-reachable negative edge weight.
func BellmanFordFrom ¶
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|).
Example (Negativecycles) ¶
package main
import (
"fmt"
"math"
"gonum.org/v1/gonum/graph/path"
"gonum.org/v1/gonum/graph/simple"
)
func main() {
// BellmanFordFrom can be used to find a non-exhaustive
// set of negative cycles in a graph. Enumerating the
// exhaustive list requires iterations of the procedure
// here successively omitting links from the new node
// to already found negative cycles.
// Construct a graph with a negative cycle.
edges := []simple.WeightedEdge{
{F: simple.Node('a'), T: simple.Node('b'), W: -2},
{F: simple.Node('a'), T: simple.Node('f'), W: 2},
{F: simple.Node('b'), T: simple.Node('c'), W: 6},
{F: simple.Node('c'), T: simple.Node('a'), W: -5},
{F: simple.Node('d'), T: simple.Node('c'), W: -3},
{F: simple.Node('d'), T: simple.Node('e'), W: 8},
{F: simple.Node('e'), T: simple.Node('b'), W: 9},
{F: simple.Node('e'), T: simple.Node('c'), W: 2},
}
g := simple.NewWeightedDirectedGraph(0, math.Inf(1))
for _, e := range edges {
g.SetWeightedEdge(e)
}
// Add a zero-cost path to all nodes from a new node Q.
for _, n := range g.Nodes() {
g.SetWeightedEdge(simple.WeightedEdge{F: simple.Node('Q'), T: n})
}
// Find the shortest path to each node from Q.
pt, ok := path.BellmanFordFrom(simple.Node('Q'), g)
if ok {
fmt.Println("no negative cycle present")
return
}
for _, n := range []simple.Node{'a', 'b', 'c', 'd', 'e', 'f'} {
p, w := pt.To(n.ID())
if math.IsNaN(w) {
fmt.Printf("negative cycle in path to %c path:%c\n", n, p)
}
}
}
Output: negative cycle in path to a path:[a b c a] negative cycle in path to b path:[b c a b] negative cycle in path to c path:[c a b c] negative cycle in path to f path:[a b c a f]
func DijkstraFrom ¶
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 DijkstrFrom is O(|E|.log|V|).
type UndirectedWeightLister ¶
type UndirectedWeightLister interface {
graph.WeightedUndirected
WeightedEdges() []graph.WeightedEdge
}
UndirectedWeightLister is an undirected graph that returns edge weights and the set of edges in the graph.
type Weighted ¶
type Weighted interface {
// Weight returns the weight for the edge between
// x and y with IDs xid and yid if Edge(xid, yid)
// returns a non-nil Edge.
// If x and y are the same node or there is no
// joining edge between the two nodes the weight
// value returned is implementation dependent.
// Weight returns true if an edge exists between
// x and y or if x and y have the same ID, false
// otherwise.
Weight(xid, yid int64) (w float64, ok bool)
}
Weighted is a weighted graph. It is a subset of graph.Weighted.
type WeightedBuilder ¶
type WeightedBuilder interface {
AddNode(graph.Node)
SetWeightedEdge(graph.WeightedEdge)
}
WeightedBuilder is a type that can add nodes and weighted edges.
type Weighting ¶
Weighting is a mapping between a pair of nodes and a weight. It follows the semantics of the Weighter interface.
func UniformCost ¶
UniformCost returns a Weighting that returns an edge cost of 1 for existing edges, zero for node identity and Inf for otherwise absent edges.
Source Files
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Directories
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| Path | Synopsis |
|---|---|
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Package dynamic provides incremental heuristic graph path finding functions.
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Package dynamic provides incremental heuristic graph path finding functions. |
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internal
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testgraphs
Package testsgraphs provides a number of graphs used for testing routines in the path and path/dynamic packages.
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Package testsgraphs provides a number of graphs used for testing routines in the path and path/dynamic packages. |