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.

Time complexity O(V³), gograph function path.FloydWarshall.

Downtown grid

Twenty intersections on a downtown street grid. Streets go both ways, Market is closed to cars between 2nd and 3rd, and each edge is the travel time in minutes.

A directed, weighted graph with 20 vertices and 60 edges.

How many minutes is the quickest drive between every pair of intersections, with Market closed between 2nd and 3rd?

Use it in Go

dist, err := path.FloydWarshall(g)
if err != nil {
	return err
}
fmt.Println(dist["Pine & 1st"]["River & 5th"])
fmt.Println(dist["River & 5th"]["Pine & 1st"]) // +Inf when there is no path

Example graphs

• Major currencies, 6 vertices and 20 edges
• Delivery area, 8 vertices and 12 edges
• Downtown grid, 20 vertices and 60 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.
• 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.

All algorithms