001package algs44;
002import stdlib.*;
003import algs13.Stack;
004import algs24.IndexMinPQ;
005/* ***********************************************************************
006 *  Compilation:  javac DijkstraSP.java
007 *  Execution:    java DijkstraSP input.txt s
008 *  Dependencies: EdgeWeightedDigraph.java IndexMinPQ.java Stack.java DirectedEdge.java
009 *  Data files:   http://algs4.cs.princeton.edu/44sp/tinyEWD.txt
010 *                http://algs4.cs.princeton.edu/44sp/mediumEWD.txt
011 *                http://algs4.cs.princeton.edu/44sp/largeEWD.txt
012 *
013 *  Dijkstra's algorithm. Computes the shortest path tree.
014 *  Assumes all weights are nonnegative.
015 *
016 *  % java DijkstraSP tinyEWD.txt 0
017 *  0 to 0 (0.00)
018 *  0 to 1 (1.05)  0->4  0.38   4->5  0.35   5->1  0.32
019 *  0 to 2 (0.26)  0->2  0.26
020 *  0 to 3 (0.99)  0->2  0.26   2->7  0.34   7->3  0.39
021 *  0 to 4 (0.38)  0->4  0.38
022 *  0 to 5 (0.73)  0->4  0.38   4->5  0.35
023 *  0 to 6 (1.51)  0->2  0.26   2->7  0.34   7->3  0.39   3->6  0.52
024 *  0 to 7 (0.60)  0->2  0.26   2->7  0.34
025 *
026 *  % java DijkstraSP mediumEWD.txt 0
027 *  0 to 0 (0.00)
028 *  0 to 1 (0.71)  0->44  0.06   44->93  0.07   ...  107->1  0.07
029 *  0 to 2 (0.65)  0->44  0.06   44->231  0.10  ...  42->2  0.11
030 *  0 to 3 (0.46)  0->97  0.08   97->248  0.09  ...  45->3  0.12
031 *  0 to 4 (0.42)  0->44  0.06   44->93  0.07   ...  77->4  0.11
032 *  ...
033 *
034 *************************************************************************/
035
036public class DijkstraSP {
037        private final double[] distTo;          // distTo[v] = distance  of shortest s->v path
038        private final DirectedEdge[] edgeTo;    // edgeTo[v] = last edge on shortest s->v path
039        private final IndexMinPQ<Double> pq;    // priority queue of vertices
040
041        public DijkstraSP(EdgeWeightedDigraph G, int s) {
042                for (DirectedEdge e : G.edges()) {
043                        if (e.weight() < 0)
044                                throw new IllegalArgumentException("edge " + e + " has negative weight");
045                }
046
047                distTo = new double[G.V()];
048                edgeTo = new DirectedEdge[G.V()];
049                for (int v = 0; v < G.V(); v++)
050                        distTo[v] = Double.POSITIVE_INFINITY;
051                distTo[s] = 0.0;
052
053                // relax vertices in order of distance from s
054                pq = new IndexMinPQ<>(G.V());
055                pq.insert(s, distTo[s]);
056                while (!pq.isEmpty()) {
057                        int v = pq.delMin();
058                        for (DirectedEdge e : G.adj(v))
059                                relax(e);
060                }
061
062                // check optimality conditions
063                assert check(G, s);
064        }
065
066        // relax edge e and update pq if changed
067        private void relax(DirectedEdge e) {
068                int v = e.from(), w = e.to();
069                if (distTo[w] > distTo[v] + e.weight()) {
070                        distTo[w] = distTo[v] + e.weight();
071                        edgeTo[w] = e;
072                        if (pq.contains(w)) pq.decreaseKey(w, distTo[w]);
073                        else                pq.insert(w, distTo[w]);
074                }
075        }
076
077        // length of shortest path from s to v
078        public double distTo(int v) {
079                return distTo[v];
080        }
081
082        // is there a path from s to v?
083        public boolean hasPathTo(int v) {
084                return distTo[v] < Double.POSITIVE_INFINITY;
085        }
086
087        // shortest path from s to v as an Iterable, null if no such path
088        public Iterable<DirectedEdge> pathTo(int v) {
089                if (!hasPathTo(v)) return null;
090                Stack<DirectedEdge> path = new Stack<>();
091                for (DirectedEdge e = edgeTo[v]; e != null; e = edgeTo[e.from()]) {
092                        path.push(e);
093                }
094                return path;
095        }
096
097
098        // check optimality conditions:
099        // (i) for all edges e:            distTo[e.to()] <= distTo[e.from()] + e.weight()
100        // (ii) for all edge e on the SPT: distTo[e.to()] == distTo[e.from()] + e.weight()
101        private boolean check(EdgeWeightedDigraph G, int s) {
102
103                // check that edge weights are nonnegative
104                for (DirectedEdge e : G.edges()) {
105                        if (e.weight() < 0) {
106                                System.err.println("negative edge weight detected");
107                                return false;
108                        }
109                }
110
111                // check that distTo[v] and edgeTo[v] are consistent
112                if (distTo[s] != 0.0 || edgeTo[s] != null) {
113                        System.err.println("distTo[s] and edgeTo[s] inconsistent");
114                        return false;
115                }
116                for (int v = 0; v < G.V(); v++) {
117                        if (v == s) continue;
118                        if (edgeTo[v] == null && distTo[v] != Double.POSITIVE_INFINITY) {
119                                System.err.println("distTo[] and edgeTo[] inconsistent");
120                                return false;
121                        }
122                }
123
124                // check that all edges e = v->w satisfy distTo[w] <= distTo[v] + e.weight()
125                for (int v = 0; v < G.V(); v++) {
126                        for (DirectedEdge e : G.adj(v)) {
127                                int w = e.to();
128                                if (distTo[v] + e.weight() < distTo[w]) {
129                                        System.err.println("edge " + e + " not relaxed");
130                                        return false;
131                                }
132                        }
133                }
134
135                // check that all edges e = v->w on SPT satisfy distTo[w] == distTo[v] + e.weight()
136                for (int w = 0; w < G.V(); w++) {
137                        if (edgeTo[w] == null) continue;
138                        DirectedEdge e = edgeTo[w];
139                        int v = e.from();
140                        if (w != e.to()) return false;
141                        if (distTo[v] + e.weight() != distTo[w]) {
142                                System.err.println("edge " + e + " on shortest path not tight");
143                                return false;
144                        }
145                }
146                return true;
147        }
148
149
150        public static void main(String[] args) {
151                In in = new In(args[0]);
152                EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);
153                int s = Integer.parseInt(args[1]);
154
155                // compute shortest paths
156                DijkstraSP sp = new DijkstraSP(G, s);
157
158
159                // print shortest path
160                for (int t = 0; t < G.V(); t++) {
161                        if (sp.hasPathTo(t)) {
162                                StdOut.format("%d to %d (%.2f)  ", s, t, sp.distTo(t));
163                                if (sp.hasPathTo(t)) {
164                                        for (DirectedEdge e : sp.pathTo(t)) {
165                                                StdOut.print(e + "   ");
166                                        }
167                                }
168                                StdOut.println();
169                        }
170                        else {
171                                StdOut.format("%d to %d         no path\n", s, t);
172                        }
173                }
174        }
175
176}