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BreadthFirstPaths.java
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198 lines (180 loc) · 5.29 KB
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/**
* Run breadth first search on an undirected graph.
* Runs in O(E + V) time.
*
* The `BreadthFirstPaths` class represents a data type for finding shortest paths(number
* of edges) from a source vertex `s` (or a set of source vertices) to every other vertex
* in an undirected graph.
* This implementation uses BFS search thoughts.
*
*/
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 `s` and every other vertex in the
// graph `G`
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 `sources` and
// every other vertex in graph `G`
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 `s`(or sources) and vertex `v` ?
public boolean hasPathTo(int v) {
validateVertex(v);
return marked[v];
}
// Returns the number of edges in a shortest path between the source vertex `s`(or sources) and
// vertex `v`
public int distTo(int v) {
validateVertex(v);
return distTo[v];
}
// Returns a shortest path between the source vertex `s`(or sources) and `v`, or `null`
// if no such path.
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 soruce
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 `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 unless `0 <= v < V`
private void validateVertex(Iterable<Integer> vertices) {
if(vertices == null)
throw new IllegalArgumentException("argument is null");
int V = marked.length;
for(int V:vertices) {
if(v < 0 || v >= V) {
throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V - 1));
}
}
}
// test
public static void main(String[] args) {
In in = new In(args[0]);
Graph G = new Graph(in);
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);
}
}
}
}