// 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 = GraphGenerator.fromIn (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);
			}

		}
	}


}