/**
* Unit tests the {@code FloydWarshall} data type.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
// random graph with V vertices and E edges, parallel edges allowed
int V = Integer.parseInt(args[0]);
int E = Integer.parseInt(args[1]);
AdjMatrixEdgeWeightedDigraph G = new AdjMatrixEdgeWeightedDigraph(V);
for (int i = 0; i < E; i++) {
int v = StdRandom.uniform(V);
int w = StdRandom.uniform(V);
double weight = Math.round(100 * (StdRandom.uniform() - 0.15)) / 100.0;
if (v == w) G.addEdge(new DirectedEdge(v, w, Math.abs(weight)));
else G.addEdge(new DirectedEdge(v, w, weight));
}
StdOut.println(G);
// run Floyd-Warshall algorithm
FloydWarshall spt = new FloydWarshall(G);
// print all-pairs shortest path distances
StdOut.printf(" ");
for (int v = 0; v < G.V(); v++) {
StdOut.printf("%6d ", v);
}
StdOut.println();
for (int v = 0; v < G.V(); v++) {
StdOut.printf("%3d: ", v);
for (int w = 0; w < G.V(); w++) {
if (spt.hasPath(v, w)) StdOut.printf("%6.2f ", spt.dist(v, w));
else StdOut.printf(" Inf ");
}
StdOut.println();
}
// print negative cycle
if (spt.hasNegativeCycle()) {
StdOut.println("Negative cost cycle:");
for (DirectedEdge e : spt.negativeCycle())
StdOut.println(e);
StdOut.println();
}
// print all-pairs shortest paths
else {
for (int v = 0; v < G.V(); v++) {
for (int w = 0; w < G.V(); w++) {
if (spt.hasPath(v, w)) {
StdOut.printf("%d to %d (%5.2f) ", v, w, spt.dist(v, w));
for (DirectedEdge e : spt.path(v, w))
StdOut.print(e + " ");
StdOut.println();
}
else {
StdOut.printf("%d to %d no path\n", v, w);
}
}
}
}
}
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;
}
/**
* Unit tests the {@code AdjMatrixEdgeWeightedDigraph} data type.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
int V = Integer.parseInt(args[0]);
int E = Integer.parseInt(args[1]);
AdjMatrixEdgeWeightedDigraph G = new AdjMatrixEdgeWeightedDigraph(V, E);
StdOut.println(G);
}
