// find shortest augmenting path and upate
private void augment() {
// build residual graph
EdgeWeightedDigraph G = new EdgeWeightedDigraph(2*n+2);
int s = 2*n, t = 2*n+1;
for (int i = 0; i < n; i++) {
if (xy[i] == UNMATCHED)
G.addEdge(new DirectedEdge(s, i, 0.0));
}
for (int j = 0; j < n; j++) {
if (yx[j] == UNMATCHED)
G.addEdge(new DirectedEdge(n+j, t, py[j]));
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (xy[i] == j) G.addEdge(new DirectedEdge(n+j, i, 0.0));
else G.addEdge(new DirectedEdge(i, n+j, reducedCost(i, j)));
}
}
// compute shortest path from s to every other vertex
DijkstraSP spt = new DijkstraSP(G, s);
// augment along alternating path
for (DirectedEdge e : spt.pathTo(t)) {
int i = e.from(), j = e.to() - n;
if (i < n) {
xy[i] = j;
yx[j] = i;
}
}
// update dual variables
for (int i = 0; i < n; i++)
px[i] += spt.distTo(i);
for (int j = 0; j < n; j++)
py[j] += spt.distTo(n+j);
}
/**
* Unit tests the {@code DijkstraSP} data type.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
In in = new In(args[0]);
EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);
int s = Integer.parseInt(args[1]);
// compute shortest paths
DijkstraSP sp = new DijkstraSP(G, s);
// print shortest path
for (int t = 0; t < G.V(); t++) {
if (sp.hasPathTo(t)) {
StdOut.printf("%d to %d (%.2f) ", s, t, sp.distTo(t));
for (DirectedEdge e : sp.pathTo(t)) {
StdOut.print(e + " ");
}
StdOut.println();
}
else {
StdOut.printf("%d to %d no path\n", s, t);
}
}
}
/**
* Computes a shortest paths tree from each vertex to to every other vertex in
* the edge-weighted digraph {@code G}.
* @param G the edge-weighted digraph
* @throws IllegalArgumentException if an edge weight is negative
* @throws IllegalArgumentException unless {@code 0 <= s < V}
*/
public DijkstraAllPairsSP(EdgeWeightedDigraph G) {
all = new DijkstraSP[G.V()];
for (int v = 0; v < G.V(); v++)
all[v] = new DijkstraSP(G, v);
}
