programming-examples/java/Data_Structures/Cycle.java

 

import edu.princeton.cs.introcs.In;
import edu.princeton.cs.introcs.StdOut;

/*************************************************************************
 *  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  Cycle  class represents a data type for 
 *  determining whether an undirected graph has a cycle.
 *  The  hasCycle  operation determines whether the graph has
 *  a cycle and, if so, the  cycle  operation returns one.
 *   
 *  This implementation uses depth-first search.
 *  The constructor takes time proportional to  V  +  E 
 *  (in the worst case),
 *  where  V  is the number of vertices and  E  is the number of edges.
 *  Afterwards, the  hasCycle  operation takes constant time;
 *  the  cycle  operation takes time proportional
 *  to the length of the cycle.
 *   
 *  For additional documentation, see <a href="/algs4/41graph">Section 4.1</a> of
 *   Algorithms, 4th Edition  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  G  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  true  if the graph has a cycle,  false  otherwise
     */
    public boolean hasCycle() {
        return cycle != null;
    }

     /**
     * Returns a cycle if the graph has a cycle, and  null  otherwise.
     * @return a cycle (as an iterable) if the graph has a cycle,
     *    and  null  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  Cycle  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");
        }
    }


}