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// -*- C++ -*-

// Copyright (C) 2005, 2006, 2009 Free Software Foundation, Inc.

//

// This file is part of the GNU ISO C++ Library.  This library is free

// software; you can redistribute it and/or modify it under the terms

// of the GNU General Public License as published by the Free Software

// Foundation; either version 3, or (at your option) any later

// version.

// This library is distributed in the hope that it will be useful, but

// WITHOUT ANY WARRANTY; without even the implied warranty of

// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

// General Public License for more details.

// You should have received a copy of the GNU General Public License

// along with this library; see the file COPYING3.  If not see

// <http://www.gnu.org/licenses/>.

// Copyright (C) 2004 Ami Tavory and Vladimir Dreizin, IBM-HRL.

// Permission to use, copy, modify, sell, and distribute this software

// is hereby granted without fee, provided that the above copyright

// notice appears in all copies, and that both that copyright notice

// and this permission notice appear in supporting documentation. None

// of the above authors, nor IBM Haifa Research Laboratories, make any

// representation about the suitability of this software for any

// purpose. It is provided "as is" without express or implied

// warranty.

/**

 * @file priority_queue_dijkstra_example.cpp

 * A basic example showing how to cross reference a vector and a

 * priority-queue for modify.

 */

/**

 * This example shows how to cross-reference priority queues

 * and a vector. I.e., using a vector to

 * map keys to entries in a priority queue, and using the priority

 * queue to map entries to the vector. The combination

 * can be used for fast modification of keys.

 *

 * As an example, a very simple form of Diskstra's algorithm is used. The graph

 * is represented by an adjacency matrix. Nodes and vertices are size_ts, and

 * it is assumed that the minimal path between any two nodes is less than 1000.

 */

#include <vector>

#include <iostream>

#include <ext/pb_ds/priority_queue.hpp>

using namespace std;

using namespace __gnu_pbds;

// The value type of the priority queue.

// The first entry is the node's id, and the second is the distance.

typedef std::pair<size_t, size_t> pq_value;

// Comparison functor used to compare priority-queue value types.

struct pq_value_cmp : public binary_function<pq_value, pq_value, bool>

{

  inline bool

  operator()(const pq_value& r_lhs, const pq_value& r_rhs) const

  {

    // Note that a value is considered smaller than a different value

    // if its distance is* larger*. This is because by STL

    // conventions, "larger" entries are nearer the top of the

    // priority queue.

    return r_rhs.second < r_lhs.second;

  }

};

int main()

{

  enum

    {

      // Number of vertices is hard-coded in this example.

      num_vertices = 5,

      // "Infinity".

      graph_inf = 1000

    };

  // The edge-distance matrix.

  // For example, the distance from node 0 to node 1 is 5, and the

  // distance from node 1 to node 0 is 2.

  const size_t a_a_edge_legnth[num_vertices][num_vertices] =

    {

      {0, 5, 3, 7, 6},

      {2, 0, 2, 8, 9},

      {2, 1, 0, 8, 0},

      {1, 8, 3, 0, 2},

      {2, 3, 4, 2, 0}

    };

  // The priority queue type.

  typedef __gnu_pbds::priority_queue< pq_value, pq_value_cmp> pq_t;

  // The priority queue object.

  pq_t p;

  // This vector contains for each node, a find-iterator into the

  // priority queue.

  vector<pq_t::point_iterator> a_it;

  // First we initialize the data structures.

  // For each node, we push into the priority queue a value

  // identifying it with a distance of infinity.

  for (size_t i = 0; i < num_vertices; ++i)

    a_it.push_back(p.push(pq_value(i, graph_inf)));

  // Now we take the initial node, in this case 0, and modify its

  // distance to 0.

  p.modify(a_it[0], pq_value(0, 0));

  // The priority queue contains all vertices whose final distance has

  // not been determined, so to finish the algorithm, we must loop

  // until it is empty.

  while (!p.empty())

    {

      // First we find the node whose distance is smallest.

      const pq_value& r_v = p.top();

      const size_t node_id = r_v.first;

      const size_t dist = r_v.second;

      // This is the node's final distance, so we can print it out.

      cout << "The distance from 0 to " << node_id

           << " is " << dist << endl;

      // Now we go over the node's neighbors and "relax" the

      // distances, if applicable.

      for (size_t neighbor_i = 0; neighbor_i < num_vertices; ++neighbor_i)

        {

          // Potentially, the distance to the neighbor is the distance

          // to the currently-considered node + the distance from this

          // node to the neighbor.

          const size_t pot_dist = dist + a_a_edge_legnth[node_id][neighbor_i];

          if (a_it[neighbor_i] == a_it[0])

            continue;

          // "Relax" the distance (if appropriate) through modify.

          if (pot_dist < a_it[neighbor_i]->second)

            p.modify(a_it[neighbor_i], pq_value(neighbor_i, pot_dist));

        }

      // Done with the node, so we pop it.

      a_it[node_id] = a_it[0];

      p.pop();

    }

  return 0;

}