package edu.princeton.cs.algs4;
import edu.princeton.cs.algs4.ch13.Queue;
import edu.princeton.cs.algs4.ch13.Stack;
import edu.princeton.cs.algs4.ch42.Digraph;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* Compilation: javac TarjanSCC.java
* Execution: Java TarjanSCC V E
* Dependencies: Digraph.java Stack.java TransitiveClosure.java StdOut.java
*
* Compute the strongly-connected components of a digraph using
* Tarjan's algorithm.
*
* Runs in O(E + V) time.
*
* % java TarjanSCC tinyDG.txt
* 5 components
* 1
* 0 2 3 4 5
* 9 10 11 12
* 6 8
* 7
*
*************************************************************************/
/**
* The <tt>TarjanSCC</tt> class represents a data type for
* determining the strong components in a digraph.
* The <em>id</em> operation determines in which strong component
* a given vertex lies; the <em>areStronglyConnected</em> operation
* determines whether two vertices are in the same strong component;
* and the <em>count</em> operation determines the number of strong
* components.
* The <em>component identifier</em> of a component is one of the
* vertices in the strong component: two vertices have the same component
* identifier if and only if they are in the same strong component.
* <p>
* This implementation uses Tarjan's algorithm.
* The constructor takes time proportional to <em>V</em> + <em>E</em>
* (in the worst case),
* where <em>V</em> is the number of vertices and <em>E</em> is the number of edges.
* Afterwards, the <em>id</em>, <em>count</em>, and <em>areStronglyConnected</em>
* operations take constant time.
* For alternate implementations of the same API, see
* {@link edu.princeton.cs.algs4.ch42.KosarajuSharirSCC} and {@link GabowSCC}.
* <p>
* For additional documentation, see <a href="/algs4/42digraph">Section 4.2</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class TarjanSCC {
private boolean[] marked; // marked[v] = has v been visited?
private int[] id; // id[v] = id of strong component containing v
private int[] low; // low[v] = low number of v
private int pre; // preorder number counter
private int count; // number of strongly-connected components
private Stack<Integer> stack;
/**
* Computes the strong components of the digraph <tt>G</tt>.
* @param G the digraph
*/
public TarjanSCC(Digraph G) {
marked = new boolean[G.V()];
stack = new Stack<Integer>();
id = new int[G.V()];
low = new int[G.V()];
for (int v = 0; v < G.V(); v++) {
if (!marked[v]) dfs(G, v);
}
// check that id[] gives strong components
assert check(G);
}
private void dfs(Digraph G, int v) {
marked[v] = true;
low[v] = pre++;
int min = low[v];
stack.push(v);
for (int w : G.adj(v)) {
if (!marked[w]) dfs(G, w);
if (low[w] < min) min = low[w];
}
if (min < low[v]) { low[v] = min; return; }
int w;
do {
w = stack.pop();
id[w] = count;
low[w] = G.V();
} while (w != v);
count++;
}
/**
* Returns the number of strong components.
* @return the number of strong components
*/
public int count() {
return count;
}
/**
* Are vertices <tt>v</tt> and <tt>w</tt> in the same strong component?
* @param v one vertex
* @param w the other vertex
* @return <tt>true</tt> if vertices <tt>v</tt> and <tt>w</tt> are in the same
* strong component, and <tt>false</tt> otherwise
*/
public boolean stronglyConnected(int v, int w) {
return id[v] == id[w];
}
/**
* Returns the component id of the strong component containing vertex <tt>v</tt>.
* @param v the vertex
* @return the component id of the strong component containing vertex <tt>v</tt>
*/
public int id(int v) {
return id[v];
}
// does the id[] array contain the strongly connected components?
private boolean check(Digraph G) {
TransitiveClosure tc = new TransitiveClosure(G);
for (int v = 0; v < G.V(); v++) {
for (int w = 0; w < G.V(); w++) {
if (stronglyConnected(v, w) != (tc.reachable(v, w) && tc.reachable(w, v)))
return false;
}
}
return true;
}
/**
* Unit tests the <tt>TarjanSCC</tt> data type.
*/
public static void main(String[] args) {
In in = new In(args[0]);
Digraph G = new Digraph(in);
TarjanSCC scc = new TarjanSCC(G);
// number of connected components
int M = scc.count();
StdOut.println(M + " components");
// compute list of vertices in each strong component
Queue<Integer>[] components = (Queue<Integer>[]) new Queue[M];
for (int i = 0; i < M; i++) {
components[i] = new Queue<Integer>();
}
for (int v = 0; v < G.V(); v++) {
components[scc.id(v)].enqueue(v);
}
// print results
for (int i = 0; i < M; i++) {
for (int v : components[i]) {
StdOut.print(v + " ");
}
StdOut.println();
}
}
}
/*************************************************************************
* Copyright 2002-2012, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4-package.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-package.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-package.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-package.jar. If not, see http://www.gnu.org/licenses.
*************************************************************************/