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
 
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#ifndef MIN_COST_MATCHING_H
#define MIN_COST_MATCHING_H
 
# include <ah-graph-concepts.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)
    {
      // MSVC cl has no __int128; compare directly as type T (T is unsigned
      // and at least 64-bit when need_upper is true, so LLONG_MAX fits in T).
      ah_overflow_error_if(value > static_cast<T>(std::numeric_limits<long long>::max()))
        << "Cost cannot be represented as long long";
    }
 
  if constexpr (need_lower)
    {
      // Only reachable for signed types wider than long long (e.g. __int128).
      // MSVC cl does not support __int128, so this branch is never
      // instantiated there; the cast is still guarded for GCC/Clang.
#if defined(_MSC_VER) && !defined(__clang__)
      (void) value;  // unreachable on MSVC — no type has digits > 63
#else
      ah_overflow_error_if(static_cast<__int128>(value) <
                           static_cast<__int128>(std::numeric_limits<long long>::min()))
        << "Cost cannot be represented as long long";
#endif
    }
 
  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 <AlephGraph GT, class Cost = Dft_Dist<GT>, ArcFilter<GT> 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));
#if defined(_MSC_VER) && !defined(__clang__)
      {
        const long long lo = std::numeric_limits<long long>::min();
        const long long hi = std::numeric_limits<long long>::max();
        ah_overflow_error_if((c > 0 and total_cost > hi - c) or (c < 0 and total_cost < lo - c))
          << "Minimum-cost matching total cost overflows long long";
        total_cost += c;
      }
#else
      {
        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);
      }
#endif
    }
 
  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 <AlephGraph GT, class Cost = Dft_Dist<GT>, ArcFilter<GT> 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 <AlephGraph GT, class Cost = Dft_Dist<GT>, ArcFilter<GT> 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 <AlephGraph GT, class Cost = Dft_Dist<GT>, ArcFilter<GT> 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 <AlephGraph GT, class Cost = Dft_Dist<GT>, ArcFilter<GT> 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 <AlephGraph GT, class Cost = Dft_Dist<GT>, ArcFilter<GT> 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