content: /*************************************************************************
   *  Compilation:  javac EdgeWeightedDirectedCycle.java
   *  Execution:    java EdgeWeightedDirectedCycle V E F
   *  Dependencies: EdgeWeightedDigraph.java DirectedEdge Stack.java
   *
   *  Finds a directed cycle in an edge-weighted digraph.
   *  Runs in O(E + V) time.
   *
   *
   *************************************************************************/
  
  public class EdgeWeightedDirectedCycle {
      private boolean[] marked;             // marked[v] = has vertex v been marked?
      private DirectedEdge[] edgeTo;        // edgeTo[v] = previous edge on path to v
      private boolean[] onStack;            // onStack[v] = is vertex on the stack?
      private Stack<DirectedEdge> cycle;    // directed cycle (or null if no such cycle)
  
      public EdgeWeightedDirectedCycle(EdgeWeightedDigraph G) {
          marked  = new boolean[G.V()];
          onStack = new boolean[G.V()];
          edgeTo  = new DirectedEdge[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(EdgeWeightedDigraph G, int v) {
          onStack[v] = true;
          marked[v] = true;
          for (DirectedEdge e : G.adj(v)) {
              int w = e.to();
  
              // short circuit if directed cycle found
              if (cycle != null) return;
  
              //found new vertex, so recur
              else if (!marked[w]) {
                  edgeTo[w] = e;
                  dfs(G, w);
              }
  
  
              // trace back directed cycle
              else if (onStack[w]) {
                  cycle = new Stack<DirectedEdge>();
                  while (e.from() != w) {
                      cycle.push(e);
                      e = edgeTo[e.from()];
                  }
                  cycle.push(e);
              }
          }
  
          onStack[v] = false;
      }
  
      public boolean hasCycle()             { return cycle != null;   }
      public Iterable<DirectedEdge> cycle() { return cycle;           }
  
  
      // certify that digraph is either acyclic or has a directed cycle
      private boolean check(EdgeWeightedDigraph G) {
  
          // edge-weighted digraph is cyclic
          if (hasCycle()) {
              // verify cycle
              DirectedEdge first = null, last = null;
              for (DirectedEdge e : cycle()) {
                  if (first == null) first = e;
                  if (last != null) {
                      if (last.to() != e.from()) {
                          System.err.printf("cycle edges %s and %s not incident\n", last, e);
                          return false;
                      }
                  }
                  last = e;
              }
  
              if (last.to() != first.from()) {
                  System.err.printf("cycle edges %s and %s not incident\n", last, first);
                  return false;
              }
          }
  
  
          return true;
      }
  
      public static void main(String[] args) {
  
          // create random DAG with V vertices and E edges; then add F random edges
          int V = Integer.parseInt(args[0]);
          int E = Integer.parseInt(args[1]);
          int F = Integer.parseInt(args[2]);
          EdgeWeightedDigraph G = new EdgeWeightedDigraph(V);
          int[] vertices = new int[V];
          for (int i = 0; i < V; i++) vertices[i] = i;
          StdRandom.shuffle(vertices);
          for (int i = 0; i < E; i++) {
              int v, w;
              do {
                  v = StdRandom.uniform(V);
                  w = StdRandom.uniform(V);
              } while (v >= w);
              double weight = Math.random();
              G.addEdge(new DirectedEdge(v, w, weight));
          }
  
          // add F extra edges
          for (int i = 0; i < F; i++) {
              int v = (int) (Math.random() * V);
              int w = (int) (Math.random() * V);
              double weight = Math.random();
              G.addEdge(new DirectedEdge(v, w, weight));
          }
  
          StdOut.println(G);
  
          // find a directed cycle
          EdgeWeightedDirectedCycle finder = new EdgeWeightedDirectedCycle(G);
          if (finder.hasCycle()) {
              StdOut.print("Cycle: ");
              for (DirectedEdge e : finder.cycle()) {
                  StdOut.print(e + " ");
              }
              StdOut.println();
          }
  
          // or give topologial sort
          else {
              StdOut.println("No directed cycle");
          }
      }
  
  }
  