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// Exercise 4.1.13 (Solution published at http://algs4.cs.princeton.edu/)
package algs41;
import stdlib.*;
import algs13.Queue;
import algs13.Stack;
/* ***********************************************************************
 *  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 final boolean[] marked;  // marked[v] = is there an s-v path
  private final int[] edgeTo;      // edgeTo[v] = previous edge on shortest s-v path
  private final 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<>();
    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<>();
    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<>();
    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) {
    //args = new String [] { "data/tinyAG.txt", "0"};
    args = new String [] { "data/tinyG.txt", "0" };
    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.format("%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.format("%d to %d (-):  not connected\n", s, v);
      }

    }
  }


}