edu.princeton.cs.algs4.TopologicalX Maven / Gradle / Ivy
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/******************************************************************************
* Compilation: javac TopologicalX.java
* Execution: java TopologicalX V E F
* Dependencies: Queue.java Digraph.java
*
* Compute topological ordering of a DAG using queue-based algorithm.
* Runs in O(E + V) time.
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code TopologicalX} class represents a data type for
* determining a topological order of a directed acyclic graph (DAG).
* Recall, a digraph has a topological order if and only if it is a DAG.
* The hasOrder operation determines whether the digraph has
* a topological order, and if so, the order 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 hasOrder and rank operations takes constant time;
* the order operation takes time proportional to V.
*
* See {@link DirectedCycle}, {@link DirectedCycleX}, and
* {@link EdgeWeightedDirectedCycle} to compute a
* directed cycle if the digraph is not a DAG.
* See {@link Topological} for a recursive version that uses depth-first search.
*
* 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 TopologicalX {
private Queue order; // vertices in topological order
private int[] ranks; // ranks[v] = order where vertex v appers in order
/**
* Determines whether the digraph {@code G} has a topological order and, if so,
* finds such a topological order.
* @param G the digraph
*/
public TopologicalX(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
ranks = new int[G.V()];
order = new Queue();
int count = 0;
// 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();
order.enqueue(v);
ranks[v] = count++;
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.
if (count != G.V()) {
order = null;
}
assert check(G);
}
/**
* Determines whether the edge-weighted digraph {@code G} has a
* topological order and, if so, finds such a topological order.
* @param G the digraph
*/
public TopologicalX(EdgeWeightedDigraph 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
ranks = new int[G.V()];
order = new Queue();
int count = 0;
// 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();
order.enqueue(v);
ranks[v] = count++;
for (DirectedEdge e : G.adj(v)) {
int w = e.to();
indegree[w]--;
if (indegree[w] == 0) queue.enqueue(w);
}
}
// there is a directed cycle in subgraph of vertices with indegree >= 1.
if (count != G.V()) {
order = null;
}
assert check(G);
}
/**
* Returns a topological order if the digraph has a topologial order,
* and {@code null} otherwise.
* @return a topological order of the vertices (as an interable) if the
* digraph has a topological order (or equivalently, if the digraph is a DAG),
* and {@code null} otherwise
*/
public Iterable order() {
return order;
}
/**
* Does the digraph have a topological order?
* @return {@code true} if the digraph has a topological order (or equivalently,
* if the digraph is a DAG), and {@code false} otherwise
*/
public boolean hasOrder() {
return order != null;
}
/**
* The the rank of vertex {@code v} in the topological order;
* -1 if the digraph is not a DAG
*
* @param v vertex
* @return the position of vertex {@code v} in a topological order
* of the digraph; -1 if the digraph is not a DAG
* @throws IllegalArgumentException unless {@code 0 <= v < V}
*/
public int rank(int v) {
validateVertex(v);
if (hasOrder()) return ranks[v];
else return -1;
}
// certify that digraph is acyclic
private boolean check(Digraph G) {
// digraph is acyclic
if (hasOrder()) {
// check that ranks are a permutation of 0 to V-1
boolean[] found = new boolean[G.V()];
for (int i = 0; i < G.V(); i++) {
found[rank(i)] = true;
}
for (int i = 0; i < G.V(); i++) {
if (!found[i]) {
System.err.println("No vertex with rank " + i);
return false;
}
}
// check that ranks provide a valid topological order
for (int v = 0; v < G.V(); v++) {
for (int w : G.adj(v)) {
if (rank(v) > rank(w)) {
System.err.printf("%d-%d: rank(%d) = %d, rank(%d) = %d\n",
v, w, v, rank(v), w, rank(w));
return false;
}
}
}
// check that order() is consistent with rank()
int r = 0;
for (int v : order()) {
if (rank(v) != r) {
System.err.println("order() and rank() inconsistent");
return false;
}
r++;
}
}
return true;
}
// certify that digraph is acyclic
private boolean check(EdgeWeightedDigraph G) {
// digraph is acyclic
if (hasOrder()) {
// check that ranks are a permutation of 0 to V-1
boolean[] found = new boolean[G.V()];
for (int i = 0; i < G.V(); i++) {
found[rank(i)] = true;
}
for (int i = 0; i < G.V(); i++) {
if (!found[i]) {
System.err.println("No vertex with rank " + i);
return false;
}
}
// check that ranks provide a valid topological order
for (int v = 0; v < G.V(); v++) {
for (DirectedEdge e : G.adj(v)) {
int w = e.to();
if (rank(v) > rank(w)) {
System.err.printf("%d-%d: rank(%d) = %d, rank(%d) = %d\n",
v, w, v, rank(v), w, rank(w));
return false;
}
}
}
// check that order() is consistent with rank()
int r = 0;
for (int v : order()) {
if (rank(v) != r) {
System.err.println("order() and rank() inconsistent");
return false;
}
r++;
}
}
return true;
}
// throw an IllegalArgumentException unless {@code 0 <= v < V}
private void validateVertex(int v) {
int V = ranks.length;
if (v < 0 || v >= V)
throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V-1));
}
/**
* Unit tests the {@code TopologicalX} data type.
*
* @param args the command-line arguments
*/
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 G1 = DigraphGenerator.dag(V, E);
// corresponding edge-weighted digraph
EdgeWeightedDigraph G2 = new EdgeWeightedDigraph(V);
for (int v = 0; v < G1.V(); v++)
for (int w : G1.adj(v))
G2.addEdge(new DirectedEdge(v, w, 0.0));
// add F extra edges
for (int i = 0; i < F; i++) {
int v = StdRandom.uniform(V);
int w = StdRandom.uniform(V);
G1.addEdge(v, w);
G2.addEdge(new DirectedEdge(v, w, 0.0));
}
StdOut.println(G1);
StdOut.println();
StdOut.println(G2);
// find a directed cycle
TopologicalX topological1 = new TopologicalX(G1);
if (!topological1.hasOrder()) {
StdOut.println("Not a DAG");
}
// or give topologial sort
else {
StdOut.print("Topological order: ");
for (int v : topological1.order()) {
StdOut.print(v + " ");
}
StdOut.println();
}
// find a directed cycle
TopologicalX topological2 = new TopologicalX(G2);
if (!topological2.hasOrder()) {
StdOut.println("Not a DAG");
}
// or give topologial sort
else {
StdOut.print("Topological order: ");
for (int v : topological2.order()) {
StdOut.print(v + " ");
}
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.
******************************************************************************/