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/******************************************************************************
* Compilation: javac AcyclicLP.java
* Execution: java AcyclicP V E
* Dependencies: EdgeWeightedDigraph.java DirectedEdge.java Topological.java
* Data files: https://algs4.cs.princeton.edu/44sp/tinyEWDAG.txt
*
* Computes longeset paths in an edge-weighted acyclic digraph.
*
* Remark: should probably check that graph is a DAG before running
*
* % java AcyclicLP tinyEWDAG.txt 5
* 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
* 5 to 1 (0.32) 5->1 0.32
* 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
* 5 to 3 (0.61) 5->1 0.32 1->3 0.29
* 5 to 4 (2.06) 5->1 0.32 1->3 0.29 3->6 0.52 6->4 0.93
* 5 to 5 (0.00)
* 5 to 6 (1.13) 5->1 0.32 1->3 0.29 3->6 0.52
* 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
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code AcyclicLP} class represents a data type for solving the
* single-source longest paths problem in edge-weighted directed
* acyclic graphs (DAGs). The edge weights can be positive, negative, or zero.
*
* This implementation uses a topological-sort based algorithm.
* The constructor takes time proportional to V + E,
* where V is the number of vertices and E is the number of edges.
* Each call to {@code distTo(int)} and {@code hasPathTo(int)} takes constant time;
* each call to {@code pathTo(int)} takes time proportional to the number of
* edges in the shortest path returned.
*
* For additional documentation,
* see Section 4.4 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class AcyclicLP {
private double[] distTo; // distTo[v] = distance of longest s->v path
private DirectedEdge[] edgeTo; // edgeTo[v] = last edge on longest s->v path
/**
* Computes a longest paths tree from {@code s} to every other vertex in
* the directed acyclic graph {@code G}.
* @param G the acyclic digraph
* @param s the source vertex
* @throws IllegalArgumentException if the digraph is not acyclic
* @throws IllegalArgumentException unless {@code 0 <= s < V}
*/
public AcyclicLP(EdgeWeightedDigraph G, int s) {
distTo = new double[G.V()];
edgeTo = new DirectedEdge[G.V()];
validateVertex(s);
for (int v = 0; v < G.V(); v++)
distTo[v] = Double.NEGATIVE_INFINITY;
distTo[s] = 0.0;
// relax vertices in topological order
Topological topological = new Topological(G);
if (!topological.hasOrder())
throw new IllegalArgumentException("Digraph is not acyclic.");
for (int v : topological.order()) {
for (DirectedEdge e : G.adj(v))
relax(e);
}
}
// relax edge e, but update if you find a *longer* path
private void relax(DirectedEdge e) {
int v = e.from(), w = e.to();
if (distTo[w] < distTo[v] + e.weight()) {
distTo[w] = distTo[v] + e.weight();
edgeTo[w] = e;
}
}
/**
* Returns the length of a longest path from the source vertex {@code s} to vertex {@code v}.
* @param v the destination vertex
* @return the length of a longest path from the source vertex {@code s} to vertex {@code v};
* {@code Double.NEGATIVE_INFINITY} if no such path
* @throws IllegalArgumentException unless {@code 0 <= v < V}
*/
public double distTo(int v) {
validateVertex(v);
return distTo[v];
}
/**
* Is there a path from the source vertex {@code s} to vertex {@code v}?
* @param v the destination vertex
* @return {@code true} if there is a path from the source vertex
* {@code s} to vertex {@code v}, and {@code false} otherwise
* @throws IllegalArgumentException unless {@code 0 <= v < V}
*/
public boolean hasPathTo(int v) {
validateVertex(v);
return distTo[v] > Double.NEGATIVE_INFINITY;
}
/**
* Returns a longest path from the source vertex {@code s} to vertex {@code v}.
* @param v the destination vertex
* @return a longest path from the source vertex {@code s} to vertex {@code v}
* as an iterable of edges, and {@code null} if no such path
* @throws IllegalArgumentException unless {@code 0 <= v < V}
*/
public Iterable pathTo(int v) {
validateVertex(v);
if (!hasPathTo(v)) return null;
Stack path = new Stack();
for (DirectedEdge e = edgeTo[v]; e != null; e = edgeTo[e.from()]) {
path.push(e);
}
return path;
}
// throw an IllegalArgumentException unless {@code 0 <= v < V}
private void validateVertex(int v) {
int V = distTo.length;
if (v < 0 || v >= V)
throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V-1));
}
/**
* Unit tests the {@code AcyclicLP} data type.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
In in = new In(args[0]);
int s = Integer.parseInt(args[1]);
EdgeWeightedDigraph G = new EdgeWeightedDigraph(in);
AcyclicLP lp = new AcyclicLP(G, s);
for (int v = 0; v < G.V(); v++) {
if (lp.hasPathTo(v)) {
StdOut.printf("%d to %d (%.2f) ", s, v, lp.distTo(v));
for (DirectedEdge e : lp.pathTo(v)) {
StdOut.print(e + " ");
}
StdOut.println();
}
else {
StdOut.printf("%d to %d no path\n", s, v);
}
}
}
}
/******************************************************************************
* Copyright 2002-2018, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/