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/******************************************************************************
* Compilation: javac CPM.java
* Execution: java CPM < input.txt
* Dependencies: EdgeWeightedDigraph.java AcyclicDigraphLP.java StdOut.java
* Data files: https://algs4.cs.princeton.edu/44sp/jobsPC.txt
*
* Critical path method.
*
* % java CPM < jobsPC.txt
* job start finish
* --------------------
* 0 0.0 41.0
* 1 41.0 92.0
* 2 123.0 173.0
* 3 91.0 127.0
* 4 70.0 108.0
* 5 0.0 45.0
* 6 70.0 91.0
* 7 41.0 73.0
* 8 91.0 123.0
* 9 41.0 70.0
* Finish time: 173.0
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code CPM} class provides a client that solves the
* parallel precedence-constrained job scheduling problem
* via the critical path method. It reduces the problem
* to the longest-paths problem in edge-weighted DAGs.
* It builds an edge-weighted digraph (which must be a DAG)
* from the job-scheduling problem specification,
* finds the longest-paths tree, and computes the longest-paths
* lengths (which are precisely the start times for each job).
*
* This implementation uses {@link AcyclicLP} to find a longest
* path in a DAG.
* The running time is proportional to V + E,
* where V is the number of jobs and E is the
* number of precedence constraints.
*
* 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 CPM {
// this class cannot be instantiated
private CPM() { }
/**
* Reads the precedence constraints from standard input
* and prints a feasible schedule to standard output.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
// number of jobs
int n = StdIn.readInt();
// source and sink
int source = 2*n;
int sink = 2*n + 1;
// build network
EdgeWeightedDigraph G = new EdgeWeightedDigraph(2*n + 2);
for (int i = 0; i < n; i++) {
double duration = StdIn.readDouble();
G.addEdge(new DirectedEdge(source, i, 0.0));
G.addEdge(new DirectedEdge(i+n, sink, 0.0));
G.addEdge(new DirectedEdge(i, i+n, duration));
// precedence constraints
int m = StdIn.readInt();
for (int j = 0; j < m; j++) {
int precedent = StdIn.readInt();
G.addEdge(new DirectedEdge(n+i, precedent, 0.0));
}
}
// compute longest path
AcyclicLP lp = new AcyclicLP(G, source);
// print results
StdOut.println(" job start finish");
StdOut.println("--------------------");
for (int i = 0; i < n; i++) {
StdOut.printf("%4d %7.1f %7.1f\n", i, lp.distTo(i), lp.distTo(i+n));
}
StdOut.printf("Finish time: %7.1f\n", lp.distTo(sink));
}
}
/******************************************************************************
* 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.
******************************************************************************/