Below is the syntax highlighted version of GabowSCC.java
from §4.2 Directed Graphs.
/****************************************************************************** * Compilation: javac GabowSCC.java * Execution: java GabowSCC V E * Dependencies: Digraph.java Stack.java TransitiveClosure.java StdOut.java * Data files: https://algs4.cs.princeton.edu/42digraph/tinyDG.txt * https://algs4.cs.princeton.edu/42digraph/mediumDG.txt * https://algs4.cs.princeton.edu/42digraph/largeDG.txt * * Compute the strongly-connected components of a digraph using * Gabow's algorithm (aka Cheriyan-Mehlhorn algorithm). * * Runs in O(E + V) time. * * % java GabowSCC tinyDG.txt * 5 components * 1 * 0 2 3 4 5 * 9 10 11 12 * 6 8 * 7 * ******************************************************************************/ /** * The {@code GabowSCC} class represents a data type for * determining the strong components in a digraph. * The <em>id</em> operation determines in which strong component * a given vertex lies; the <em>areStronglyConnected</em> operation * determines whether two vertices are in the same strong component; * and the <em>count</em> operation determines the number of strong * components. * The <em>component identifier</em> of a component is one of the * vertices in the strong component: two vertices have the same component * identifier if and only if they are in the same strong component. * <p> * This implementation uses the Gabow's algorithm. * The constructor takes Θ(<em>V</em> + <em>E</em>) time, * where <em>V</em> is the number of vertices and <em>E</em> is * the number of edges. * Each instance method takes Θ(1) time. * It uses Θ(<em>V</em>) extra space (not including the digraph). * For alternative implementations of the same API, see * {@link KosarajuSharirSCC} and {@link TarjanSCC}. * <p> * For additional documentation, * see <a href="https://algs4.cs.princeton.edu/42digraph">Section 4.2</a> of * <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne. * * @author Robert Sedgewick * @author Kevin Wayne */ public class GabowSCC { private boolean[] marked; // marked[v] = has v been visited? private int[] id; // id[v] = id of strong component containing v private int[] preorder; // preorder[v] = preorder of v private int pre; // preorder number counter private int count; // number of strongly-connected components private Stack<Integer> stack1; private Stack<Integer> stack2; /** * Computes the strong components of the digraph {@code G}. * @param G the digraph */ public GabowSCC(Digraph G) { marked = new boolean[G.V()]; stack1 = new Stack<Integer>(); stack2 = new Stack<Integer>(); id = new int[G.V()]; preorder = new int[G.V()]; for (int v = 0; v < G.V(); v++) id[v] = -1; for (int v = 0; v < G.V(); v++) { if (!marked[v]) dfs(G, v); } // check that id[] gives strong components assert check(G); } private void dfs(Digraph G, int v) { marked[v] = true; preorder[v] = pre++; stack1.push(v); stack2.push(v); for (int w : G.adj(v)) { if (!marked[w]) dfs(G, w); else if (id[w] == -1) { while (preorder[stack2.peek()] > preorder[w]) stack2.pop(); } } // found strong component containing v if (stack2.peek() == v) { stack2.pop(); int w; do { w = stack1.pop(); id[w] = count; } while (w != v); count++; } } /** * Returns the number of strong components. * @return the number of strong components */ public int count() { return count; } /** * Are vertices {@code v} and {@code w} in the same strong component? * @param v one vertex * @param w the other vertex * @return {@code true} if vertices {@code v} and {@code w} are in the same * strong component, and {@code false} otherwise * @throws IllegalArgumentException unless {@code 0 <= v < V} * @throws IllegalArgumentException unless {@code 0 <= w < V} */ public boolean stronglyConnected(int v, int w) { validateVertex(v); validateVertex(w); return id[v] == id[w]; } /** * Returns the component id of the strong component containing vertex {@code v}. * @param v the vertex * @return the component id of the strong component containing vertex {@code v} * @throws IllegalArgumentException unless {@code 0 <= v < V} */ public int id(int v) { validateVertex(v); return id[v]; } // does the id[] array contain the strongly connected components? private boolean check(Digraph G) { TransitiveClosure tc = new TransitiveClosure(G); for (int v = 0; v < G.V(); v++) { for (int w = 0; w < G.V(); w++) { if (stronglyConnected(v, w) != (tc.reachable(v, w) && tc.reachable(w, v))) return false; } } return true; } // throw an IllegalArgumentException unless {@code 0 <= v < V} private void validateVertex(int v) { int V = marked.length; if (v < 0 || v >= V) throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V-1)); } /** * Unit tests the {@code GabowSCC} data type. * * @param args the command-line arguments */ public static void main(String[] args) { In in = new In(args[0]); Digraph G = new Digraph(in); GabowSCC scc = new GabowSCC(G); // number of connected components int m = scc.count(); StdOut.println(m + " components"); // compute list of vertices in each strong component Queue<Integer>[] components = (Queue<Integer>[]) new Queue[m]; for (int i = 0; i < m; i++) { components[i] = new Queue<Integer>(); } for (int v = 0; v < G.V(); v++) { components[scc.id(v)].enqueue(v); } // print results for (int i = 0; i < m; i++) { for (int v : components[i]) { StdOut.print(v + " "); } StdOut.println(); } } }