package edu.princeton.cs.algs4.ch41;
import edu.princeton.cs.algs4.ch13.Queue;
import edu.princeton.cs.algs4.ch13.Stack;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* Compilation: javac BreadthFirstPaths.java
* Execution: java BreadthFirstPaths G s
* Dependencies: Graph.java Queue.java Stack.java StdOut.java
* Data files: http://algs4.cs.princeton.edu/41undirected/tinyCG.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 <tt>BreadthFirstPaths</tt> 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 time proportional to <em>V</em> + <em>E</em>,
* where <em>V</em> is the number of vertices and <em>E</em> is the number of edges.
* It uses extra space (not including the graph) proportional to <em>V</em>.
* <p>
* For additional documentation, see <a href="/algs4/41graph">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 <tt>s</tt>
* and every other vertex in the graph <tt>G</tt>.
* @param G the graph
* @param s the source vertex
*/
public BreadthFirstPaths(Graph G, int s) {
marked = new boolean[G.V()];
distTo = new int[G.V()];
edgeTo = new int[G.V()];
bfs(G, s);
assert check(G, s);
}
/**
* Computes the shortest path between any one of the source vertices in <tt>sources</tt>
* and every other vertex in graph <tt>G</tt>.
* @param G the graph
* @param sources the source vertices
*/
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;
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 <tt>s</tt> (or sources) and vertex <tt>v</tt>?
* @param v the vertex
* @return <tt>true</tt> if there is a path, and <tt>false</tt> otherwise
*/
public boolean hasPathTo(int v) {
return marked[v];
}
/**
* Returns the number of edges in a shortest path between the source vertex <tt>s</tt>
* (or sources) and vertex <tt>v</tt>?
* @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 between the source vertex <tt>s</tt> (or sources)
* and <tt>v</tt>, or <tt>null</tt> if no such path.
* @param v the vertex
* @return the sequence of vertices on a shortest path, as an Iterable
*/
public Iterable<Integer> pathTo(int 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;
}
/**
* Unit tests the <tt>BreadthFirstPaths</tt> data type.
*/
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);
}
}
}
}
/*************************************************************************
* Copyright 2002-2012, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4-package.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-package.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-package.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-package.jar. If not, see http://www.gnu.org/licenses.
*************************************************************************/