Bellman-Ford
Finds the shortest distance from a start vertex to every other vertex, even with negative weights, and reports a negative cycle when the start can reach one.
Time complexity O(V·E), gograph function path.BellmanFord.
One-way city
Forty-five intersections, I1 to I45, where I stands for intersection, numbered row by row from the top left with nine to a row. Most streets are one way, and the outer streets form a clockwise loop. Only the middle row (I19 to I27) and the middle column (I5, I14, I23, I32 and I41) go both ways, and each edge is the travel time in minutes.
A directed, weighted graph with 45 vertices and 88 edges.
How many minutes is the quickest drive from I23 to each intersection, when most streets are one way?
Use it in Go
dist, err := path.BellmanFord(g, "I23")
if err != nil {
return err // path.ErrNegativeWeightCycle
}
fmt.Println(dist["I2"])Example graphs
- School run, 6 vertices and 13 edges
- Major currencies, 6 vertices and 20 edges
- Delivery area, 8 vertices and 12 edges
- Arbitrage loop, 8 vertices and 24 edges
- One-way city, 45 vertices and 88 edges
More in Shortest paths
- Dijkstra: Finds the shortest distance from a start vertex to every other vertex when no edge weight is negative.
- Floyd-Warshall: Finds the shortest distance between every pair of vertices, even with negative weights, by letting paths stop at one more vertex in each round.