default_search.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 <cstddef>
#include <cstdint>
#include <functional>
#include <limits>
#include <memory>
#include <string>
#include <utility>
#include <vector>
 
#include "absl/container/flat_hash_set.h"
#include "absl/strings/str_format.h"
#include "ortools/base/commandlineflags.h"
#include "ortools/base/integral_types.h"
#include "ortools/base/logging.h"
#include "ortools/base/macros.h"
#include "ortools/base/stl_util.h"
#include "ortools/constraint_solver/constraint_solver.h"
#include "ortools/constraint_solver/constraint_solveri.h"
#include "ortools/util/cached_log.h"
#include "ortools/util/string_array.h"
 
ABSL_FLAG(int, cp_impact_divider, 10, "Divider for continuous update.");
 
namespace operations_research {
 
namespace {
// Default constants for search phase parameters.
const int kDefaultNumberOfSplits = 100;
const int kDefaultHeuristicPeriod = 100;
const int kDefaultHeuristicNumFailuresLimit = 30;
const bool kDefaultUseLastConflict = true;
}  // namespace
 
DefaultPhaseParameters::DefaultPhaseParameters()
    : var_selection_schema(DefaultPhaseParameters::CHOOSE_MAX_SUM_IMPACT),
      value_selection_schema(DefaultPhaseParameters::SELECT_MIN_IMPACT),
      initialization_splits(kDefaultNumberOfSplits),
      run_all_heuristics(true),
      heuristic_period(kDefaultHeuristicPeriod),
      heuristic_num_failures_limit(kDefaultHeuristicNumFailuresLimit),
      persistent_impact(true),
      random_seed(CpRandomSeed()),
      display_level(DefaultPhaseParameters::NORMAL),
      use_last_conflict(kDefaultUseLastConflict),
      decision_builder(nullptr) {}
 
namespace {
// ----- DomainWatcher -----
 
// This class follows the domains of variables and will report the log of the
// search space of all integer variables.
class DomainWatcher {
 public:
  DomainWatcher(const std::vector<IntVar*>& vars, int cache_size)
      : vars_(vars) {
    cached_log_.Init(cache_size);
  }
 
  double LogSearchSpaceSize() {
    double result = 0.0;
    for (int index = 0; index < vars_.size(); ++index) {
      result += cached_log_.Log2(vars_[index]->Size());
    }
    return result;
  }
 
  double Log2(int64_t size) const { return cached_log_.Log2(size); }
 
 private:
  std::vector<IntVar*> vars_;
  CachedLog cached_log_;
  DISALLOW_COPY_AND_ASSIGN(DomainWatcher);
};
 
// ---------- FindVar decision visitor ---------
 
class FindVar : public DecisionVisitor {
 public:
  enum Operation { NONE, ASSIGN, SPLIT_LOW, SPLIT_HIGH };
 
  FindVar() : var_(nullptr), value_(0), operation_(NONE) {}
 
  ~FindVar() override {}
 
  void VisitSetVariableValue(IntVar* const var, int64_t value) override {
    var_ = var;
    value_ = value;
    operation_ = ASSIGN;
  }
 
  void VisitSplitVariableDomain(IntVar* const var, int64_t value,
                                bool start_with_lower_half) override {
    var_ = var;
    value_ = value;
    operation_ = start_with_lower_half ? SPLIT_LOW : SPLIT_HIGH;
  }
 
  void VisitScheduleOrPostpone(IntervalVar* const var, int64_t est) override {
    operation_ = NONE;
  }
 
  virtual void VisitTryRankFirst(SequenceVar* const sequence, int index) {
    operation_ = NONE;
  }
 
  virtual void VisitTryRankLast(SequenceVar* const sequence, int index) {
    operation_ = NONE;
  }
 
  void VisitUnknownDecision() override { operation_ = NONE; }
 
  // Returns the current variable.
  IntVar* const var() const {
    CHECK_NE(operation_, NONE);
    return var_;
  }
 
  // Returns the value of the current variable.
  int64_t value() const {
    CHECK_NE(operation_, NONE);
    return value_;
  }
 
  Operation operation() const { return operation_; }
 
  std::string DebugString() const override {
    return "FindVar decision visitor";
  }
 
 private:
  IntVar* var_;
  int64_t value_;
  Operation operation_;
};
 
// ----- Auxiliary decision builders to init impacts -----
 
// This class initialize impacts by scanning each value of the domain
// of the variable.
class InitVarImpacts : public DecisionBuilder {
 public:
  // ----- main -----
  InitVarImpacts()
      : var_(nullptr),
        update_impact_callback_(nullptr),
        new_start_(false),
        var_index_(0),
        value_index_(-1),
        update_impact_closure_([this]() { UpdateImpacts(); }),
        updater_(update_impact_closure_) {
    CHECK(update_impact_closure_ != nullptr);
  }
 
  ~InitVarImpacts() override {}
 
  void UpdateImpacts() {
    // the Min is always the value we just set.
    update_impact_callback_(var_index_, var_->Min());
  }
 
  void Init(IntVar* const var, IntVarIterator* const iterator, int var_index) {
    var_ = var;
    iterator_ = iterator;
    var_index_ = var_index;
    new_start_ = true;
    value_index_ = 0;
  }
 
  Decision* Next(Solver* const solver) override {
    CHECK(var_ != nullptr);
    CHECK(iterator_ != nullptr);
    if (new_start_) {
      active_values_.clear();
      for (const int64_t value : InitAndGetValues(iterator_)) {
        active_values_.push_back(value);
      }
      new_start_ = false;
    }
    if (value_index_ == active_values_.size()) {
      return nullptr;
    }
    updater_.var_ = var_;
    updater_.value_ = active_values_[value_index_];
    value_index_++;
    return &updater_;
  }
 
  void set_update_impact_callback(std::function<void(int, int64_t)> callback) {
    update_impact_callback_ = std::move(callback);
  }
 
 private:
  // ----- helper decision -----
  class AssignCallFail : public Decision {
   public:
    explicit AssignCallFail(const std::function<void()>& update_impact_closure)
        : var_(nullptr),
          value_(0),
          update_impact_closure_(update_impact_closure) {
      CHECK(update_impact_closure_ != nullptr);
    }
    ~AssignCallFail() override {}
    void Apply(Solver* const solver) override {
      CHECK(var_ != nullptr);
      var_->SetValue(value_);
      // We call the closure on the part that cannot fail.
      update_impact_closure_();
      solver->Fail();
    }
    void Refute(Solver* const solver) override {}
    // Public data for easy access.
    IntVar* var_;
    int64_t value_;
 
   private:
    const std::function<void()>& update_impact_closure_;
    DISALLOW_COPY_AND_ASSIGN(AssignCallFail);
  };
 
  IntVar* var_;
  std::function<void(int, int64_t)> update_impact_callback_;
  bool new_start_;
  IntVarIterator* iterator_;
  int var_index_;
  std::vector<int64_t> active_values_;
  int value_index_;
  std::function<void()> update_impact_closure_;
  AssignCallFail updater_;
};
 
// This class initialize impacts by scanning at most 'split_size'
// intervals on the domain of the variable.
 
class InitVarImpactsWithSplits : public DecisionBuilder {
 public:
  // ----- helper decision -----
  class AssignIntervalCallFail : public Decision {
   public:
    explicit AssignIntervalCallFail(
        const std::function<void()>& update_impact_closure)
        : var_(nullptr),
          value_min_(0),
          value_max_(0),
          update_impact_closure_(update_impact_closure) {
      CHECK(update_impact_closure_ != nullptr);
    }
    ~AssignIntervalCallFail() override {}
    void Apply(Solver* const solver) override {
      CHECK(var_ != nullptr);
      var_->SetRange(value_min_, value_max_);
      // We call the closure on the part that cannot fail.
      update_impact_closure_();
      solver->Fail();
    }
    void Refute(Solver* const solver) override {}
 
    // Public for easy access.
    IntVar* var_;
    int64_t value_min_;
    int64_t value_max_;
 
   private:
    const std::function<void()>& update_impact_closure_;
    DISALLOW_COPY_AND_ASSIGN(AssignIntervalCallFail);
  };
 
  // ----- main -----
 
  explicit InitVarImpactsWithSplits(int split_size)
      : var_(nullptr),
        update_impact_callback_(nullptr),
        new_start_(false),
        var_index_(0),
        min_value_(0),
        max_value_(0),
        split_size_(split_size),
        split_index_(-1),
        update_impact_closure_([this]() { UpdateImpacts(); }),
        updater_(update_impact_closure_) {
    CHECK(update_impact_closure_ != nullptr);
  }
 
  ~InitVarImpactsWithSplits() override {}
 
  void UpdateImpacts() {
    for (const int64_t value : InitAndGetValues(iterator_)) {
      update_impact_callback_(var_index_, value);
    }
  }
 
  void Init(IntVar* const var, IntVarIterator* const iterator, int var_index) {
    var_ = var;
    iterator_ = iterator;
    var_index_ = var_index;
    new_start_ = true;
    split_index_ = 0;
  }
 
  int64_t IntervalStart(int index) const {
    const int64_t length = max_value_ - min_value_ + 1;
    return (min_value_ + length * index / split_size_);
  }
 
  Decision* Next(Solver* const solver) override {
    if (new_start_) {
      min_value_ = var_->Min();
      max_value_ = var_->Max();
      new_start_ = false;
    }
    if (split_index_ == split_size_) {
      return nullptr;
    }
    updater_.var_ = var_;
    updater_.value_min_ = IntervalStart(split_index_);
    split_index_++;
    if (split_index_ == split_size_) {
      updater_.value_max_ = max_value_;
    } else {
      updater_.value_max_ = IntervalStart(split_index_) - 1;
    }
    return &updater_;
  }
 
  void set_update_impact_callback(std::function<void(int, int64_t)> callback) {
    update_impact_callback_ = std::move(callback);
  }
 
 private:
  IntVar* var_;
  std::function<void(int, int64_t)> update_impact_callback_;
  bool new_start_;
  IntVarIterator* iterator_;
  int var_index_;
  int64_t min_value_;
  int64_t max_value_;
  const int split_size_;
  int split_index_;
  std::function<void()> update_impact_closure_;
  AssignIntervalCallFail updater_;
};
 
// ----- ImpactRecorder
 
// This class will record the impacts of all assignment of values to
// variables. Its main output is to find the optimal pair (variable/value)
// based on default phase parameters.
class ImpactRecorder : public SearchMonitor {
 public:
  static const int kLogCacheSize;
  static const double kPerfectImpact;
  static const double kFailureImpact;
  static const double kInitFailureImpact;
  static const int kUninitializedVarIndex;
 
  ImpactRecorder(Solver* const solver, DomainWatcher* const domain_watcher,
                 const std::vector<IntVar*>& vars,
                 DefaultPhaseParameters::DisplayLevel display_level)
      : SearchMonitor(solver),
        domain_watcher_(domain_watcher),
        vars_(vars),
        size_(vars.size()),
        current_log_space_(0.0),
        impacts_(size_),
        original_min_(size_, 0LL),
        domain_iterators_(new IntVarIterator*[size_]),
        display_level_(display_level),
        current_var_(kUninitializedVarIndex),
        current_value_(0),
        init_done_(false) {
    for (int i = 0; i < size_; ++i) {
      domain_iterators_[i] = vars_[i]->MakeDomainIterator(true);
      var_map_[vars_[i]] = i;
    }
  }
 
  void ApplyDecision(Decision* const d) override {
    if (!init_done_) {
      return;
    }
    d->Accept(&find_var_);
    if (find_var_.operation() == FindVar::ASSIGN &&
        gtl::ContainsKey(var_map_, find_var_.var())) {
      current_var_ = var_map_[find_var_.var()];
      current_value_ = find_var_.value();
      current_log_space_ = domain_watcher_->LogSearchSpaceSize();
    } else {
      current_var_ = kUninitializedVarIndex;
      current_value_ = 0;
    }
  }
 
  void AfterDecision(Decision* const d, bool apply) override {
    if (init_done_ && current_var_ != kUninitializedVarIndex) {
      if (current_log_space_ > 0.0) {
        const double log_space = domain_watcher_->LogSearchSpaceSize();
        if (apply) {
          const double impact = kPerfectImpact - log_space / current_log_space_;
          UpdateImpact(current_var_, current_value_, impact);
          current_var_ = kUninitializedVarIndex;
          current_value_ = 0;
        }
        current_log_space_ = log_space;
      }
    }
  }
 
  void BeginFail() override {
    if (init_done_ && current_var_ != kUninitializedVarIndex) {
      UpdateImpact(current_var_, current_value_, kFailureImpact);
      current_var_ = kUninitializedVarIndex;
      current_value_ = 0;
    }
  }
 
  void ResetAllImpacts() {
    for (int i = 0; i < size_; ++i) {
      original_min_[i] = vars_[i]->Min();
      // By default, we init impacts to 2.0 -> equivalent to failure.
      // This will be overwritten to real impact values on valid domain
      // values during the FirstRun() method.
      impacts_[i].resize(vars_[i]->Max() - vars_[i]->Min() + 1,
                         kInitFailureImpact);
    }
 
    for (int i = 0; i < size_; ++i) {
      for (int j = 0; j < impacts_[i].size(); ++j) {
        impacts_[i][j] = kInitFailureImpact;
      }
    }
  }
 
  void UpdateImpact(int var_index, int64_t value, double impact) {
    const int64_t value_index = value - original_min_[var_index];
    const double current_impact = impacts_[var_index][value_index];
    const double new_impact =
        (current_impact * (absl::GetFlag(FLAGS_cp_impact_divider) - 1) +
         impact) /
        absl::GetFlag(FLAGS_cp_impact_divider);
    impacts_[var_index][value_index] = new_impact;
  }
 
  void InitImpact(int var_index, int64_t value) {
    const double log_space = domain_watcher_->LogSearchSpaceSize();
    const double impact = kPerfectImpact - log_space / current_log_space_;
    const int64_t value_index = value - original_min_[var_index];
    DCHECK_LT(var_index, size_);
    DCHECK_LT(value_index, impacts_[var_index].size());
    impacts_[var_index][value_index] = impact;
    init_count_++;
  }
 
  void FirstRun(int64_t splits) {
    Solver* const s = solver();
    current_log_space_ = domain_watcher_->LogSearchSpaceSize();
    if (display_level_ != DefaultPhaseParameters::NONE) {
      LOG(INFO) << "  - initial log2(SearchSpace) = " << current_log_space_;
    }
    const int64_t init_time = s->wall_time();
    ResetAllImpacts();
    int64_t removed_counter = 0;
    FirstRunVariableContainers* container =
        s->RevAlloc(new FirstRunVariableContainers(this, splits));
    // Loop on the variables, scan domains and initialize impacts.
    for (int var_index = 0; var_index < size_; ++var_index) {
      IntVar* const var = vars_[var_index];
      if (var->Bound()) {
        continue;
      }
      IntVarIterator* const iterator = domain_iterators_[var_index];
      DecisionBuilder* init_decision_builder = nullptr;
      const bool no_split = var->Size() < splits;
      if (no_split) {
        // The domain is small enough, we scan it completely.
        container->without_split()->set_update_impact_callback(
            container->update_impact_callback());
        container->without_split()->Init(var, iterator, var_index);
        init_decision_builder = container->without_split();
      } else {
        // The domain is too big, we scan it in initialization_splits
        // intervals.
        container->with_splits()->set_update_impact_callback(
            container->update_impact_callback());
        container->with_splits()->Init(var, iterator, var_index);
        init_decision_builder = container->with_splits();
      }
      // Reset the number of impacts initialized.
      init_count_ = 0;
      // Use Solve() to scan all values of one variable.
      s->Solve(init_decision_builder);
 
      // If we have not initialized all values, then they can be removed.
      // As the iterator is not stable w.r.t. deletion, we need to store
      // removed values in an intermediate vector.
      if (init_count_ != var->Size() && no_split) {
        container->ClearRemovedValues();
        for (const int64_t value : InitAndGetValues(iterator)) {
          const int64_t value_index = value - original_min_[var_index];
          if (impacts_[var_index][value_index] == kInitFailureImpact) {
            container->PushBackRemovedValue(value);
          }
        }
        CHECK(container->HasRemovedValues()) << var->DebugString();
        removed_counter += container->NumRemovedValues();
        const double old_log = domain_watcher_->Log2(var->Size());
        var->RemoveValues(container->removed_values());
        current_log_space_ += domain_watcher_->Log2(var->Size()) - old_log;
      }
    }
    if (display_level_ != DefaultPhaseParameters::NONE) {
      if (removed_counter) {
        LOG(INFO) << "  - init done, time = " << s->wall_time() - init_time
                  << " ms, " << removed_counter
                  << " values removed, log2(SearchSpace) = "
                  << current_log_space_;
      } else {
        LOG(INFO) << "  - init done, time = " << s->wall_time() - init_time
                  << " ms";
      }
    }
    s->SaveAndSetValue(&init_done_, true);
  }
 
  // This method scans the domain of one variable and returns the sum
  // of the impacts of all values in its domain, along with the value
  // with minimal impact.
  void ScanVarImpacts(int var_index, int64_t* const best_impact_value,
                      double* const var_impacts,
                      DefaultPhaseParameters::VariableSelection var_select,
                      DefaultPhaseParameters::ValueSelection value_select) {
    CHECK(best_impact_value != nullptr);
    CHECK(var_impacts != nullptr);
    double max_impact = -std::numeric_limits<double>::max();
    double min_impact = std::numeric_limits<double>::max();
    double sum_var_impact = 0.0;
    int64_t min_impact_value = -1;
    int64_t max_impact_value = -1;
    for (const int64_t value : InitAndGetValues(domain_iterators_[var_index])) {
      const int64_t value_index = value - original_min_[var_index];
      DCHECK_LT(var_index, size_);
      DCHECK_LT(value_index, impacts_[var_index].size());
      const double current_impact = impacts_[var_index][value_index];
      sum_var_impact += current_impact;
      if (current_impact > max_impact) {
        max_impact = current_impact;
        max_impact_value = value;
      }
      if (current_impact < min_impact) {
        min_impact = current_impact;
        min_impact_value = value;
      }
    }
 
    switch (var_select) {
      case DefaultPhaseParameters::CHOOSE_MAX_AVERAGE_IMPACT: {
        *var_impacts = sum_var_impact / vars_[var_index]->Size();
        break;
      }
      case DefaultPhaseParameters::CHOOSE_MAX_VALUE_IMPACT: {
        *var_impacts = max_impact;
        break;
      }
      default: {
        *var_impacts = sum_var_impact;
        break;
      }
    }
 
    switch (value_select) {
      case DefaultPhaseParameters::SELECT_MIN_IMPACT: {
        *best_impact_value = min_impact_value;
        break;
      }
      case DefaultPhaseParameters::SELECT_MAX_IMPACT: {
        *best_impact_value = max_impact_value;
        break;
      }
    }
  }
 
  std::string DebugString() const override { return "ImpactRecorder"; }
 
 private:
  // A container for the variables needed in FirstRun that is reversibly
  // allocable.
  class FirstRunVariableContainers : public BaseObject {
   public:
    FirstRunVariableContainers(ImpactRecorder* impact_recorder, int64_t splits)
        : update_impact_callback_(
              [impact_recorder](int var_index, int64_t value) {
                impact_recorder->InitImpact(var_index, value);
              }),
          removed_values_(),
          without_splits_(),
          with_splits_(splits) {}
    std::function<void(int, int64_t)> update_impact_callback() const {
      return update_impact_callback_;
    }
    void PushBackRemovedValue(int64_t value) {
      removed_values_.push_back(value);
    }
    bool HasRemovedValues() const { return !removed_values_.empty(); }
    void ClearRemovedValues() { removed_values_.clear(); }
    size_t NumRemovedValues() const { return removed_values_.size(); }
    const std::vector<int64_t>& removed_values() const {
      return removed_values_;
    }
    InitVarImpacts* without_split() { return &without_splits_; }
    InitVarImpactsWithSplits* with_splits() { return &with_splits_; }
 
    std::string DebugString() const override {
      return "FirstRunVariableContainers";
    }
 
   private:
    const std::function<void(int, int64_t)> update_impact_callback_;
    std::vector<int64_t> removed_values_;
    InitVarImpacts without_splits_;
    InitVarImpactsWithSplits with_splits_;
  };
 
  DomainWatcher* const domain_watcher_;
  std::vector<IntVar*> vars_;
  const int size_;
  double current_log_space_;
  // impacts_[i][j] stores the average search space reduction when assigning
  // original_min_[i] + j to variable i.
  std::vector<std::vector<double> > impacts_;
  std::vector<int64_t> original_min_;
  std::unique_ptr<IntVarIterator*[]> domain_iterators_;
  int64_t init_count_;
  const DefaultPhaseParameters::DisplayLevel display_level_;
  int current_var_;
  int64_t current_value_;
  FindVar find_var_;
  absl::flat_hash_map<const IntVar*, int> var_map_;
  bool init_done_;
 
  DISALLOW_COPY_AND_ASSIGN(ImpactRecorder);
};
 
const int ImpactRecorder::kLogCacheSize = 1000;
const double ImpactRecorder::kPerfectImpact = 1.0;
const double ImpactRecorder::kFailureImpact = 1.0;
const double ImpactRecorder::kInitFailureImpact = 2.0;
const int ImpactRecorder::kUninitializedVarIndex = -1;
 
// This structure stores 'var[index] (left?==:!=) value'.
class ChoiceInfo {
 public:
  ChoiceInfo() : value_(0), var_(nullptr), left_(false) {}
 
  ChoiceInfo(IntVar* const var, int64_t value, bool left)
      : value_(value), var_(var), left_(left) {}
 
  std::string DebugString() const {
    return absl::StrFormat("%s %s %d", var_->name(), (left_ ? "==" : "!="),
                           value_);
  }
 
  IntVar* var() const { return var_; }
 
  bool left() const { return left_; }
 
  int64_t value() const { return value_; }
 
  void set_left(bool left) { left_ = left; }
 
 private:
  int64_t value_;
  IntVar* var_;
  bool left_;
};
 
// ---------- Heuristics ----------
 
class RunHeuristicsAsDives : public Decision {
 public:
  RunHeuristicsAsDives(Solver* const solver, const std::vector<IntVar*>& vars,
                       DefaultPhaseParameters::DisplayLevel level,
                       bool run_all_heuristics, int random_seed,
                       int heuristic_period, int heuristic_num_failures_limit)
      : heuristic_limit_(nullptr),
        display_level_(level),
        run_all_heuristics_(run_all_heuristics),
        random_(random_seed),
        heuristic_period_(heuristic_period),
        heuristic_branch_count_(0),
        heuristic_runs_(0) {
    Init(solver, vars, heuristic_num_failures_limit);
  }
 
  ~RunHeuristicsAsDives() override { gtl::STLDeleteElements(&heuristics_); }
 
  void Apply(Solver* const solver) override {
    if (!RunAllHeuristics(solver)) {
      solver->Fail();
    }
  }
 
  void Refute(Solver* const solver) override {}
 
  bool ShouldRun() {
    if (heuristic_period_ <= 0) {
      return false;
    }
    ++heuristic_branch_count_;
    return heuristic_branch_count_ % heuristic_period_ == 0;
  }
 
  bool RunOneHeuristic(Solver* const solver, int index) {
    HeuristicWrapper* const wrapper = heuristics_[index];
    heuristic_runs_++;
 
    const bool result =
        solver->SolveAndCommit(wrapper->phase, heuristic_limit_);
    if (result && display_level_ != DefaultPhaseParameters::NONE) {
      LOG(INFO) << "  --- solution found by heuristic " << wrapper->name
                << " --- ";
    }
    return result;
  }
 
  bool RunAllHeuristics(Solver* const solver) {
    if (run_all_heuristics_) {
      for (int index = 0; index < heuristics_.size(); ++index) {
        for (int run = 0; run < heuristics_[index]->runs; ++run) {
          if (RunOneHeuristic(solver, index)) {
            return true;
          }
        }
      }
      return false;
    } else {
      DCHECK_GT(heuristics_.size(), 0);
      const int index = absl::Uniform<int>(random_, 0, heuristics_.size());
      return RunOneHeuristic(solver, index);
    }
  }
 
  int Rand32(int size) {
    DCHECK_GT(size, 0);
    return absl::Uniform<int>(random_, 0, size);
  }
 
  void Init(Solver* const solver, const std::vector<IntVar*>& vars,
            int heuristic_num_failures_limit) {
    const int kRunOnce = 1;
    const int kRunMore = 2;
    const int kRunALot = 3;
 
    heuristics_.push_back(new HeuristicWrapper(
        solver, vars, Solver::CHOOSE_MIN_SIZE_LOWEST_MIN,
        Solver::ASSIGN_MIN_VALUE, "AssignMinValueToMinDomainSize", kRunOnce));
 
    heuristics_.push_back(new HeuristicWrapper(
        solver, vars, Solver::CHOOSE_MIN_SIZE_HIGHEST_MAX,
        Solver::ASSIGN_MAX_VALUE, "AssignMaxValueToMinDomainSize", kRunOnce));
 
    heuristics_.push_back(
        new HeuristicWrapper(solver, vars, Solver::CHOOSE_MIN_SIZE_LOWEST_MIN,
                             Solver::ASSIGN_CENTER_VALUE,
                             "AssignCenterValueToMinDomainSize", kRunOnce));
 
    heuristics_.push_back(new HeuristicWrapper(
        solver, vars, Solver::CHOOSE_FIRST_UNBOUND, Solver::ASSIGN_RANDOM_VALUE,
        "AssignRandomValueToFirstUnbound", kRunALot));
 
    heuristics_.push_back(new HeuristicWrapper(
        solver, vars, Solver::CHOOSE_RANDOM, Solver::ASSIGN_MIN_VALUE,
        "AssignMinValueToRandomVariable", kRunMore));
 
    heuristics_.push_back(new HeuristicWrapper(
        solver, vars, Solver::CHOOSE_RANDOM, Solver::ASSIGN_MAX_VALUE,
        "AssignMaxValueToRandomVariable", kRunMore));
 
    heuristics_.push_back(new HeuristicWrapper(
        solver, vars, Solver::CHOOSE_RANDOM, Solver::ASSIGN_RANDOM_VALUE,
        "AssignRandomValueToRandomVariable", kRunMore));
 
    heuristic_limit_ = solver->MakeFailuresLimit(heuristic_num_failures_limit);
  }
 
  int heuristic_runs() const { return heuristic_runs_; }
 
 private:
  // This class wraps one heuristic with extra information: name and
  // number of runs.
  struct HeuristicWrapper {
    HeuristicWrapper(Solver* const solver, const std::vector<IntVar*>& vars,
                     Solver::IntVarStrategy var_strategy,
                     Solver::IntValueStrategy value_strategy,
                     const std::string& heuristic_name, int heuristic_runs)
        : phase(solver->MakePhase(vars, var_strategy, value_strategy)),
          name(heuristic_name),
          runs(heuristic_runs) {}
 
    // The decision builder we are going to use in this dive.
    DecisionBuilder* const phase;
    // A name for logging purposes.
    const std::string name;
    // How many times we will run this particular heuristic in case the
    // parameter run_all_heuristics is true. This is useful for random
    // heuristics where it makes sense to run them more than once.
    const int runs;
  };
 
  std::vector<HeuristicWrapper*> heuristics_;
  SearchMonitor* heuristic_limit_;
  DefaultPhaseParameters::DisplayLevel display_level_;
  bool run_all_heuristics_;
  std::mt19937 random_;
  const int heuristic_period_;
  int heuristic_branch_count_;
  int heuristic_runs_;
};
 
// ---------- DefaultIntegerSearch ----------
 
// Default phase decision builder.
class DefaultIntegerSearch : public DecisionBuilder {
 public:
  static const double kSmallSearchSpaceLimit;
 
  DefaultIntegerSearch(Solver* const solver, const std::vector<IntVar*>& vars,
                       const DefaultPhaseParameters& parameters)
      : vars_(vars),
        parameters_(parameters),
        domain_watcher_(vars, ImpactRecorder::kLogCacheSize),
        impact_recorder_(solver, &domain_watcher_, vars,
                         parameters.display_level),
        heuristics_(solver, vars_, parameters_.display_level,
                    parameters_.run_all_heuristics, parameters_.random_seed,
                    parameters_.heuristic_period,
                    parameters_.heuristic_num_failures_limit),
        find_var_(),
        last_int_var_(nullptr),
        last_int_value_(0),
        last_operation_(FindVar::NONE),
        last_conflict_count_(0),
        init_done_(false) {}
 
  ~DefaultIntegerSearch() override {}
 
  Decision* Next(Solver* const solver) override {
    CheckInit(solver);
 
    if (heuristics_.ShouldRun()) {
      return &heuristics_;
    }
 
    Decision* const decision = parameters_.decision_builder != nullptr
                                   ? parameters_.decision_builder->Next(solver)
                                   : ImpactNext(solver);
 
    // Returns early if the search tree is finished anyway.
    if (decision == nullptr) {
      ClearLastDecision();
      return nullptr;
    }
 
    // The main goal of last conflict is to branch on a decision
    // variable different from the one being evaluated. We need to
    // retrieve first the variable in the current decision.
    decision->Accept(&find_var_);
    IntVar* const decision_var =
        find_var_.operation() != FindVar::NONE ? find_var_.var() : nullptr;
 
    // We will hijack the search heuristics if
    //  - we use last conflict
    //  - we have stored the last decision from the search heuristics
    //  - the variable stored is different from the variable of the current
    //    decision
    //  - this variable is not bound already
    // Furthermore, each case will also verify that the stored decision is
    // compatible with the current domain variable.
    if (parameters_.use_last_conflict && last_int_var_ != nullptr &&
        !last_int_var_->Bound() &&
        (decision_var == nullptr || decision_var != last_int_var_)) {
      switch (last_operation_) {
        case FindVar::ASSIGN: {
          if (last_int_var_->Contains(last_int_value_)) {
            Decision* const assign =
                solver->MakeAssignVariableValue(last_int_var_, last_int_value_);
            ClearLastDecision();
            last_conflict_count_++;
            return assign;
          }
          break;
        }
        case FindVar::SPLIT_LOW: {
          if (last_int_var_->Max() > last_int_value_ &&
              last_int_var_->Min() <= last_int_value_) {
            Decision* const split = solver->MakeVariableLessOrEqualValue(
                last_int_var_, last_int_value_);
            ClearLastDecision();
            last_conflict_count_++;
            return split;
          }
          break;
        }
        case FindVar::SPLIT_HIGH: {
          if (last_int_var_->Min() < last_int_value_ &&
              last_int_var_->Max() >= last_int_value_) {
            Decision* const split = solver->MakeVariableGreaterOrEqualValue(
                last_int_var_, last_int_value_);
            ClearLastDecision();
            last_conflict_count_++;
            return split;
          }
          break;
        }
        default: {
          break;
        }
      }
    }
 
    if (parameters_.use_last_conflict) {
      // Store the last decision to replay it upon failure.
      decision->Accept(&find_var_);
      if (find_var_.operation() != FindVar::NONE) {
        last_int_var_ = find_var_.var();
        last_int_value_ = find_var_.value();
        last_operation_ = find_var_.operation();
      }
    }
 
    return decision;
  }
 
  void ClearLastDecision() {
    last_int_var_ = nullptr;
    last_int_value_ = 0;
    last_operation_ = FindVar::NONE;
  }
 
  void AppendMonitors(Solver* const solver,
                      std::vector<SearchMonitor*>* const extras) override {
    CHECK(solver != nullptr);
    CHECK(extras != nullptr);
    if (parameters_.decision_builder == nullptr) {
      extras->push_back(&impact_recorder_);
    }
  }
 
  void Accept(ModelVisitor* const visitor) const override {
    visitor->BeginVisitExtension(ModelVisitor::kVariableGroupExtension);
    visitor->VisitIntegerVariableArrayArgument(ModelVisitor::kVarsArgument,
                                               vars_);
    visitor->EndVisitExtension(ModelVisitor::kVariableGroupExtension);
  }
 
  std::string DebugString() const override {
    std::string out = "DefaultIntegerSearch(";
 
    if (parameters_.decision_builder == nullptr) {
      out.append("Impact Based Search, ");
    } else {
      out.append(parameters_.decision_builder->DebugString());
      out.append(", ");
    }
    out.append(JoinDebugStringPtr(vars_, ", "));
    out.append(")");
    return out;
  }
 
  std::string StatString() const {
    const int runs = heuristics_.heuristic_runs();
    std::string result;
    if (runs > 0) {
      if (!result.empty()) {
        result.append(", ");
      }
      if (runs == 1) {
        result.append("1 heuristic run");
      } else {
        absl::StrAppendFormat(&result, "%d heuristic runs", runs);
      }
    }
    if (last_conflict_count_ > 0) {
      if (!result.empty()) {
        result.append(", ");
      }
      if (last_conflict_count_ == 1) {
        result.append("1 last conflict hint");
      } else {
        absl::StrAppendFormat(&result, "%d last conflict hints",
                              last_conflict_count_);
      }
    }
    return result;
  }
 
 private:
  void CheckInit(Solver* const solver) {
    if (init_done_) {
      return;
    }
    if (parameters_.decision_builder == nullptr) {
      // Decide if we are doing impacts, no if one variable is too big.
      for (int i = 0; i < vars_.size(); ++i) {
        if (vars_[i]->Max() - vars_[i]->Min() > 0xFFFFFF) {
          if (parameters_.display_level == DefaultPhaseParameters::VERBOSE) {
            LOG(INFO) << "Domains are too large, switching to simple "
                      << "heuristics";
          }
          solver->SaveValue(
              reinterpret_cast<void**>(&parameters_.decision_builder));
          parameters_.decision_builder =
              solver->MakePhase(vars_, Solver::CHOOSE_MIN_SIZE_LOWEST_MIN,
                                Solver::ASSIGN_MIN_VALUE);
          solver->SaveAndSetValue(&init_done_, true);
          return;
        }
      }
      // No if the search space is too small.
      if (domain_watcher_.LogSearchSpaceSize() < kSmallSearchSpaceLimit) {
        if (parameters_.display_level == DefaultPhaseParameters::VERBOSE) {
          LOG(INFO) << "Search space is too small, switching to simple "
                    << "heuristics";
        }
        solver->SaveValue(
            reinterpret_cast<void**>(&parameters_.decision_builder));
        parameters_.decision_builder = solver->MakePhase(
            vars_, Solver::CHOOSE_FIRST_UNBOUND, Solver::ASSIGN_MIN_VALUE);
        solver->SaveAndSetValue(&init_done_, true);
        return;
      }
 
      if (parameters_.display_level != DefaultPhaseParameters::NONE) {
        LOG(INFO) << "Init impact based search phase on " << vars_.size()
                  << " variables, initialization splits = "
                  << parameters_.initialization_splits
                  << ", heuristic_period = " << parameters_.heuristic_period
                  << ", run_all_heuristics = "
                  << parameters_.run_all_heuristics;
      }
      // Init the impacts.
      impact_recorder_.FirstRun(parameters_.initialization_splits);
    }
    if (parameters_.persistent_impact) {
      init_done_ = true;
    } else {
      solver->SaveAndSetValue(&init_done_, true);
    }
  }
 
  // This method will do an exhaustive scan of all domains of all
  // variables to select the variable with the maximal sum of impacts
  // per value in its domain, and then select the value with the
  // minimal impact.
  Decision* ImpactNext(Solver* const solver) {
    IntVar* var = nullptr;
    int64_t value = 0;
    double best_var_impact = -std::numeric_limits<double>::max();
    for (int i = 0; i < vars_.size(); ++i) {
      if (!vars_[i]->Bound()) {
        int64_t current_value = 0;
        double current_var_impact = 0.0;
        impact_recorder_.ScanVarImpacts(i, &current_value, &current_var_impact,
                                        parameters_.var_selection_schema,
                                        parameters_.value_selection_schema);
        if (current_var_impact > best_var_impact) {
          var = vars_[i];
          value = current_value;
          best_var_impact = current_var_impact;
        }
      }
    }
    if (var == nullptr) {
      return nullptr;
    } else {
      return solver->MakeAssignVariableValue(var, value);
    }
  }
 
  // ----- data members -----
 
  std::vector<IntVar*> vars_;
  DefaultPhaseParameters parameters_;
  DomainWatcher domain_watcher_;
  ImpactRecorder impact_recorder_;
  RunHeuristicsAsDives heuristics_;
  FindVar find_var_;
  IntVar* last_int_var_;
  int64_t last_int_value_;
  FindVar::Operation last_operation_;
  int last_conflict_count_;
  bool init_done_;
};
 
const double DefaultIntegerSearch::kSmallSearchSpaceLimit = 10.0;
}  // namespace
 
// ---------- API ----------
 
std::string DefaultPhaseStatString(DecisionBuilder* db) {
  DefaultIntegerSearch* const dis = dynamic_cast<DefaultIntegerSearch*>(db);
  return dis != nullptr ? dis->StatString() : "";
}
 
DecisionBuilder* Solver::MakeDefaultPhase(const std::vector<IntVar*>& vars) {
  DefaultPhaseParameters parameters;
  return MakeDefaultPhase(vars, parameters);
}
 
DecisionBuilder* Solver::MakeDefaultPhase(
    const std::vector<IntVar*>& vars,
    const DefaultPhaseParameters& parameters) {
  return RevAlloc(new DefaultIntegerSearch(this, vars, parameters));
}
}  // namespace operations_research