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