Johnson.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
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  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
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  SOFTWARE.
*/
 
 
#ifndef JOHNSON_H
#define JOHNSON_H
 
#include <Dijkstra.H>
#include <Bellman_Ford.H>
#include <tpl_graph.H>
#include <tpl_dynList.H>
#include <ah-errors.H>
#include <limits>
#include <type_traits>
 
namespace Aleph
{
 
template <class GT,
          class Distance = Dft_Dist<GT>,
          template <class, class> class Ait = Arc_Iterator,
          template <class, class> class NAit = Node_Arc_Iterator,
          class SA = Dft_Show_Arc<GT>>
class Johnson
{
public:
  using Node = typename GT::Node;
  using Arc = typename GT::Arc;
  using Distance_Type = typename Distance::Distance_Type;
 
private:
  const GT* orig_graph = nullptr;
  GraphCopyWithMapping<GT> graph_copy;  
  DynMapTree<Node*, Node*> copy_to_orig_node;
  DynMapTree<Arc*, Arc*> copy_to_orig_arc;
  DynMapTree<Node*, Distance_Type> h;   
  Distance dist;
  SA sa;
  bool initialized = false;
 
  struct Reweighted_Dist
  {
    using Distance_Type = typename Johnson::Distance_Type;
 
    static_assert(std::is_convertible_v<typename GT::Arc_Type, Distance_Type>,
                  "Reweighted_Dist requires arc info convertible to Distance_Type");
 
    Distance_Type operator()(Arc* arc) const
    {
      return static_cast<Distance_Type>(arc->get_info());
    }
  };
 
  static Distance_Type checked_add(const Distance_Type& a, const Distance_Type& b)
  {
    return shortest_path_detail::checked_add(a, b);
  }
 
  static Distance_Type checked_sub(const Distance_Type& a, const Distance_Type& b)
  {
    if constexpr (std::is_integral_v<Distance_Type>)
      {
        ah_overflow_error_if(b > 0 and
                             a < std::numeric_limits<Distance_Type>::min() + b)
          << "Integer underflow in distance subtraction: " << a << " - " << b;
 
        ah_overflow_error_if(b < 0 and
                             a > std::numeric_limits<Distance_Type>::max() + b)
          << "Integer overflow in distance subtraction: " << a << " - " << b;
      }
 
    return a - b;
  }
 
  void reweight_arcs()
  {
    GT& g = graph_copy.get_graph();
    
    for (Ait<GT, SA> it(g, sa); it.has_curr(); it.next())
      {
        auto arc = it.get_curr();
        auto u = g.get_src_node(arc);
        auto v = g.get_tgt_node(arc);
        
        Distance_Type w = dist(arc);
        if (auto* orig = copy_to_orig_arc.search(arc))
          w = dist(orig->second);
 
        Distance_Type hu = h.find(u);
        Distance_Type hv = h.find(v);
        Distance_Type w_prime = checked_sub(checked_add(w, hu), hv);
        
        // Store reweighted value in the arc
        arc->get_info() = w_prime;
      }
  }
 
  void build_reverse_mappings(const GT& orig)
  {
    copy_to_orig_node.empty();
    copy_to_orig_arc.empty();
 
    graph_copy.for_each_mapping([this](Node* orig_node, Node* copy_node) {
      copy_to_orig_node.insert(copy_node, orig_node);
    });
 
    DynMapTree<std::pair<Node*, Node*>, DynList<Arc*>> buckets;
    GT& copy_g = graph_copy.get_graph();
 
    for (typename GT::Arc_Iterator it(copy_g); it.has_curr(); it.next_ne())
      {
        Arc* copy_arc = it.get_curr();
        Node* csrc = copy_g.get_src_node(copy_arc);
        Node* ctgt = copy_g.get_tgt_node(copy_arc);
        buckets[std::make_pair(csrc, ctgt)].append(copy_arc);
      }
 
    for (typename GT::Arc_Iterator it(orig); it.has_curr(); it.next_ne())
      {
        Arc* orig_arc = it.get_curr();
        Node* osrc = const_cast<GT&>(orig).get_src_node(orig_arc);
        Node* otgt = const_cast<GT&>(orig).get_tgt_node(orig_arc);
 
        Node* csrc = graph_copy.get_copy(osrc);
        Node* ctgt = graph_copy.get_copy(otgt);
 
        auto* bucket = buckets.search(std::make_pair(csrc, ctgt));
        ah_domain_error_if(bucket == nullptr or bucket->second.is_empty())
          << "Arc mapping mismatch between original and copied graph";
 
        Arc* copy_arc = bucket->second.remove_first();
        copy_to_orig_arc.insert(copy_arc, orig_arc);
      }
 
    ah_domain_error_if(copy_to_orig_arc.size() != copy_g.get_num_arcs())
      << "Arc mapping mismatch between original and copied graph";
  }
 
  Path<GT> map_copy_path_to_original(const Path<GT>& copy_path) const
  {
    ah_domain_error_if(orig_graph == nullptr)
      << "Original graph not available";
 
    Path<GT> orig_path(*orig_graph);
 
    if (copy_path.is_empty())
      return orig_path;
 
    auto it = copy_path.get_it();
    auto* node_pair = copy_to_orig_node.search(it.get_current_node());
    ah_domain_error_if(node_pair == nullptr)
      << "Node not found in mapping";
 
    orig_path.init(node_pair->second);
 
    for (; it.has_curr() and it.has_current_arc(); it.next())
      {
        auto* arc_pair = copy_to_orig_arc.search(it.get_current_arc());
        ah_domain_error_if(arc_pair == nullptr)
          << "Arc not found in mapping";
 
        orig_path.append(arc_pair->second);
      }
 
    return orig_path;
  }
 
public:
  explicit Johnson(const GT& g, Distance d = Distance(), SA __sa = SA())
    : orig_graph(&g), graph_copy(g), dist(d), sa(__sa)
  {
    GT& gc = graph_copy.get_graph();
 
    build_reverse_mappings(g);
    
    // Compute node potentials using Bellman-Ford
    // This will throw domain_error if negative cycle exists
    Bellman_Ford<GT, Distance, Ait, NAit, SA> bf(gc, dist, sa);
    h = bf.compute_nodes_weights();
    
    // Reweight all arcs
    reweight_arcs();
    
    initialized = true;
  }
 
  Johnson() = default;
 
  [[nodiscard]] bool is_initialized() const noexcept { return initialized; }
 
  Distance_Type get_distance(Node* src, Node* tgt)
  {
    ah_domain_error_if(!initialized) << "Johnson not initialized";
    ah_domain_error_if(src == nullptr or tgt == nullptr) << "Source or target node is null";
 
    // Same node - distance is 0
    if (src == tgt)
      return Distance_Type(0);
 
    // Get corresponding nodes in the copy
    Node* csrc = graph_copy.get_copy(src);
    Node* ctgt = graph_copy.get_copy(tgt);
    
    GT& gc = graph_copy.get_graph();
    
    // Run Dijkstra from csrc on reweighted graph
    Dijkstra_Min_Paths<GT, Reweighted_Dist, NAit, SA> dijkstra(Reweighted_Dist(), sa);
    dijkstra.paint_min_paths_tree(gc, csrc);
    
    if (not IS_NODE_VISITED(ctgt, Aleph::Spanning_Tree))
      return std::numeric_limits<Distance_Type>::infinity();
 
    // Get reweighted distance (may throw if unreachable)
    Path<GT> path(gc);
    Distance_Type d_prime = dijkstra.get_min_path(ctgt, path);
    
    // Adjust back: d(s,t) = d'(s,t) - h(s) + h(t)
    Distance_Type hs = h.find(csrc);
    Distance_Type ht = h.find(ctgt);
    
    return d_prime - hs + ht;
  }
 
  Path<GT> find_path(Node* src, Node* tgt)
  {
    ah_domain_error_if(!initialized) << "Johnson not initialized";
    ah_domain_error_if(src == nullptr or tgt == nullptr) << "Source or target node is null";
 
    // Get corresponding nodes in the copy
    Node* csrc = graph_copy.get_copy(src);
    Node* ctgt = graph_copy.get_copy(tgt);
    
    GT& gc = graph_copy.get_graph();
    
    // Run Dijkstra from csrc on reweighted graph
    Dijkstra_Min_Paths<GT, Reweighted_Dist, NAit, SA> dijkstra(Reweighted_Dist(), sa);
    dijkstra.paint_min_paths_tree(gc, csrc);
 
    if (not IS_NODE_VISITED(ctgt, Aleph::Spanning_Tree))
      return Path<GT>(*orig_graph);
    
    // Get path in copy graph
    Path<GT> copy_path(gc);
    dijkstra.get_min_path(ctgt, copy_path);
 
    return map_copy_path_to_original(copy_path);
  }
 
  DynMapTree<std::pair<Node*, Node*>, Distance_Type> 
  compute_all_pairs_distances()
  {
    ah_domain_error_if(!initialized) << "Johnson not initialized";
    
    DynMapTree<std::pair<Node*, Node*>, Distance_Type> result;
    GT& gc = graph_copy.get_graph();
    
    // For each node as source
    graph_copy.for_each_mapping([&](Node* orig_src, Node* copy_src) {
      // Run Dijkstra from copy_src
      Dijkstra_Min_Paths<GT, Reweighted_Dist, NAit, SA> dijkstra(Reweighted_Dist(), sa);
      dijkstra.paint_min_paths_tree(gc, copy_src);
      
      Distance_Type hs = h.find(copy_src);
      
      // Get distance to all targets
      graph_copy.for_each_mapping([&](Node* orig_tgt, Node* copy_tgt) {
        if (not IS_NODE_VISITED(copy_tgt, Aleph::Spanning_Tree))
          {
            result.insert(std::make_pair(orig_src, orig_tgt),
                          std::numeric_limits<Distance_Type>::infinity());
            return;
          }
 
        Path<GT> path(gc);
        Distance_Type d_prime = dijkstra.get_min_path(copy_tgt, path);
        Distance_Type ht = h.find(copy_tgt);
        Distance_Type d = d_prime - hs + ht;
        result.insert(std::make_pair(orig_src, orig_tgt), d);
      });
    });
    
    return result;
  }
 
  Distance_Type get_potential(Node* node) const
  {
    ah_domain_error_if(!initialized) << "Johnson not initialized";
    Node* copy_node = graph_copy.get_copy(node);
    return h.find(copy_node);
  }
 
  GT& get_reweighted_graph() noexcept { return graph_copy.get_graph(); }
 
  const GT& get_reweighted_graph() const noexcept { return graph_copy.get_graph(); }
 
  Node* get_copy_node(Node* orig) const { return graph_copy.get_copy(orig); }
};
 
} // namespace Aleph
 
#endif // JOHNSON_H