latex_floyd.H

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
 
#ifndef LATEX_FLOYD_H
#define LATEX_FLOYD_H
 
#include <ahFunction.H>
#include <tpl_matgraph.H>
#include <mat_latex.H>
 
namespace Aleph
{
 
template <class AM>
struct Initialize_Dist
{
  typedef typename AM::Graph_Type::Arc_Type Arc_Type;
 
  typedef typename AM::Graph_Type GT;
 
  typedef typename GT::Node Node;
 
  typedef typename GT::Arc Arc;
 
  typedef typename AM::Arc_Type::Distance_Type Distance_Type;
 
  void operator () (AM &            mat,
        Node *          src,
        Node *          tgt,
        const long &    i,
        const long &    j,
        Distance_Type & entry,
        void *          p)
  {
    Ady_Mat<typename AM::Graph_Type, long> & path = 
      * reinterpret_cast<Ady_Mat<typename AM::Graph_Type, long> *>(p);
 
    if (i == j)
      {
  entry = AM::Graph_Type::Arc_Type::Zero_Distance;
  path(i, j) = j;
 
  return;
      }
 
    GT & g = mat.get_list_graph();
 
    Arc * arc = search_arc(g, src, tgt);
 
    if (arc == nullptr)
      {
  entry = AM::Graph_Type::Arc_Type::Max_Distance;
  return;
      }
 
    entry = arc->get_info().get_distance();
 
    path(i, j) = j;
  }
};
 
template <class GT, class Compare, class Plus> 
void floyd_all_shortest_paths(
    GT &                                                g, 
    Ady_Mat<GT, typename GT::Arc_Type::Distance_Type> & dist,
    Ady_Mat<GT, long> &                                 path)
{
  typedef Ady_Mat<GT, typename GT::Arc_Type::Distance_Type> Dist_Mat;
 
  typedef typename GT::Arc_Type::Distance_Type Dist_Type;
 
  dist.
    template operate_all_arcs_matrix<Initialize_Dist<Dist_Mat> > (&path);
 
  const Dist_Type & max = GT::Arc_Type::Max_Distance;
 
  const long & n = g.get_num_nodes();
 
  for (int i = 0; i < n; ++i)
    for (int s = 0; s < n; ++s)
      if (dist(s, i) < max)
  for (int t = 0; t < n; ++t)
    {
            if (!(dist(i, t) < max))
              continue;
 
      Dist_Type new_dist = Plus () (dist(s, i), dist(i, t));
 
      if (Compare () (new_dist, dist(s, t)))
        {
    path(s, t) = path(s, i);
    dist(s, t) = new_dist;
        }
    }
}
 
template <class GT> 
void floyd_all_shortest_paths(
    GT &                                                g, 
    Ady_Mat<GT, typename GT::Arc_Type::Distance_Type> & dist,
    Ady_Mat<GT, long> &                                 path)
{
  using Dist_T = typename GT::Arc_Type::Distance_Type;
  floyd_all_shortest_paths<GT, Aleph::less<Dist_T>, Aleph::plus<Dist_T>>(g, dist, path);
}
 
template <class Mat>
void find_min_path(Mat &                           p, 
                   const long                      src_index,
                   const long                      tgt_index,
                   Path<typename Mat::Graph_Type>& path)
{
  using GT = typename Mat::Graph_Type;
  using Node = typename GT::Node;
 
  GT & g = p.get_list_graph();
  Node * src = p(src_index);
  path.set_graph(g, src);
  
  // NOTE: Initialize j properly to avoid undefined behavior
  for (long i = src_index, j = p(i, tgt_index); i != tgt_index; i = j, j = p(i, tgt_index))
  {
    Node * next = p(j);
    path.append(next);
  }
}
 
template <class Mat>
void find_min_path(Mat &                           p, 
                   typename Mat::Node *            src_node,
                   typename Mat::Node *            tgt_node,
                   Path<typename Mat::Graph_Type>& path)
{
  const long src_index = p(src_node);
  const long tgt_index = p(tgt_node);
  find_min_path(p, src_index, tgt_index, path);
}
 
 
template <class GT, class Compare, class Plus, 
          template <class> class P_i,   // Row/column index format for dist and path
          template <class> class P_ij,  // Path matrix entry format
          template <class> class D_ij>  // Distance matrix entry format
void floyd_all_shortest_paths_latex(
    GT &                                                g, 
    Ady_Mat<GT, typename GT::Arc_Type::Distance_Type> & dist,
    Ady_Mat<GT, long> &                                 path,
    std::ofstream &                                     output)
{
  typedef Ady_Mat<GT, typename GT::Arc_Type::Distance_Type> Dist_Mat;
  typedef Ady_Mat<GT, long>                                 Path_Mat;
 
  typedef typename GT::Arc_Type::Distance_Type Dist_Type;
 
  dist.
    template operate_all_arcs_matrix<Initialize_Dist<Dist_Mat> > (&path);
 
  const Dist_Type & max = GT::Arc_Type::Max_Distance;
 
  const long & n = g.get_num_nodes();
 
  output << "\\begin{figure}[H]{\\tiny " << std::endl
   << "\\begin{tabular}{ll}" << std::endl
   << "\\begin{tabular}{ll}" << std::endl;
  mat_to_latex <Dist_Mat, P_i<Dist_Mat>, P_i<Dist_Mat>, D_ij<Dist_Mat> >
    (dist, n, n, output, "\\hskip -5mm $D_0=$", "\\\\ ");
  output << "\\end{tabular}" << std::endl
   << " & \\begin{tabular}{ll}" << std::endl;
  mat_to_latex <Path_Mat, P_i<Path_Mat>, P_i<Path_Mat>, P_ij<Path_Mat> >
    (path, n, n, output, "\\hskip -7mm $P_0=$", "\\\\ ");
  output << "\\end{tabular}" << std::endl 
       << "\\end{tabular}" << std::endl
   << "}\\end{figure}" << std::endl;
 
  for (int i = 0; i < n; ++i)
    {
      for (int s = 0; s < n; ++s)
  if (dist(s, i) < max)
    for (int t = 0; t < n; ++t)
      {
              if (!(dist(i, t) < max))
                continue;
 
        Dist_Type new_dist = Plus() (dist(s, i), dist(i, t));
 
        if (Compare () (new_dist, dist(s, t)))
    {
      path(s, t) = path(s, i);
      dist(s, t) = new_dist;
    }
      }
      char buf[256];
 
      snprintf(buf, 256, "\\hskip -5mm $D_%d=$ ", i + 1);
 
      output << "\\begin{figure}[H]{\\tiny " << std::endl
       << "\\begin{tabular}{ll}" << std::endl
       << "\\begin{tabular}{ll}" << std::endl;
      mat_to_latex <Dist_Mat, P_i<Dist_Mat>, P_i<Dist_Mat>, D_ij<Dist_Mat> >
  (dist, n, n, output, buf, "\\\\ ");
      output << "\\end{tabular}" << std::endl
       << " & \\begin{tabular}{ll}" << std::endl;
 
      snprintf(buf, 256, "\\hskip -7mm $P_%d=$ ", i + 1);
 
      mat_to_latex <Path_Mat, P_i<Path_Mat>, P_i<Path_Mat>, P_ij<Path_Mat> >
  (path, n, n, output, buf, "\\\\");
      output << "\\end{tabular}" << std::endl 
       << "\\end{tabular}" << std::endl
       << "}\\end{figure}" << std::endl;
    }
}
 
 
template <class GT, 
          template <class> class P_i,   // Row/column index format
          template <class> class P_ij,  // Path matrix entry format
          template <class> class D_ij>  // Distance matrix entry format
void floyd_all_shortest_paths_latex(
    GT &                                                g, 
    Ady_Mat<GT, typename GT::Arc_Type::Distance_Type> & dist,
    Ady_Mat<GT, long> &                                 path,
    std::ofstream &                                     output)
{
  using Dist_T = typename GT::Arc_Type::Distance_Type;
  floyd_all_shortest_paths_latex<GT, Aleph::less<Dist_T>, Aleph::plus<Dist_T>, 
                                  P_i, P_ij, D_ij>(g, dist, path, output);
}
 
} // end namespace Aleph
 
#endif // LATEX_FLOYD_H