cp_model_solver.cc

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// Copyright 2010-2021 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
 
#include "ortools/sat/cp_model_solver.h"
 
#include <algorithm>
#include <atomic>
#include <cmath>
#include <cstdint>
#include <functional>
#include <limits>
#include <map>
#include <memory>
#include <random>
#include <set>
#include <string>
#include <thread>
#include <utility>
#include <vector>
 
#if !defined(__PORTABLE_PLATFORM__)
#include "absl/synchronization/notification.h"
#include "google/protobuf/text_format.h"
#include "ortools/base/file.h"
#include "ortools/util/sigint.h"
#endif  // __PORTABLE_PLATFORM__
 
#include "absl/container/flat_hash_set.h"
#include "absl/memory/memory.h"
#include "absl/status/status.h"
#include "absl/strings/str_cat.h"
#include "absl/strings/str_format.h"
#include "absl/strings/str_join.h"
#include "absl/strings/str_split.h"
#include "absl/synchronization/mutex.h"
#include "ortools/base/cleanup.h"
#include "ortools/base/commandlineflags.h"
#include "ortools/base/int_type.h"
#include "ortools/base/integral_types.h"
#include "ortools/base/logging.h"
#include "ortools/base/map_util.h"
#include "ortools/base/threadpool.h"
#include "ortools/base/timer.h"
#include "ortools/base/vlog_is_on.h"
#include "ortools/graph/connected_components.h"
#include "ortools/port/proto_utils.h"
#include "ortools/sat/circuit.h"
#include "ortools/sat/clause.h"
#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_checker.h"
#include "ortools/sat/cp_model_lns.h"
#include "ortools/sat/cp_model_loader.h"
#include "ortools/sat/cp_model_postsolve.h"
#include "ortools/sat/cp_model_presolve.h"
#include "ortools/sat/cp_model_search.h"
#include "ortools/sat/cp_model_symmetries.h"
#include "ortools/sat/cp_model_utils.h"
#include "ortools/sat/cuts.h"
#include "ortools/sat/drat_checker.h"
#include "ortools/sat/drat_proof_handler.h"
#include "ortools/sat/feasibility_pump.h"
#include "ortools/sat/integer.h"
#include "ortools/sat/integer_expr.h"
#include "ortools/sat/integer_search.h"
#include "ortools/sat/intervals.h"
#include "ortools/sat/lb_tree_search.h"
#include "ortools/sat/linear_programming_constraint.h"
#include "ortools/sat/linear_relaxation.h"
#include "ortools/sat/optimization.h"
#include "ortools/sat/parameters_validation.h"
#include "ortools/sat/precedences.h"
#include "ortools/sat/probing.h"
#include "ortools/sat/rins.h"
#include "ortools/sat/sat_base.h"
#include "ortools/sat/sat_inprocessing.h"
#include "ortools/sat/sat_parameters.pb.h"
#include "ortools/sat/sat_solver.h"
#include "ortools/sat/simplification.h"
#include "ortools/sat/subsolver.h"
#include "ortools/sat/synchronization.h"
#include "ortools/util/logging.h"
#include "ortools/util/sorted_interval_list.h"
#include "ortools/util/time_limit.h"
 
#if defined(_MSC_VER)
ABSL_FLAG(std::string, cp_model_dump_prefix, ".\\",
          "Prefix filename for all dumped files");
#else
ABSL_FLAG(std::string, cp_model_dump_prefix, "/tmp/",
          "Prefix filename for all dumped files");
#endif
ABSL_FLAG(bool, cp_model_dump_models, false,
          "DEBUG ONLY. When set to true, SolveCpModel() will dump its model "
          "protos (original model, presolved model, mapping model) in text "
          "format to 'FLAGS_cp_model_dump_prefix'{model|presolved_model|"
          "mapping_model}.pb.txt.");
 
ABSL_FLAG(bool, cp_model_dump_lns, false,
          "DEBUG ONLY. When set to true, solve will dump all "
          "lns models proto in text format to "
          "'FLAGS_cp_model_dump_prefix'lns_xxx.pb.txt.");
 
ABSL_FLAG(
    bool, cp_model_dump_problematic_lns, false,
    "DEBUG ONLY. Similar to --cp_model_dump_lns, but only dump fragment for "
    "which we got an issue while validating the postsolved solution. This "
    "allows to debug presolve issues without dumping all the models.");
 
ABSL_FLAG(bool, cp_model_dump_response, false,
          "DEBUG ONLY. If true, the final response of each solve will be "
          "dumped to 'FLAGS_cp_model_dump_prefix'response.pb.txt");
 
ABSL_FLAG(std::string, cp_model_params, "",
          "This is interpreted as a text SatParameters proto. The "
          "specified fields will override the normal ones for all solves.");
 
ABSL_FLAG(std::string, drat_output, "",
          "If non-empty, a proof in DRAT format will be written to this file. "
          "This will only be used for pure-SAT problems.");
 
ABSL_FLAG(bool, drat_check, false,
          "If true, a proof in DRAT format will be stored in memory and "
          "checked if the problem is UNSAT. This will only be used for "
          "pure-SAT problems.");
 
ABSL_FLAG(double, max_drat_time_in_seconds,
          std::numeric_limits<double>::infinity(),
          "Maximum time in seconds to check the DRAT proof. This will only "
          "be used is the drat_check flag is enabled.");
 
ABSL_FLAG(bool, cp_model_check_intermediate_solutions, false,
          "When true, all intermediate solutions found by the solver will be "
          "checked. This can be expensive, therefore it is off by default.");
 
ABSL_FLAG(std::string, contention_profile, "",
          "If non-empty, dump a contention pprof proto to the specified "
          "destination at the end of the solve.");
 
namespace operations_research {
namespace sat {
 
namespace {
 
// Makes the string fit in one line by cutting it in the middle if necessary.
std::string Summarize(const std::string& input) {
  if (input.size() < 105) return input;
  const int half = 50;
  return absl::StrCat(input.substr(0, half), " ... ",
                      input.substr(input.size() - half, half));
}
 
}  // namespace.
 
// =============================================================================
// Public API.
// =============================================================================
 
std::string CpModelStats(const CpModelProto& model_proto) {
  std::map<std::string, int> num_constraints_by_name;
  std::map<std::string, int> num_reif_constraints_by_name;
  std::map<std::string, int> name_to_num_literals;
  std::map<std::string, int> name_to_num_terms;
 
  int no_overlap_2d_num_rectangles = 0;
  int no_overlap_2d_num_optional_rectangles = 0;
  int no_overlap_2d_num_linear_areas = 0;
  int no_overlap_2d_num_quadratic_areas = 0;
 
  int cumulative_num_intervals = 0;
  int cumulative_num_optional_intervals = 0;
  int cumulative_num_variable_sizes = 0;
  int cumulative_num_variable_demands = 0;
 
  int no_overlap_num_intervals = 0;
  int no_overlap_num_optional_intervals = 0;
  int no_overlap_num_variable_sizes = 0;
 
  for (const ConstraintProto& ct : model_proto.constraints()) {
    std::string name = ConstraintCaseName(ct.constraint_case());
 
    // We split the linear constraints into 3 buckets has it gives more insight
    // on the type of problem we are facing.
    if (ct.constraint_case() == ConstraintProto::ConstraintCase::kLinear) {
      if (ct.linear().vars_size() == 1) name += "1";
      if (ct.linear().vars_size() == 2) name += "2";
      if (ct.linear().vars_size() == 3) name += "3";
      if (ct.linear().vars_size() > 3) name += "N";
    }
 
    num_constraints_by_name[name]++;
    if (!ct.enforcement_literal().empty()) {
      num_reif_constraints_by_name[name]++;
    }
 
    auto variable_is_fixed = [&model_proto](int ref) {
      const IntegerVariableProto& proto =
          model_proto.variables(PositiveRef(ref));
      return proto.domain_size() == 2 && proto.domain(0) == proto.domain(1);
    };
 
    auto interval_has_fixed_size = [&model_proto, &variable_is_fixed](int c) {
      const IntervalConstraintProto& proto =
          model_proto.constraints(c).interval();
      if (proto.has_size_view()) {
        for (const int ref : proto.size_view().vars()) {
          if (!variable_is_fixed(ref)) {
            return false;
          }
        }
        return true;
      } else {
        return variable_is_fixed(proto.size());
      }
    };
 
    auto constraint_is_optional = [&model_proto](int i) {
      return !model_proto.constraints(i).enforcement_literal().empty();
    };
 
    // For pure Boolean constraints, we also display the total number of literal
    // involved as this gives a good idea of the problem size.
    if (ct.constraint_case() == ConstraintProto::ConstraintCase::kBoolOr) {
      name_to_num_literals[name] += ct.bool_or().literals().size();
    } else if (ct.constraint_case() ==
               ConstraintProto::ConstraintCase::kBoolAnd) {
      name_to_num_literals[name] += ct.bool_and().literals().size();
    } else if (ct.constraint_case() ==
               ConstraintProto::ConstraintCase::kAtMostOne) {
      name_to_num_literals[name] += ct.at_most_one().literals().size();
    } else if (ct.constraint_case() ==
               ConstraintProto::ConstraintCase::kExactlyOne) {
      name_to_num_literals[name] += ct.exactly_one().literals().size();
    } else if (ct.constraint_case() ==
               ConstraintProto::ConstraintCase::kNoOverlap2D) {
      const int num_boxes = ct.no_overlap_2d().x_intervals_size();
      no_overlap_2d_num_rectangles += num_boxes;
      for (int i = 0; i < num_boxes; ++i) {
        const int x_interval = ct.no_overlap_2d().x_intervals(i);
        const int y_interval = ct.no_overlap_2d().y_intervals(i);
        if (constraint_is_optional(x_interval) ||
            constraint_is_optional(y_interval)) {
          no_overlap_2d_num_optional_rectangles++;
        }
        const int num_fixed = interval_has_fixed_size(x_interval) +
                              interval_has_fixed_size(y_interval);
        if (num_fixed == 0) {
          no_overlap_2d_num_quadratic_areas++;
        } else if (num_fixed == 1) {
          no_overlap_2d_num_linear_areas++;
        }
      }
    } else if (ct.constraint_case() ==
               ConstraintProto::ConstraintCase::kNoOverlap) {
      const int num_intervals = ct.no_overlap().intervals_size();
      no_overlap_num_intervals += num_intervals;
      for (int i = 0; i < num_intervals; ++i) {
        const int interval = ct.no_overlap().intervals(i);
        if (constraint_is_optional(interval)) {
          no_overlap_num_optional_intervals++;
        }
        if (!interval_has_fixed_size(interval)) {
          no_overlap_num_variable_sizes++;
        }
      }
    } else if (ct.constraint_case() ==
               ConstraintProto::ConstraintCase::kCumulative) {
      const int num_intervals = ct.cumulative().intervals_size();
      cumulative_num_intervals += num_intervals;
      for (int i = 0; i < num_intervals; ++i) {
        const int interval = ct.cumulative().intervals(i);
        if (constraint_is_optional(interval)) {
          cumulative_num_optional_intervals++;
        }
        if (!interval_has_fixed_size(interval)) {
          cumulative_num_variable_sizes++;
        }
        if (!variable_is_fixed(ct.cumulative().demands(i))) {
          cumulative_num_variable_demands++;
        }
      }
    }
 
    if (ct.constraint_case() == ConstraintProto::ConstraintCase::kLinear &&
        ct.linear().vars_size() > 3) {
      name_to_num_terms[name] += ct.linear().vars_size();
    }
  }
 
  int num_constants = 0;
  std::set<int64_t> constant_values;
  std::map<Domain, int> num_vars_per_domains;
  for (const IntegerVariableProto& var : model_proto.variables()) {
    if (var.domain_size() == 2 && var.domain(0) == var.domain(1)) {
      ++num_constants;
      constant_values.insert(var.domain(0));
    } else {
      num_vars_per_domains[ReadDomainFromProto(var)]++;
    }
  }
 
  std::string result;
  if (model_proto.has_objective()) {
    absl::StrAppend(&result, "optimization model '", model_proto.name(),
                    "':\n");
  } else {
    absl::StrAppend(&result, "satisfaction model '", model_proto.name(),
                    "':\n");
  }
 
  for (const DecisionStrategyProto& strategy : model_proto.search_strategy()) {
    absl::StrAppend(
        &result, "Search strategy: on ", strategy.variables_size(),
        " variables, ",
        ProtoEnumToString<DecisionStrategyProto::VariableSelectionStrategy>(
            strategy.variable_selection_strategy()),
        ", ",
        ProtoEnumToString<DecisionStrategyProto::DomainReductionStrategy>(
            strategy.domain_reduction_strategy()),
        "\n");
  }
 
  const std::string objective_string =
      model_proto.has_objective()
          ? absl::StrCat(" (", model_proto.objective().vars_size(),
                         " in objective)")
          : "";
  absl::StrAppend(&result, "#Variables: ", model_proto.variables_size(),
                  objective_string, "\n");
  if (num_vars_per_domains.size() < 100) {
    for (const auto& entry : num_vars_per_domains) {
      const std::string temp = absl::StrCat("  - ", entry.second, " in ",
                                            entry.first.ToString(), "\n");
      absl::StrAppend(&result, Summarize(temp));
    }
  } else {
    int64_t max_complexity = 0;
    int64_t min = std::numeric_limits<int64_t>::max();
    int64_t max = std::numeric_limits<int64_t>::min();
    for (const auto& entry : num_vars_per_domains) {
      min = std::min(min, entry.first.Min());
      max = std::max(max, entry.first.Max());
      max_complexity = std::max(
          max_complexity, static_cast<int64_t>(entry.first.NumIntervals()));
    }
    absl::StrAppend(&result, "  - ", num_vars_per_domains.size(),
                    " different domains in [", min, ",", max,
                    "] with a largest complexity of ", max_complexity, ".\n");
  }
 
  if (num_constants > 0) {
    const std::string temp =
        absl::StrCat("  - ", num_constants, " constants in {",
                     absl::StrJoin(constant_values, ","), "} \n");
    absl::StrAppend(&result, Summarize(temp));
  }
 
  std::vector<std::string> constraints;
  constraints.reserve(num_constraints_by_name.size());
  for (const auto& entry : num_constraints_by_name) {
    const std::string& name = entry.first;
    constraints.push_back(absl::StrCat("#", name, ": ", entry.second));
    if (gtl::ContainsKey(num_reif_constraints_by_name, name)) {
      absl::StrAppend(&constraints.back(),
                      " (#enforced: ", num_reif_constraints_by_name[name], ")");
    }
    if (gtl::ContainsKey(name_to_num_literals, name)) {
      absl::StrAppend(&constraints.back(),
                      " (#literals: ", name_to_num_literals[name], ")");
    }
    if (gtl::ContainsKey(name_to_num_terms, name)) {
      absl::StrAppend(&constraints.back(),
                      " (#terms: ", name_to_num_terms[name], ")");
    }
    if (name == "kNoOverlap2D") {
      absl::StrAppend(&constraints.back(),
                      " (#rectangles: ", no_overlap_2d_num_rectangles);
      if (no_overlap_2d_num_optional_rectangles > 0) {
        absl::StrAppend(&constraints.back(),
                        ", #optional: ", no_overlap_2d_num_optional_rectangles);
      }
      if (no_overlap_2d_num_linear_areas > 0) {
        absl::StrAppend(&constraints.back(),
                        ", #linear_areas: ", no_overlap_2d_num_linear_areas);
      }
      if (no_overlap_2d_num_quadratic_areas > 0) {
        absl::StrAppend(&constraints.back(), ", #quadratic_areas: ",
                        no_overlap_2d_num_quadratic_areas);
      }
      absl::StrAppend(&constraints.back(), ")");
    } else if (name == "kCumulative") {
      absl::StrAppend(&constraints.back(),
                      " (#intervals: ", cumulative_num_intervals);
      if (cumulative_num_optional_intervals > 0) {
        absl::StrAppend(&constraints.back(),
                        ", #optional: ", cumulative_num_optional_intervals);
      }
      if (cumulative_num_variable_sizes > 0) {
        absl::StrAppend(&constraints.back(),
                        ", #variable_sizes: ", cumulative_num_variable_sizes);
      }
      if (cumulative_num_variable_demands > 0) {
        absl::StrAppend(&constraints.back(), ", #variable_demands: ",
                        cumulative_num_variable_demands);
      }
      absl::StrAppend(&constraints.back(), ")");
    } else if (name == "kNoOverlap") {
      absl::StrAppend(&constraints.back(),
                      " (#intervals: ", no_overlap_num_intervals);
      if (no_overlap_num_optional_intervals > 0) {
        absl::StrAppend(&constraints.back(),
                        ", #optional: ", no_overlap_num_optional_intervals);
      }
      if (no_overlap_num_variable_sizes > 0) {
        absl::StrAppend(&constraints.back(),
                        ", #variable_sizes: ", no_overlap_num_variable_sizes);
      }
      absl::StrAppend(&constraints.back(), ")");
    }
  }
  std::sort(constraints.begin(), constraints.end());
  absl::StrAppend(&result, absl::StrJoin(constraints, "\n"));
 
  return result;
}
 
std::string CpSolverResponseStats(const CpSolverResponse& response,
                                  bool has_objective) {
  std::string result;
  absl::StrAppend(&result, "CpSolverResponse summary:");
  absl::StrAppend(&result, "\nstatus: ",
                  ProtoEnumToString<CpSolverStatus>(response.status()));
 
  if (has_objective && response.status() != CpSolverStatus::INFEASIBLE) {
    absl::StrAppendFormat(&result, "\nobjective: %.16g",
                          response.objective_value());
    absl::StrAppendFormat(&result, "\nbest_bound: %.16g",
                          response.best_objective_bound());
  } else {
    absl::StrAppend(&result, "\nobjective: NA");
    absl::StrAppend(&result, "\nbest_bound: NA");
  }
 
  absl::StrAppend(&result, "\nbooleans: ", response.num_booleans());
  absl::StrAppend(&result, "\nconflicts: ", response.num_conflicts());
  absl::StrAppend(&result, "\nbranches: ", response.num_branches());
 
  // TODO(user): This is probably better named "binary_propagation", but we just
  // output "propagations" to be consistent with sat/analyze.sh.
  absl::StrAppend(&result,
                  "\npropagations: ", response.num_binary_propagations());
  absl::StrAppend(
      &result, "\ninteger_propagations: ", response.num_integer_propagations());
 
  absl::StrAppend(&result, "\nrestarts: ", response.num_restarts());
  absl::StrAppend(&result, "\nlp_iterations: ", response.num_lp_iterations());
  absl::StrAppend(&result, "\nwalltime: ", response.wall_time());
  absl::StrAppend(&result, "\nusertime: ", response.user_time());
  absl::StrAppend(&result,
                  "\ndeterministic_time: ", response.deterministic_time());
  absl::StrAppend(&result, "\nprimal_integral: ", response.primal_integral());
  absl::StrAppend(&result, "\n");
  return result;
}
 
namespace {
 
#if !defined(__PORTABLE_PLATFORM__)
#endif  // __PORTABLE_PLATFORM__
 
void FillSolutionInResponse(const CpModelProto& model_proto, const Model& model,
                            CpSolverResponse* response) {
  response->clear_solution();
  response->clear_solution_lower_bounds();
  response->clear_solution_upper_bounds();
 
  auto* mapping = model.Get<CpModelMapping>();
  auto* trail = model.Get<Trail>();
  auto* integer_trail = model.Get<IntegerTrail>();
 
  std::vector<int64_t> solution;
  for (int i = 0; i < model_proto.variables_size(); ++i) {
    if (mapping->IsInteger(i)) {
      const IntegerVariable var = mapping->Integer(i);
      if (integer_trail->IsCurrentlyIgnored(var)) {
        // This variable is "ignored" so it may not be fixed, simply use
        // the current lower bound. Any value in its domain should lead to
        // a feasible solution.
        solution.push_back(model.Get(LowerBound(var)));
      } else {
        if (model.Get(LowerBound(var)) != model.Get(UpperBound(var))) {
          solution.clear();
          break;
        }
        solution.push_back(model.Get(Value(var)));
      }
    } else {
      DCHECK(mapping->IsBoolean(i));
      const Literal literal = mapping->Literal(i);
      if (trail->Assignment().LiteralIsAssigned(literal)) {
        solution.push_back(model.Get(Value(literal)));
      } else {
        solution.clear();
        break;
      }
    }
  }
 
  if (!solution.empty()) {
    if (DEBUG_MODE ||
        absl::GetFlag(FLAGS_cp_model_check_intermediate_solutions)) {
      // TODO(user): Checks against initial model.
      CHECK(SolutionIsFeasible(model_proto, solution));
    }
    for (const int64_t value : solution) response->add_solution(value);
  } else {
    // Not all variables are fixed.
    // We fill instead the lb/ub of each variables.
    const auto& assignment = trail->Assignment();
    for (int i = 0; i < model_proto.variables_size(); ++i) {
      if (mapping->IsBoolean(i)) {
        if (assignment.VariableIsAssigned(mapping->Literal(i).Variable())) {
          const int64_t value = model.Get(Value(mapping->Literal(i)));
          response->add_solution_lower_bounds(value);
          response->add_solution_upper_bounds(value);
        } else {
          response->add_solution_lower_bounds(0);
          response->add_solution_upper_bounds(1);
        }
      } else {
        response->add_solution_lower_bounds(
            model.Get(LowerBound(mapping->Integer(i))));
        response->add_solution_upper_bounds(
            model.Get(UpperBound(mapping->Integer(i))));
      }
    }
  }
}
 
namespace {
 
IntegerVariable GetOrCreateVariableWithTightBound(
    const std::vector<std::pair<IntegerVariable, int64_t>>& terms,
    Model* model) {
  if (terms.empty()) return model->Add(ConstantIntegerVariable(0));
  if (terms.size() == 1 && terms.front().second == 1) {
    return terms.front().first;
  }
  if (terms.size() == 1 && terms.front().second == -1) {
    return NegationOf(terms.front().first);
  }
 
  int64_t sum_min = 0;
  int64_t sum_max = 0;
  for (const std::pair<IntegerVariable, int64_t> var_coeff : terms) {
    const int64_t min_domain = model->Get(LowerBound(var_coeff.first));
    const int64_t max_domain = model->Get(UpperBound(var_coeff.first));
    const int64_t coeff = var_coeff.second;
    const int64_t prod1 = min_domain * coeff;
    const int64_t prod2 = max_domain * coeff;
    sum_min += std::min(prod1, prod2);
    sum_max += std::max(prod1, prod2);
  }
  return model->Add(NewIntegerVariable(sum_min, sum_max));
}
 
IntegerVariable GetOrCreateVariableGreaterOrEqualToSumOf(
    const std::vector<std::pair<IntegerVariable, int64_t>>& terms,
    Model* model) {
  if (terms.empty()) return model->Add(ConstantIntegerVariable(0));
  if (terms.size() == 1 && terms.front().second == 1) {
    return terms.front().first;
  }
  if (terms.size() == 1 && terms.front().second == -1) {
    return NegationOf(terms.front().first);
  }
 
  // Create a new variable and link it with the linear terms.
  const IntegerVariable new_var =
      GetOrCreateVariableWithTightBound(terms, model);
  std::vector<IntegerVariable> vars;
  std::vector<int64_t> coeffs;
  for (const auto& term : terms) {
    vars.push_back(term.first);
    coeffs.push_back(term.second);
  }
  vars.push_back(new_var);
  coeffs.push_back(-1);
  model->Add(WeightedSumLowerOrEqual(vars, coeffs, 0));
  return new_var;
}
 
}  // namespace
 
// Adds one LinearProgrammingConstraint per connected component of the model.
IntegerVariable AddLPConstraints(const CpModelProto& model_proto,
                                 int linearization_level, Model* m) {
  LinearRelaxation relaxation;
  ComputeLinearRelaxation(model_proto, linearization_level, m, &relaxation);
 
  // The bipartite graph of LP constraints might be disconnected:
  // make a partition of the variables into connected components.
  // Constraint nodes are indexed by [0..num_lp_constraints),
  // variable nodes by [num_lp_constraints..num_lp_constraints+num_variables).
  //
  // TODO(user): look into biconnected components.
  const int num_lp_constraints = relaxation.linear_constraints.size();
  const int num_lp_cut_generators = relaxation.cut_generators.size();
  const int num_integer_variables =
      m->GetOrCreate<IntegerTrail>()->NumIntegerVariables().value();
  DenseConnectedComponentsFinder components;
  components.SetNumberOfNodes(num_lp_constraints + num_lp_cut_generators +
                              num_integer_variables);
  auto get_constraint_index = [](int ct_index) { return ct_index; };
  auto get_cut_generator_index = [num_lp_constraints](int cut_index) {
    return num_lp_constraints + cut_index;
  };
  auto get_var_index = [num_lp_constraints,
                        num_lp_cut_generators](IntegerVariable var) {
    return num_lp_constraints + num_lp_cut_generators + var.value();
  };
  for (int i = 0; i < num_lp_constraints; i++) {
    for (const IntegerVariable var : relaxation.linear_constraints[i].vars) {
      components.AddEdge(get_constraint_index(i), get_var_index(var));
    }
  }
  for (int i = 0; i < num_lp_cut_generators; ++i) {
    for (const IntegerVariable var : relaxation.cut_generators[i].vars) {
      components.AddEdge(get_cut_generator_index(i), get_var_index(var));
    }
  }
 
  // Add edges for at most ones that we do not statically add to the LP.
  //
  // TODO(user): Because we currently add every at_most_ones (and we clear it)
  // this code is unused outside of experiments.
  for (const std::vector<Literal>& at_most_one : relaxation.at_most_ones) {
    LinearConstraintBuilder builder(m, kMinIntegerValue, IntegerValue(1));
    for (const Literal literal : at_most_one) {
      // Note that it is okay to simply ignore the literal if it has no
      // integer view.
      const bool unused ABSL_ATTRIBUTE_UNUSED =
          builder.AddLiteralTerm(literal, IntegerValue(1));
    }
    LinearConstraint lc = builder.Build();
    for (int i = 1; i < lc.vars.size(); ++i) {
      components.AddEdge(get_var_index(lc.vars[0]), get_var_index(lc.vars[i]));
    }
  }
 
  const int num_components = components.GetNumberOfComponents();
  std::vector<int> component_sizes(num_components, 0);
  const std::vector<int> index_to_component = components.GetComponentIds();
  for (int i = 0; i < num_lp_constraints; i++) {
    ++component_sizes[index_to_component[get_constraint_index(i)]];
  }
  for (int i = 0; i < num_lp_cut_generators; i++) {
    ++component_sizes[index_to_component[get_cut_generator_index(i)]];
  }
 
  // Make sure any constraint that touch the objective is not discarded even
  // if it is the only one in its component. This is important to propagate
  // as much as possible the objective bound by using any bounds the LP give
  // us on one of its components. This is critical on the zephyrus problems for
  // instance.
  auto* mapping = m->GetOrCreate<CpModelMapping>();
  for (int i = 0; i < model_proto.objective().coeffs_size(); ++i) {
    const IntegerVariable var =
        mapping->Integer(model_proto.objective().vars(i));
    ++component_sizes[index_to_component[get_var_index(var)]];
  }
 
  // Dispatch every constraint to its LinearProgrammingConstraint.
  std::vector<LinearProgrammingConstraint*> lp_constraints(num_components,
                                                           nullptr);
  std::vector<std::vector<LinearConstraint>> component_to_constraints(
      num_components);
  for (int i = 0; i < num_lp_constraints; i++) {
    const int c = index_to_component[get_constraint_index(i)];
    if (component_sizes[c] <= 1) continue;
    component_to_constraints[c].push_back(relaxation.linear_constraints[i]);
    if (lp_constraints[c] == nullptr) {
      lp_constraints[c] = m->Create<LinearProgrammingConstraint>();
    }
    // Load the constraint.
    lp_constraints[c]->AddLinearConstraint(relaxation.linear_constraints[i]);
  }
 
  // Dispatch every cut generator to its LinearProgrammingConstraint.
  for (int i = 0; i < num_lp_cut_generators; i++) {
    const int c = index_to_component[get_cut_generator_index(i)];
    if (lp_constraints[c] == nullptr) {
      lp_constraints[c] = m->Create<LinearProgrammingConstraint>();
    }
    lp_constraints[c]->AddCutGenerator(std::move(relaxation.cut_generators[i]));
  }
 
  // Register "generic" clique (i.e. at most one) cut generator.
  const SatParameters& params = *(m->GetOrCreate<SatParameters>());
  if (params.add_clique_cuts() && params.linearization_level() > 1) {
    for (LinearProgrammingConstraint* lp : lp_constraints) {
      if (lp == nullptr) continue;
      lp->AddCutGenerator(CreateCliqueCutGenerator(lp->integer_variables(), m));
    }
  }
 
  if (params.add_knapsack_cuts() && params.linearization_level() > 1) {
    for (int c = 0; c < num_components; ++c) {
      if (component_to_constraints[c].empty()) continue;
      lp_constraints[c]->AddCutGenerator(CreateKnapsackCoverCutGenerator(
          component_to_constraints[c], lp_constraints[c]->integer_variables(),
          m));
    }
  }
 
  // Add the objective.
  std::vector<std::vector<std::pair<IntegerVariable, int64_t>>>
      component_to_cp_terms(num_components);
  std::vector<std::pair<IntegerVariable, int64_t>> top_level_cp_terms;
  int num_components_containing_objective = 0;
  if (model_proto.has_objective()) {
    // First pass: set objective coefficients on the lp constraints, and store
    // the cp terms in one vector per component.
    for (int i = 0; i < model_proto.objective().coeffs_size(); ++i) {
      const IntegerVariable var =
          mapping->Integer(model_proto.objective().vars(i));
      const int64_t coeff = model_proto.objective().coeffs(i);
      const int c = index_to_component[get_var_index(var)];
      if (lp_constraints[c] != nullptr) {
        lp_constraints[c]->SetObjectiveCoefficient(var, IntegerValue(coeff));
        component_to_cp_terms[c].push_back(std::make_pair(var, coeff));
      } else {
        // Component is too small. We still need to store the objective term.
        top_level_cp_terms.push_back(std::make_pair(var, coeff));
      }
    }
    // Second pass: Build the cp sub-objectives per component.
    for (int c = 0; c < num_components; ++c) {
      if (component_to_cp_terms[c].empty()) continue;
      const IntegerVariable sub_obj_var =
          GetOrCreateVariableGreaterOrEqualToSumOf(component_to_cp_terms[c], m);
      top_level_cp_terms.push_back(std::make_pair(sub_obj_var, 1));
      lp_constraints[c]->SetMainObjectiveVariable(sub_obj_var);
      num_components_containing_objective++;
    }
  }
 
  const IntegerVariable main_objective_var =
      model_proto.has_objective()
          ? GetOrCreateVariableGreaterOrEqualToSumOf(top_level_cp_terms, m)
          : kNoIntegerVariable;
 
  // Register LP constraints. Note that this needs to be done after all the
  // constraints have been added.
  for (LinearProgrammingConstraint* lp_constraint : lp_constraints) {
    if (lp_constraint == nullptr) continue;
    lp_constraint->RegisterWith(m);
    VLOG(3) << "LP constraint: " << lp_constraint->DimensionString() << ".";
  }
 
  VLOG(3) << top_level_cp_terms.size()
          << " terms in the main objective linear equation ("
          << num_components_containing_objective << " from LP constraints).";
  return main_objective_var;
}
 
}  // namespace
 
// Used by NewFeasibleSolutionObserver to register observers.
struct SolutionObservers {
  explicit SolutionObservers(Model* model) {}
  std::vector<std::function<void(const CpSolverResponse& response)>> observers;
};
 
std::function<void(Model*)> NewFeasibleSolutionObserver(
    const std::function<void(const CpSolverResponse& response)>& observer) {
  return [=](Model* model) {
    model->GetOrCreate<SolutionObservers>()->observers.push_back(observer);
  };
}
 
#if !defined(__PORTABLE_PLATFORM__)
// TODO(user): Support it on android.
std::function<SatParameters(Model*)> NewSatParameters(
    const std::string& params) {
  sat::SatParameters parameters;
  if (!params.empty()) {
    CHECK(google::protobuf::TextFormat::ParseFromString(params, &parameters))
        << params;
  }
  return NewSatParameters(parameters);
}
#endif  // __PORTABLE_PLATFORM__
 
std::function<SatParameters(Model*)> NewSatParameters(
    const sat::SatParameters& parameters) {
  return [=](Model* model) {
    // Tricky: It is important to initialize the model parameters before any
    // of the solver object are created, so that by default they use the given
    // parameters.
    //
    // TODO(user): A notable exception to this is the TimeLimit which is
    // currently not initializing itself from the SatParameters in the model. It
    // will also starts counting from the time of its creation. It will be good
    // to find a solution that is less error prone.
    *model->GetOrCreate<SatParameters>() = parameters;
    return parameters;
  };
}
 
namespace {
 
// Registers a callback that will export variables bounds fixed at level 0 of
// the search. This should not be registered to a LNS search.
void RegisterVariableBoundsLevelZeroExport(
    const CpModelProto& model_proto, SharedBoundsManager* shared_bounds_manager,
    Model* model) {
  CHECK(shared_bounds_manager != nullptr);
  int saved_trail_index = 0;
  auto broadcast_level_zero_bounds =
      [&model_proto, saved_trail_index, model, shared_bounds_manager](
          const std::vector<IntegerVariable>& modified_vars) mutable {
        CpModelMapping* const mapping = model->GetOrCreate<CpModelMapping>();
 
        std::vector<int> model_variables;
        std::vector<int64_t> new_lower_bounds;
        std::vector<int64_t> new_upper_bounds;
        absl::flat_hash_set<int> visited_variables;
 
        // Inspect the modified IntegerVariables.
        auto* integer_trail = model->Get<IntegerTrail>();
        for (const IntegerVariable& var : modified_vars) {
          const IntegerVariable positive_var = PositiveVariable(var);
          const int model_var =
              mapping->GetProtoVariableFromIntegerVariable(positive_var);
          if (model_var == -1 || visited_variables.contains(model_var)) {
            // TODO(user): I don't think we should see the same model_var twice
            // here so maybe we don't need the visited_variables.contains()
            // part.
            continue;
          }
 
          visited_variables.insert(model_var);
          const int64_t new_lb =
              integer_trail->LevelZeroLowerBound(positive_var).value();
          const int64_t new_ub =
              integer_trail->LevelZeroUpperBound(positive_var).value();
          // TODO(user): We could imagine an API based on atomic<int64_t>
          // that could preemptively check if this new bounds are improving.
          model_variables.push_back(model_var);
          new_lower_bounds.push_back(new_lb);
          new_upper_bounds.push_back(new_ub);
        }
 
        // Inspect the newly modified Booleans.
        auto* trail = model->Get<Trail>();
        for (; saved_trail_index < trail->Index(); ++saved_trail_index) {
          const Literal fixed_literal = (*trail)[saved_trail_index];
          const int model_var = mapping->GetProtoVariableFromBooleanVariable(
              fixed_literal.Variable());
          if (model_var == -1 || visited_variables.contains(model_var)) {
            // If the variable is already visited, it should mean that this
            // Boolean also has an IntegerVariable view, and we should already
            // have set its bound correctly.
            continue;
          }
 
          visited_variables.insert(model_var);
          model_variables.push_back(model_var);
          if (fixed_literal.IsPositive()) {
            new_lower_bounds.push_back(1);
            new_upper_bounds.push_back(1);
          } else {
            new_lower_bounds.push_back(0);
            new_upper_bounds.push_back(0);
          }
        }
 
        if (!model_variables.empty()) {
          shared_bounds_manager->ReportPotentialNewBounds(
              model_proto, model->Name(), model_variables, new_lower_bounds,
              new_upper_bounds);
 
          // If we are not in interleave_search we synchronize right away.
          if (!model->Get<SatParameters>()->interleave_search()) {
            shared_bounds_manager->Synchronize();
          }
        }
      };
 
  // The callback will just be called on NEWLY modified var. So initially,
  // we do want to read all variables.
  //
  // TODO(user): Find a better way? It seems nicer to register this before
  // any variable is modified. But then we don't want to call it each time
  // we reach level zero during probing. It should be better to only call
  // it when a new variable has been fixed.
  const IntegerVariable num_vars =
      model->GetOrCreate<IntegerTrail>()->NumIntegerVariables();
  std::vector<IntegerVariable> all_variables;
  all_variables.reserve(num_vars.value());
  for (IntegerVariable var(0); var < num_vars; ++var) {
    all_variables.push_back(var);
  }
  broadcast_level_zero_bounds(all_variables);
 
  model->GetOrCreate<GenericLiteralWatcher>()
      ->RegisterLevelZeroModifiedVariablesCallback(broadcast_level_zero_bounds);
}
 
// Registers a callback to import new variables bounds stored in the
// shared_bounds_manager. These bounds are imported at level 0 of the search
// in the linear scan minimize function.
void RegisterVariableBoundsLevelZeroImport(
    const CpModelProto& model_proto, SharedBoundsManager* shared_bounds_manager,
    Model* model) {
  CHECK(shared_bounds_manager != nullptr);
  auto* integer_trail = model->GetOrCreate<IntegerTrail>();
  CpModelMapping* const mapping = model->GetOrCreate<CpModelMapping>();
  const int id = shared_bounds_manager->RegisterNewId();
 
  const auto& import_level_zero_bounds = [&model_proto, shared_bounds_manager,
                                          model, integer_trail, id, mapping]() {
    std::vector<int> model_variables;
    std::vector<int64_t> new_lower_bounds;
    std::vector<int64_t> new_upper_bounds;
    shared_bounds_manager->GetChangedBounds(
        id, &model_variables, &new_lower_bounds, &new_upper_bounds);
    bool new_bounds_have_been_imported = false;
    for (int i = 0; i < model_variables.size(); ++i) {
      const int model_var = model_variables[i];
      // This can happen if a boolean variables is forced to have an
      // integer view in one thread, and not in another thread.
      if (!mapping->IsInteger(model_var)) continue;
      const IntegerVariable var = mapping->Integer(model_var);
      const IntegerValue new_lb(new_lower_bounds[i]);
      const IntegerValue new_ub(new_upper_bounds[i]);
      const IntegerValue old_lb = integer_trail->LowerBound(var);
      const IntegerValue old_ub = integer_trail->UpperBound(var);
      const bool changed_lb = new_lb > old_lb;
      const bool changed_ub = new_ub < old_ub;
      if (!changed_lb && !changed_ub) continue;
 
      new_bounds_have_been_imported = true;
      if (VLOG_IS_ON(3)) {
        const IntegerVariableProto& var_proto =
            model_proto.variables(model_var);
        const std::string& var_name =
            var_proto.name().empty()
                ? absl::StrCat("anonymous_var(", model_var, ")")
                : var_proto.name();
        LOG(INFO) << "  '" << model->Name() << "' imports new bounds for "
                  << var_name << ": from [" << old_lb << ", " << old_ub
                  << "] to [" << new_lb << ", " << new_ub << "]";
      }
 
      if (changed_lb &&
          !integer_trail->Enqueue(IntegerLiteral::GreaterOrEqual(var, new_lb),
                                  {}, {})) {
        return false;
      }
      if (changed_ub &&
          !integer_trail->Enqueue(IntegerLiteral::LowerOrEqual(var, new_ub), {},
                                  {})) {
        return false;
      }
    }
    if (new_bounds_have_been_imported &&
        !model->GetOrCreate<SatSolver>()->FinishPropagation()) {
      return false;
    }
    return true;
  };
  model->GetOrCreate<LevelZeroCallbackHelper>()->callbacks.push_back(
      import_level_zero_bounds);
}
 
// Registers a callback that will report improving objective best bound.
// It will be called each time new objective bound are propagated at level zero.
void RegisterObjectiveBestBoundExport(
    IntegerVariable objective_var,
    SharedResponseManager* shared_response_manager, Model* model) {
  auto* integer_trail = model->Get<IntegerTrail>();
  const auto broadcast_objective_lower_bound =
      [objective_var, integer_trail, shared_response_manager,
       model](const std::vector<IntegerVariable>& unused) {
        shared_response_manager->UpdateInnerObjectiveBounds(
            model->Name(), integer_trail->LevelZeroLowerBound(objective_var),
            integer_trail->LevelZeroUpperBound(objective_var));
        // If we are not in interleave_search we synchronize right away.
        if (!model->Get<SatParameters>()->interleave_search()) {
          shared_response_manager->Synchronize();
        }
      };
  model->GetOrCreate<GenericLiteralWatcher>()
      ->RegisterLevelZeroModifiedVariablesCallback(
          broadcast_objective_lower_bound);
}
 
// Registers a callback to import new objective bounds. It will be called each
// time the search main loop is back to level zero. Note that it the presence of
// assumptions, this will not happen until the set of assumptions is changed.
void RegisterObjectiveBoundsImport(
    SharedResponseManager* shared_response_manager, Model* model) {
  auto* solver = model->GetOrCreate<SatSolver>();
  auto* integer_trail = model->GetOrCreate<IntegerTrail>();
  auto* objective = model->GetOrCreate<ObjectiveDefinition>();
  const std::string name = model->Name();
  const auto import_objective_bounds = [name, solver, integer_trail, objective,
                                        shared_response_manager]() {
    if (solver->AssumptionLevel() != 0) return true;
    bool propagate = false;
 
    const IntegerValue external_lb =
        shared_response_manager->SynchronizedInnerObjectiveLowerBound();
    const IntegerValue current_lb =
        integer_trail->LowerBound(objective->objective_var);
    if (external_lb > current_lb) {
      if (!integer_trail->Enqueue(IntegerLiteral::GreaterOrEqual(
                                      objective->objective_var, external_lb),
                                  {}, {})) {
        return false;
      }
      propagate = true;
    }
 
    const IntegerValue external_ub =
        shared_response_manager->SynchronizedInnerObjectiveUpperBound();
    const IntegerValue current_ub =
        integer_trail->UpperBound(objective->objective_var);
    if (external_ub < current_ub) {
      if (!integer_trail->Enqueue(IntegerLiteral::LowerOrEqual(
                                      objective->objective_var, external_ub),
                                  {}, {})) {
        return false;
      }
      propagate = true;
    }
 
    if (!propagate) return true;
 
    VLOG(2) << "'" << name << "' imports objective bounds: external ["
            << objective->ScaleIntegerObjective(external_lb) << ", "
            << objective->ScaleIntegerObjective(external_ub) << "], current ["
            << objective->ScaleIntegerObjective(current_lb) << ", "
            << objective->ScaleIntegerObjective(current_ub) << "]";
 
    return solver->FinishPropagation();
  };
 
  model->GetOrCreate<LevelZeroCallbackHelper>()->callbacks.push_back(
      import_objective_bounds);
}
 
void LoadBaseModel(const CpModelProto& model_proto, Model* model) {
  auto* shared_response_manager = model->GetOrCreate<SharedResponseManager>();
  CHECK(shared_response_manager != nullptr);
  auto* sat_solver = model->GetOrCreate<SatSolver>();
 
  // Simple function for the few places where we do "return unsat()".
  const auto unsat = [shared_response_manager, sat_solver, model] {
    sat_solver->NotifyThatModelIsUnsat();
    shared_response_manager->NotifyThatImprovingProblemIsInfeasible(
        absl::StrCat(model->Name(), " [loading]"));
  };
 
  // We will add them all at once after model_proto is loaded.
  model->GetOrCreate<IntegerEncoder>()->DisableImplicationBetweenLiteral();
 
  auto* mapping = model->GetOrCreate<CpModelMapping>();
  const SatParameters& parameters = *(model->GetOrCreate<SatParameters>());
  const bool view_all_booleans_as_integers =
      (parameters.linearization_level() >= 2) ||
      (parameters.search_branching() == SatParameters::FIXED_SEARCH &&
       model_proto.search_strategy().empty());
  LoadVariables(model_proto, view_all_booleans_as_integers, model);
  DetectOptionalVariables(model_proto, model);
 
  // TODO(user): The core algo and symmetries seems to be problematic in some
  // cases. See for instance: neos-691058.mps.gz. This is probably because as
  // we modify the model, our symmetry might be wrong? investigate.
  if (!parameters.optimize_with_core() && parameters.symmetry_level() > 1 &&
      !parameters.enumerate_all_solutions()) {
    LoadBooleanSymmetries(model_proto, model);
  }
 
  ExtractEncoding(model_proto, model);
  PropagateEncodingFromEquivalenceRelations(model_proto, model);
 
  // Check the model is still feasible before continuing.
  if (sat_solver->IsModelUnsat()) return unsat();
 
  // Fully encode variables as needed by the search strategy.
  AddFullEncodingFromSearchBranching(model_proto, model);
 
  // Force some variables to be fully encoded.
  MaybeFullyEncodeMoreVariables(model_proto, model);
 
  // Load the constraints.
  std::set<std::string> unsupported_types;
  int num_ignored_constraints = 0;
  for (const ConstraintProto& ct : model_proto.constraints()) {
    if (mapping->ConstraintIsAlreadyLoaded(&ct)) {
      ++num_ignored_constraints;
      continue;
    }
 
    if (!LoadConstraint(ct, model)) {
      unsupported_types.insert(ConstraintCaseName(ct.constraint_case()));
      continue;
    }
 
    // We propagate after each new Boolean constraint but not the integer
    // ones. So we call FinishPropagation() manually here.
    //
    // Note that we only do that in debug mode as this can be really slow on
    // certain types of problems with millions of constraints.
    if (DEBUG_MODE) {
      if (sat_solver->FinishPropagation()) {
        Trail* trail = model->GetOrCreate<Trail>();
        const int old_num_fixed = trail->Index();
        if (trail->Index() > old_num_fixed) {
          VLOG(3) << "Constraint fixed " << trail->Index() - old_num_fixed
                  << " Boolean variable(s): " << ProtobufDebugString(ct);
        }
      }
    }
    if (sat_solver->IsModelUnsat()) {
      VLOG(2) << "UNSAT during extraction (after adding '"
              << ConstraintCaseName(ct.constraint_case()) << "'). "
              << ProtobufDebugString(ct);
      break;
    }
  }
  if (num_ignored_constraints > 0) {
    VLOG(3) << num_ignored_constraints << " constraints were skipped.";
  }
  if (!unsupported_types.empty()) {
    VLOG(1) << "There is unsupported constraints types in this model: ";
    for (const std::string& type : unsupported_types) {
      VLOG(1) << " - " << type;
    }
    return unsat();
  }
 
  model->GetOrCreate<IntegerEncoder>()
      ->AddAllImplicationsBetweenAssociatedLiterals();
  if (!sat_solver->FinishPropagation()) return unsat();
}
 
void LoadFeasibilityPump(const CpModelProto& model_proto, Model* model) {
  LoadBaseModel(model_proto, model);
 
  auto* mapping = model->GetOrCreate<CpModelMapping>();
  const SatParameters& parameters = *(model->GetOrCreate<SatParameters>());
  if (parameters.linearization_level() == 0) return;
 
  // Add linear constraints to Feasibility Pump.
  LinearRelaxation relaxation;
  ComputeLinearRelaxation(model_proto, parameters.linearization_level(), model,
                          &relaxation);
  const int num_lp_constraints = relaxation.linear_constraints.size();
  if (num_lp_constraints == 0) return;
  auto* feasibility_pump = model->GetOrCreate<FeasibilityPump>();
  for (int i = 0; i < num_lp_constraints; i++) {
    feasibility_pump->AddLinearConstraint(relaxation.linear_constraints[i]);
  }
 
  if (model_proto.has_objective()) {
    for (int i = 0; i < model_proto.objective().coeffs_size(); ++i) {
      const IntegerVariable var =
          mapping->Integer(model_proto.objective().vars(i));
      const int64_t coeff = model_proto.objective().coeffs(i);
      feasibility_pump->SetObjectiveCoefficient(var, IntegerValue(coeff));
    }
  }
}
 
// Loads a CpModelProto inside the given model.
// This should only be called once on a given 'Model' class.
//
// TODO(user): move to cp_model_loader.h/.cc
void LoadCpModel(const CpModelProto& model_proto, Model* model) {
  auto* shared_response_manager = model->GetOrCreate<SharedResponseManager>();
 
  LoadBaseModel(model_proto, model);
 
  // Simple function for the few places where we do "return unsat()".
  auto* sat_solver = model->GetOrCreate<SatSolver>();
  const auto unsat = [shared_response_manager, sat_solver, model] {
    sat_solver->NotifyThatModelIsUnsat();
    shared_response_manager->NotifyThatImprovingProblemIsInfeasible(
        absl::StrCat(model->Name(), " [loading]"));
  };
 
  auto* mapping = model->GetOrCreate<CpModelMapping>();
  const SatParameters& parameters = *(model->GetOrCreate<SatParameters>());
 
  // Auto detect "at least one of" constraints in the PrecedencesPropagator.
  // Note that we do that before we finish loading the problem (objective and
  // LP relaxation), because propagation will be faster at this point and it
  // should be enough for the purpose of this auto-detection.
  if (model->Mutable<PrecedencesPropagator>() != nullptr &&
      parameters.auto_detect_greater_than_at_least_one_of()) {
    model->Mutable<PrecedencesPropagator>()
        ->AddGreaterThanAtLeastOneOfConstraints(model);
    if (!sat_solver->FinishPropagation()) return unsat();
  }
 
  // TODO(user): This should be done in the presolve instead.
  // TODO(user): We don't have a good deterministic time on all constraints,
  // so this might take more time than wanted.
  if (parameters.cp_model_probing_level() > 1) {
    Prober* prober = model->GetOrCreate<Prober>();
    prober->ProbeBooleanVariables(/*deterministic_time_limit=*/1.0);
    if (model->GetOrCreate<SatSolver>()->IsModelUnsat()) {
      return unsat();
    }
    if (!model->GetOrCreate<BinaryImplicationGraph>()
             ->ComputeTransitiveReduction()) {
      return unsat();
    }
  }
 
  // Create an objective variable and its associated linear constraint if
  // needed.
  IntegerVariable objective_var = kNoIntegerVariable;
  if (parameters.linearization_level() > 0) {
    // Linearize some part of the problem and register LP constraint(s).
    objective_var =
        AddLPConstraints(model_proto, parameters.linearization_level(), model);
  } else if (model_proto.has_objective()) {
    const CpObjectiveProto& obj = model_proto.objective();
    std::vector<std::pair<IntegerVariable, int64_t>> terms;
    terms.reserve(obj.vars_size());
    for (int i = 0; i < obj.vars_size(); ++i) {
      terms.push_back(
          std::make_pair(mapping->Integer(obj.vars(i)), obj.coeffs(i)));
    }
    if (parameters.optimize_with_core()) {
      objective_var = GetOrCreateVariableWithTightBound(terms, model);
    } else {
      objective_var = GetOrCreateVariableGreaterOrEqualToSumOf(terms, model);
    }
  }
 
  // Create the objective definition inside the Model so that it can be accessed
  // by the heuristics than needs it.
  if (objective_var != kNoIntegerVariable) {
    const CpObjectiveProto& objective_proto = model_proto.objective();
    auto* objective_definition = model->GetOrCreate<ObjectiveDefinition>();
 
    objective_definition->scaling_factor = objective_proto.scaling_factor();
    if (objective_definition->scaling_factor == 0.0) {
      objective_definition->scaling_factor = 1.0;
    }
    objective_definition->offset = objective_proto.offset();
    objective_definition->objective_var = objective_var;
 
    const int size = objective_proto.vars_size();
    objective_definition->vars.resize(size);
    objective_definition->coeffs.resize(size);
    for (int i = 0; i < objective_proto.vars_size(); ++i) {
      // Note that if there is no mapping, then the variable will be
      // kNoIntegerVariable.
      objective_definition->vars[i] = mapping->Integer(objective_proto.vars(i));
      objective_definition->coeffs[i] = IntegerValue(objective_proto.coeffs(i));
 
      // Fill the objective heuristics data.
      const int ref = objective_proto.vars(i);
      if (mapping->IsInteger(ref)) {
        const IntegerVariable var = mapping->Integer(objective_proto.vars(i));
        objective_definition->objective_impacting_variables.insert(
            objective_proto.coeffs(i) > 0 ? var : NegationOf(var));
      }
    }
 
    // Register an objective special propagator.
    model->TakeOwnership(
        new LevelZeroEquality(objective_var, objective_definition->vars,
                              objective_definition->coeffs, model));
  }
 
  // Intersect the objective domain with the given one if any.
  if (!model_proto.objective().domain().empty()) {
    const Domain user_domain = ReadDomainFromProto(model_proto.objective());
    const Domain automatic_domain =
        model->GetOrCreate<IntegerTrail>()->InitialVariableDomain(
            objective_var);
    VLOG(3) << "Objective offset:" << model_proto.objective().offset()
            << " scaling_factor:" << model_proto.objective().scaling_factor();
    VLOG(3) << "Automatic internal objective domain: " << automatic_domain;
    VLOG(3) << "User specified internal objective domain: " << user_domain;
    CHECK_NE(objective_var, kNoIntegerVariable);
    const bool ok = model->GetOrCreate<IntegerTrail>()->UpdateInitialDomain(
        objective_var, user_domain);
    if (!ok) {
      VLOG(2) << "UNSAT due to the objective domain.";
      return unsat();
    }
 
    // Make sure the sum take a value inside the objective domain by adding
    // the other side: objective <= sum terms.
    //
    // TODO(user): Use a better condition to detect when this is not useful.
    // Note also that for the core algorithm, we might need the other side too,
    // otherwise we could return feasible solution with an objective above the
    // user specified upper bound.
    if (!automatic_domain.IsIncludedIn(user_domain)) {
      std::vector<IntegerVariable> vars;
      std::vector<int64_t> coeffs;
      const CpObjectiveProto& obj = model_proto.objective();
      for (int i = 0; i < obj.vars_size(); ++i) {
        vars.push_back(mapping->Integer(obj.vars(i)));
        coeffs.push_back(obj.coeffs(i));
      }
      vars.push_back(objective_var);
      coeffs.push_back(-1);
      model->Add(WeightedSumGreaterOrEqual(vars, coeffs, 0));
    }
  }
 
  // Note that we do one last propagation at level zero once all the
  // constraints were added.
  SOLVER_LOG(model->GetOrCreate<SolverLogger>(),
             "Initial num_bool: ", sat_solver->NumVariables());
  if (!sat_solver->FinishPropagation()) return unsat();
 
  if (model_proto.has_objective()) {
    // Report the initial objective variable bounds.
    auto* integer_trail = model->GetOrCreate<IntegerTrail>();
    shared_response_manager->UpdateInnerObjectiveBounds(
        absl::StrCat(model->Name(), " initial_propagation"),
        integer_trail->LowerBound(objective_var),
        integer_trail->UpperBound(objective_var));
 
    // Watch improved objective best bounds.
    RegisterObjectiveBestBoundExport(objective_var, shared_response_manager,
                                     model);
 
    // Import objective bounds.
    // TODO(user): Support objective bounds import in LNS and Core based
    // search.
    if (model->GetOrCreate<SatParameters>()->share_objective_bounds()) {
      RegisterObjectiveBoundsImport(shared_response_manager, model);
    }
  }
 
  // Cache the links between model vars, IntegerVariables and lp constraints.
  // TODO(user): Cache this only if it is actually used.
  auto* integer_trail = model->GetOrCreate<IntegerTrail>();
  auto* lp_dispatcher = model->GetOrCreate<LinearProgrammingDispatcher>();
  auto* lp_vars = model->GetOrCreate<LPVariables>();
  IntegerVariable size = integer_trail->NumIntegerVariables();
  for (IntegerVariable positive_var(0); positive_var < size;
       positive_var += 2) {
    LPVariable lp_var;
    lp_var.positive_var = positive_var;
    lp_var.model_var =
        mapping->GetProtoVariableFromIntegerVariable(positive_var);
    lp_var.lp = gtl::FindWithDefault(*lp_dispatcher, positive_var, nullptr);
 
    if (lp_var.model_var >= 0) {
      lp_vars->vars.push_back(lp_var);
      lp_vars->model_vars_size =
          std::max(lp_vars->model_vars_size, lp_var.model_var + 1);
    }
  }
 
  // Initialize the fixed_search strategy.
  auto* search_heuristics = model->GetOrCreate<SearchHeuristics>();
  search_heuristics->fixed_search = ConstructSearchStrategy(
      model_proto, mapping->GetVariableMapping(), objective_var, model);
  if (VLOG_IS_ON(3)) {
    search_heuristics->fixed_search =
        InstrumentSearchStrategy(model_proto, mapping->GetVariableMapping(),
                                 search_heuristics->fixed_search, model);
  }
 
  // Initialize the "follow hint" strategy.
  std::vector<BooleanOrIntegerVariable> vars;
  std::vector<IntegerValue> values;
  for (int i = 0; i < model_proto.solution_hint().vars_size(); ++i) {
    const int ref = model_proto.solution_hint().vars(i);
    CHECK(RefIsPositive(ref));
    BooleanOrIntegerVariable var;
    if (mapping->IsBoolean(ref)) {
      var.bool_var = mapping->Literal(ref).Variable();
    } else {
      var.int_var = mapping->Integer(ref);
    }
    vars.push_back(var);
    values.push_back(IntegerValue(model_proto.solution_hint().values(i)));
  }
  search_heuristics->hint_search = FollowHint(vars, values, model);
 
  // Create the CoreBasedOptimizer class if needed.
  if (parameters.optimize_with_core()) {
    // TODO(user): Remove code duplication with the solution_observer in
    // SolveLoadedCpModel().
    const std::string solution_info = model->Name();
    const auto solution_observer = [&model_proto, model, solution_info,
                                    shared_response_manager]() {
      CpSolverResponse response;
      FillSolutionInResponse(model_proto, *model, &response);
      response.set_solution_info(solution_info);
      shared_response_manager->NewSolution(response, model);
    };
 
    const auto& objective = *model->GetOrCreate<ObjectiveDefinition>();
    CoreBasedOptimizer* core =
        new CoreBasedOptimizer(objective_var, objective.vars, objective.coeffs,
                               solution_observer, model);
    model->Register<CoreBasedOptimizer>(core);
    model->TakeOwnership(core);
  }
}
 
// Solves an already loaded cp_model_proto.
// The final CpSolverResponse must be read from the shared_response_manager.
//
// TODO(user): This should be transformed so that it can be called many times
// and resume from the last search state as if it wasn't interuped. That would
// allow use to easily interleave different heuristics in the same thread.
void SolveLoadedCpModel(const CpModelProto& model_proto, Model* model) {
  auto* shared_response_manager = model->GetOrCreate<SharedResponseManager>();
  if (shared_response_manager->ProblemIsSolved()) return;
 
  const std::string& solution_info = model->Name();
  const auto solution_observer = [&model_proto, &model, &solution_info,
                                  &shared_response_manager]() {
    CpSolverResponse response;
    FillSolutionInResponse(model_proto, *model, &response);
    response.set_solution_info(solution_info);
    shared_response_manager->NewSolution(response, model);
  };
 
  // Reconfigure search heuristic if it was changed.
  ConfigureSearchHeuristics(model);
 
  const auto& mapping = *model->GetOrCreate<CpModelMapping>();
  SatSolver::Status status;
  const SatParameters& parameters = *model->GetOrCreate<SatParameters>();
  if (parameters.use_probing_search()) {
    std::vector<BooleanVariable> bool_vars;
    std::vector<IntegerVariable> int_vars;
    IntegerTrail* integer_trail = model->GetOrCreate<IntegerTrail>();
    absl::flat_hash_set<BooleanVariable> visited;
    for (int v = 0; v < model_proto.variables_size(); ++v) {
      if (mapping.IsBoolean(v)) {
        const BooleanVariable bool_var = mapping.Literal(v).Variable();
        if (!visited.contains(bool_var)) {
          visited.insert(bool_var);
          bool_vars.push_back(bool_var);
        }
      } else {
        IntegerVariable var = mapping.Integer(v);
        if (integer_trail->IsFixed(var)) continue;
        int_vars.push_back(var);
      }
    }
    status = ContinuousProbing(bool_vars, int_vars, solution_observer, model);
  } else if (!model_proto.has_objective()) {
    while (true) {
      status = ResetAndSolveIntegerProblem(
          mapping.Literals(model_proto.assumptions()), model);
      if (status != SatSolver::Status::FEASIBLE) break;
      solution_observer();
      if (!parameters.enumerate_all_solutions()) break;
      model->Add(ExcludeCurrentSolutionWithoutIgnoredVariableAndBacktrack());
    }
    if (status == SatSolver::INFEASIBLE) {
      shared_response_manager->NotifyThatImprovingProblemIsInfeasible(
          solution_info);
    }
    if (status == SatSolver::ASSUMPTIONS_UNSAT) {
      shared_response_manager->NotifyThatImprovingProblemIsInfeasible(
          solution_info);
 
      // Extract a good subset of assumptions and add it to the response.
      auto* time_limit = model->GetOrCreate<TimeLimit>();
      auto* sat_solver = model->GetOrCreate<SatSolver>();
      std::vector<Literal> core = sat_solver->GetLastIncompatibleDecisions();
      MinimizeCoreWithPropagation(time_limit, sat_solver, &core);
      std::vector<int> core_in_proto_format;
      for (const Literal l : core) {
        core_in_proto_format.push_back(
            mapping.GetProtoVariableFromBooleanVariable(l.Variable()));
        if (!l.IsPositive()) {
          core_in_proto_format.back() = NegatedRef(core_in_proto_format.back());
        }
      }
      shared_response_manager->AddUnsatCore(core_in_proto_format);
    }
  } else {
    // Optimization problem.
    const auto& objective = *model->GetOrCreate<ObjectiveDefinition>();
    const IntegerVariable objective_var = objective.objective_var;
    CHECK_NE(objective_var, kNoIntegerVariable);
 
    if (parameters.optimize_with_lb_tree_search()) {
      auto* search = model->GetOrCreate<LbTreeSearch>();
      status = search->Search(solution_observer);
    } else if (parameters.optimize_with_core()) {
      // TODO(user): This doesn't work with splitting in chunk for now. It
      // shouldn't be too hard to fix.
      if (parameters.optimize_with_max_hs()) {
        status = MinimizeWithHittingSetAndLazyEncoding(
            objective, solution_observer, model);
      } else {
        status = model->Mutable<CoreBasedOptimizer>()->Optimize();
      }
    } else {
      // TODO(user): This parameter break the splitting in chunk of a Solve().
      // It should probably be moved into another SubSolver altogether.
      if (parameters.binary_search_num_conflicts() >= 0) {
        RestrictObjectiveDomainWithBinarySearch(objective_var,
                                                solution_observer, model);
      }
      status = MinimizeIntegerVariableWithLinearScanAndLazyEncoding(
          objective_var, solution_observer, model);
    }
 
    // The search is done in both case.
    //
    // TODO(user): Remove the weird translation INFEASIBLE->FEASIBLE in the
    // function above?
    if (status == SatSolver::INFEASIBLE || status == SatSolver::FEASIBLE) {
      shared_response_manager->NotifyThatImprovingProblemIsInfeasible(
          solution_info);
    }
  }
 
  // TODO(user): Remove from here when we split in chunk. We just want to
  // do that at the end.
  shared_response_manager->SetStatsFromModel(model);
}
 
// Try to find a solution by following the hint and using a low conflict limit.
// The CpModelProto must already be loaded in the Model.
void QuickSolveWithHint(const CpModelProto& model_proto, Model* model) {
  if (!model_proto.has_solution_hint()) return;
 
  auto* shared_response_manager = model->GetOrCreate<SharedResponseManager>();
  if (shared_response_manager->ProblemIsSolved()) return;
 
  // Temporarily change the parameters.
  auto* parameters = model->GetOrCreate<SatParameters>();
  const SatParameters saved_params = *parameters;
  parameters->set_max_number_of_conflicts(parameters->hint_conflict_limit());
  parameters->set_search_branching(SatParameters::HINT_SEARCH);
  parameters->set_optimize_with_core(false);
  auto cleanup = ::absl::MakeCleanup(
      [parameters, saved_params]() { *parameters = saved_params; });
 
  // Solve decision problem.
  ConfigureSearchHeuristics(model);
  const auto& mapping = *model->GetOrCreate<CpModelMapping>();
  const SatSolver::Status status = ResetAndSolveIntegerProblem(
      mapping.Literals(model_proto.assumptions()), model);
 
  const std::string& solution_info = model->Name();
  if (status == SatSolver::Status::FEASIBLE) {
    CpSolverResponse response;
    FillSolutionInResponse(model_proto, *model, &response);
    response.set_solution_info(absl::StrCat(solution_info, " [hint]"));
    shared_response_manager->NewSolution(response, model);
 
    if (!model_proto.has_objective()) {
      if (parameters->enumerate_all_solutions()) {
        model->Add(ExcludeCurrentSolutionWithoutIgnoredVariableAndBacktrack());
      }
    } else {
      // Restrict the objective.
      const IntegerVariable objective_var =
          model->GetOrCreate<ObjectiveDefinition>()->objective_var;
      model->GetOrCreate<SatSolver>()->Backtrack(0);
      IntegerTrail* integer_trail = model->GetOrCreate<IntegerTrail>();
      if (!integer_trail->Enqueue(
              IntegerLiteral::LowerOrEqual(
                  objective_var,
                  shared_response_manager->GetInnerObjectiveUpperBound()),
              {}, {})) {
        shared_response_manager->NotifyThatImprovingProblemIsInfeasible(
            absl::StrCat(solution_info, " [hint]"));
        shared_response_manager->SetStatsFromModel(model);
        return;
      }
    }
  }
}
 
// Solve a model with a different objective consisting of minimizing the L1
// distance with the provided hint. Note that this method creates an in-memory
// copy of the model and loads a local Model object from the copied model.
void MinimizeL1DistanceWithHint(const CpModelProto& model_proto, Model* model) {
  Model local_model;
 
  // Forward some shared class.
  local_model.Register<ModelSharedTimeLimit>(
      model->GetOrCreate<ModelSharedTimeLimit>());
  local_model.Register<WallTimer>(model->GetOrCreate<WallTimer>());
 
  if (!model_proto.has_solution_hint()) return;
 
  auto* shared_response_manager = model->GetOrCreate<SharedResponseManager>();
  if (shared_response_manager->ProblemIsSolved()) return;
 
  auto* parameters = local_model.GetOrCreate<SatParameters>();
  // TODO(user): As of now the repair hint doesn't support when
  // enumerate_all_solutions is set since the solution is created on a different
  // model.
  if (parameters->enumerate_all_solutions()) return;
 
  // Change the parameters.
  const SatParameters saved_params = *model->GetOrCreate<SatParameters>();
  *parameters = saved_params;
  parameters->set_max_number_of_conflicts(parameters->hint_conflict_limit());
  parameters->set_optimize_with_core(false);
 
  // Update the model to introduce penalties to go away from hinted values.
  CpModelProto updated_model_proto = model_proto;
  updated_model_proto.clear_objective();
 
  // TODO(user): For boolean variables we can avoid creating new variables.
  for (int i = 0; i < model_proto.solution_hint().vars_size(); ++i) {
    const int var = model_proto.solution_hint().vars(i);
    const int64_t value = model_proto.solution_hint().values(i);
 
    // Add a new var to represent the difference between var and value.
    const int new_var_index = updated_model_proto.variables_size();
    IntegerVariableProto* var_proto = updated_model_proto.add_variables();
    const int64_t min_domain = model_proto.variables(var).domain(0) - value;
    const int64_t max_domain =
        model_proto.variables(var).domain(
            model_proto.variables(var).domain_size() - 1) -
        value;
    var_proto->add_domain(min_domain);
    var_proto->add_domain(max_domain);
 
    // new_var = var - value.
    ConstraintProto* const linear_constraint_proto =
        updated_model_proto.add_constraints();
    LinearConstraintProto* linear = linear_constraint_proto->mutable_linear();
    linear->add_vars(new_var_index);
    linear->add_coeffs(1);
    linear->add_vars(var);
    linear->add_coeffs(-1);
    linear->add_domain(-value);
    linear->add_domain(-value);
 
    // abs_var = abs(new_var).
    const int abs_var_index = updated_model_proto.variables_size();
    IntegerVariableProto* abs_var_proto = updated_model_proto.add_variables();
    const int64_t abs_min_domain = 0;
    const int64_t abs_max_domain =
        std::max(std::abs(min_domain), std::abs(max_domain));
    abs_var_proto->add_domain(abs_min_domain);
    abs_var_proto->add_domain(abs_max_domain);
    ConstraintProto* const abs_constraint_proto =
        updated_model_proto.add_constraints();
    abs_constraint_proto->mutable_int_max()->set_target(abs_var_index);
    abs_constraint_proto->mutable_int_max()->add_vars(new_var_index);
    abs_constraint_proto->mutable_int_max()->add_vars(
        NegatedRef(new_var_index));
 
    updated_model_proto.mutable_objective()->add_vars(abs_var_index);
    updated_model_proto.mutable_objective()->add_coeffs(1);
  }
 
  auto* local_response_manager =
      local_model.GetOrCreate<SharedResponseManager>();
  local_response_manager->InitializeObjective(updated_model_proto);
 
  // Solve optimization problem.
  LoadCpModel(updated_model_proto, &local_model);
 
  ConfigureSearchHeuristics(&local_model);
  const auto& mapping = *local_model.GetOrCreate<CpModelMapping>();
  const SatSolver::Status status = ResetAndSolveIntegerProblem(
      mapping.Literals(updated_model_proto.assumptions()), &local_model);
 
  const std::string& solution_info = model->Name();
  if (status == SatSolver::Status::FEASIBLE) {
    CpSolverResponse response;
    FillSolutionInResponse(model_proto, local_model, &response);
    if (DEBUG_MODE) {
      CpSolverResponse updated_response;
      FillSolutionInResponse(updated_model_proto, local_model,
                             &updated_response);
      LOG(INFO) << "Found solution with repaired hint penalty = "
                << ComputeInnerObjective(updated_model_proto.objective(),
                                         updated_response);
    }
    response.set_solution_info(absl::StrCat(solution_info, " [repaired]"));
    shared_response_manager->NewSolution(response, &local_model);
  }
}
 
// TODO(user): If this ever shows up in the profile, we could avoid copying
// the mapping_proto if we are careful about how we modify the variable domain
// before postsolving it. Note that 'num_variables_in_original_model' refers to
// the model before presolve.
void PostsolveResponseWithFullSolver(
    const int64_t num_variables_in_original_model, CpModelProto mapping_proto,
    const std::vector<int>& postsolve_mapping, WallTimer* wall_timer,
    CpSolverResponse* response) {
  if (response->status() != CpSolverStatus::FEASIBLE &&
      response->status() != CpSolverStatus::OPTIMAL) {
    return;
  }
 
  // If presolve was not called, the mapping model is empty.
  if (mapping_proto.variables_size() == 0) {
    return;
  }
 
  // Postsolve.
  for (int i = 0; i < response->solution_size(); ++i) {
    auto* var_proto = mapping_proto.mutable_variables(postsolve_mapping[i]);
    var_proto->clear_domain();
    var_proto->add_domain(response->solution(i));
    var_proto->add_domain(response->solution(i));
  }
  for (int i = 0; i < response->solution_lower_bounds_size(); ++i) {
    auto* var_proto = mapping_proto.mutable_variables(postsolve_mapping[i]);
    FillDomainInProto(
        ReadDomainFromProto(*var_proto)
            .IntersectionWith({response->solution_lower_bounds(i),
                               response->solution_upper_bounds(i)}),
        var_proto);
  }
 
  // Postosolve parameters.
  // TODO(user): this problem is usually trivial, but we may still want to
  // impose a time limit or copy some of the parameters passed by the user.
  Model postsolve_model;
  postsolve_model.Register<WallTimer>(wall_timer);
  {
    SatParameters& params = *postsolve_model.GetOrCreate<SatParameters>();
    params.set_linearization_level(0);
    params.set_cp_model_probing_level(0);
  }
 
  LoadCpModel(mapping_proto, &postsolve_model);
  SolveLoadedCpModel(mapping_proto, &postsolve_model);
  const CpSolverResponse postsolve_response =
      postsolve_model.GetOrCreate<SharedResponseManager>()->GetResponse();
  CHECK(postsolve_response.status() == CpSolverStatus::FEASIBLE ||
        postsolve_response.status() == CpSolverStatus::OPTIMAL)
      << response->solution_info();
 
  // We only copy the solution from the postsolve_response to the response.
  response->clear_solution();
  response->clear_solution_lower_bounds();
  response->clear_solution_upper_bounds();
  if (!postsolve_response.solution().empty()) {
    for (int i = 0; i < num_variables_in_original_model; ++i) {
      response->add_solution(postsolve_response.solution(i));
    }
  } else {
    for (int i = 0; i < num_variables_in_original_model; ++i) {
      response->add_solution_lower_bounds(
          postsolve_response.solution_lower_bounds(i));
      response->add_solution_upper_bounds(
          postsolve_response.solution_upper_bounds(i));
    }
  }
}
 
void PostsolveResponseWrapper(const SatParameters& params,
                              const int64_t num_variables_in_original_model,
                              const CpModelProto& mapping_proto,
                              const std::vector<int>& postsolve_mapping,
                              WallTimer* wall_timer,
                              CpSolverResponse* response) {
  if (params.cp_model_postsolve_with_full_solver()) {
    PostsolveResponseWithFullSolver(num_variables_in_original_model,
                                    mapping_proto, postsolve_mapping,
                                    wall_timer, response);
  } else {
    PostsolveResponse(num_variables_in_original_model, mapping_proto,
                      postsolve_mapping, response);
  }
}
 
// TODO(user): Uniformize this function with the other one.
CpSolverResponse SolvePureSatModel(const CpModelProto& model_proto,
                                   WallTimer* wall_timer, Model* model,
                                   SolverLogger* logger) {
  std::unique_ptr<SatSolver> solver(new SatSolver());
  SatParameters parameters = *model->GetOrCreate<SatParameters>();
  solver->SetParameters(parameters);
  model->GetOrCreate<TimeLimit>()->ResetLimitFromParameters(parameters);
 
  // Create a DratProofHandler?
  std::unique_ptr<DratProofHandler> drat_proof_handler;
#if !defined(__PORTABLE_PLATFORM__)
  if (!absl::GetFlag(FLAGS_drat_output).empty() ||
      absl::GetFlag(FLAGS_drat_check)) {
    if (!absl::GetFlag(FLAGS_drat_output).empty()) {
      File* output;
      CHECK_OK(file::Open(absl::GetFlag(FLAGS_drat_output), "w", &output,
                          file::Defaults()));
      drat_proof_handler = absl::make_unique<DratProofHandler>(
          /*in_binary_format=*/false, output, absl::GetFlag(FLAGS_drat_check));
    } else {
      drat_proof_handler = absl::make_unique<DratProofHandler>();
    }
    solver->SetDratProofHandler(drat_proof_handler.get());
  }
#endif  // __PORTABLE_PLATFORM__
 
  auto get_literal = [](int ref) {
    if (ref >= 0) return Literal(BooleanVariable(ref), true);
    return Literal(BooleanVariable(NegatedRef(ref)), false);
  };
 
  std::vector<Literal> temp;
  const int num_variables = model_proto.variables_size();
  solver->SetNumVariables(num_variables);
  if (drat_proof_handler != nullptr) {
    drat_proof_handler->SetNumVariables(num_variables);
 
    // We load the model in the drat_proof_handler for the case where we want
    // to do in-memory checking.
    for (int ref = 0; ref < num_variables; ++ref) {
      const Domain domain = ReadDomainFromProto(model_proto.variables(ref));
      if (domain.IsFixed()) {
        const Literal ref_literal =
            domain.Min() == 0 ? get_literal(ref).Negated() : get_literal(ref);
        drat_proof_handler->AddProblemClause({ref_literal});
      }
    }
    for (const ConstraintProto& ct : model_proto.constraints()) {
      switch (ct.constraint_case()) {
        case ConstraintProto::ConstraintCase::kBoolAnd: {
          if (ct.enforcement_literal_size() == 0) {
            for (const int ref : ct.bool_and().literals()) {
              drat_proof_handler->AddProblemClause({get_literal(ref)});
            }
          } else {
            // a => b
            const Literal not_a =
                get_literal(ct.enforcement_literal(0)).Negated();
            for (const int ref : ct.bool_and().literals()) {
              drat_proof_handler->AddProblemClause({not_a, get_literal(ref)});
            }
          }
          break;
        }
        case ConstraintProto::ConstraintCase::kBoolOr:
          temp.clear();
          for (const int ref : ct.bool_or().literals()) {
            temp.push_back(get_literal(ref));
          }
          for (const int ref : ct.enforcement_literal()) {
            temp.push_back(get_literal(ref).Negated());
          }
          drat_proof_handler->AddProblemClause(temp);
          break;
        default:
          LOG(FATAL) << "Not supported";
      }
    }
  }
 
  for (const ConstraintProto& ct : model_proto.constraints()) {
    switch (ct.constraint_case()) {
      case ConstraintProto::ConstraintCase::kBoolAnd: {
        if (ct.enforcement_literal_size() == 0) {
          for (const int ref : ct.bool_and().literals()) {
            const Literal b = get_literal(ref);
            solver->AddUnitClause(b);
          }
        } else {
          // a => b
          const Literal not_a =
              get_literal(ct.enforcement_literal(0)).Negated();
          for (const int ref : ct.bool_and().literals()) {
            const Literal b = get_literal(ref);
            solver->AddProblemClause({not_a, b});
          }
        }
        break;
      }
      case ConstraintProto::ConstraintCase::kBoolOr:
        temp.clear();
        for (const int ref : ct.bool_or().literals()) {
          temp.push_back(get_literal(ref));
        }
        for (const int ref : ct.enforcement_literal()) {
          temp.push_back(get_literal(ref).Negated());
        }
        solver->AddProblemClause(temp);
        break;
      default:
        LOG(FATAL) << "Not supported";
    }
  }
 
  // Deal with fixed variables.
  for (int ref = 0; ref < num_variables; ++ref) {
    const Domain domain = ReadDomainFromProto(model_proto.variables(ref));
    if (domain.Min() == domain.Max()) {
      const Literal ref_literal =
          domain.Min() == 0 ? get_literal(ref).Negated() : get_literal(ref);
      solver->AddUnitClause(ref_literal);
    }
  }
 
  SatSolver::Status status;
  CpSolverResponse response;
  if (parameters.cp_model_presolve()) {
    std::vector<bool> solution;
    status = SolveWithPresolve(&solver, model->GetOrCreate<TimeLimit>(),
                               &solution, drat_proof_handler.get(), logger);
    if (status == SatSolver::FEASIBLE) {
      response.clear_solution();
      for (int ref = 0; ref < num_variables; ++ref) {
        response.add_solution(solution[ref]);
      }
    }
  } else {
    status = solver->SolveWithTimeLimit(model->GetOrCreate<TimeLimit>());
    if (status == SatSolver::FEASIBLE) {
      response.clear_solution();
      for (int ref = 0; ref < num_variables; ++ref) {
        response.add_solution(
            solver->Assignment().LiteralIsTrue(get_literal(ref)) ? 1 : 0);
      }
    }
  }
 
  // Tricky: the model local time limit is updated by the new functions, but
  // the old ones update time_limit directly.
  model->GetOrCreate<TimeLimit>()->AdvanceDeterministicTime(
      solver->model()->GetOrCreate<TimeLimit>()->GetElapsedDeterministicTime());
 
  switch (status) {
    case SatSolver::LIMIT_REACHED: {
      response.set_status(CpSolverStatus::UNKNOWN);
      break;
    }
    case SatSolver::FEASIBLE: {
      CHECK(SolutionIsFeasible(
          model_proto, std::vector<int64_t>(response.solution().begin(),
                                            response.solution().end())));
      response.set_status(CpSolverStatus::OPTIMAL);
      break;
    }
    case SatSolver::INFEASIBLE: {
      response.set_status(CpSolverStatus::INFEASIBLE);
      break;
    }
    default:
      LOG(FATAL) << "Unexpected SatSolver::Status " << status;
  }
  response.set_num_booleans(solver->NumVariables());
  response.set_num_branches(solver->num_branches());
  response.set_num_conflicts(solver->num_failures());
  response.set_num_binary_propagations(solver->num_propagations());
  response.set_num_integer_propagations(0);
  response.set_wall_time(wall_timer->Get());
  response.set_deterministic_time(
      model->Get<TimeLimit>()->GetElapsedDeterministicTime());
 
  if (status == SatSolver::INFEASIBLE && drat_proof_handler != nullptr) {
    WallTimer drat_timer;
    drat_timer.Start();
    DratChecker::Status drat_status = drat_proof_handler->Check(
        absl::GetFlag(FLAGS_max_drat_time_in_seconds));
    switch (drat_status) {
      case DratChecker::UNKNOWN:
        LOG(INFO) << "DRAT status: UNKNOWN";
        break;
      case DratChecker::VALID:
        LOG(INFO) << "DRAT status: VALID";
        break;
      case DratChecker::INVALID:
        LOG(ERROR) << "DRAT status: INVALID";
        break;
      default:
        // Should not happen.
        break;
    }
    LOG(INFO) << "DRAT wall time: " << drat_timer.Get();
  } else if (drat_proof_handler != nullptr) {
    // Always log a DRAT status to make it easier to extract it from a multirun
    // result with awk.
    LOG(INFO) << "DRAT status: NA";
    LOG(INFO) << "DRAT wall time: NA";
    LOG(INFO) << "DRAT user time: NA";
  }
  return response;
}
 
#if !defined(__PORTABLE_PLATFORM__)
 
// Small wrapper to simplify the constructions of the two SubSolver below.
struct SharedClasses {
  CpModelProto const* model_proto;
  WallTimer* wall_timer;
  ModelSharedTimeLimit* time_limit;
  SharedBoundsManager* bounds;
  SharedResponseManager* response;
  SharedRelaxationSolutionRepository* relaxation_solutions;
  SharedLPSolutionRepository* lp_solutions;
  SharedIncompleteSolutionManager* incomplete_solutions;
  Model* global_model;
 
  bool SearchIsDone() {
    if (response->ProblemIsSolved()) return true;
    if (time_limit->LimitReached()) return true;
    return false;
  }
};
 
// Encapsulate a full CP-SAT solve without presolve in the SubSolver API.
class FullProblemSolver : public SubSolver {
 public:
  FullProblemSolver(const std::string& name,
                    const SatParameters& local_parameters, bool split_in_chunks,
                    SharedClasses* shared)
      : SubSolver(name),
        shared_(shared),
        split_in_chunks_(split_in_chunks),
        local_model_(absl::make_unique<Model>(name)) {
    // Setup the local model parameters and time limit.
    *(local_model_->GetOrCreate<SatParameters>()) = local_parameters;
    shared_->time_limit->UpdateLocalLimit(
        local_model_->GetOrCreate<TimeLimit>());
 
    if (shared->response != nullptr) {
      local_model_->Register<SharedResponseManager>(shared->response);
    }
 
    if (shared->relaxation_solutions != nullptr) {
      local_model_->Register<SharedRelaxationSolutionRepository>(
          shared->relaxation_solutions);
    }
 
    if (shared->lp_solutions != nullptr) {
      local_model_->Register<SharedLPSolutionRepository>(shared->lp_solutions);
    }
 
    if (shared->incomplete_solutions != nullptr) {
      local_model_->Register<SharedIncompleteSolutionManager>(
          shared->incomplete_solutions);
    }
  }
 
  bool TaskIsAvailable() override {
    if (shared_->SearchIsDone()) return false;
 
    absl::MutexLock mutex_lock(&mutex_);
    return previous_task_is_completed_;
  }
 
  std::function<void()> GenerateTask(int64_t task_id) override {
    {
      absl::MutexLock mutex_lock(&mutex_);
      previous_task_is_completed_ = false;
    }
    return [this]() {
      if (solving_first_chunk_) {
        LoadCpModel(*shared_->model_proto, local_model_.get());
 
        // Level zero variable bounds sharing. It is important to register
        // that after the probing that takes place in LoadCpModel() otherwise
        // we will have a mutex contention issue when all the thread probes
        // at the same time.
        if (shared_->bounds != nullptr) {
          RegisterVariableBoundsLevelZeroExport(
              *shared_->model_proto, shared_->bounds, local_model_.get());
          RegisterVariableBoundsLevelZeroImport(
              *shared_->model_proto, shared_->bounds, local_model_.get());
        }
 
        if (local_model_->GetOrCreate<SatParameters>()->repair_hint()) {
          MinimizeL1DistanceWithHint(*shared_->model_proto, local_model_.get());
        } else {
          QuickSolveWithHint(*shared_->model_proto, local_model_.get());
        }
 
        // No need for mutex since we only run one task at the time.
        solving_first_chunk_ = false;
 
        if (split_in_chunks_) {
          // Abort first chunk and allow to schedule the next.
          absl::MutexLock mutex_lock(&mutex_);
          previous_task_is_completed_ = true;
          return;
        }
      }
 
      auto* time_limit = local_model_->GetOrCreate<TimeLimit>();
      if (split_in_chunks_) {
        // Configure time limit for chunk solving. Note that we do not want
        // to do that for the hint search for now.
        auto* params = local_model_->GetOrCreate<SatParameters>();
        params->set_max_deterministic_time(1);
        time_limit->ResetLimitFromParameters(*params);
        shared_->time_limit->UpdateLocalLimit(time_limit);
      }
 
      const double saved_dtime = time_limit->GetElapsedDeterministicTime();
      SolveLoadedCpModel(*shared_->model_proto, local_model_.get());
      {
        absl::MutexLock mutex_lock(&mutex_);
        deterministic_time_since_last_synchronize_ +=
            time_limit->GetElapsedDeterministicTime() - saved_dtime;
      }
 
      // Abort if the problem is solved.
      if (shared_->SearchIsDone()) {
        shared_->time_limit->Stop();
        return;
      }
 
      // In this mode, we allow to generate more task.
      if (split_in_chunks_) {
        absl::MutexLock mutex_lock(&mutex_);
        previous_task_is_completed_ = true;
        return;
      }
 
      // Once a solver is done clear its memory and do not wait for the
      // destruction of the SubSolver. This is important because the full solve
      // might not be done at all, for instance this might have been configured
      // with stop_after_first_solution.
      local_model_.reset();
    };
  }
 
  // TODO(user): A few of the information sharing we do between threads does not
  // happen here (bound sharing, RINS neighborhood, objective). Fix that so we
  // can have a deterministic parallel mode.
  void Synchronize() override {
    absl::MutexLock mutex_lock(&mutex_);
    deterministic_time_ += deterministic_time_since_last_synchronize_;
    shared_->time_limit->AdvanceDeterministicTime(
        deterministic_time_since_last_synchronize_);
    deterministic_time_since_last_synchronize_ = 0.0;
  }
 
  std::string StatisticsString() const override {
    // The local model may have been deleted at the end of GenerateTask.
    // Do not crash in this case.
    // TODO(user): Revisit this case.
    if (local_model_ == nullptr) return std::string();
 
    const auto& lps =
        *local_model_->GetOrCreate<LinearProgrammingConstraintCollection>();
    std::string lp_stats;
    if (!lps.empty() &&
        local_model_->GetOrCreate<SatParameters>()->linearization_level() >=
            2) {
      for (const auto* lp : lps) {
        const std::string raw_statistics = lp->Statistics();
        const std::vector<absl::string_view> lines =
            absl::StrSplit(raw_statistics, '\n', absl::SkipEmpty());
        for (const absl::string_view& line : lines) {
          absl::StrAppend(&lp_stats, "     ", line, "\n");
        }
      }
    }
    return lp_stats;
  }
 
 private:
  SharedClasses* shared_;
  const bool split_in_chunks_;
  std::unique_ptr<Model> local_model_;
 
  // The first chunk is special. It is the one in which we load the model and
  // try to follow the hint.
  bool solving_first_chunk_ = true;
 
  absl::Mutex mutex_;
  double deterministic_time_since_last_synchronize_ ABSL_GUARDED_BY(mutex_) =
      0.0;
  bool previous_task_is_completed_ ABSL_GUARDED_BY(mutex_) = true;
};
 
class FeasibilityPumpSolver : public SubSolver {
 public:
  FeasibilityPumpSolver(const SatParameters& local_parameters,
                        SharedClasses* shared)
      : SubSolver("feasibility_pump"),
        shared_(shared),
        local_model_(absl::make_unique<Model>(name_)) {
    // Setup the local model parameters and time limit.
    *(local_model_->GetOrCreate<SatParameters>()) = local_parameters;
    shared_->time_limit->UpdateLocalLimit(
        local_model_->GetOrCreate<TimeLimit>());
 
    if (shared->response != nullptr) {
      local_model_->Register<SharedResponseManager>(shared->response);
    }
 
    if (shared->relaxation_solutions != nullptr) {
      local_model_->Register<SharedRelaxationSolutionRepository>(
          shared->relaxation_solutions);
    }
 
    if (shared->lp_solutions != nullptr) {
      local_model_->Register<SharedLPSolutionRepository>(shared->lp_solutions);
    }
 
    if (shared->incomplete_solutions != nullptr) {
      local_model_->Register<SharedIncompleteSolutionManager>(
          shared->incomplete_solutions);
    }
 
    // Level zero variable bounds sharing.
    if (shared_->bounds != nullptr) {
      RegisterVariableBoundsLevelZeroImport(
          *shared_->model_proto, shared_->bounds, local_model_.get());
    }
  }
 
  bool TaskIsAvailable() override {
    if (shared_->SearchIsDone()) return false;
    absl::MutexLock mutex_lock(&mutex_);
    return previous_task_is_completed_;
  }
 
  std::function<void()> GenerateTask(int64_t task_id) override {
    return [this]() {
      {
        absl::MutexLock mutex_lock(&mutex_);
        if (!previous_task_is_completed_) return;
        previous_task_is_completed_ = false;
      }
      {
        absl::MutexLock mutex_lock(&mutex_);
        if (solving_first_chunk_) {
          LoadFeasibilityPump(*shared_->model_proto, local_model_.get());
          // No new task will be scheduled for this worker if there is no
          // linear relaxation.
          if (local_model_->Get<FeasibilityPump>() == nullptr) return;
          solving_first_chunk_ = false;
          // Abort first chunk and allow to schedule the next.
          previous_task_is_completed_ = true;
          return;
        }
      }
 
      auto* time_limit = local_model_->GetOrCreate<TimeLimit>();
      const double saved_dtime = time_limit->GetElapsedDeterministicTime();
      auto* feasibility_pump = local_model_->Mutable<FeasibilityPump>();
      if (!feasibility_pump->Solve()) {
        shared_->response->NotifyThatImprovingProblemIsInfeasible(name_);
      }
 
      {
        absl::MutexLock mutex_lock(&mutex_);
        deterministic_time_since_last_synchronize_ +=
            time_limit->GetElapsedDeterministicTime() - saved_dtime;
      }
 
      // Abort if the problem is solved.
      if (shared_->SearchIsDone()) {
        shared_->time_limit->Stop();
        return;
      }
 
      absl::MutexLock mutex_lock(&mutex_);
      previous_task_is_completed_ = true;
    };
  }
 
  void Synchronize() override {
    absl::MutexLock mutex_lock(&mutex_);
    deterministic_time_ += deterministic_time_since_last_synchronize_;
    shared_->time_limit->AdvanceDeterministicTime(
        deterministic_time_since_last_synchronize_);
    deterministic_time_since_last_synchronize_ = 0.0;
  }
 
  // TODO(user, fdid): Display feasibility pump statistics.
 
 private:
  SharedClasses* shared_;
  std::unique_ptr<Model> local_model_;
 
  absl::Mutex mutex_;
 
  // The first chunk is special. It is the one in which we load the linear
  // constraints.
  bool solving_first_chunk_ ABSL_GUARDED_BY(mutex_) = true;
 
  double deterministic_time_since_last_synchronize_ ABSL_GUARDED_BY(mutex_) =
      0.0;
  bool previous_task_is_completed_ ABSL_GUARDED_BY(mutex_) = true;
};
 
// A Subsolver that generate LNS solve from a given neighborhood.
class LnsSolver : public SubSolver {
 public:
  LnsSolver(std::unique_ptr<NeighborhoodGenerator> generator,
            const SatParameters& parameters,
            NeighborhoodGeneratorHelper* helper, SharedClasses* shared)
      : SubSolver(generator->name()),
        generator_(std::move(generator)),
        helper_(helper),
        parameters_(parameters),
        shared_(shared) {}
 
  bool TaskIsAvailable() override {
    if (shared_->SearchIsDone()) return false;
    return generator_->ReadyToGenerate();
  }
 
  std::function<void()> GenerateTask(int64_t task_id) override {
    return [task_id, this]() {
      if (shared_->SearchIsDone()) return;
 
      // Create a random number generator whose seed depends both on the task_id
      // and on the parameters_.random_seed() so that changing the later will
      // change the LNS behavior.
      const int32_t low = static_cast<int32_t>(task_id);
      const int32_t high = static_cast<int32_t>(task_id >> 32);
      std::seed_seq seed{low, high, parameters_.random_seed()};
      random_engine_t random(seed);
 
      NeighborhoodGenerator::SolveData data;
      data.difficulty = generator_->difficulty();
      data.deterministic_limit = generator_->deterministic_limit();
 
      // Choose a base solution for this neighborhood.
      CpSolverResponse base_response;
      {
        const SharedSolutionRepository<int64_t>& repo =
            shared_->response->SolutionsRepository();
        if (repo.NumSolutions() > 0) {
          base_response.set_status(CpSolverStatus::FEASIBLE);
          const SharedSolutionRepository<int64_t>::Solution solution =
              repo.GetRandomBiasedSolution(random);
          for (const int64_t value : solution.variable_values) {
            base_response.add_solution(value);
          }
          // Note: We assume that the solution rank is the solution internal
          // objective.
          data.initial_best_objective = repo.GetSolution(0).rank;
          data.base_objective = solution.rank;
        } else {
          base_response.set_status(CpSolverStatus::UNKNOWN);
 
          // If we do not have a solution, we use the current objective upper
          // bound so that our code that compute an "objective" improvement
          // works.
          //
          // TODO(user): this is non-deterministic. Fix.
          data.initial_best_objective =
              shared_->response->GetInnerObjectiveUpperBound();
          data.base_objective = data.initial_best_objective;
        }
      }
 
      Neighborhood neighborhood =
          generator_->Generate(base_response, data.difficulty, random);
 
      if (!neighborhood.is_generated) return;
 
      data.neighborhood_id = neighborhood.id;
 
      const int64_t num_calls = std::max(int64_t{1}, generator_->num_calls());
      const double fully_solved_proportion =
          static_cast<double>(generator_->num_fully_solved_calls()) /
          static_cast<double>(num_calls);
      std::string source_info = name();
      if (!neighborhood.source_info.empty()) {
        absl::StrAppend(&source_info, "_", neighborhood.source_info);
      }
      const std::string solution_info = absl::StrFormat(
          "%s(d=%0.2f s=%i t=%0.2f p=%0.2f)", source_info, data.difficulty,
          task_id, data.deterministic_limit, fully_solved_proportion);
 
      SatParameters local_params(parameters_);
      local_params.set_max_deterministic_time(data.deterministic_limit);
      local_params.set_stop_after_first_solution(false);
      local_params.set_log_search_progress(false);
      local_params.set_cp_model_probing_level(0);
      local_params.set_symmetry_level(0);
      local_params.set_solution_pool_size(1);
 
      Model local_model(solution_info);
      *(local_model.GetOrCreate<SatParameters>()) = local_params;
      TimeLimit* local_time_limit = local_model.GetOrCreate<TimeLimit>();
      local_time_limit->ResetLimitFromParameters(local_params);
      shared_->time_limit->UpdateLocalLimit(local_time_limit);
 
      // Presolve and solve the LNS fragment.
      CpModelProto lns_fragment;
      CpModelProto mapping_proto;
      auto context = absl::make_unique<PresolveContext>(
          &local_model, &lns_fragment, &mapping_proto);
 
      *lns_fragment.mutable_variables() = neighborhood.delta.variables();
      {
        ModelCopy copier(context.get());
 
        // Copy and simplify the constraints from the initial model.
        if (!copier.ImportAndSimplifyConstraints(
                helper_->ModelProto(), neighborhood.constraints_to_ignore)) {
          return;
        }
 
        // Copy and simplify the constraints from the delta model.
        if (!neighborhood.delta.constraints().empty() &&
            !copier.ImportAndSimplifyConstraints(neighborhood.delta, {})) {
          return;
        }
      }
 
      // Copy the rest of the model and overwrite the name.
      CopyEverythingExceptVariablesAndConstraintsFieldsIntoContext(
          helper_->ModelProto(), context.get());
      lns_fragment.set_name(absl::StrCat("lns_", task_id));
 
      // Overwrite solution hinting.
      if (neighborhood.delta.has_solution_hint()) {
        *lns_fragment.mutable_solution_hint() =
            neighborhood.delta.solution_hint();
      }
 
      CpModelProto debug_copy;
      if (absl::GetFlag(FLAGS_cp_model_dump_problematic_lns)) {
        // We need to make a copy because the presolve is destructive.
        // It is why we do not do that by default.
        debug_copy = lns_fragment;
      }
 
#if !defined(__PORTABLE_PLATFORM__)
#endif  // __PORTABLE_PLATFORM__
 
      if (absl::GetFlag(FLAGS_cp_model_dump_lns)) {
        // TODO(user): export the delta too if needed.
        const std::string lns_name =
            absl::StrCat(absl::GetFlag(FLAGS_cp_model_dump_prefix),
                         lns_fragment.name(), ".pb.txt");
        LOG(INFO) << "Dumping LNS model to '" << lns_name << "'.";
        CHECK_OK(file::SetTextProto(lns_name, lns_fragment, file::Defaults()));
      }
 
      std::vector<int> postsolve_mapping;
      PresolveCpModel(context.get(), &postsolve_mapping);
 
      // Release the context.
      context.reset(nullptr);
      neighborhood.delta.Clear();
 
      // TODO(user): Depending on the problem, we should probably use the
      // parameters that work bests (core, linearization_level, etc...) or
      // maybe we can just randomize them like for the base solution used.
      auto* local_response_manager =
          local_model.GetOrCreate<SharedResponseManager>();
      local_response_manager->InitializeObjective(lns_fragment);
      LoadCpModel(lns_fragment, &local_model);
      QuickSolveWithHint(lns_fragment, &local_model);
      SolveLoadedCpModel(lns_fragment, &local_model);
      CpSolverResponse local_response = local_response_manager->GetResponse();
 
      // TODO(user): we actually do not need to postsolve if the solution is
      // not going to be used...
      PostsolveResponseWrapper(
          local_params, helper_->ModelProto().variables_size(), mapping_proto,
          postsolve_mapping, shared_->wall_timer, &local_response);
      data.status = local_response.status();
      data.deterministic_time = local_time_limit->GetElapsedDeterministicTime();
 
      if (generator_->IsRelaxationGenerator()) {
        bool has_feasible_solution = false;
        if (local_response.status() == CpSolverStatus::OPTIMAL ||
            local_response.status() == CpSolverStatus::FEASIBLE) {
          has_feasible_solution = true;
        }
 
        if (local_response.status() == CpSolverStatus::INFEASIBLE) {
          shared_->response->NotifyThatImprovingProblemIsInfeasible(
              local_response.solution_info());
        }
 
        if (shared_->model_proto->has_objective()) {
          // TODO(user): This is not deterministic since it is updated without
          // synchronization! So we shouldn't base the LNS score out of that.
          const IntegerValue current_obj_lb =
              shared_->response->GetInnerObjectiveLowerBound();
 
          const IntegerValue local_obj_lb =
              local_response_manager->GetInnerObjectiveLowerBound();
 
          const double scaled_local_obj_bound = ScaleObjectiveValue(
              lns_fragment.objective(), local_obj_lb.value());
 
          // Update the bound.
          const IntegerValue new_inner_obj_lb = IntegerValue(
              std::ceil(UnscaleObjectiveValue(shared_->model_proto->objective(),
                                              scaled_local_obj_bound) -
                        1e-6));
          data.new_objective_bound = new_inner_obj_lb;
          data.initial_best_objective_bound = current_obj_lb;
          if (new_inner_obj_lb > current_obj_lb) {
            shared_->response->UpdateInnerObjectiveBounds(
                solution_info, new_inner_obj_lb, kMaxIntegerValue);
          }
        }
 
        // If we have a solution of the relaxed problem, we check if it is also
        // a valid solution of the non-relaxed one.
        if (has_feasible_solution) {
          if (SolutionIsFeasible(
                  *shared_->model_proto,
                  std::vector<int64_t>(local_response.solution().begin(),
                                       local_response.solution().end()))) {
            shared_->response->NewSolution(local_response,
                                           /*model=*/nullptr);
 
            // Mark the solution optimal if the relaxation status is optimal.
            if (local_response.status() == CpSolverStatus::OPTIMAL) {
              shared_->response->NotifyThatImprovingProblemIsInfeasible(
                  local_response.solution_info());
              shared_->time_limit->Stop();
            }
          }
          shared_->relaxation_solutions->NewRelaxationSolution(local_response);
        }
      } else {
        if (!local_response.solution().empty()) {
          // A solution that does not pass our validator indicates a bug. We
          // abort and dump the problematic model to facilitate debugging.
          //
          // TODO(user): In a production environment, we should probably just
          // ignore this fragment and continue.
          const bool feasible = SolutionIsFeasible(
              *shared_->model_proto,
              std::vector<int64_t>(local_response.solution().begin(),
                                   local_response.solution().end()));
          if (!feasible) {
            if (absl::GetFlag(FLAGS_cp_model_dump_problematic_lns)) {
              const std::string name =
                  absl::StrCat(absl::GetFlag(FLAGS_cp_model_dump_prefix),
                               debug_copy.name(), ".pb.txt");
              LOG(INFO) << "Dumping problematic LNS model to '" << name << "'.";
              CHECK_OK(file::SetTextProto(name, debug_copy, file::Defaults()));
            }
            LOG(FATAL) << "Infeasible LNS solution! " << solution_info
                       << " solved with params "
                       << local_params.ShortDebugString();
          }
        }
 
        // Finish to fill the SolveData now that the local solve is done.
        data.new_objective = data.base_objective;
        if (local_response.status() == CpSolverStatus::OPTIMAL ||
            local_response.status() == CpSolverStatus::FEASIBLE) {
          data.new_objective = IntegerValue(ComputeInnerObjective(
              shared_->model_proto->objective(), local_response));
        }
 
        // Report any feasible solution we have.
        if (local_response.status() == CpSolverStatus::OPTIMAL ||
            local_response.status() == CpSolverStatus::FEASIBLE) {
          shared_->response->NewSolution(local_response,
                                         /*model=*/nullptr);
        }
        if (!neighborhood.is_reduced &&
            (local_response.status() == CpSolverStatus::OPTIMAL ||
             local_response.status() == CpSolverStatus::INFEASIBLE)) {
          shared_->response->NotifyThatImprovingProblemIsInfeasible(
              local_response.solution_info());
          shared_->time_limit->Stop();
        }
      }
 
      generator_->AddSolveData(data);
 
      // The total number of call when this was called is the same as task_id.
      const int64_t total_num_calls = task_id;
      VLOG(2) << name() << ": [difficulty: " << data.difficulty
              << ", id: " << task_id
              << ", deterministic_time: " << data.deterministic_time << " / "
              << data.deterministic_limit
              << ", status: " << ProtoEnumToString<CpSolverStatus>(data.status)
              << ", num calls: " << generator_->num_calls()
              << ", UCB1 Score: " << generator_->GetUCBScore(total_num_calls)
              << ", p: " << fully_solved_proportion << "]";
    };
  }
 
  void Synchronize() override {
    generator_->Synchronize();
    const double old = deterministic_time_;
    deterministic_time_ = generator_->deterministic_time();
    shared_->time_limit->AdvanceDeterministicTime(deterministic_time_ - old);
  }
 
  // TODO(user): Display LNS success rate.
 
 private:
  std::unique_ptr<NeighborhoodGenerator> generator_;
  NeighborhoodGeneratorHelper* helper_;
  const SatParameters parameters_;
  SharedClasses* shared_;
};
 
void SolveCpModelParallel(const CpModelProto& model_proto,
                          Model* global_model) {
  const SatParameters& parameters = *global_model->GetOrCreate<SatParameters>();
  const int num_search_workers = parameters.num_search_workers();
  CHECK(!parameters.enumerate_all_solutions())
      << "Enumerating all solutions in parallel is not supported.";
 
  std::unique_ptr<SharedBoundsManager> shared_bounds_manager;
  if (parameters.share_level_zero_bounds()) {
    shared_bounds_manager = absl::make_unique<SharedBoundsManager>(model_proto);
  }
 
  std::unique_ptr<SharedRelaxationSolutionRepository>
      shared_relaxation_solutions;
  if (parameters.use_relaxation_lns()) {
    shared_relaxation_solutions =
        absl::make_unique<SharedRelaxationSolutionRepository>(
            /*num_solutions_to_keep=*/10);
    global_model->Register<SharedRelaxationSolutionRepository>(
        shared_relaxation_solutions.get());
  }
 
  auto shared_lp_solutions = absl::make_unique<SharedLPSolutionRepository>(
      /*num_solutions_to_keep=*/10);
  global_model->Register<SharedLPSolutionRepository>(shared_lp_solutions.get());
 
  // We currently only use the feasiblity pump if it is enabled and some other
  // parameters are not on.
  std::unique_ptr<SharedIncompleteSolutionManager> shared_incomplete_solutions;
  const bool use_feasibility_pump = parameters.use_feasibility_pump() &&
                                    parameters.linearization_level() > 0 &&
                                    !parameters.use_lns_only() &&
                                    !parameters.interleave_search();
  if (use_feasibility_pump) {
    shared_incomplete_solutions =
        absl::make_unique<SharedIncompleteSolutionManager>();
    global_model->Register<SharedIncompleteSolutionManager>(
        shared_incomplete_solutions.get());
  }
 
  SharedClasses shared;
  shared.model_proto = &model_proto;
  shared.wall_timer = global_model->GetOrCreate<WallTimer>();
  shared.time_limit = global_model->GetOrCreate<ModelSharedTimeLimit>();
  shared.bounds = shared_bounds_manager.get();
  shared.response = global_model->GetOrCreate<SharedResponseManager>();
  shared.relaxation_solutions = shared_relaxation_solutions.get();
  shared.lp_solutions = shared_lp_solutions.get();
  shared.incomplete_solutions = shared_incomplete_solutions.get();
  shared.global_model = global_model;
 
  // The list of all the SubSolver that will be used in this parallel search.
  std::vector<std::unique_ptr<SubSolver>> subsolvers;
 
  // Add a synchronization point for the shared classes.
  subsolvers.push_back(absl::make_unique<SynchronizationPoint>([&shared]() {
    shared.response->Synchronize();
    shared.response->MutableSolutionsRepository()->Synchronize();
    if (shared.bounds != nullptr) {
      shared.bounds->Synchronize();
    }
    if (shared.relaxation_solutions != nullptr) {
      shared.relaxation_solutions->Synchronize();
    }
    if (shared.lp_solutions != nullptr) {
      shared.lp_solutions->Synchronize();
    }
  }));
 
  if (parameters.use_lns_only()) {
    // Register something to find a first solution. Note that this is mainly
    // used for experimentation, and using no LP ususally result in a faster
    // first solution.
    SatParameters local_params = parameters;
    local_params.set_stop_after_first_solution(true);
    local_params.set_linearization_level(0);
    subsolvers.push_back(absl::make_unique<FullProblemSolver>(
        "first_solution", local_params,
        /*split_in_chunks=*/false, &shared));
  } else {
    for (const SatParameters& local_params : GetDiverseSetOfParameters(
             parameters, model_proto, num_search_workers)) {
      // TODO(user): This is currently not supported here.
      if (parameters.optimize_with_max_hs()) continue;
 
      subsolvers.push_back(absl::make_unique<FullProblemSolver>(
          local_params.name(), local_params,
          /*split_in_chunks=*/parameters.interleave_search(), &shared));
    }
  }
 
  // Add FeasibilityPumpSolver if enabled.
  if (use_feasibility_pump) {
    subsolvers.push_back(
        absl::make_unique<FeasibilityPumpSolver>(parameters, &shared));
  }
 
  // Add LNS SubSolver(s).
 
  // Add the NeighborhoodGeneratorHelper as a special subsolver so that its
  // Synchronize() is called before any LNS neighborhood solvers.
  auto unique_helper = absl::make_unique<NeighborhoodGeneratorHelper>(
      &model_proto, &parameters, shared.response, shared.time_limit,
      shared.bounds);
  NeighborhoodGeneratorHelper* helper = unique_helper.get();
  subsolvers.push_back(std::move(unique_helper));
 
  // By default we use the user provided parameters.
  std::vector<SatParameters> lns_params = {parameters};
  lns_params.back().set_name("default");
  if (parameters.diversify_lns_params()) {
    std::vector<SatParameters> lns_params =
        GetDiverseSetOfParameters(parameters, model_proto, 6);
  }
  for (const SatParameters& local_params : lns_params) {
    // Only register following LNS SubSolver if there is an objective.
    if (model_proto.has_objective()) {
      // Enqueue all the possible LNS neighborhood subsolvers.
      // Each will have their own metrics.
      subsolvers.push_back(absl::make_unique<LnsSolver>(
          absl::make_unique<RelaxRandomVariablesGenerator>(
              helper, absl::StrCat("rnd_var_lns_", local_params.name())),
          local_params, helper, &shared));
      subsolvers.push_back(absl::make_unique<LnsSolver>(
          absl::make_unique<RelaxRandomConstraintsGenerator>(
              helper, absl::StrCat("rnd_cst_lns_", local_params.name())),
          local_params, helper, &shared));
      subsolvers.push_back(absl::make_unique<LnsSolver>(
          absl::make_unique<VariableGraphNeighborhoodGenerator>(
              helper, absl::StrCat("graph_var_lns_", local_params.name())),
          local_params, helper, &shared));
      subsolvers.push_back(absl::make_unique<LnsSolver>(
          absl::make_unique<ConstraintGraphNeighborhoodGenerator>(
              helper, absl::StrCat("graph_cst_lns_", local_params.name())),
          local_params, helper, &shared));
 
      // TODO(user): If we have a model with scheduling + routing. We create
      // a lot of LNS generators. Investigate if we can reduce this number.
      if (!helper->TypeToConstraints(ConstraintProto::kNoOverlap).empty() ||
          !helper->TypeToConstraints(ConstraintProto::kNoOverlap2D).empty() ||
          !helper->TypeToConstraints(ConstraintProto::kCumulative).empty()) {
        subsolvers.push_back(absl::make_unique<LnsSolver>(
            absl::make_unique<SchedulingTimeWindowNeighborhoodGenerator>(
                helper, absl::StrCat("scheduling_time_window_lns_",
                                     local_params.name())),
            local_params, helper, &shared));
        subsolvers.push_back(absl::make_unique<LnsSolver>(
            absl::make_unique<SchedulingNeighborhoodGenerator>(
                helper,
                absl::StrCat("scheduling_random_lns_", local_params.name())),
            local_params, helper, &shared));
      }
    }
 
    const int num_circuit =
        helper->TypeToConstraints(ConstraintProto::kCircuit).size();
    const int num_routes =
        helper->TypeToConstraints(ConstraintProto::kRoutes).size();
    if (num_circuit + num_routes > 0) {
      subsolvers.push_back(absl::make_unique<LnsSolver>(
          absl::make_unique<RoutingRandomNeighborhoodGenerator>(
              helper, absl::StrCat("routing_random_lns_", local_params.name())),
          local_params, helper, &shared));
 
      subsolvers.push_back(absl::make_unique<LnsSolver>(
          absl::make_unique<RoutingPathNeighborhoodGenerator>(
              helper, absl::StrCat("routing_path_lns_", local_params.name())),
          local_params, helper, &shared));
    }
    if (num_routes > 0 || num_circuit > 1) {
      subsolvers.push_back(absl::make_unique<LnsSolver>(
          absl::make_unique<RoutingFullPathNeighborhoodGenerator>(
              helper,
              absl::StrCat("routing_full_path_lns_", local_params.name())),
          local_params, helper, &shared));
    }
 
    // TODO(user): for now this is not deterministic so we disable it on
    // interleave search. Fix.
    if (parameters.use_rins_lns() && !parameters.interleave_search()) {
      // Note that we always create the SharedLPSolutionRepository. This meets
      // the requirement of having at least one of
      // SharedRelaxationSolutionRepository or SharedLPSolutionRepository to
      // create RINS/RENS lns generators.
 
      // RINS.
      subsolvers.push_back(absl::make_unique<LnsSolver>(
          absl::make_unique<RelaxationInducedNeighborhoodGenerator>(
              helper, shared.response, shared.relaxation_solutions,
              shared.lp_solutions, /*incomplete_solutions=*/nullptr,
              absl::StrCat("rins_lns_", local_params.name())),
          local_params, helper, &shared));
 
      // RENS.
      subsolvers.push_back(absl::make_unique<LnsSolver>(
          absl::make_unique<RelaxationInducedNeighborhoodGenerator>(
              helper, /*respons_manager=*/nullptr, shared.relaxation_solutions,
              shared.lp_solutions, shared.incomplete_solutions,
              absl::StrCat("rens_lns_", local_params.name())),
          local_params, helper, &shared));
    }
 
    if (parameters.use_relaxation_lns()) {
      subsolvers.push_back(absl::make_unique<LnsSolver>(
          absl::make_unique<
              ConsecutiveConstraintsRelaxationNeighborhoodGenerator>(
              helper, absl::StrCat("rnd_rel_lns_", local_params.name())),
          local_params, helper, &shared));
 
      subsolvers.push_back(absl::make_unique<LnsSolver>(
          absl::make_unique<WeightedRandomRelaxationNeighborhoodGenerator>(
              helper, absl::StrCat("wgt_rel_lns_", local_params.name())),
          local_params, helper, &shared));
    }
  }
 
  // Add a synchronization point for the primal integral that is executed last.
  // This way, after each batch, the proper deterministic time is updated and
  // then the function to integrate take the value of the new gap.
  subsolvers.push_back(absl::make_unique<SynchronizationPoint>(
      [&shared]() { shared.response->UpdatePrimalIntegral(); }));
 
  // Log the name of all our SubSolvers.
  auto* logger = global_model->GetOrCreate<SolverLogger>();
  if (logger->LoggingIsEnabled()) {
    std::vector<std::string> names;
    for (const auto& subsolver : subsolvers) {
      if (!subsolver->name().empty()) names.push_back(subsolver->name());
    }
    SOLVER_LOG(logger, "");
    SOLVER_LOG(logger,
               absl::StrFormat("Starting Search at %.2fs with %i "
                               "workers and subsolvers: [ %s ]",
                               shared.wall_timer->Get(), num_search_workers,
                               absl::StrJoin(names, ", ")));
  }
 
  // Launch the main search loop.
  if (parameters.interleave_search()) {
    DeterministicLoop(subsolvers, num_search_workers,
                      parameters.interleave_batch_size());
  } else {
    NonDeterministicLoop(subsolvers, num_search_workers);
  }
 
  if (parameters.log_subsolver_statistics()) {
    SOLVER_LOG(logger, "");
    SOLVER_LOG(logger, "Sub-solver search statistics:");
    for (const auto& subsolver : subsolvers) {
      const std::string stats = subsolver->StatisticsString();
      if (stats.empty()) continue;
      SOLVER_LOG(logger, absl::StrCat("  '", subsolver->name(), "':\n", stats));
    }
  }
}
 
#endif  // __PORTABLE_PLATFORM__
 
// If the option use_sat_inprocessing is true, then before postsolving a
// solution, we need to make sure we add any new clause required for postsolving
// to the mapping_model.
void AddPostsolveClauses(const std::vector<int>& postsolve_mapping,
                         Model* model, CpModelProto* mapping_proto) {
  auto* mapping = model->GetOrCreate<CpModelMapping>();
  auto* postsolve = model->GetOrCreate<PostsolveClauses>();
  for (const auto& clause : postsolve->clauses) {
    auto* ct = mapping_proto->add_constraints()->mutable_bool_or();
    for (const Literal l : clause) {
      int var = mapping->GetProtoVariableFromBooleanVariable(l.Variable());
      CHECK_NE(var, -1);
      var = postsolve_mapping[var];
      ct->add_literals(l.IsPositive() ? var : NegatedRef(var));
    }
  }
  postsolve->clauses.clear();
}
 
}  // namespace
 
CpSolverResponse SolveCpModel(const CpModelProto& model_proto, Model* model) {
  auto* wall_timer = model->GetOrCreate<WallTimer>();
  auto* user_timer = model->GetOrCreate<UserTimer>();
  wall_timer->Start();
  user_timer->Start();
 
#if !defined(__PORTABLE_PLATFORM__)
#endif  // __PORTABLE_PLATFORM__
 
#if !defined(__PORTABLE_PLATFORM__)
  // Dump initial model?
  if (absl::GetFlag(FLAGS_cp_model_dump_models)) {
    const std::string file =
        absl::StrCat(absl::GetFlag(FLAGS_cp_model_dump_prefix), "model.pb.txt");
    LOG(INFO) << "Dumping cp model proto to '" << file << "'.";
    CHECK_OK(file::SetTextProto(file, model_proto, file::Defaults()));
  }
#endif  // __PORTABLE_PLATFORM__
 
#if !defined(__PORTABLE_PLATFORM__)
  // Override parameters?
  if (!absl::GetFlag(FLAGS_cp_model_params).empty()) {
    SatParameters params = *model->GetOrCreate<SatParameters>();
    SatParameters flag_params;
    CHECK(google::protobuf::TextFormat::ParseFromString(
        absl::GetFlag(FLAGS_cp_model_params), &flag_params));
    params.MergeFrom(flag_params);
    *(model->GetOrCreate<SatParameters>()) = params;
  }
#endif  // __PORTABLE_PLATFORM__
 
  // Enable the logging component.
  const SatParameters& params = *model->GetOrCreate<SatParameters>();
  SolverLogger* logger = model->GetOrCreate<SolverLogger>();
  logger->EnableLogging(params.log_search_progress() || VLOG_IS_ON(1));
  logger->SetLogToStdOut(params.log_to_stdout());
  std::string log_string;
  if (params.log_to_response()) {
    logger->AddInfoLoggingCallback([&log_string](const std::string& message) {
      absl::StrAppend(&log_string, message, "\n");
    });
  }
 
  auto* shared_response_manager = model->GetOrCreate<SharedResponseManager>();
  shared_response_manager->set_dump_prefix(
      absl::GetFlag(FLAGS_cp_model_dump_prefix));
 
#if !defined(__PORTABLE_PLATFORM__)
  // Note that the postprocessors are executed in reverse order, so this
  // will always dump the response just before it is returned since it is
  // the first one we register.
  if (absl::GetFlag(FLAGS_cp_model_dump_response)) {
    shared_response_manager->AddFinalSolutionPostprocessor(
        [](CpSolverResponse* response) {
          const std::string file = absl::StrCat(
              absl::GetFlag(FLAGS_cp_model_dump_prefix), "response.pbtxt");
          LOG(INFO) << "Dumping response proto to '" << file << "'.";
          CHECK_OK(file::SetTextProto(file, *response, file::Defaults()));
        });
  }
#endif  // __PORTABLE_PLATFORM__
 
  // Always display the final response stats if requested.
  // This also copy the logs to the response if requested.
  shared_response_manager->AddFinalSolutionPostprocessor(
      [logger, &model_proto, &log_string](CpSolverResponse* response) {
        SOLVER_LOG(logger, "");
        SOLVER_LOG(logger, CpSolverResponseStats(*response,
                                                 model_proto.has_objective()));
        if (!log_string.empty()) {
          response->set_solve_log(log_string);
        }
      });
 
  // Always add the timing information to a response. Note that it is important
  // to add this after the log/dump postprocessor since we execute them in
  // reverse order.
  auto* shared_time_limit = model->GetOrCreate<ModelSharedTimeLimit>();
  shared_response_manager->AddSolutionPostprocessor(
      [&wall_timer, &user_timer,
       &shared_time_limit](CpSolverResponse* response) {
        response->set_wall_time(wall_timer->Get());
        response->set_user_time(user_timer->Get());
        response->set_deterministic_time(
            shared_time_limit->GetElapsedDeterministicTime());
      });
 
  // Validate parameters.
  //
  // Note that the few parameters we use before that are Booleans and thus
  // "safe". We need to delay the validation to return a proper response.
  {
    const std::string error = ValidateParameters(params);
    if (!error.empty()) {
      SOLVER_LOG(logger, "Invalid parameters: ", error);
 
      // TODO(user): We currently reuse the MODEL_INVALID status even though it
      // is not the best name for this. Maybe we can add a PARAMETERS_INVALID
      // when it become needed. Or rename to INVALID_INPUT ?
      shared_response_manager->MutableResponse()->set_status(
          CpSolverStatus::MODEL_INVALID);
      return shared_response_manager->GetResponse();
    }
  }
 
  // Initialize the time limit from the parameters.
  model->GetOrCreate<TimeLimit>()->ResetLimitFromParameters(params);
 
#if !defined(__PORTABLE_PLATFORM__)
  // Register SIGINT handler if requested by the parameters.
  if (params.catch_sigint_signal()) {
    model->GetOrCreate<SigintHandler>()->Register(
        [&shared_time_limit]() { shared_time_limit->Stop(); });
  }
#endif  // __PORTABLE_PLATFORM__
 
  SOLVER_LOG(logger, "");
  SOLVER_LOG(logger, "Starting CP-SAT solver.");
 
  // Initialize the number of workers if set to 0.
  if (params.num_search_workers() == 0) {
#if !defined(__PORTABLE_PLATFORM__)
    // Sometimes, hardware_concurrency will return 0. So always default to 1.
    const int num_cores =
        params.enumerate_all_solutions()
            ? 1
            : std::max<int>(std::thread::hardware_concurrency(), 1);
#else
    const int num_cores = 1;
#endif
    SOLVER_LOG(logger, "Setting number of workers to ", num_cores);
    model->GetOrCreate<SatParameters>()->set_num_search_workers(num_cores);
  }
 
  SOLVER_LOG(logger, "Parameters: ", params.ShortDebugString());
  if (logger->LoggingIsEnabled() && params.use_absl_random()) {
    model->GetOrCreate<ModelRandomGenerator>()->LogSalt();
  }
 
  // Validate model_proto.
  // TODO(user): provide an option to skip this step for speed?
  {
    const std::string error = ValidateCpModel(model_proto);
    if (!error.empty()) {
      SOLVER_LOG(logger, "Invalid model: ", error);
      shared_response_manager->MutableResponse()->set_status(
          CpSolverStatus::MODEL_INVALID);
      return shared_response_manager->GetResponse();
    }
  }
 
  SOLVER_LOG(logger, "");
  SOLVER_LOG(logger, "Initial ", CpModelStats(model_proto));
 
  // Special case for pure-sat problem.
  // TODO(user): improve the normal presolver to do the same thing.
  // TODO(user): Support solution hint, but then the first TODO will make it
  // automatic.
  if (!params.use_sat_inprocessing() && !model_proto.has_objective() &&
      !model_proto.has_solution_hint() && !params.enumerate_all_solutions() &&
      !params.use_lns_only() && params.num_search_workers() <= 1 &&
      model_proto.assumptions().empty()) {
    bool is_pure_sat = true;
    for (const IntegerVariableProto& var : model_proto.variables()) {
      if (var.domain_size() != 2 || var.domain(0) < 0 || var.domain(1) > 1) {
        is_pure_sat = false;
        break;
      }
    }
    if (is_pure_sat) {
      for (const ConstraintProto& ct : model_proto.constraints()) {
        if (ct.constraint_case() != ConstraintProto::ConstraintCase::kBoolOr &&
            ct.constraint_case() != ConstraintProto::ConstraintCase::kBoolAnd) {
          is_pure_sat = false;
          break;
        }
      }
    }
    if (is_pure_sat) {
      // TODO(user): All this duplication will go away when we are fast enough
      // on pure-sat model with the CpModel presolve...
      *shared_response_manager->MutableResponse() =
          SolvePureSatModel(model_proto, wall_timer, model, logger);
      if (params.fill_tightened_domains_in_response()) {
        *shared_response_manager->MutableResponse()
             ->mutable_tightened_variables() = model_proto.variables();
      }
      return shared_response_manager->GetResponse();
    }
  }
 
  // Presolve and expansions.
  SOLVER_LOG(logger, "");
  SOLVER_LOG(logger,
             absl::StrFormat("Starting presolve at %.2fs", wall_timer->Get()));
  CpModelProto new_cp_model_proto;
  CpModelProto mapping_proto;
  auto context = absl::make_unique<PresolveContext>(model, &new_cp_model_proto,
                                                    &mapping_proto);
 
  *context->working_model->mutable_variables() = model_proto.variables();
  if (!ImportConstraintsWithBasicPresolveIntoContext(model_proto,
                                                     context.get())) {
    VLOG(1) << "Model found infeasible during copy";
    // TODO(user): At this point, the model is trivial, but we could exit
    // early.
  }
  CopyEverythingExceptVariablesAndConstraintsFieldsIntoContext(model_proto,
                                                               context.get());
 
  // Checks for hints early in case they are forced to be hard constraints.
  if (params.fix_variables_to_their_hinted_value() &&
      model_proto.has_solution_hint()) {
    SOLVER_LOG(context->logger(), "Fixing ",
               model_proto.solution_hint().vars().size(),
               " variables to their value in the solution hints.");
    for (int i = 0; i < model_proto.solution_hint().vars_size(); ++i) {
      const int var = model_proto.solution_hint().vars(i);
      const int64_t value = model_proto.solution_hint().values(i);
      if (!context->IntersectDomainWith(var, Domain(value))) {
        const IntegerVariableProto& var_proto =
            context->working_model->variables(var);
        const std::string var_name = var_proto.name().empty()
                                         ? absl::StrCat("var(", var, ")")
                                         : var_proto.name();
 
        const Domain var_domain = ReadDomainFromProto(var_proto);
        SOLVER_LOG(context->logger(),
                   "Hint found infeasible when assigning variable '", var_name,
                   "' with domain", var_domain.ToString(), " the value ",
                   value);
        break;
      }
    }
  }
 
  // If the hint is complete, we can use the solution checker to do more
  // validation.
  if (model_proto.has_solution_hint() && !context->ModelIsUnsat()) {
    // TODO(user): Add a parameter and change the code to make the solution
    // checker more informative.
    // After the model has been validated, we are sure there are do duplicate
    // variables in the solution hint.
    if (model_proto.solution_hint().vars().size() ==
        model_proto.variables_size()) {
      std::vector<int64_t> solution(model_proto.variables_size(), 0);
      for (int i = 0; i < model_proto.solution_hint().vars_size(); ++i) {
        const int ref = model_proto.solution_hint().vars(i);
        const int64_t value = model_proto.solution_hint().values(i);
        solution[PositiveRef(ref)] = RefIsPositive(ref) ? value : -value;
      }
      if (SolutionIsFeasible(model_proto, solution)) {
        SOLVER_LOG(context->logger(),
                   "The solution hint is complete and is feasible.");
 
      } else {
        SOLVER_LOG(context->logger(),
                   "The solution hint is complete, but it is infeasible! we "
                   "will try to repair it.");
      }
    }
  }
 
  if (params.num_search_workers() > 1 || model_proto.has_objective()) {
    // For the case where the assumptions are currently not supported, we just
    // assume they are fixed, and will always report all of them in the UNSAT
    // core if the problem turn out to be UNSAT.
    //
    // If the mode is not degraded, we will hopefully report a small subset
    // in case there is no feasible solution under these assumptions.
    shared_response_manager->AddFinalSolutionPostprocessor(
        [&model_proto](CpSolverResponse* response) {
          if (response->status() != CpSolverStatus::INFEASIBLE) return;
 
          // For now, just pass in all assumptions.
          *response->mutable_sufficient_assumptions_for_infeasibility() =
              model_proto.assumptions();
        });
 
    context->InitializeNewDomains();
    for (const int ref : model_proto.assumptions()) {
      if (!context->SetLiteralToTrue(ref)) {
        shared_response_manager->MutableResponse()->set_status(
            CpSolverStatus::INFEASIBLE);
        shared_response_manager->MutableResponse()
            ->add_sufficient_assumptions_for_infeasibility(ref);
        return shared_response_manager->GetResponse();
      }
    }
  }
 
  // Do the actual presolve.
  std::vector<int> postsolve_mapping;
  const bool ok = PresolveCpModel(context.get(), &postsolve_mapping);
  if (!ok) {
    LOG(ERROR) << "Error while presolving, likely due to integer overflow.";
    shared_response_manager->MutableResponse()->set_status(
        CpSolverStatus::MODEL_INVALID);
    return shared_response_manager->GetResponse();
  }
 
  SOLVER_LOG(logger, "");
  SOLVER_LOG(logger, "Presolved ", CpModelStats(new_cp_model_proto));
  SOLVER_LOG(logger, "");
  SOLVER_LOG(logger, "Preloading model.");
 
  if (params.cp_model_presolve()) {
    shared_response_manager->AddSolutionPostprocessor(
        [&model_proto, &params, &mapping_proto, &postsolve_mapping, wall_timer,
         model](CpSolverResponse* response) {
          AddPostsolveClauses(postsolve_mapping, model, &mapping_proto);
          PostsolveResponseWrapper(params, model_proto.variables_size(),
                                   mapping_proto, postsolve_mapping, wall_timer,
                                   response);
          if (!response->solution().empty()) {
            CHECK(SolutionIsFeasible(
                model_proto,
                std::vector<int64_t>(response->solution().begin(),
                                     response->solution().end()),
                &mapping_proto, &postsolve_mapping))
                << "postsolved solution";
          }
          if (params.fill_tightened_domains_in_response()) {
            // TODO(user): for now, we just use the domain infered during
            // presolve.
            if (mapping_proto.variables().size() >=
                model_proto.variables().size()) {
              for (int i = 0; i < model_proto.variables().size(); ++i) {
                *response->add_tightened_variables() =
                    mapping_proto.variables(i);
              }
            }
          }
        });
  } else {
    shared_response_manager->AddFinalSolutionPostprocessor(
        [&model_proto](CpSolverResponse* response) {
          if (!response->solution().empty()) {
            CHECK(SolutionIsFeasible(
                model_proto, std::vector<int64_t>(response->solution().begin(),
                                                  response->solution().end())));
          }
        });
    shared_response_manager->AddSolutionPostprocessor(
        [&model_proto, &params](CpSolverResponse* response) {
          // Truncate the solution in case model expansion added more variables.
          const int initial_size = model_proto.variables_size();
          if (response->solution_size() > 0) {
            response->mutable_solution()->Truncate(initial_size);
            if (DEBUG_MODE ||
                absl::GetFlag(FLAGS_cp_model_check_intermediate_solutions)) {
              CHECK(SolutionIsFeasible(
                  model_proto,
                  std::vector<int64_t>(response->solution().begin(),
                                       response->solution().end())));
            }
          } else if (response->solution_lower_bounds_size() > 0) {
            response->mutable_solution_lower_bounds()->Truncate(initial_size);
            response->mutable_solution_upper_bounds()->Truncate(initial_size);
          }
          if (params.fill_tightened_domains_in_response()) {
            *response->mutable_tightened_variables() = model_proto.variables();
          }
        });
  }
 
  // Delete the context.
  context.reset(nullptr);
 
  if (params.symmetry_level() > 1) {
    DetectAndAddSymmetryToProto(params, &new_cp_model_proto, logger);
  }
 
  const auto& observers = model->GetOrCreate<SolutionObservers>()->observers;
  if (!observers.empty()) {
    shared_response_manager->AddSolutionCallback(
        [&observers](const CpSolverResponse& response) {
          for (const auto& observer : observers) {
            observer(response);
          }
        });
  }
 
  // If specified, we load the initial objective domain right away in the
  // response manager. Note that the presolve will always fill it with the
  // trivial min/max value if the user left it empty. This avoids to display
  // [-infinity, infinity] for the initial objective search space.
  if (new_cp_model_proto.has_objective()) {
    shared_response_manager->InitializeObjective(new_cp_model_proto);
    shared_response_manager->SetGapLimitsFromParameters(params);
  }
 
  // Start counting the primal integral from the current determistic time and
  // initial objective domain gap that we just filled.
  shared_response_manager->UpdatePrimalIntegral();
 
#if !defined(__PORTABLE_PLATFORM__)
  if (absl::GetFlag(FLAGS_cp_model_dump_models)) {
    const std::string presolved_file = absl::StrCat(
        absl::GetFlag(FLAGS_cp_model_dump_prefix), "presolved_model.pb.txt");
    LOG(INFO) << "Dumping presolved cp model proto to '" << presolved_file
              << "'.";
    CHECK_OK(file::SetTextProto(presolved_file, new_cp_model_proto,
                                file::Defaults()));
 
    const std::string mapping_file = absl::StrCat(
        absl::GetFlag(FLAGS_cp_model_dump_prefix), "mapping_model.pb.txt");
    LOG(INFO) << "Dumping mapping cp model proto to '" << mapping_file << "'.";
    CHECK_OK(file::SetTextProto(mapping_file, mapping_proto, file::Defaults()));
  }
#endif  // __PORTABLE_PLATFORM__
 
  if (params.stop_after_presolve() || shared_time_limit->LimitReached()) {
    int64_t num_terms = 0;
    for (const ConstraintProto& ct : new_cp_model_proto.constraints()) {
      num_terms += UsedVariables(ct).size();
    }
    SOLVER_LOG(
        logger, "Stopped after presolve.",
        "\nPresolvedNumVariables: ", new_cp_model_proto.variables().size(),
        "\nPresolvedNumConstraints: ", new_cp_model_proto.constraints().size(),
        "\nPresolvedNumTerms: ", num_terms);
 
    shared_response_manager->SetStatsFromModel(model);
    return shared_response_manager->GetResponse();
  }
 
  // Make sure everything stops when we have a first solution if requested.
  if (params.stop_after_first_solution()) {
    shared_response_manager->AddSolutionCallback(
        [shared_time_limit](const CpSolverResponse& response) {
          shared_time_limit->Stop();
        });
  }
 
#if defined(__PORTABLE_PLATFORM__)
  if (/* DISABLES CODE */ (false)) {
    // We ignore the multithreading parameter in this case.
#else   // __PORTABLE_PLATFORM__
  if (params.num_search_workers() > 1 || params.interleave_search()) {
    SolveCpModelParallel(new_cp_model_proto, model);
#endif  // __PORTABLE_PLATFORM__
  } else {
    SOLVER_LOG(logger, "");
    SOLVER_LOG(logger, absl::StrFormat("Starting to load the model at %.2fs",
                                       wall_timer->Get()));
    shared_response_manager->SetUpdatePrimalIntegralOnEachChange(true);
    LoadCpModel(new_cp_model_proto, model);
    shared_response_manager->LoadDebugSolution(model);
 
    SOLVER_LOG(logger, "");
    SOLVER_LOG(logger, absl::StrFormat("Starting sequential search at %.2fs",
                                       wall_timer->Get()));
    if (params.repair_hint()) {
      MinimizeL1DistanceWithHint(new_cp_model_proto, model);
    } else {
      QuickSolveWithHint(new_cp_model_proto, model);
    }
    SolveLoadedCpModel(new_cp_model_proto, model);
  }
 
  if (logger->LoggingIsEnabled()) {
    if (params.num_search_workers() <= 1) {
      const auto& lps =
          *model->GetOrCreate<LinearProgrammingConstraintCollection>();
      if (!lps.empty()) {
        SOLVER_LOG(logger, "");
        for (const auto* lp : lps) {
          SOLVER_LOG(logger, lp->Statistics());
        }
      }
    }
 
    if (params.num_search_workers() > 1) {
      SOLVER_LOG(logger, "");
      shared_response_manager->DisplayImprovementStatistics();
    }
  }
 
  return shared_response_manager->GetResponse();
}
 
CpSolverResponse Solve(const CpModelProto& model_proto) {
  Model model;
  return SolveCpModel(model_proto, &model);
}
 
CpSolverResponse SolveWithParameters(const CpModelProto& model_proto,
                                     const SatParameters& params) {
  Model model;
  model.Add(NewSatParameters(params));
  return SolveCpModel(model_proto, &model);
}
 
#if !defined(__PORTABLE_PLATFORM__)
CpSolverResponse SolveWithParameters(const CpModelProto& model_proto,
                                     const std::string& params) {
  Model model;
  model.Add(NewSatParameters(params));
  return SolveCpModel(model_proto, &model);
}
#endif  // !__PORTABLE_PLATFORM__
 
}  // namespace sat
}  // namespace operations_research