Blossom_Weighted.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
 
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  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
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*/
 
#ifndef BLOSSOM_WEIGHTED_H
#define BLOSSOM_WEIGHTED_H
 
# include <ah-graph-concepts.H>
 
#include <algorithm>
#include <cstddef>
#include <cstdint>
#include <functional>
#include <limits>
#include <type_traits>
#include <utility>
 
#include <ah-errors.H>
#include <ahSort.H>
#include <cookie_guard.H>
#include <tpl_array.H>
#include <tpl_dynDlist.H>
#include <tpl_graph.H>
#include <tpl_graph_utils.H>
 
#include <blossom_weighted_mwmatching.H>
 
namespace Aleph {
template <typename Weight_Type = long long>
struct Blossom_Weighted_Result
{
  Weight_Type total_weight = Weight_Type{0};  
  size_t cardinality = 0;                     
};
 
namespace blossom_weighted_detail {
template <typename T>
long long to_ll_checked(T value)
{
  static_assert(std::is_integral_v<T>, "Blossom_Weighted requires integral arc weights");
 
  if constexpr (std::is_signed_v<T>)
    {
      using Common = std::common_type_t<T, long long>;
      constexpr auto ll_max = std::numeric_limits<long long>::max();
      constexpr auto ll_min = std::numeric_limits<long long>::min();
 
      const auto v = static_cast<Common>(value);
      ah_overflow_error_if(v > static_cast<Common>(ll_max) or v < static_cast<Common>(ll_min))
        << "Weight cannot be represented as long long";
    }
  else
    {
      using Common = std::common_type_t<T, long long>;
      constexpr auto ll_max = std::numeric_limits<long long>::max();
 
      const auto v = static_cast<Common>(value);
      ah_overflow_error_if(v > static_cast<Common>(ll_max))
        << "Weight cannot be represented as long long";
    }
 
  return static_cast<long long>(value);
}
}  // namespace blossom_weighted_detail
 
template <AlephGraph GT, class Weight = Dft_Dist<GT>, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
Blossom_Weighted_Result<long long> compute_maximum_weight_general_matching(
  const GT &g,
  DynDlist<typename GT::Arc *> &matching,
  Weight weight = Weight(),
  SA sa = SA(),
  const bool max_cardinality = false)
{
  using Node = typename GT::Node;
  using Arc = typename GT::Arc;
  using Raw_Weight = std::decay_t<decltype(weight(static_cast<Arc *>(nullptr)))>;
  using MwVertex = blossom_weighted_detail::mwmatching::VertexId;
  using MwEdge = blossom_weighted_detail::mwmatching::Edge<long long>;
  using MwPair = blossom_weighted_detail::mwmatching::VertexPair;
 
  static_assert(std::is_integral_v<Raw_Weight>, "Blossom_Weighted requires integral arc weights");
 
  ah_domain_error_if(g.is_digraph()) << "compute_maximum_weight_general_matching(): g is a digraph";
 
  matching.empty();
 
  if (g.get_num_nodes() == 0)
    return Blossom_Weighted_Result<long long>{0, 0};
 
  constexpr auto max_vertex = static_cast<size_t>(std::numeric_limits<MwVertex>::max());
  ah_overflow_error_if(g.get_num_nodes() > max_vertex)
    << "Graph has too many vertices for weighted blossom implementation";
 
  Cookie_Saver<GT> cookie_saver(g, true, false);
 
  size_t num_nodes = 0;
  for (Node_Iterator<GT> it(g); it.has_curr(); it.next_ne())
    {
      Node *p = it.get_curr();
      ++num_nodes;
      const auto encoded = num_nodes;  // index + 1
      NODE_COOKIE(p) = reinterpret_cast<void *>(encoded);
    }
 
  struct Arc_Record
  {
    size_t u = 0;
    size_t v = 0;
    long long weight = 0;
    Arc *arc = nullptr;
  };
 
  Array<Arc_Record> records;
  records.reserve(g.get_num_arcs() + 1);
 
  for (Arc_Iterator<GT, SA> it(g, sa); it.has_curr(); it.next_ne())
    {
      Arc *arc = it.get_curr_ne();
      Node *src = g.get_src_node(arc);
      Node *tgt = g.get_tgt_node(arc);
 
      const auto src_idx_plus_one = reinterpret_cast<uintptr_t>(NODE_COOKIE(src));
      const auto tgt_idx_plus_one = reinterpret_cast<uintptr_t>(NODE_COOKIE(tgt));
 
      ah_runtime_error_unless(src_idx_plus_one != 0 and tgt_idx_plus_one != 0)
        << "Weighted blossom internal node index mapping is invalid";
 
      auto u = src_idx_plus_one - 1;
      auto v = tgt_idx_plus_one - 1;
      if (u == v)
        continue;  // Loops are irrelevant to matchings.
 
      if (u > v)
        std::swap(u, v);
 
      const long long w = blossom_weighted_detail::to_ll_checked(weight(arc));
      records.append(Arc_Record{u, v, w, arc});
    }
 
  if (records.is_empty())
    return Blossom_Weighted_Result<long long>{0, 0};
 
  struct Arc_Record_Less
  {
    bool operator()(const Arc_Record &a, const Arc_Record &b) const noexcept
    {
      if (a.u != b.u)
        return a.u < b.u;
      if (a.v != b.v)
        return a.v < b.v;
      return a.weight > b.weight;
    }
  };
  in_place_sort(records, Arc_Record_Less());
 
  Array<Arc_Record> best_edges;
  best_edges.reserve(records.size());
  for (size_t i = 0; i < records.size();)
    {
      const Arc_Record &best = records[i];
      best_edges.append(best);
      ++i;
      while (i < records.size() and records[i].u == best.u and records[i].v == best.v)
        ++i;
    }
 
  Array<MwEdge> edges;
  edges.reserve(best_edges.size());
  for (const Arc_Record &e : best_edges)
    edges.append(MwEdge(static_cast<MwVertex>(e.u), static_cast<MwVertex>(e.v), e.weight));
 
  Array<MwEdge> solver_edges;
  if (max_cardinality)
    solver_edges =
      blossom_weighted_detail::mwmatching::adjust_weights_for_maximum_cardinality_matching(edges);
  else
    solver_edges = edges;
 
  const Array<MwPair> matched_pairs =
    blossom_weighted_detail::mwmatching::maximum_weight_matching(solver_edges);
 
  long long total_weight = 0;
  size_t cardinality = 0;
 
  auto find_edge = [&best_edges](size_t u, size_t v) -> const Arc_Record *
  {
    size_t lo = 0;
    size_t hi = best_edges.size();
 
    while (lo < hi)
      {
        const size_t mid = lo + (hi - lo) / 2;
        if (const Arc_Record &cur = best_edges[mid]; cur.u < u or (cur.u == u and cur.v < v))
          lo = mid + 1;
        else
          hi = mid;
      }
 
    if (lo < best_edges.size())
      {
        const Arc_Record &cand = best_edges[lo];
        if (cand.u == u and cand.v == v)
          return &cand;
      }
 
    return nullptr;
  };
 
  for (const auto &[fst, snd] : matched_pairs)
    {
      auto u = static_cast<size_t>(fst);
      auto v = static_cast<size_t>(snd);
      if (u > v)
        std::swap(u, v);
 
      const Arc_Record *arc_info = find_edge(u, v);
      ah_runtime_error_unless(arc_info != nullptr)
        << "Weighted blossom returned an unknown matched pair";
 
      matching.append(arc_info->arc);
#if defined(_MSC_VER) && !defined(__clang__)
      // MSVC has no __int128; detect long long overflow without it.
      {
        const long long w = arc_info->weight;
        const long long lo = std::numeric_limits<long long>::min();
        const long long hi = std::numeric_limits<long long>::max();
        ah_overflow_error_if((w > 0 and total_weight > hi - w) or (w < 0 and total_weight < lo - w))
          << "Matching total weight overflows long long";
        total_weight += w;
      }
#else
      const __int128 sum =
        static_cast<__int128>(total_weight) + static_cast<__int128>(arc_info->weight);
      ah_overflow_error_if(sum > static_cast<__int128>(std::numeric_limits<long long>::max()) or
                           sum < static_cast<__int128>(std::numeric_limits<long long>::min()))
        << "Matching total weight overflows long long";
      total_weight = static_cast<long long>(sum);
#endif
      ++cardinality;
    }
 
  return Blossom_Weighted_Result<long long>{total_weight, cardinality};
}
 
template <AlephGraph GT, class Weight = Dft_Dist<GT>, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
Blossom_Weighted_Result<long long> blossom_maximum_weight_matching(const GT &g,
                                                                   DynDlist<typename GT::Arc *> &matching,
                                                                   Weight weight = Weight(),
                                                                   SA sa = SA(),
                                                                   const bool max_cardinality = false)
{
  return compute_maximum_weight_general_matching<GT, Weight, SA>(g, matching, std::move(weight),
                                                                 std::move(sa), max_cardinality);
}
 
template <AlephGraph GT, class Weight = Dft_Dist<GT>, ArcFilter<GT> SA = Dft_Show_Arc<GT>>
class Compute_Maximum_Weight_General_Matching
{
  Weight weight_;
  SA sa_;
  bool max_cardinality_ = false;
 
public:
  Compute_Maximum_Weight_General_Matching(Weight weight = Weight(),
                                          SA sa = SA(),
                                          const bool max_cardinality = false)
    : weight_(std::move(weight)), sa_(std::move(sa)), max_cardinality_(max_cardinality)
  {
    // empty
  }
 
  Blossom_Weighted_Result<long long> operator()(const GT &g, DynDlist<typename GT::Arc *> &matching)
  {
    return compute_maximum_weight_general_matching<GT, Weight, SA>(g, matching, weight_, sa_,
                                                                   max_cardinality_);
  }
};
}  // namespace Aleph
 
#endif  // BLOSSOM_WEIGHTED_H