/*************************************************************************
* Compilation: javac BreadthFirstDirectedPaths.java
* Execution: java BreadthFirstDirectedPaths V E
* Dependencies: Digraph.java Queue.java Stack.java
*
* Run breadth first search on a digraph.
* Runs in O(E + V) time.
*
* % java BreadthFirstDirectedPaths tinyDG.txt 3
* 3 to 0 (2): 3->2->0
* 3 to 1 (3): 3->2->0->1
* 3 to 2 (1): 3->2
* 3 to 3 (0): 3
* 3 to 4 (2): 3->5->4
* 3 to 5 (1): 3->5
* 3 to 6 (-): not connected
* 3 to 7 (-): not connected
* 3 to 8 (-): not connected
* 3 to 9 (-): not connected
* 3 to 10 (-): not connected
* 3 to 11 (-): not connected
* 3 to 12 (-): not connected
*
*************************************************************************/
/**
* The BreadthDirectedFirstPaths class represents a data type for finding
* shortest paths (number of edges) from a source vertex s
* (or set of source vertices) to every other vertex in the digraph.
*
* This implementation uses breadth-first search.
* The constructor takes time proportional to V + E,
* where V is the number of vertices and E is the number of edges.
* It uses extra space (not including the digraph) proportional to V.
*
* For additional documentation, see Section 4.1 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class BreadthFirstDirectedPaths {
private static final int INFINITY = Integer.MAX_VALUE;
private boolean[] marked; // marked[v] = is there an s->v path?
private int[] edgeTo; // edgeTo[v] = last edge on shortest s->v path
private int[] distTo; // distTo[v] = length of shortest s->v path
/**
* Computes the shortest path from s and every other vertex in graph G.
* @param G the digraph
* @param s the source vertex
*/
public BreadthFirstDirectedPaths(Digraph G, int s) {
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;
bfs(G, s);
}
/**
* Computes the shortest path from any one of the source vertices in sources
* to every other vertex in graph G.
* @param G the digraph
* @param sources the source vertices
*/
public BreadthFirstDirectedPaths(Digraph G, Iterable 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;
bfs(G, sources);
}
// BFS from single source
private void bfs(Digraph G, int s) {
Queue q = new Queue();
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);
}
}
}
}
// BFS from multiple sources
private void bfs(Digraph G, Iterable sources) {
Queue q = new Queue();
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 directed path from the source s (or sources) to vertex v?
* @param v the vertex
* @return true if there is a directed path, false otherwise
*/
public boolean hasPathTo(int v) {
return marked[v];
}
/**
* Returns the number of edges in a shortest path from the source s
* (or sources) to vertex v?
* @param v the vertex
* @return the number of edges in a shortest path
*/
public int distTo(int v) {
return distTo[v];
}
/**
* Returns a shortest path from s (or sources) to v, or
* null if no such path.
* @param v the vertex
* @return the sequence of vertices on a shortest path, as an Iterable
*/
public Iterable pathTo(int v) {
if (!hasPathTo(v)) return null;
Stack path = new Stack();
int x;
for (x = v; distTo[x] != 0; x = edgeTo[x])
path.push(x);
path.push(x);
return path;
}
/**
* Unit tests the BreadthFirstDirectedPaths data type.
*/
public static void main(String[] args) {
In in = new In(args[0]);
Digraph G = new Digraph(in);
// StdOut.println(G);
int s = Integer.parseInt(args[1]);
BreadthFirstDirectedPaths bfs = new BreadthFirstDirectedPaths(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);
}
}
}
}