Min_Cost_Matching.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:
 
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  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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*/
 
 
# ifndef MIN_COST_MATCHING_H
# define MIN_COST_MATCHING_H
 
# include <cstddef>
# include <limits>
# include <type_traits>
# include <utility>
 
# include <ah-errors.H>
# include <Blossom_Weighted.H>
 
namespace Aleph
{
  template <typename Cost_Type = long long>
  struct Min_Cost_Matching_Result
  {
    Cost_Type total_cost = Cost_Type{0}; 
    size_t cardinality = 0; 
  };
 
 
  template <typename Cost_Type = long long>
  struct Min_Cost_Perfect_Matching_Result
  {
    bool feasible = false; 
    Cost_Type total_cost = Cost_Type{0}; 
    size_t cardinality = 0; 
  };
 
 
  namespace min_cost_matching_detail
  {
    template <typename T>
    long long to_ll_checked(T value)
    {
      static_assert(std::is_integral_v<T>,
                    "Min_Cost_Matching requires integral arc costs");
 
      // Number of value bits in T and in long long (excludes the sign bit).
      constexpr int T_digits  = std::numeric_limits<T>::digits;
      constexpr int LL_digits = std::numeric_limits<long long>::digits; // 63
 
      // Upper check: T can hold values > LLONG_MAX when
      //   unsigned T: T_digits >= LL_digits  (e.g. unsigned long long: 64 >= 63)
      //   signed   T: T_digits >  LL_digits  (e.g. __int128: 127 > 63)
      constexpr bool need_upper =
          std::is_unsigned_v<T> ? (T_digits >= LL_digits)
                                : (T_digits >  LL_digits);
 
      // Lower check: only signed T wider than long long can go below LLONG_MIN.
      constexpr bool need_lower =
          std::is_signed_v<T> and (T_digits > LL_digits);
 
      if constexpr (need_upper)
        {
          ah_overflow_error_if(static_cast<__int128>(value)
                               > static_cast<__int128>(std::numeric_limits<long long>::max()))
            << "Cost cannot be represented as long long";
        }
 
      if constexpr (need_lower)
        {
          ah_overflow_error_if(static_cast<__int128>(value)
                               < static_cast<__int128>(std::numeric_limits<long long>::min()))
            << "Cost cannot be represented as long long";
        }
 
      return static_cast<long long>(value);
    }
 
 
    template <class Cost_Accessor>
    class Negated_Cost_Accessor
    {
      Cost_Accessor cost_;
 
    public:
      explicit Negated_Cost_Accessor(Cost_Accessor cost = Cost_Accessor())
        : cost_(std::move(cost))
      {
        // empty
      }
 
      template <class Arc>
      long long operator()(Arc *arc) const
      {
        const long long c = to_ll_checked(cost_(arc));
        ah_overflow_error_if(c == std::numeric_limits<long long>::min())
          << "Minimum-cost matching cannot negate LLONG_MIN cost";
        return -c;
      }
    };
  } // namespace min_cost_matching_detail
 
 
  template <class GT,
            class Cost = Dft_Dist<GT>,
            class SA = Dft_Show_Arc<GT>>
  Min_Cost_Matching_Result<long long>
  compute_minimum_cost_general_matching(const GT & g,
                                        DynDlist<typename GT::Arc *> & matching,
                                        Cost cost = Cost(),
                                        SA sa = SA(),
                                        const bool max_cardinality = false)
  {
    ah_domain_error_if(g.is_digraph())
      << "compute_minimum_cost_general_matching(): g is a digraph";
 
    using Arc = typename GT::Arc;
    using Raw_Cost = std::decay_t<decltype(cost(static_cast<Arc *>(nullptr)))>;
 
    static_assert(std::is_integral_v<Raw_Cost>,
                  "Min_Cost_Matching requires integral arc costs");
 
    Cost cost_accessor = std::move(cost);
 
    const auto weighted_result =
        compute_maximum_weight_general_matching<
          GT,
          min_cost_matching_detail::Negated_Cost_Accessor<Cost>,
          SA>(g,
              matching,
              min_cost_matching_detail::Negated_Cost_Accessor<Cost>(cost_accessor),
              std::move(sa),
              max_cardinality);
 
    long long total_cost = 0;
    for (auto it = matching.get_it(); it.has_curr(); it.next_ne())
      {
        Arc *arc = it.get_curr();
        const long long c = min_cost_matching_detail::to_ll_checked(cost_accessor(arc));
        const __int128 sum = static_cast<__int128>(total_cost)
                             + static_cast<__int128>(c);
        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()))
          << "Minimum-cost matching total cost overflows long long";
        total_cost = static_cast<long long>(sum);
      }
 
    ah_runtime_error_unless(weighted_result.cardinality == matching.size())
      << "Minimum-cost matching internal cardinality mismatch";
 
    return Min_Cost_Matching_Result<long long>{total_cost, weighted_result.cardinality};
  }
 
 
  template <class GT,
            class Cost = Dft_Dist<GT>,
            class SA = Dft_Show_Arc<GT>>
  Min_Cost_Matching_Result<long long>
  blossom_minimum_cost_matching(const GT & g,
                                DynDlist<typename GT::Arc *> & matching,
                                Cost cost = Cost(),
                                SA sa = SA(),
                                const bool max_cardinality = false)
  {
    return compute_minimum_cost_general_matching<GT, Cost, SA>(
                                                               g, matching, std::move(cost), std::move(sa),
                                                               max_cardinality);
  }
 
 
  template <class GT,
            class Cost = Dft_Dist<GT>,
            class SA = Dft_Show_Arc<GT>>
  Min_Cost_Perfect_Matching_Result<long long>
  compute_minimum_cost_perfect_general_matching(const GT & g,
                                                DynDlist<typename GT::Arc *> & matching,
                                                Cost cost = Cost(),
                                                SA sa = SA())
  {
    ah_domain_error_if(g.is_digraph())
      << "compute_minimum_cost_perfect_general_matching(): g is a digraph";
 
    matching.empty();
 
    const size_t num_nodes = g.get_num_nodes();
    if (num_nodes == 0)
      return Min_Cost_Perfect_Matching_Result<long long>{true, 0, 0};
 
    if (num_nodes % 2 == 1)
      return Min_Cost_Perfect_Matching_Result<long long>{false, 0, 0};
 
    const auto best = compute_minimum_cost_general_matching<GT, Cost, SA>(
                                                                          g, matching, std::move(cost), std::move(sa),
                                                                          true);
 
    const size_t expected = num_nodes / 2;
    if (best.cardinality != expected)
      {
        matching.empty();
        return Min_Cost_Perfect_Matching_Result<long long>{false, 0, 0};
      }
 
    return Min_Cost_Perfect_Matching_Result<long long>{
          true, best.total_cost, best.cardinality
        };
  }
 
 
  template <class GT,
            class Cost = Dft_Dist<GT>,
            class SA = Dft_Show_Arc<GT>>
  Min_Cost_Perfect_Matching_Result<long long>
  blossom_minimum_cost_perfect_matching(const GT & g,
                                        DynDlist<typename GT::Arc *> & matching,
                                        Cost cost = Cost(),
                                        SA sa = SA())
  {
    return compute_minimum_cost_perfect_general_matching<GT, Cost, SA>(
                                                                       g, matching, std::move(cost), std::move(sa));
  }
 
 
  template <class GT,
            class Cost = Dft_Dist<GT>,
            class SA = Dft_Show_Arc<GT>>
  class Compute_Minimum_Cost_General_Matching
  {
    Cost cost_;
    SA sa_;
    bool max_cardinality_ = false;
 
  public:
    Compute_Minimum_Cost_General_Matching(Cost cost = Cost(),
                                          SA sa = SA(),
                                          const bool max_cardinality = false)
      : cost_(std::move(cost)),
        sa_(std::move(sa)),
        max_cardinality_(max_cardinality)
    {
      // empty
    }
 
    Min_Cost_Matching_Result<long long>
    operator()(const GT & g, DynDlist<typename GT::Arc *> & matching)
    {
      return compute_minimum_cost_general_matching<GT, Cost, SA>(
                                                                 g, matching, cost_, sa_, max_cardinality_);
    }
  };
 
 
  template <class GT,
            class Cost = Dft_Dist<GT>,
            class SA = Dft_Show_Arc<GT>>
  class Compute_Minimum_Cost_Perfect_General_Matching
  {
    Cost cost_;
    SA sa_;
 
  public:
    Compute_Minimum_Cost_Perfect_General_Matching(Cost cost = Cost(), SA sa = SA())
      : cost_(std::move(cost)),
        sa_(std::move(sa))
    {
      // empty
    }
 
    Min_Cost_Perfect_Matching_Result<long long>
    operator()(const GT & g, DynDlist<typename GT::Arc *> & matching)
    {
      return compute_minimum_cost_perfect_general_matching<GT, Cost, SA>(g, matching, cost_, sa_);
    }
  };
} // namespace Aleph
 
# endif // MIN_COST_MATCHING_H