private DirectedEdge[][] edgeTo; // edgeTo[v][w] = last edge on shortest v->w path
/**
* Computes a shortest paths tree from each vertex to to every other vertex in
* the edge-weighted digraph {@code G}. If no such shortest path exists for
* some pair of vertices, it computes a negative cycle.
* @param G the edge-weighted digraph
*/
public FloydWarshall(AdjMatrixEdgeWeightedDigraph G) {
int V = G.V();
distTo = new double[V][V];
edgeTo = new DirectedEdge[V][V];
// initialize distances to infinity
for (int v = 0; v < V; v++) {
for (int w = 0; w < V; w++) {
distTo[v][w] = Double.POSITIVE_INFINITY;
}
}
// initialize distances using edge-weighted digraph's
for (int v = 0; v < G.V(); v++) {
for (DirectedEdge e : G.adj(v)) {
distTo[e.from()][e.to()] = e.weight();
edgeTo[e.from()][e.to()] = e;
}
// in case of self-loops
if (distTo[v][v] >= 0.0) {
distTo[v][v] = 0.0;
edgeTo[v][v] = null;
}
}
// Floyd-Warshall updates
for (int i = 0; i < V; i++) {
// compute shortest paths using only 0, 1, ..., i as intermediate vertices
for (int v = 0; v < V; v++) {
if (edgeTo[v][i] == null) continue; // optimization
for (int w = 0; w < V; w++) {
if (distTo[v][w] > distTo[v][i] + distTo[i][w]) {
distTo[v][w] = distTo[v][i] + distTo[i][w];
edgeTo[v][w] = edgeTo[i][w];
}
}
// check for negative cycle
if (distTo[v][v] < 0.0) {
hasNegativeCycle = true;
return;
}
}
}
assert check(G);
}
// check optimality conditions
private boolean check(AdjMatrixEdgeWeightedDigraph G) {
// no negative cycle
if (!hasNegativeCycle()) {
for (int v = 0; v < G.V(); v++) {
for (DirectedEdge e : G.adj(v)) {
int w = e.to();
for (int i = 0; i < G.V(); i++) {
if (distTo[i][w] > distTo[i][v] + e.weight()) {
System.err.println("edge " + e + " is eligible");
return false;
}
}
}
}
}
return true;
}