package edu.princeton.cs.algs4.ch43;
import edu.princeton.cs.algs4.ch13.Stack;
import edu.princeton.cs.algs4.ch42.DirectedEdge;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* 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.
*
*
*************************************************************************/
/**
* The <tt>EdgeWeightedDirectedCycle</tt> class represents a data type for
* determining whether an edge-weighted digraph has a directed cycle.
* The <em>hasCycle</em> operation determines whether the edge-weighted
* digraph has a directed 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>
* See {@link edu.princeton.cs.algs4.ch42.Topological} to compute a topological order if the edge-weighted
* digraph is acyclic.
* <p>
* For additional documentation, see <a href="/algs4/44sp">Section 4.4</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
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)
/**
* Determines whether the edge-weighted digraph <tt>G</tt> has a directed cycle and,
* if so, finds such a cycle.
* @param G the edge-weighted digraph
*/
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;
}
/**
* Does the edge-weighted digraph have a directed cycle?
* @return <tt>true</tt> if the edge-weighted digraph has a directed cycle,
* <tt>false</tt> otherwise
*/
public boolean hasCycle() {
return cycle != null;
}
/**
* Returns a directed cycle if the edge-weighted digraph has a directed cycle,
* and <tt>null</tt> otherwise.
* @return a directed cycle (as an iterable) if the edge-weighted digraph
* has a directed cycle, and <tt>null</tt> otherwise
*/
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;
}
/**
* Unit tests the <tt>EdgeWeightedDirectedCycle</tt> data type.
*/
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");
}
}
}
/*************************************************************************
* 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.
*************************************************************************/