edu.princeton.cs.algs4.DirectedCycleX Maven / Gradle / Ivy
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/******************************************************************************
* Compilation: javac DirectedCycleX.java
* Execution: java DirectedCycleX V E F
* Dependencies: Queue.java Digraph.java Stack.java
*
* Find a directed cycle in a digraph, using a nonrecursive, queue-based
* algorithm. Runs in O(E + V) time.
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code DirectedCycleX} class represents a data type for
* determining whether a digraph has a directed cycle.
* The hasCycle operation determines whether the digraph has
* a simple directed cycle and, if so, the cycle operation
* returns one.
*
* This implementation uses a nonrecursive, queue-based algorithm.
* 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.
*
* See {@link DirectedCycle} for a recursive version that uses depth-first search.
* See {@link Topological} or {@link TopologicalX} to compute a topological order
* when the digraph is acyclic.
*
* For additional documentation,
* see Section 4.2 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class DirectedCycleX {
private Stack cycle; // the directed cycle; null if digraph is acyclic
public DirectedCycleX(Digraph G) {
// indegrees of remaining vertices
int[] indegree = new int[G.V()];
for (int v = 0; v < G.V(); v++) {
indegree[v] = G.indegree(v);
}
// initialize queue to contain all vertices with indegree = 0
Queue queue = new Queue();
for (int v = 0; v < G.V(); v++)
if (indegree[v] == 0) queue.enqueue(v);
while (!queue.isEmpty()) {
int v = queue.dequeue();
for (int w : G.adj(v)) {
indegree[w]--;
if (indegree[w] == 0) queue.enqueue(w);
}
}
// there is a directed cycle in subgraph of vertices with indegree >= 1.
int[] edgeTo = new int[G.V()];
int root = -1; // any vertex with indegree >= -1
for (int v = 0; v < G.V(); v++) {
if (indegree[v] == 0) continue;
else root = v;
for (int w : G.adj(v)) {
if (indegree[w] > 0) {
edgeTo[w] = v;
}
}
}
if (root != -1) {
// find any vertex on cycle
boolean[] visited = new boolean[G.V()];
while (!visited[root]) {
visited[root] = true;
root = edgeTo[root];
}
// extract cycle
cycle = new Stack();
int v = root;
do {
cycle.push(v);
v = edgeTo[v];
} while (v != root);
cycle.push(root);
}
assert check();
}
/**
* Returns a directed cycle if the digraph has a directed cycle, and {@code null} otherwise.
* @return a directed cycle (as an iterable) if the digraph has a directed cycle,
* and {@code null} otherwise
*/
public Iterable cycle() {
return cycle;
}
/**
* Does the digraph have a directed cycle?
* @return {@code true} if the digraph has a directed cycle, {@code false} otherwise
*/
public boolean hasCycle() {
return cycle != null;
}
// certify that digraph has a directed cycle if it reports one
private boolean check() {
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) {
// 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]);
Digraph G = DigraphGenerator.dag(V, E);
// add F extra edges
for (int i = 0; i < F; i++) {
int v = StdRandom.uniform(V);
int w = StdRandom.uniform(V);
G.addEdge(v, w);
}
StdOut.println(G);
DirectedCycleX finder = new DirectedCycleX(G);
if (finder.hasCycle()) {
StdOut.print("Directed cycle: ");
for (int v : finder.cycle()) {
StdOut.print(v + " ");
}
StdOut.println();
}
else {
StdOut.println("No directed cycle");
}
StdOut.println();
}
}
/******************************************************************************
* Copyright 2002-2018, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.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.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.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.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/