kosaraju.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
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
 
# ifndef KOSARAJU_H
# define KOSARAJU_H
 
# include <ah-graph-concepts.H>
 
# include <tpl_graph_utils.H>
 
namespace Aleph {
 
template <AlephGraph GT>
inline static void __dfp_phase1(const GT & g,
                                 typename GT::Node * p,
                                 DynArray<typename GT::Node*> & df)
{
  if (IS_NODE_VISITED(p, Depth_First))
    return;
 
  NODE_BITS(p).set_bit(Depth_First, true);
 
  // Traverse outgoing arcs in depth-first order
  for (auto it = g.get_out_it(p); it.has_curr(); it.next_ne())
    {
      auto a = it.get_current_arc_ne();
      if (IS_ARC_VISITED(a, Depth_First))
        continue;
 
      ARC_BITS(a).set_bit(Depth_First, true);
 
      __dfp_phase1(g, it.get_tgt_node(), df);
    }
 
  df.append(p); // Append node in postorder (finish time)
  NODE_COUNTER(p) = df.size();
}
 
template <AlephGraph GT>
inline static void __dfp_phase2_subgraph(const GT & g,
                                          typename GT::Node * p,
                                          GT & blk,
                                          const int & color)
{
  if (IS_NODE_VISITED(p, Depth_First))
    return;
 
  NODE_BITS(p).set_bit(Depth_First, true);
 
  auto q = blk.insert_node(p->get_info());
  NODE_COUNTER(q) = color;
  GT::map_nodes(p, q);
 
  for (auto it = g.get_out_it(p); it.has_curr(); it.next_ne())
    {
      auto a = it.get_current_arc_ne();
      if (IS_ARC_VISITED(a, Depth_First))
        continue;
      ARC_BITS(a).set_bit(Depth_First, true);
 
      __dfp_phase2_subgraph(g, it.get_tgt_node(), blk, color);
    }
}
 
template <AlephGraph GT>
inline static void __dfp_phase2_list(const GT & g,
                                      typename GT::Node * p,
                                      DynList<typename GT::Node *> & list)
{
  if (IS_NODE_VISITED(p, Depth_First))
    return;
 
  NODE_BITS(p).set_bit(Depth_First, true);
 
  list.append(mapped_node<GT>(p));
 
  for (auto it = g.get_out_it(p); it.has_curr(); it.next_ne())
    {
      auto a = it.get_current_arc_ne();
      if (IS_ARC_VISITED(a, Depth_First))
        continue;
      ARC_BITS(a).set_bit(Depth_First, true);
 
      __dfp_phase2_list(g, it.get_tgt_node(), list);
    }
}
 
template <AlephGraph GT>
inline void kosaraju_connected_components(const GT & g,
                                          DynList<GT> & blk_list,
                                          DynList<typename GT::Arc *> & arc_list)
{
  g.reset_nodes();
  g.reset_arcs();
 
  DynArray<typename GT::Node*> df; // Array for postorder (finish times)
 
  // First DFS: compute finish times in postorder
  for (auto it = g.get_node_it(); it.has_curr(); it.next_ne())
    __dfp_phase1(g, it.get_curr(), df);
 
  GT gi = invert_digraph(g); // Transposed graph
 
  DynArray<GT*> array; // Array of subgraph pointers indexed by color
 
  // Second DFS: process nodes in decreasing order of finish time
  for (long i = static_cast<long>(df.size()) - 1, color = 0; i >= 0; --i)
    {
      auto gp = df.access(i);
      auto bp = mapped_node<GT>(gp);
      if (IS_NODE_VISITED(bp, Depth_First))
        continue;
 
      GT & blk = blk_list.append(GT());
      array[color] = &blk;
 
      __dfp_phase2_subgraph(gi, bp, blk, color++); // DFS on transposed graph
 
      assert(NODE_COLOR(mapped_node<GT>(bp)) == color - 1);
    }
 
  // Classify arcs: internal to SCC or crossing between SCCs
  for (auto it = g.get_arc_it(); it.has_curr(); it.next_ne())
    {
      auto a  = it.get_curr();
      auto gs = g.get_src_node(a);
      auto gt = g.get_tgt_node(a);
 
      // Double mapping: original graph → transposed graph → SCC subgraph
      // First mapped_node: original node → transposed graph node
      // Second mapped_node: transposed graph node → SCC subgraph node
      auto bs = mapped_node<GT>(mapped_node<GT>(gs));
      auto bt = mapped_node<GT>(mapped_node<GT>(gt));
 
      const long & color = NODE_COLOR(bs);
 
      if (color == NODE_COLOR(bt))
        {
          typename GT::Arc * ba = array.access(color)->insert_arc(bs, bt);
          GT::map_arcs(a, ba);
        }
      else
        arc_list.append(a);
    }
}
 
template <AlephGraph GT>
inline DynList<DynList<typename GT::Node*>>
kosaraju_connected_components(const GT & g)
{
  DynList<DynList<typename GT::Node*>> list;
 
  g.reset_nodes();
  g.reset_arcs();
 
  DynArray<typename GT::Node*> df; // Array for postorder (finish times)
 
  // First DFS: compute finish times in postorder
  for (auto it = g.get_node_it(); it.has_curr(); it.next_ne())
    __dfp_phase1(g, it.get_curr(), df);
 
  GT gi = invert_digraph(g); // Transposed graph
 
  // Second DFS: process nodes in decreasing order of finish time
  for (long i = static_cast<long>(df.size()) - 1; i >= 0; --i)
    {
      auto gp = df.access(i);
      auto bp = mapped_node<GT>(gp);
      if (IS_NODE_VISITED(bp, Depth_First))
        continue;
 
      auto & blk = list.append(DynList<typename GT::Node*>());
 
      __dfp_phase2_list(gi, bp, blk);
    }
 
  return list;
}
 
template <AlephGraph GT>
struct Kosaraju_Connected_Components
{
  void operator () (const GT & g,
                    DynList<GT> & blk_list,
                    DynList<typename GT::Arc *> & arc_list) const
  {
    kosaraju_connected_components(g, blk_list, arc_list);
  }
 
  DynList<DynList<typename GT::Node*>> operator () (const GT & g) const
  {
    return kosaraju_connected_components(g);
  }
};
 
template <AlephGraph GT>
inline size_t kosaraju_scc_count(const GT & g)
{
  return kosaraju_connected_components(g).size();
}
 
template <AlephGraph GT>
inline bool is_strongly_connected(const GT & g)
{
  if (g.get_num_nodes() <= 1)
    return true;
 
  return kosaraju_scc_count(g) == 1;
}
 
} // end namespace Aleph
 
# endif // KOSARAJU_H