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BreadthFirstSearch.java
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BreadthFirstSearch.java
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import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Stack;
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 multiple sources
private void bfs(Graph G, Iterable<Integer> sources) {
Queue<Integer> q = new PriorityQueue<Integer>();
for (int s : sources) {
marked[s] = true;
distTo[s] = 0;
q.add(s);
}
while (!q.isEmpty()) {
int v = q.poll();
for (int w : G.adj(v)) {
if (!marked[w]) {
edgeTo[w] = v;
distTo[w] = distTo[v] + 1;
marked[w] = true;
q.add(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) {
System.out.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)) {
System.out.println("edge " + v + "-" + w);
System.out.println("hasPathTo(" + v + ") = " + hasPathTo(v));
System.out.println("hasPathTo(" + w + ") = " + hasPathTo(w));
return false;
}
if (hasPathTo(v) && (distTo[w] > distTo[v] + 1)) {
System.out.println("edge " + v + "-" + w);
System.out.println("distTo[" + v + "] = " + distTo[v]);
System.out.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) {
System.out.println("shortest path edge " + v + "-" + w);
System.out.println("distTo[" + v + "] = " + distTo[v]);
System.out.println("distTo[" + w + "] = " + distTo[w]);
return false;
}
}
return true;
}
private void BFS(Graph G, int s){
Queue<Integer> q = new PriorityQueue<Integer>();
for (int v = 0; v < G.V(); v++)
distTo[v] = INFINITY;
q.add(s);
distTo[s] = 0;
marked[s] = true;
while (!q.isEmpty()) {
int v = q.poll();
for (int w : G.adj(v)) {
if (!marked[w]) {
edgeTo[w] = v;
distTo[w] = distTo[v] + 1;
marked[w] = true;
q.add(w);
}
}
}
}
}