//=======================================================================

// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.

// Copyright 2004 The Trustees of Indiana University

// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek

//

// Distributed under the Boost Software License, Version 1.0. (See

// accompanying file LICENSE_1_0.txt or copy at

// http://www.boost.org/LICENSE_1_0.txt)

//=======================================================================

#ifndef BOOST_GRAPH_SEQUENTIAL_VERTEX_COLORING_HPP

#define BOOST_GRAPH_SEQUENTIAL_VERTEX_COLORING_HPP

#include <vector>

#include <boost/graph/graph_traits.hpp>

#include <boost/tuple/tuple.hpp>

#include <boost/property_map.hpp>

#include <boost/limits.hpp>

#ifdef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS

#  include <iterator>

#endif

/* This algorithm is to find coloring of a graph

   Algorithm: 

   Let G = (V,E) be a graph with vertices (somehow) ordered v_1, v_2, ...,

   v_n. For k = 1, 2, ..., n the sequential algorithm assigns v_k to the

   smallest possible color. 

   Reference:

   Thomas F. Coleman and Jorge J. More, Estimation of sparse Jacobian

   matrices and graph coloring problems. J. Numer. Anal. V20, P187-209, 1983

   v_k is stored as o[k] here. 

   The color of the vertex v will be stored in color[v].

   i.e., vertex v belongs to coloring color[v] */

namespace boost {

  template <class VertexListGraph, class OrderPA, class ColorMap>

  typename property_traits<ColorMap>::value_type

  sequential_vertex_coloring(const VertexListGraph& G, OrderPA order, 

                             ColorMap color)

  {

    typedef graph_traits<VertexListGraph> GraphTraits;

    typedef typename GraphTraits::vertex_descriptor Vertex;

    typedef typename property_traits<ColorMap>::value_type size_type;

    size_type max_color = 0;

    const size_type V = num_vertices(G);

    // We need to keep track of which colors are used by

    // adjacent vertices. We do this by marking the colors

    // that are used. The mark array contains the mark

    // for each color. The length of mark is the

    // number of vertices since the maximum possible number of colors

    // is the number of vertices.

    std::vector<size_type> mark(V, 

                                std::numeric_limits<size_type>::max BOOST_PREVENT_MACRO_SUBSTITUTION());

    //Initialize colors 

    typename GraphTraits::vertex_iterator v, vend;

    for (tie(v, vend) = vertices(G); v != vend; ++v)

      put(color, *v, V-1);

    //Determine the color for every vertex one by one

    for ( size_type i = 0; i < V; i++) {

      Vertex current = get(order,i);

      typename GraphTraits::adjacency_iterator v, vend;

      //Mark the colors of vertices adjacent to current.

      //i can be the value for marking since i increases successively

      for (tie(v,vend) = adjacent_vertices(current, G); v != vend; ++v)

        mark[get(color,*v)] = i; 

      //Next step is to assign the smallest un-marked color

      //to the current vertex.

      size_type j = 0;

      //Scan through all useable colors, find the smallest possible

      //color that is not used by neighbors.  Note that if mark[j]

      //is equal to i, color j is used by one of the current vertex's

      //neighbors.

      while ( j < max_color && mark[j] == i ) 

        ++j;

      if ( j == max_color )  //All colors are used up. Add one more color

        ++max_color;

      //At this point, j is the smallest possible color

      put(color, current, j);  //Save the color of vertex current

    }

    return max_color;

  }

  template<class VertexListGraph, class ColorMap>

  typename property_traits<ColorMap>::value_type

  sequential_vertex_coloring(const VertexListGraph& G, ColorMap color)

  {

    typedef typename graph_traits<VertexListGraph>::vertex_descriptor

      vertex_descriptor;

    typedef typename graph_traits<VertexListGraph>::vertex_iterator

      vertex_iterator;

    std::pair<vertex_iterator, vertex_iterator> v = vertices(G);

#ifndef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS

    std::vector<vertex_descriptor> order(v.first, v.second);

#else

    std::vector<vertex_descriptor> order;

    order.reserve(std::distance(v.first, v.second));

    while (v.first != v.second) order.push_back(*v.first++);

#endif

    return sequential_vertex_coloring

             (G, 

              make_iterator_property_map

              (order.begin(), identity_property_map(), 

               graph_traits<VertexListGraph>::null_vertex()), 

              color);

  }

}

#endif