content: /*************************************************************************
   *  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
   *
   *************************************************************************/
  
  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
  
      // single source
      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);
      }
  
      // multiple sources
      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);
      }
  
  
      // BFS from single soruce
      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);
                  }
              }
          }
      }
  
      // BFS 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 s (or sources) and v?
      public boolean hasPathTo(int v) {
          return marked[v];
      }
  
      // length of shortest path between s (or sources) and v
      public int distTo(int v) {
          return distTo[v];
      }
  
      // shortest path bewteen s (or sources) and v; null if no such path
      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;
      }
  
  
      // test client
      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);
              }
  
          }
      }
  
  
  }
  