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// 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

#include <vector>
#include <boost/graph/graph_traits.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/property_map.hpp>
#include <boost/limits.hpp>

#  include <iterator>

/* This algorithm is to find coloring of a graph

   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. 


   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
      while ( j < max_color && mark[j] == i ) 
      if ( j == max_color )  //All colors are used up. Add one more 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
    typedef typename graph_traits<VertexListGraph>::vertex_iterator

    std::pair<vertex_iterator, vertex_iterator> v = vertices(G);
    std::vector<vertex_descriptor> order(v.first, v.second);
    std::vector<vertex_descriptor> order;
    order.reserve(std::distance(v.first, v.second));
    while (v.first != v.second) order.push_back(*v.first++);
    return sequential_vertex_coloring
              (order.begin(), identity_property_map(),