content: /*************************************************************************
   *  Compilation:  javac DirectedCycle.java
   *  Execution:    java DirectedCycle < input.txt
   *  Dependencies: Digraph.java Stack.java StdOut.java In.java
   *  Data files:   http://algs.cs.princeton.edu/42digraph/tinyDG.txt
   *                http://algs.cs.princeton.edu/42digraph/tinyDAG.txt
   *
   *  Finds a directed cycle in a digraph.
   *  Runs in O(E + V) time.
   *
   *  % java DirectedCycle tinyDG.txt 
   *  Cycle: 3 5 4 3 
   *
   *  %  java DirectedCycle tinyDAG.txt 
   *  No cycle
   *
   *************************************************************************/
  
  public class DirectedCycle {
      private boolean[] marked;        // marked[v] = has vertex v been marked?
      private int[] edgeTo;            // edgeTo[v] = previous vertex on path to v
      private boolean[] onStack;       // onStack[v] = is vertex on the stack?
      private Stack<Integer> cycle;    // directed cycle (or null if no such cycle)
  
      public DirectedCycle(Digraph G) {
          marked  = new boolean[G.V()];
          onStack = new boolean[G.V()];
          edgeTo  = new int[G.V()];
          for (int v = 0; v < G.V(); v++)
              if (!marked[v]) dfs(G, v);
  
          // check that digraph has a cycle
          assert check(G);
      }
  
  
      // check that algorithm computes either the topological order or finds a directed cycle
      private void dfs(Digraph G, int v) {
          onStack[v] = true;
          marked[v] = true;
          for (int w : G.adj(v)) {
  
              // short circuit if directed cycle found
              if (cycle != null) return;
  
              //found new vertex, so recur
              else if (!marked[w]) {
                  edgeTo[w] = v;
                  dfs(G, w);
              }
  
              // trace back directed cycle
              else if (onStack[w]) {
                  cycle = new Stack<Integer>();
                  for (int x = v; x != w; x = edgeTo[x]) {
                      cycle.push(x);
                  }
                  cycle.push(w);
                  cycle.push(v);
              }
          }
  
          onStack[v] = false;
      }
  
      public boolean hasCycle()        { return cycle != null;   }
      public Iterable<Integer> cycle() { return cycle;           }
  
  
      // certify that digraph is either acyclic or has a directed cycle
      private boolean check(Digraph G) {
  
          if (hasCycle()) {
              // verify cycle
              int first = -1, last = -1;
              for (int v : cycle()) {
                  if (first == -1) first = v;
                  last = v;
              }
              if (first != last) {
                  System.err.printf("cycle begins with %d and ends with %d\n", first, last);
                  return false;
              }
          }
  
  
          return true;
      }
  
      public static void main(String[] args) {
          In in = new In(args[0]);
          Digraph G = new Digraph(in);
  
          DirectedCycle finder = new DirectedCycle(G);
          if (finder.hasCycle()) {
              StdOut.print("Cycle: ");
              for (int v : finder.cycle()) {
                  StdOut.print(v + " ");
              }
              StdOut.println();
          }
  
          else {
              StdOut.println("No cycle");
          }
      }
  
  }
  