Below is the syntax highlighted version of BreadthFirstPaths.java
from §4.1 Undirected Graphs.
/****************************************************************************** * Compilation: javac BreadthFirstPaths.java * Execution: java BreadthFirstPaths G s * Dependencies: Graph.java Queue.java Stack.java StdOut.java * Data files: https://algs4.cs.princeton.edu/41graph/tinyCG.txt * https://algs4.cs.princeton.edu/41graph/tinyG.txt * https://algs4.cs.princeton.edu/41graph/mediumG.txt * https://algs4.cs.princeton.edu/41graph/largeG.txt * * Run breadth first search on an undirected graph. * Runs in O(E + V) time. * * % java Graph tinyCG.txt * 6 8 * 0: 2 1 5 * 1: 0 2 * 2: 0 1 3 4 * 3: 5 4 2 * 4: 3 2 * 5: 3 0 * * % java BreadthFirstPaths tinyCG.txt 0 * 0 to 0 (0): 0 * 0 to 1 (1): 0-1 * 0 to 2 (1): 0-2 * 0 to 3 (2): 0-2-3 * 0 to 4 (2): 0-2-4 * 0 to 5 (1): 0-5 * * % java BreadthFirstPaths largeG.txt 0 * 0 to 0 (0): 0 * 0 to 1 (418): 0-932942-474885-82707-879889-971961-... * 0 to 2 (323): 0-460790-53370-594358-780059-287921-... * 0 to 3 (168): 0-713461-75230-953125-568284-350405-... * 0 to 4 (144): 0-460790-53370-310931-440226-380102-... * 0 to 5 (566): 0-932942-474885-82707-879889-971961-... * 0 to 6 (349): 0-932942-474885-82707-879889-971961-... * ******************************************************************************/ /** * The {@code BreadthFirstPaths} class represents a data type for finding * shortest paths (number of edges) from a source vertex <em>s</em> * (or a set of source vertices) * to every other vertex in an undirected graph. * <p> * This implementation uses breadth-first search. * The constructor takes Θ(<em>V</em> + <em>E</em>) time in the * worst case, 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 graph). * <p> * For additional documentation, * see <a href="https://algs4.cs.princeton.edu/41graph">Section 4.1</a> * of <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne. * * @author Robert Sedgewick * @author Kevin Wayne */ public class BreadthFirstPaths { private static final int INFINITY = Integer.MAX_VALUE; private boolean[] marked; // marked[v] = is there an s-v path private int[] edgeTo; // edgeTo[v] = previous edge on shortest s-v path private int[] distTo; // distTo[v] = number of edges shortest s-v path /** * Computes the shortest path between the source vertex {@code s} * and every other vertex in the graph {@code G}. * @param G the graph * @param s the source vertex * @throws IllegalArgumentException unless {@code 0 <= s < V} */ public BreadthFirstPaths(Graph G, int s) { marked = new boolean[G.V()]; distTo = new int[G.V()]; edgeTo = new int[G.V()]; validateVertex(s); bfs(G, s); assert check(G, s); } /** * Computes the shortest path between any one of the source vertices in {@code sources} * and every other vertex in graph {@code G}. * @param G the graph * @param sources the source vertices * @throws IllegalArgumentException if {@code sources} is {@code null} * @throws IllegalArgumentException if {@code sources} contains no vertices * @throws IllegalArgumentException unless {@code 0 <= s < V} for each vertex * {@code s} in {@code sources} */ public BreadthFirstPaths(Graph G, Iterable<Integer> sources) { marked = new boolean[G.V()]; distTo = new int[G.V()]; edgeTo = new int[G.V()]; for (int v = 0; v < G.V(); v++) distTo[v] = INFINITY; validateVertices(sources); bfs(G, sources); } // breadth-first search from a single source private void bfs(Graph G, int s) { Queue<Integer> q = new Queue<Integer>(); for (int v = 0; v < G.V(); v++) distTo[v] = INFINITY; distTo[s] = 0; marked[s] = true; q.enqueue(s); while (!q.isEmpty()) { int v = q.dequeue(); for (int w : G.adj(v)) { if (!marked[w]) { edgeTo[w] = v; distTo[w] = distTo[v] + 1; marked[w] = true; q.enqueue(w); } } } } // breadth-first search from multiple sources private void bfs(Graph G, Iterable<Integer> sources) { Queue<Integer> q = new Queue<Integer>(); for (int s : sources) { marked[s] = true; distTo[s] = 0; q.enqueue(s); } while (!q.isEmpty()) { int v = q.dequeue(); for (int w : G.adj(v)) { if (!marked[w]) { edgeTo[w] = v; distTo[w] = distTo[v] + 1; marked[w] = true; q.enqueue(w); } } } } /** * Is there a path between the source vertex {@code s} (or sources) and vertex {@code v}? * @param v the vertex * @return {@code true} if there is a path, and {@code false} otherwise * @throws IllegalArgumentException unless {@code 0 <= v < V} */ public boolean hasPathTo(int v) { validateVertex(v); return marked[v]; } /** * Returns the number of edges in a shortest path between the source vertex {@code s} * (or sources) and vertex {@code v}? * @param v the vertex * @return the number of edges in such a shortest path * (or {@code Integer.MAX_VALUE} if there is no such path) * @throws IllegalArgumentException unless {@code 0 <= v < V} */ public int distTo(int v) { validateVertex(v); return distTo[v]; } /** * Returns a shortest path between the source vertex {@code s} (or sources) * and {@code v}, or {@code null} if no such path. * @param v the vertex * @return the sequence of vertices on a shortest path, as an Iterable * @throws IllegalArgumentException unless {@code 0 <= v < V} */ public Iterable<Integer> pathTo(int v) { validateVertex(v); if (!hasPathTo(v)) return null; Stack<Integer> path = new Stack<Integer>(); int x; for (x = v; distTo[x] != 0; x = edgeTo[x]) path.push(x); path.push(x); return path; } // check optimality conditions for single source private boolean check(Graph G, int s) { // check that the distance of s = 0 if (distTo[s] != 0) { StdOut.println("distance of source " + s + " to itself = " + distTo[s]); return false; } // check that for each edge v-w dist[w] <= dist[v] + 1 // provided v is reachable from s for (int v = 0; v < G.V(); v++) { for (int w : G.adj(v)) { if (hasPathTo(v) != hasPathTo(w)) { StdOut.println("edge " + v + "-" + w); StdOut.println("hasPathTo(" + v + ") = " + hasPathTo(v)); StdOut.println("hasPathTo(" + w + ") = " + hasPathTo(w)); return false; } if (hasPathTo(v) && (distTo[w] > distTo[v] + 1)) { StdOut.println("edge " + v + "-" + w); StdOut.println("distTo[" + v + "] = " + distTo[v]); StdOut.println("distTo[" + w + "] = " + distTo[w]); return false; } } } // check that v = edgeTo[w] satisfies distTo[w] = distTo[v] + 1 // provided v is reachable from s for (int w = 0; w < G.V(); w++) { if (!hasPathTo(w) || w == s) continue; int v = edgeTo[w]; if (distTo[w] != distTo[v] + 1) { StdOut.println("shortest path edge " + v + "-" + w); StdOut.println("distTo[" + v + "] = " + distTo[v]); StdOut.println("distTo[" + w + "] = " + distTo[w]); 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)); } // throw an IllegalArgumentException if vertices is null, has zero vertices, // or has a vertex not between 0 and V-1 private void validateVertices(Iterable<Integer> vertices) { if (vertices == null) { throw new IllegalArgumentException("argument is null"); } int vertexCount = 0; for (Integer v : vertices) { vertexCount++; if (v == null) { throw new IllegalArgumentException("vertex is null"); } validateVertex(v); } if (vertexCount == 0) { throw new IllegalArgumentException("zero vertices"); } } /** * Unit tests the {@code BreadthFirstPaths} data type. * * @param args the command-line arguments */ public static void main(String[] args) { In in = new In(args[0]); Graph G = new Graph(in); // StdOut.println(G); int s = Integer.parseInt(args[1]); BreadthFirstPaths bfs = new BreadthFirstPaths(G, s); for (int v = 0; v < G.V(); v++) { if (bfs.hasPathTo(v)) { StdOut.printf("%d to %d (%d): ", s, v, bfs.distTo(v)); for (int x : bfs.pathTo(v)) { if (x == s) StdOut.print(x); else StdOut.print("-" + x); } StdOut.println(); } else { StdOut.printf("%d to %d (-): not connected\n", s, v); } } } }