package edu.princeton.cs.algs4.ch41;
import edu.princeton.cs.algs4.ch13.Stack;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* Compilation: javac Cycle.java
* Dependencies: Graph.java Stack.java
*
* Identifies a cycle.
* Runs in O(E + V) time.
*
* % java Cycle tinyG.txt
* 3 4 5 3
*
* % java Cycle mediumG.txt
* 15 0 225 15
*
* % java Cycle largeG.txt
* 996673 762 840164 4619 785187 194717 996673
*
*************************************************************************/
/**
* The <tt>Cycle</tt> class represents a data type for
* determining whether an undirected graph has a cycle.
* The <em>hasCycle</em> operation determines whether the graph has
* a cycle and, if so, the <em>cycle</em> operation returns one.
* <p>
* This implementation uses depth-first search.
* 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>hasCycle</em> operation takes constant time;
* the <em>cycle</em> operation takes time proportional
* to the length of the cycle.
* <p>
* For additional documentation, see <a href="/algs4/41graph">Section 4.1</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class Cycle {
private boolean[] marked;
private int[] edgeTo;
private Stack<Integer> cycle;
/**
* Determines whether the undirected graph <tt>G</tt> has a cycle and, if so,
* finds such a cycle.
* @param G the graph
*/
public Cycle(Graph G) {
if (hasSelfLoop(G)) return;
if (hasParallelEdges(G)) return;
marked = new boolean[G.V()];
edgeTo = new int[G.V()];
for (int v = 0; v < G.V(); v++)
if (!marked[v])
dfs(G, -1, v);
}
// does this graph have a self loop?
// side effect: initialize cycle to be self loop
private boolean hasSelfLoop(Graph G) {
for (int v = 0; v < G.V(); v++) {
for (int w : G.adj(v)) {
if (v == w) {
cycle = new Stack<Integer>();
cycle.push(v);
cycle.push(v);
return true;
}
}
}
return false;
}
// does this graph have two parallel edges?
// side effect: initialize cycle to be two parallel edges
private boolean hasParallelEdges(Graph G) {
marked = new boolean[G.V()];
for (int v = 0; v < G.V(); v++) {
// check for parallel edges incident to v
for (int w : G.adj(v)) {
if (marked[w]) {
cycle = new Stack<Integer>();
cycle.push(v);
cycle.push(w);
cycle.push(v);
return true;
}
marked[w] = true;
}
// reset so marked[v] = false for all v
for (int w : G.adj(v)) {
marked[w] = false;
}
}
return false;
}
/**
* Does the graph have a cycle?
* @return <tt>true</tt> if the graph has a cycle, <tt>false</tt> otherwise
*/
public boolean hasCycle() {
return cycle != null;
}
/**
* Returns a cycle if the graph has a cycle, and <tt>null</tt> otherwise.
* @return a cycle (as an iterable) if the graph has a cycle,
* and <tt>null</tt> otherwise
*/
public Iterable<Integer> cycle() {
return cycle;
}
private void dfs(Graph G, int u, int v) {
marked[v] = true;
for (int w : G.adj(v)) {
// short circuit if cycle already found
if (cycle != null) return;
if (!marked[w]) {
edgeTo[w] = v;
dfs(G, v, w);
}
// check for cycle (but disregard reverse of edge leading to v)
else if (w != u) {
cycle = new Stack<Integer>();
for (int x = v; x != w; x = edgeTo[x]) {
cycle.push(x);
}
cycle.push(w);
cycle.push(v);
}
}
}
/**
* Unit tests the <tt>Cycle</tt> data type.
*/
public static void main(String[] args) {
In in = new In(args[0]);
Graph G = new Graph(in);
Cycle finder = new Cycle(G);
if (finder.hasCycle()) {
for (int v : finder.cycle()) {
StdOut.print(v + " ");
}
StdOut.println();
}
else {
StdOut.println("Graph is acyclic");
}
}
}
/*************************************************************************
* 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.
*************************************************************************/