private IndexMinPQ<Double> pq; // priority queue of vertices /** * Computes a shortest-paths tree from the source vertex {@code s} to every other * vertex in the edge-weighted digraph {@code G}. * * @param G the edge-weighted digraph * @param s the source vertex * @throws IllegalArgumentException if an edge weight is negative * @throws IllegalArgumentException unless {@code 0 <= s < V} */ public DijkstraSP(EdgeWeightedDigraph G, int s) { for (DirectedEdge e : G.edges()) { if (e.weight() < 0) throw new IllegalArgumentException("edge " + e + " has negative weight"); } distTo = new double[G.V()]; edgeTo = new DirectedEdge[G.V()]; validateVertex(s); for (int v = 0; v < G.V(); v++) distTo[v] = Double.POSITIVE_INFINITY; distTo[s] = 0.0; // relax vertices in order of distance from s pq = new IndexMinPQ<Double>(G.V()); pq.insert(s, distTo[s]); while (!pq.isEmpty()) { int v = pq.delMin(); for (DirectedEdge e : G.adj(v)) relax(e); } // check optimality conditions assert check(G, s); }
// check optimality conditions: // (i) for all edges e: distTo[e.to()] <= distTo[e.from()] + e.weight() // (ii) for all edge e on the SPT: distTo[e.to()] == distTo[e.from()] + e.weight() private boolean check(EdgeWeightedDigraph G, int s) { // check that edge weights are nonnegative for (DirectedEdge e : G.edges()) { if (e.weight() < 0) { System.err.println("negative edge weight detected"); return false; } } // check that distTo[v] and edgeTo[v] are consistent if (distTo[s] != 0.0 || edgeTo[s] != null) { System.err.println("distTo[s] and edgeTo[s] inconsistent"); return false; } for (int v = 0; v < G.V(); v++) { if (v == s) continue; if (edgeTo[v] == null && distTo[v] != Double.POSITIVE_INFINITY) { System.err.println("distTo[] and edgeTo[] inconsistent"); return false; } } // check that all edges e = v->w satisfy distTo[w] <= distTo[v] + e.weight() for (int v = 0; v < G.V(); v++) { for (DirectedEdge e : G.adj(v)) { int w = e.to(); if (distTo[v] + e.weight() < distTo[w]) { System.err.println("edge " + e + " not relaxed"); return false; } } } // check that all edges e = v->w on SPT satisfy distTo[w] == distTo[v] + e.weight() for (int w = 0; w < G.V(); w++) { if (edgeTo[w] == null) continue; DirectedEdge e = edgeTo[w]; int v = e.from(); if (w != e.to()) return false; if (distTo[v] + e.weight() != distTo[w]) { System.err.println("edge " + e + " on shortest path not tight"); return false; } } return true; }