edu.princeton.cs.algs4.TransitiveClosure Maven / Gradle / Ivy
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/******************************************************************************
* Compilation: javac TransitiveClosure.java
* Execution: java TransitiveClosure filename.txt
* Dependencies: Digraph.java DepthFirstDirectedPaths.java In.java StdOut.java
* Data files: https://algs4.cs.princeton.edu/42digraph/tinyDG.txt
*
* Compute transitive closure of a digraph and support
* reachability queries.
*
* Preprocessing time: O(V(E + V)) time.
* Query time: O(1).
* Space: O(V^2).
*
* % java TransitiveClosure tinyDG.txt
* 0 1 2 3 4 5 6 7 8 9 10 11 12
* --------------------------------------------
* 0: T T T T T T
* 1: T
* 2: T T T T T T
* 3: T T T T T T
* 4: T T T T T T
* 5: T T T T T T
* 6: T T T T T T T T T T T
* 7: T T T T T T T T T T T T T
* 8: T T T T T T T T T T T T T
* 9: T T T T T T T T T T
* 10: T T T T T T T T T T
* 11: T T T T T T T T T T
* 12: T T T T T T T T T T
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code TransitiveClosure} class represents a data type for
* computing the transitive closure of a digraph.
*
* This implementation runs depth-first search from each vertex.
* The constructor takes time proportional to V(V + E)
* (in the worst case) and uses space proportional to V2,
* where V is the number of vertices and E is the number of edges.
*
* For large digraphs, you may want to consider a more sophisticated algorithm.
* Nuutila proposes two
* algorithm for the problem (based on strong components and an interval representation)
* that runs in E + V time on typical digraphs.
*
* For additional documentation,
* see Section 4.2 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class TransitiveClosure {
private DirectedDFS[] tc; // tc[v] = reachable from v
/**
* Computes the transitive closure of the digraph {@code G}.
* @param G the digraph
*/
public TransitiveClosure(Digraph G) {
tc = new DirectedDFS[G.V()];
for (int v = 0; v < G.V(); v++)
tc[v] = new DirectedDFS(G, v);
}
/**
* Is there a directed path from vertex {@code v} to vertex {@code w} in the digraph?
* @param v the source vertex
* @param w the target vertex
* @return {@code true} if there is a directed path from {@code v} to {@code w},
* {@code false} otherwise
* @throws IllegalArgumentException unless {@code 0 <= v < V}
* @throws IllegalArgumentException unless {@code 0 <= w < V}
*/
public boolean reachable(int v, int w) {
validateVertex(v);
validateVertex(w);
return tc[v].marked(w);
}
// throw an IllegalArgumentException unless {@code 0 <= v < V}
private void validateVertex(int v) {
int V = tc.length;
if (v < 0 || v >= V)
throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V-1));
}
/**
* Unit tests the {@code TransitiveClosure} data type.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
In in = new In(args[0]);
Digraph G = new Digraph(in);
TransitiveClosure tc = new TransitiveClosure(G);
// print header
StdOut.print(" ");
for (int v = 0; v < G.V(); v++)
StdOut.printf("%3d", v);
StdOut.println();
StdOut.println("--------------------------------------------");
// print transitive closure
for (int v = 0; v < G.V(); v++) {
StdOut.printf("%3d: ", v);
for (int w = 0; w < G.V(); w++) {
if (tc.reachable(v, w)) StdOut.printf(" T");
else StdOut.printf(" ");
}
StdOut.println();
}
}
}
/******************************************************************************
* 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.
******************************************************************************/