```001// Exercise 4.4.28 (Solution published at http://algs4.cs.princeton.edu/)
002package algs44;
003import stdlib.*;
004import algs13.Stack;
005import algs42.Topological;
006/* ***********************************************************************
007 *  Compilation:  javac AcyclicLP.java
008 *  Execution:    java AcyclicP V E
009 *  Dependencies: EdgeWeightedDigraph.java DirectedEdge.java Topological.java
010 *  Data files:   http://algs4.cs.princeton.edu/44sp/tinyEWDAG.txt
011 *
012 *  Computes longest paths in an edge-weighted acyclic digraph.
013 *
014 *  Remark: should probably check that graph is a DAG before running
015 *
016 *  % java AcyclicLP tinyEWDAG.txt 5
017 *  5 to 0 (2.44)  5->1  0.32   1->3  0.29   3->6  0.52   6->4  0.93   4->0  0.38
018 *  5 to 1 (0.32)  5->1  0.32
019 *  5 to 2 (2.77)  5->1  0.32   1->3  0.29   3->6  0.52   6->4  0.93   4->7  0.37   7->2  0.34
020 *  5 to 3 (0.61)  5->1  0.32   1->3  0.29
021 *  5 to 4 (2.06)  5->1  0.32   1->3  0.29   3->6  0.52   6->4  0.93
022 *  5 to 5 (0.00)
023 *  5 to 6 (1.13)  5->1  0.32   1->3  0.29   3->6  0.52
024 *  5 to 7 (2.43)  5->1  0.32   1->3  0.29   3->6  0.52   6->4  0.93   4->7  0.37
025 *
026 *************************************************************************/
027
028public class AcyclicLP {
029        private final double[] distTo;          // distTo[v] = distance  of longest s->v path
030        private final DirectedEdge[] edgeTo;    // edgeTo[v] = last edge on longest s->v path
031
032        public AcyclicLP(EdgeWeightedDigraph G, int s) {
033                distTo = new double[G.V()];
034                edgeTo = new DirectedEdge[G.V()];
035                for (int v = 0; v < G.V(); v++) distTo[v] = Double.NEGATIVE_INFINITY;
036                distTo[s] = 0.0;
037
038                // relax vertices in toplogical order
039                Topological topological = new Topological(G);
040                for (int v : topological.order()) {
041                        for (DirectedEdge e : G.adj(v))
042                                relax(e);
043                }
044        }
045
046        // relax edge e, but update if you find a *longer* path
047        private void relax(DirectedEdge e) {
048                int v = e.from(), w = e.to();
049                if (distTo[w] < distTo[v] + e.weight()) {
050                        distTo[w] = distTo[v] + e.weight();
051                        edgeTo[w] = e;
052                }
053        }
054
055        // return length of the longest path from s to v, -infinity if no such path
056        public double distTo(int v) {
057                return distTo[v];
058        }
059
060        //  is there a  path from s to v?
061        public boolean hasPathTo(int v) {
062                return distTo[v] > Double.NEGATIVE_INFINITY;
063        }
064
065        // return view of longest path from s to v, null if no such path
066        public Iterable<DirectedEdge> pathTo(int v) {
067                if (!hasPathTo(v)) return null;
068                Stack<DirectedEdge> path = new Stack<>();
069                for (DirectedEdge e = edgeTo[v]; e != null; e = edgeTo[e.from()]) {
070                        path.push(e);
071                }
072                return path;
073        }
074
075
076
077        public static void main(String[] args) {
078                In in = new In(args[0]);
079                int s = Integer.parseInt(args[1]);
080                EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);
081
082                AcyclicLP lp = new AcyclicLP(G, s);
083
084                for (int v = 0; v < G.V(); v++) {
085                        if (lp.hasPathTo(v)) {
086                                StdOut.format("%d to %d (%.2f)  ", s, v, lp.distTo(v));
087                                for (DirectedEdge e : lp.pathTo(v)) {
088                                        StdOut.print(e + "   ");
089                                }
090                                StdOut.println();
091                        }
092                        else {
093                                StdOut.format("%d to %d         no path\n", s, v);
094                        }
095                }
096        }
097}

```