constraint_solveri.h

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// Copyright 2010-2024 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.
 
 
#ifndef OR_TOOLS_CONSTRAINT_SOLVER_CONSTRAINT_SOLVERI_H_
#define OR_TOOLS_CONSTRAINT_SOLVER_CONSTRAINT_SOLVERI_H_
 
#include <stdint.h>
#include <string.h>
 
#include <algorithm>
#include <functional>
#include <initializer_list>
#include <memory>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
 
#include "absl/algorithm/container.h"
#include "absl/container/flat_hash_map.h"
#include "absl/strings/str_cat.h"
#include "ortools/base/logging.h"
#include "ortools/base/strong_int.h"
#include "ortools/base/strong_vector.h"
#include "ortools/base/timer.h"
#include "ortools/base/types.h"
#include "ortools/constraint_solver/constraint_solver.h"
#include "ortools/util/bitset.h"
#include "ortools/util/tuple_set.h"
 
namespace operations_research {
 
class LocalSearchMonitor;
 
class BaseIntExpr : public IntExpr {
 public:
  explicit BaseIntExpr(Solver* const s) : IntExpr(s), var_(nullptr) {}
  ~BaseIntExpr() override {}
 
  IntVar* Var() override;
  virtual IntVar* CastToVar();
 
 private:
  IntVar* var_;
};
 
enum VarTypes {
  UNSPECIFIED,
  DOMAIN_INT_VAR,
  BOOLEAN_VAR,
  CONST_VAR,
  VAR_ADD_CST,
  VAR_TIMES_CST,
  CST_SUB_VAR,
  OPP_VAR,
  TRACE_VAR
};
 
#ifndef SWIG
template <class T>
class SimpleRevFIFO {
 private:
  enum { CHUNK_SIZE = 16 };  // TODO(user): could be an extra template param
  struct Chunk {
    T data_[CHUNK_SIZE];
    const Chunk* const next_;
    explicit Chunk(const Chunk* next) : next_(next) {}
  };
 
 public:
  class Iterator {
   public:
    explicit Iterator(const SimpleRevFIFO<T>* l)
        : chunk_(l->chunks_), value_(l->Last()) {}
    bool ok() const { return (value_ != nullptr); }
    T operator*() const { return *value_; }
    void operator++() {
      ++value_;
      if (value_ == chunk_->data_ + CHUNK_SIZE) {
        chunk_ = chunk_->next_;
        value_ = chunk_ ? chunk_->data_ : nullptr;
      }
    }
 
   private:
    const Chunk* chunk_;
    const T* value_;
  };
 
  SimpleRevFIFO() : chunks_(nullptr), pos_(0) {}
 
  void Push(Solver* const s, T val) {
    if (pos_.Value() == 0) {
      Chunk* const chunk = s->UnsafeRevAlloc(new Chunk(chunks_));
      s->SaveAndSetValue(reinterpret_cast<void**>(&chunks_),
                         reinterpret_cast<void*>(chunk));
      pos_.SetValue(s, CHUNK_SIZE - 1);
    } else {
      pos_.Decr(s);
    }
    chunks_->data_[pos_.Value()] = val;
  }
 
  void PushIfNotTop(Solver* const s, T val) {
    if (chunks_ == nullptr || LastValue() != val) {
      Push(s, val);
    }
  }
 
  const T* Last() const {
    return chunks_ ? &chunks_->data_[pos_.Value()] : nullptr;
  }
 
  T* MutableLast() { return chunks_ ? &chunks_->data_[pos_.Value()] : nullptr; }
 
  const T& LastValue() const {
    DCHECK(chunks_);
    return chunks_->data_[pos_.Value()];
  }
 
  void SetLastValue(const T& v) {
    DCHECK(Last());
    chunks_->data_[pos_.Value()] = v;
  }
 
 private:
  Chunk* chunks_;
  NumericalRev<int> pos_;
};
 
// TODO(user): use murmurhash.
inline uint64_t Hash1(uint64_t value) {
  value = (~value) + (value << 21);  
  value ^= value >> 24;
  value += (value << 3) + (value << 8);  
  value ^= value >> 14;
  value += (value << 2) + (value << 4);  
  value ^= value >> 28;
  value += (value << 31);
  return value;
}
 
inline uint64_t Hash1(uint32_t value) {
  uint64_t a = value;
  a = (a + 0x7ed55d16) + (a << 12);
  a = (a ^ 0xc761c23c) ^ (a >> 19);
  a = (a + 0x165667b1) + (a << 5);
  a = (a + 0xd3a2646c) ^ (a << 9);
  a = (a + 0xfd7046c5) + (a << 3);
  a = (a ^ 0xb55a4f09) ^ (a >> 16);
  return a;
}
 
inline uint64_t Hash1(int64_t value) {
  return Hash1(static_cast<uint64_t>(value));
}
 
inline uint64_t Hash1(int value) { return Hash1(static_cast<uint32_t>(value)); }
 
inline uint64_t Hash1(void* const ptr) {
#if defined(__x86_64__) || defined(_M_X64) || defined(__powerpc64__) || \
    defined(__aarch64__) || (defined(_MIPS_SZPTR) && (_MIPS_SZPTR == 64))
  return Hash1(reinterpret_cast<uint64_t>(ptr));
#else
  return Hash1(reinterpret_cast<uint32_t>(ptr));
#endif
}
 
template <class T>
uint64_t Hash1(const std::vector<T*>& ptrs) {
  if (ptrs.empty()) return 0;
  if (ptrs.size() == 1) return Hash1(ptrs[0]);
  uint64_t hash = Hash1(ptrs[0]);
  for (int i = 1; i < ptrs.size(); ++i) {
    hash = hash * i + Hash1(ptrs[i]);
  }
  return hash;
}
 
inline uint64_t Hash1(const std::vector<int64_t>& ptrs) {
  if (ptrs.empty()) return 0;
  if (ptrs.size() == 1) return Hash1(ptrs[0]);
  uint64_t hash = Hash1(ptrs[0]);
  for (int i = 1; i < ptrs.size(); ++i) {
    hash = hash * i + Hash1(ptrs[i]);
  }
  return hash;
}
 
template <class K, class V>
class RevImmutableMultiMap {
 public:
  RevImmutableMultiMap(Solver* const solver, int initial_size)
      : solver_(solver),
        array_(solver->UnsafeRevAllocArray(new Cell*[initial_size])),
        size_(initial_size),
        num_items_(0) {
    memset(array_, 0, sizeof(*array_) * size_.Value());
  }
 
  ~RevImmutableMultiMap() {}
 
  int num_items() const { return num_items_.Value(); }
 
  bool ContainsKey(const K& key) const {
    uint64_t code = Hash1(key) % size_.Value();
    Cell* tmp = array_[code];
    while (tmp) {
      if (tmp->key() == key) {
        return true;
      }
      tmp = tmp->next();
    }
    return false;
  }
 
  const V& FindWithDefault(const K& key, const V& default_value) const {
    uint64_t code = Hash1(key) % size_.Value();
    Cell* tmp = array_[code];
    while (tmp) {
      if (tmp->key() == key) {
        return tmp->value();
      }
      tmp = tmp->next();
    }
    return default_value;
  }
 
  void Insert(const K& key, const V& value) {
    const int position = Hash1(key) % size_.Value();
    Cell* const cell =
        solver_->UnsafeRevAlloc(new Cell(key, value, array_[position]));
    solver_->SaveAndSetValue(reinterpret_cast<void**>(&array_[position]),
                             reinterpret_cast<void*>(cell));
    num_items_.Incr(solver_);
    if (num_items_.Value() > 2 * size_.Value()) {
      Double();
    }
  }
 
 private:
  class Cell {
   public:
    Cell(const K& key, const V& value, Cell* const next)
        : key_(key), value_(value), next_(next) {}
 
    void SetRevNext(Solver* const solver, Cell* const next) {
      solver->SaveAndSetValue(reinterpret_cast<void**>(&next_),
                              reinterpret_cast<void*>(next));
    }
 
    Cell* next() const { return next_; }
 
    const K& key() const { return key_; }
 
    const V& value() const { return value_; }
 
   private:
    const K key_;
    const V value_;
    Cell* next_;
  };
 
  void Double() {
    Cell** const old_cell_array = array_;
    const int old_size = size_.Value();
    size_.SetValue(solver_, size_.Value() * 2);
    solver_->SaveAndSetValue(
        reinterpret_cast<void**>(&array_),
        reinterpret_cast<void*>(
            solver_->UnsafeRevAllocArray(new Cell*[size_.Value()])));
    memset(array_, 0, size_.Value() * sizeof(*array_));
    for (int i = 0; i < old_size; ++i) {
      Cell* tmp = old_cell_array[i];
      while (tmp != nullptr) {
        Cell* const to_reinsert = tmp;
        tmp = tmp->next();
        const uint64_t new_position = Hash1(to_reinsert->key()) % size_.Value();
        to_reinsert->SetRevNext(solver_, array_[new_position]);
        solver_->SaveAndSetValue(
            reinterpret_cast<void**>(&array_[new_position]),
            reinterpret_cast<void*>(to_reinsert));
      }
    }
  }
 
  Solver* const solver_;
  Cell** array_;
  NumericalRev<int> size_;
  NumericalRev<int> num_items_;
};
 
class RevSwitch {
 public:
  RevSwitch() : value_(false) {}
 
  bool Switched() const { return value_; }
 
  void Switch(Solver* const solver) { solver->SaveAndSetValue(&value_, true); }
 
 private:
  bool value_;
};
 
class SmallRevBitSet {
 public:
  explicit SmallRevBitSet(int64_t size);
  void SetToOne(Solver* solver, int64_t pos);
  void SetToZero(Solver* solver, int64_t pos);
  int64_t Cardinality() const;
  bool IsCardinalityZero() const { return bits_.Value() == uint64_t{0}; }
  bool IsCardinalityOne() const {
    return (bits_.Value() != 0) && !(bits_.Value() & (bits_.Value() - 1));
  }
  int64_t GetFirstOne() const;
 
 private:
  Rev<uint64_t> bits_;
};
 
class RevBitSet {
 public:
  explicit RevBitSet(int64_t size);
  ~RevBitSet();
 
  void SetToOne(Solver* solver, int64_t index);
  void SetToZero(Solver* solver, int64_t index);
  bool IsSet(int64_t index) const;
  int64_t Cardinality() const;
  bool IsCardinalityZero() const;
  bool IsCardinalityOne() const;
  int64_t GetFirstBit(int start) const;
  void ClearAll(Solver* solver);
 
  friend class RevBitMatrix;
 
 private:
  void Save(Solver* solver, int offset);
  const int64_t size_;
  const int64_t length_;
  uint64_t* bits_;
  uint64_t* stamps_;
};
 
class RevBitMatrix : private RevBitSet {
 public:
  RevBitMatrix(int64_t rows, int64_t columns);
  ~RevBitMatrix();
 
  void SetToOne(Solver* solver, int64_t row, int64_t column);
  void SetToZero(Solver* solver, int64_t row, int64_t column);
  bool IsSet(int64_t row, int64_t column) const {
    DCHECK_GE(row, 0);
    DCHECK_LT(row, rows_);
    DCHECK_GE(column, 0);
    DCHECK_LT(column, columns_);
    return RevBitSet::IsSet(row * columns_ + column);
  }
  int64_t Cardinality(int row) const;
  bool IsCardinalityZero(int row) const;
  bool IsCardinalityOne(int row) const;
  int64_t GetFirstBit(int row, int start) const;
  void ClearAll(Solver* solver);
 
 private:
  const int64_t rows_;
  const int64_t columns_;
};
 
 
template <class T>
class CallMethod0 : public Demon {
 public:
  CallMethod0(T* const ct, void (T::*method)(), const std::string& name)
      : constraint_(ct), method_(method), name_(name) {}
 
  ~CallMethod0() override {}
 
  void Run(Solver* const s) override { (constraint_->*method_)(); }
 
  std::string DebugString() const override {
    return "CallMethod_" + name_ + "(" + constraint_->DebugString() + ")";
  }
 
 private:
  T* const constraint_;
  void (T::*const method_)();
  const std::string name_;
};
 
template <class T>
Demon* MakeConstraintDemon0(Solver* const s, T* const ct, void (T::*method)(),
                            const std::string& name) {
  return s->RevAlloc(new CallMethod0<T>(ct, method, name));
}
 
template <class P>
std::string ParameterDebugString(P param) {
  return absl::StrCat(param);
}
 
template <class P>
std::string ParameterDebugString(P* param) {
  return param->DebugString();
}
 
template <class T, class P>
class CallMethod1 : public Demon {
 public:
  CallMethod1(T* const ct, void (T::*method)(P), const std::string& name,
              P param1)
      : constraint_(ct), method_(method), name_(name), param1_(param1) {}
 
  ~CallMethod1() override {}
 
  void Run(Solver* const s) override { (constraint_->*method_)(param1_); }
 
  std::string DebugString() const override {
    return absl::StrCat("CallMethod_", name_, "(", constraint_->DebugString(),
                        ", ", ParameterDebugString(param1_), ")");
  }
 
 private:
  T* const constraint_;
  void (T::*const method_)(P);
  const std::string name_;
  P param1_;
};
 
template <class T, class P>
Demon* MakeConstraintDemon1(Solver* const s, T* const ct, void (T::*method)(P),
                            const std::string& name, P param1) {
  return s->RevAlloc(new CallMethod1<T, P>(ct, method, name, param1));
}
 
template <class T, class P, class Q>
class CallMethod2 : public Demon {
 public:
  CallMethod2(T* const ct, void (T::*method)(P, Q), const std::string& name,
              P param1, Q param2)
      : constraint_(ct),
        method_(method),
        name_(name),
        param1_(param1),
        param2_(param2) {}
 
  ~CallMethod2() override {}
 
  void Run(Solver* const s) override {
    (constraint_->*method_)(param1_, param2_);
  }
 
  std::string DebugString() const override {
    return absl::StrCat(absl::StrCat("CallMethod_", name_),
                        absl::StrCat("(", constraint_->DebugString()),
                        absl::StrCat(", ", ParameterDebugString(param1_)),
                        absl::StrCat(", ", ParameterDebugString(param2_), ")"));
  }
 
 private:
  T* const constraint_;
  void (T::*const method_)(P, Q);
  const std::string name_;
  P param1_;
  Q param2_;
};
 
template <class T, class P, class Q>
Demon* MakeConstraintDemon2(Solver* const s, T* const ct,
                            void (T::*method)(P, Q), const std::string& name,
                            P param1, Q param2) {
  return s->RevAlloc(
      new CallMethod2<T, P, Q>(ct, method, name, param1, param2));
}
template <class T, class P, class Q, class R>
class CallMethod3 : public Demon {
 public:
  CallMethod3(T* const ct, void (T::*method)(P, Q, R), const std::string& name,
              P param1, Q param2, R param3)
      : constraint_(ct),
        method_(method),
        name_(name),
        param1_(param1),
        param2_(param2),
        param3_(param3) {}
 
  ~CallMethod3() override {}
 
  void Run(Solver* const s) override {
    (constraint_->*method_)(param1_, param2_, param3_);
  }
 
  std::string DebugString() const override {
    return absl::StrCat(absl::StrCat("CallMethod_", name_),
                        absl::StrCat("(", constraint_->DebugString()),
                        absl::StrCat(", ", ParameterDebugString(param1_)),
                        absl::StrCat(", ", ParameterDebugString(param2_)),
                        absl::StrCat(", ", ParameterDebugString(param3_), ")"));
  }
 
 private:
  T* const constraint_;
  void (T::*const method_)(P, Q, R);
  const std::string name_;
  P param1_;
  Q param2_;
  R param3_;
};
 
template <class T, class P, class Q, class R>
Demon* MakeConstraintDemon3(Solver* const s, T* const ct,
                            void (T::*method)(P, Q, R), const std::string& name,
                            P param1, Q param2, R param3) {
  return s->RevAlloc(
      new CallMethod3<T, P, Q, R>(ct, method, name, param1, param2, param3));
}
 
 
template <class T>
class DelayedCallMethod0 : public Demon {
 public:
  DelayedCallMethod0(T* const ct, void (T::*method)(), const std::string& name)
      : constraint_(ct), method_(method), name_(name) {}
 
  ~DelayedCallMethod0() override {}
 
  void Run(Solver* const s) override { (constraint_->*method_)(); }
 
  Solver::DemonPriority priority() const override {
    return Solver::DELAYED_PRIORITY;
  }
 
  std::string DebugString() const override {
    return "DelayedCallMethod_" + name_ + "(" + constraint_->DebugString() +
           ")";
  }
 
 private:
  T* const constraint_;
  void (T::*const method_)();
  const std::string name_;
};
 
template <class T>
Demon* MakeDelayedConstraintDemon0(Solver* const s, T* const ct,
                                   void (T::*method)(),
                                   const std::string& name) {
  return s->RevAlloc(new DelayedCallMethod0<T>(ct, method, name));
}
 
template <class T, class P>
class DelayedCallMethod1 : public Demon {
 public:
  DelayedCallMethod1(T* const ct, void (T::*method)(P), const std::string& name,
                     P param1)
      : constraint_(ct), method_(method), name_(name), param1_(param1) {}
 
  ~DelayedCallMethod1() override {}
 
  void Run(Solver* const s) override { (constraint_->*method_)(param1_); }
 
  Solver::DemonPriority priority() const override {
    return Solver::DELAYED_PRIORITY;
  }
 
  std::string DebugString() const override {
    return absl::StrCat("DelayedCallMethod_", name_, "(",
                        constraint_->DebugString(), ", ",
                        ParameterDebugString(param1_), ")");
  }
 
 private:
  T* const constraint_;
  void (T::*const method_)(P);
  const std::string name_;
  P param1_;
};
 
template <class T, class P>
Demon* MakeDelayedConstraintDemon1(Solver* const s, T* const ct,
                                   void (T::*method)(P),
                                   const std::string& name, P param1) {
  return s->RevAlloc(new DelayedCallMethod1<T, P>(ct, method, name, param1));
}
 
template <class T, class P, class Q>
class DelayedCallMethod2 : public Demon {
 public:
  DelayedCallMethod2(T* const ct, void (T::*method)(P, Q),
                     const std::string& name, P param1, Q param2)
      : constraint_(ct),
        method_(method),
        name_(name),
        param1_(param1),
        param2_(param2) {}
 
  ~DelayedCallMethod2() override {}
 
  void Run(Solver* const s) override {
    (constraint_->*method_)(param1_, param2_);
  }
 
  Solver::DemonPriority priority() const override {
    return Solver::DELAYED_PRIORITY;
  }
 
  std::string DebugString() const override {
    return absl::StrCat(absl::StrCat("DelayedCallMethod_", name_),
                        absl::StrCat("(", constraint_->DebugString()),
                        absl::StrCat(", ", ParameterDebugString(param1_)),
                        absl::StrCat(", ", ParameterDebugString(param2_), ")"));
  }
 
 private:
  T* const constraint_;
  void (T::*const method_)(P, Q);
  const std::string name_;
  P param1_;
  Q param2_;
};
 
template <class T, class P, class Q>
Demon* MakeDelayedConstraintDemon2(Solver* const s, T* const ct,
                                   void (T::*method)(P, Q),
                                   const std::string& name, P param1,
                                   Q param2) {
  return s->RevAlloc(
      new DelayedCallMethod2<T, P, Q>(ct, method, name, param1, param2));
}
 
#endif  // !defined(SWIG)
 
// ----- LightIntFunctionElementCt -----
 
template <typename F>
class LightIntFunctionElementCt : public Constraint {
 public:
  LightIntFunctionElementCt(Solver* const solver, IntVar* const var,
                            IntVar* const index, F values,
                            std::function<bool()> deep_serialize)
      : Constraint(solver),
        var_(var),
        index_(index),
        values_(std::move(values)),
        deep_serialize_(std::move(deep_serialize)) {}
  ~LightIntFunctionElementCt() override {}
 
  void Post() override {
    Demon* demon = MakeConstraintDemon0(
        solver(), this, &LightIntFunctionElementCt::IndexBound, "IndexBound");
    index_->WhenBound(demon);
  }
 
  void InitialPropagate() override {
    if (index_->Bound()) {
      IndexBound();
    }
  }
 
  std::string DebugString() const override {
    return absl::StrFormat("LightIntFunctionElementCt(%s, %s)",
                           var_->DebugString(), index_->DebugString());
  }
 
  void Accept(ModelVisitor* const visitor) const override {
    visitor->BeginVisitConstraint(ModelVisitor::kLightElementEqual, this);
    visitor->VisitIntegerExpressionArgument(ModelVisitor::kTargetArgument,
                                            var_);
    visitor->VisitIntegerExpressionArgument(ModelVisitor::kIndexArgument,
                                            index_);
    // Warning: This will expand all values into a vector.
    if (deep_serialize_ == nullptr || deep_serialize_()) {
      visitor->VisitInt64ToInt64Extension(values_, index_->Min(),
                                          index_->Max());
    }
    visitor->EndVisitConstraint(ModelVisitor::kLightElementEqual, this);
  }
 
 private:
  void IndexBound() { var_->SetValue(values_(index_->Min())); }
 
  IntVar* const var_;
  IntVar* const index_;
  F values_;
  std::function<bool()> deep_serialize_;
};
 
// ----- LightIntIntFunctionElementCt -----
 
template <typename F>
class LightIntIntFunctionElementCt : public Constraint {
 public:
  LightIntIntFunctionElementCt(Solver* const solver, IntVar* const var,
                               IntVar* const index1, IntVar* const index2,
                               F values, std::function<bool()> deep_serialize)
      : Constraint(solver),
        var_(var),
        index1_(index1),
        index2_(index2),
        values_(std::move(values)),
        deep_serialize_(std::move(deep_serialize)) {}
  ~LightIntIntFunctionElementCt() override {}
  void Post() override {
    Demon* demon = MakeConstraintDemon0(
        solver(), this, &LightIntIntFunctionElementCt::IndexBound,
        "IndexBound");
    index1_->WhenBound(demon);
    index2_->WhenBound(demon);
  }
  void InitialPropagate() override { IndexBound(); }
 
  std::string DebugString() const override {
    return "LightIntIntFunctionElementCt";
  }
 
  void Accept(ModelVisitor* const visitor) const override {
    visitor->BeginVisitConstraint(ModelVisitor::kLightElementEqual, this);
    visitor->VisitIntegerExpressionArgument(ModelVisitor::kTargetArgument,
                                            var_);
    visitor->VisitIntegerExpressionArgument(ModelVisitor::kIndexArgument,
                                            index1_);
    visitor->VisitIntegerExpressionArgument(ModelVisitor::kIndex2Argument,
                                            index2_);
    // Warning: This will expand all values into a vector.
    const int64_t index1_min = index1_->Min();
    const int64_t index1_max = index1_->Max();
    visitor->VisitIntegerArgument(ModelVisitor::kMinArgument, index1_min);
    visitor->VisitIntegerArgument(ModelVisitor::kMaxArgument, index1_max);
    if (deep_serialize_ == nullptr || deep_serialize_()) {
      for (int i = index1_min; i <= index1_max; ++i) {
        visitor->VisitInt64ToInt64Extension(
            [this, i](int64_t j) { return values_(i, j); }, index2_->Min(),
            index2_->Max());
      }
    }
    visitor->EndVisitConstraint(ModelVisitor::kLightElementEqual, this);
  }
 
 private:
  void IndexBound() {
    if (index1_->Bound() && index2_->Bound()) {
      var_->SetValue(values_(index1_->Min(), index2_->Min()));
    }
  }
 
  IntVar* const var_;
  IntVar* const index1_;
  IntVar* const index2_;
  Solver::IndexEvaluator2 values_;
  std::function<bool()> deep_serialize_;
};
 
// TODO(user): rename Start to Synchronize ?
// TODO(user): decouple the iterating from the defining of a neighbor.
class LocalSearchOperator : public BaseObject {
 public:
  LocalSearchOperator() {}
  ~LocalSearchOperator() override {}
  virtual bool MakeNextNeighbor(Assignment* delta, Assignment* deltadelta) = 0;
  virtual void Start(const Assignment* assignment) = 0;
  virtual void Reset() {}
#ifndef SWIG
  virtual const LocalSearchOperator* Self() const { return this; }
#endif  // SWIG
  virtual bool HasFragments() const { return false; }
  virtual bool HoldsDelta() const { return false; }
};
 
class LocalSearchOperatorState {
 public:
  LocalSearchOperatorState() {}
 
  void SetCurrentDomainInjectiveAndKeepInverseValues(int max_value) {
    max_inversible_index_ = candidate_values_.size();
    candidate_value_to_index_.resize(max_value + 1, -1);
    committed_value_to_index_.resize(max_value + 1, -1);
  }
 
  int64_t CandidateValue(int64_t index) const {
    DCHECK_LT(index, candidate_values_.size());
    return candidate_values_[index];
  }
  int64_t CommittedValue(int64_t index) const {
    return committed_values_[index];
  }
  int64_t CheckPointValue(int64_t index) const {
    return checkpoint_values_[index];
  }
  void SetCandidateValue(int64_t index, int64_t value) {
    candidate_values_[index] = value;
    if (index < max_inversible_index_) {
      candidate_value_to_index_[value] = index;
    }
    MarkChange(index);
  }
 
  bool CandidateIsActive(int64_t index) const {
    return candidate_is_active_[index];
  }
  void SetCandidateActive(int64_t index, bool active) {
    if (active) {
      candidate_is_active_.Set(index);
    } else {
      candidate_is_active_.Clear(index);
    }
    MarkChange(index);
  }
 
  void Commit() {
    for (const int64_t index : changes_.PositionsSetAtLeastOnce()) {
      const int64_t value = candidate_values_[index];
      committed_values_[index] = value;
      if (index < max_inversible_index_) {
        committed_value_to_index_[value] = index;
      }
      committed_is_active_.CopyBucket(candidate_is_active_, index);
    }
    changes_.SparseClearAll();
    incremental_changes_.SparseClearAll();
  }
 
  void CheckPoint() { checkpoint_values_ = committed_values_; }
 
  void Revert(bool only_incremental) {
    incremental_changes_.SparseClearAll();
    if (only_incremental) return;
 
    for (const int64_t index : changes_.PositionsSetAtLeastOnce()) {
      const int64_t committed_value = committed_values_[index];
      candidate_values_[index] = committed_value;
      if (index < max_inversible_index_) {
        candidate_value_to_index_[committed_value] = index;
      }
      candidate_is_active_.CopyBucket(committed_is_active_, index);
    }
    changes_.SparseClearAll();
  }
 
  const std::vector<int64_t>& CandidateIndicesChanged() const {
    return changes_.PositionsSetAtLeastOnce();
  }
  const std::vector<int64_t>& IncrementalIndicesChanged() const {
    return incremental_changes_.PositionsSetAtLeastOnce();
  }
 
  void Resize(int size) {
    candidate_values_.resize(size);
    committed_values_.resize(size);
    checkpoint_values_.resize(size);
    candidate_is_active_.Resize(size);
    committed_is_active_.Resize(size);
    changes_.ClearAndResize(size);
    incremental_changes_.ClearAndResize(size);
  }
 
  int64_t CandidateInverseValue(int64_t value) const {
    return candidate_value_to_index_[value];
  }
  int64_t CommittedInverseValue(int64_t value) const {
    return committed_value_to_index_[value];
  }
 
 private:
  void MarkChange(int64_t index) {
    incremental_changes_.Set(index);
    changes_.Set(index);
  }
 
  std::vector<int64_t> candidate_values_;
  std::vector<int64_t> committed_values_;
  std::vector<int64_t> checkpoint_values_;
 
  Bitset64<> candidate_is_active_;
  Bitset64<> committed_is_active_;
 
  SparseBitset<> changes_;
  SparseBitset<> incremental_changes_;
 
  int64_t max_inversible_index_ = -1;
  std::vector<int64_t> candidate_value_to_index_;
  std::vector<int64_t> committed_value_to_index_;
};
 
class IntVarLocalSearchOperator : public LocalSearchOperator {
 public:
  // If keep_inverse_values is true, assumes that vars models an injective
  // function f with domain [0, vars.size()) in which case the operator will
  // maintain the inverse function.
  explicit IntVarLocalSearchOperator(const std::vector<IntVar*>& vars,
                                     bool keep_inverse_values = false) {
    AddVars(vars);
    if (keep_inverse_values) {
      int64_t max_value = -1;
      for (const IntVar* const var : vars) {
        max_value = std::max(max_value, var->Max());
      }
      state_.SetCurrentDomainInjectiveAndKeepInverseValues(max_value);
    }
  }
  ~IntVarLocalSearchOperator() override {}
 
  bool HoldsDelta() const override { return true; }
  void Start(const Assignment* assignment) override {
    state_.CheckPoint();
    RevertChanges(false);
    const int size = Size();
    CHECK_LE(size, assignment->Size())
        << "Assignment contains fewer variables than operator";
    const Assignment::IntContainer& container = assignment->IntVarContainer();
    for (int i = 0; i < size; ++i) {
      const IntVarElement* element = &(container.Element(i));
      if (element->Var() != vars_[i]) {
        CHECK(container.Contains(vars_[i]))
            << "Assignment does not contain operator variable " << vars_[i];
        element = &(container.Element(vars_[i]));
      }
      state_.SetCandidateValue(i, element->Value());
      state_.SetCandidateActive(i, element->Activated());
    }
    state_.Commit();
    OnStart();
  }
  virtual bool IsIncremental() const { return false; }
 
  int Size() const { return vars_.size(); }
  int64_t Value(int64_t index) const {
    DCHECK_LT(index, vars_.size());
    return state_.CandidateValue(index);
  }
  IntVar* Var(int64_t index) const { return vars_[index]; }
  virtual bool SkipUnchanged(int index) const { return false; }
  int64_t OldValue(int64_t index) const { return state_.CommittedValue(index); }
  int64_t PrevValue(int64_t index) const {
    return state_.CheckPointValue(index);
  }
  void SetValue(int64_t index, int64_t value) {
    state_.SetCandidateValue(index, value);
  }
  bool Activated(int64_t index) const {
    return state_.CandidateIsActive(index);
  }
  void Activate(int64_t index) { state_.SetCandidateActive(index, true); }
  void Deactivate(int64_t index) { state_.SetCandidateActive(index, false); }
 
  bool ApplyChanges(Assignment* delta, Assignment* deltadelta) const {
    if (IsIncremental() && candidate_has_changes_) {
      for (const int64_t index : state_.IncrementalIndicesChanged()) {
        IntVar* var = Var(index);
        const int64_t value = Value(index);
        const bool activated = Activated(index);
        AddToAssignment(var, value, activated, nullptr, index, deltadelta);
        AddToAssignment(var, value, activated, &assignment_indices_, index,
                        delta);
      }
    } else {
      delta->Clear();
      for (const int64_t index : state_.CandidateIndicesChanged()) {
        const int64_t value = Value(index);
        const bool activated = Activated(index);
        if (!activated || value != OldValue(index) || !SkipUnchanged(index)) {
          AddToAssignment(Var(index), value, activated, &assignment_indices_,
                          index, delta);
        }
      }
    }
    return true;
  }
 
  void RevertChanges(bool change_was_incremental) {
    candidate_has_changes_ = change_was_incremental && IsIncremental();
 
    if (!candidate_has_changes_) {
      for (const int64_t index : state_.CandidateIndicesChanged()) {
        assignment_indices_[index] = -1;
      }
    }
    state_.Revert(candidate_has_changes_);
  }
 
  void AddVars(const std::vector<IntVar*>& vars) {
    if (!vars.empty()) {
      vars_.insert(vars_.end(), vars.begin(), vars.end());
      const int64_t size = Size();
      assignment_indices_.resize(size, -1);
      state_.Resize(size);
    }
  }
 
  virtual void OnStart() {}
 
 
  bool MakeNextNeighbor(Assignment* delta, Assignment* deltadelta) override;
 
 protected:
  // TODO(user): make it pure virtual, implies porting all apps overriding
  virtual bool MakeOneNeighbor();
 
  int64_t InverseValue(int64_t index) const {
    return state_.CandidateInverseValue(index);
  }
  int64_t OldInverseValue(int64_t index) const {
    return state_.CommittedInverseValue(index);
  }
 
  void AddToAssignment(IntVar* var, int64_t value, bool active,
                       std::vector<int>* assignment_indices, int64_t index,
                       Assignment* assignment) const {
    Assignment::IntContainer* const container =
        assignment->MutableIntVarContainer();
    IntVarElement* element = nullptr;
    if (assignment_indices != nullptr) {
      if ((*assignment_indices)[index] == -1) {
        (*assignment_indices)[index] = container->Size();
        element = assignment->FastAdd(var);
      } else {
        element = container->MutableElement((*assignment_indices)[index]);
      }
    } else {
      element = assignment->FastAdd(var);
    }
    if (active) {
      element->SetValue(value);
      element->Activate();
    } else {
      element->Deactivate();
    }
  }
 
 private:
  std::vector<IntVar*> vars_;
  mutable std::vector<int> assignment_indices_;
  bool candidate_has_changes_ = false;
 
  LocalSearchOperatorState state_;
};
 
class BaseLns : public IntVarLocalSearchOperator {
 public:
  explicit BaseLns(const std::vector<IntVar*>& vars);
  ~BaseLns() override;
  virtual void InitFragments();
  virtual bool NextFragment() = 0;
  void AppendToFragment(int index);
  int FragmentSize() const;
  bool HasFragments() const override { return true; }
 
 protected:
  bool MakeOneNeighbor() override;
 
 private:
  void OnStart() override;
  std::vector<int> fragment_;
};
 
class ChangeValue : public IntVarLocalSearchOperator {
 public:
  explicit ChangeValue(const std::vector<IntVar*>& vars);
  ~ChangeValue() override;
  virtual int64_t ModifyValue(int64_t index, int64_t value) = 0;
 
 protected:
  bool MakeOneNeighbor() override;
 
 private:
  void OnStart() override;
 
  int index_;
};
 
class PathOperator : public IntVarLocalSearchOperator {
 public:
  struct IterationParameters {
    int number_of_base_nodes;
    bool skip_locally_optimal_paths;
    bool accept_path_end_base;
    std::function<int(int64_t)> start_empty_path_class;
    std::function<const std::vector<int>&(/*node=*/int, /*start_node=*/int)>
        get_neighbors;
  };
  PathOperator(const std::vector<IntVar*>& next_vars,
               const std::vector<IntVar*>& path_vars,
               IterationParameters iteration_parameters);
  PathOperator(const std::vector<IntVar*>& next_vars,
               const std::vector<IntVar*>& path_vars, int number_of_base_nodes,
               bool skip_locally_optimal_paths, bool accept_path_end_base,
               std::function<int(int64_t)> start_empty_path_class,
               std::function<const std::vector<int>&(int, int)> get_neighbors)
      : PathOperator(next_vars, path_vars,
                     {number_of_base_nodes, skip_locally_optimal_paths,
                      accept_path_end_base, std::move(start_empty_path_class),
                      std::move(get_neighbors)}) {}
  ~PathOperator() override {}
  virtual bool MakeNeighbor() = 0;
  void Reset() override;
 
  // TODO(user): Make the following methods protected.
  bool SkipUnchanged(int index) const override;
 
  int64_t Next(int64_t node) const {
    DCHECK(!IsPathEnd(node));
    return Value(node);
  }
 
  int64_t Prev(int64_t node) const {
    DCHECK(!IsPathStart(node));
    DCHECK_EQ(Next(InverseValue(node)), node);
    return InverseValue(node);
  }
 
  int64_t Path(int64_t node) const {
    return ignore_path_vars_ ? 0LL : Value(node + number_of_nexts_);
  }
 
  int number_of_nexts() const { return number_of_nexts_; }
 
 protected:
  bool MakeOneNeighbor() override;
  virtual void OnNodeInitialization() {}
 
  int64_t BaseNode(int i) const { return base_nodes_[i]; }
  int BaseAlternative(int i) const { return base_alternatives_[i]; }
  int64_t BaseAlternativeNode(int i) const {
    if (!ConsiderAlternatives(i)) return BaseNode(i);
    const int alternative_index = alternative_index_[BaseNode(i)];
    return alternative_index >= 0
               ? alternative_sets_[alternative_index][base_alternatives_[i]]
               : BaseNode(i);
  }
  int BaseSiblingAlternative(int i) const {
    return base_sibling_alternatives_[i];
  }
  int64_t BaseSiblingAlternativeNode(int i) const {
    if (!ConsiderAlternatives(i)) return BaseNode(i);
    const int sibling_alternative_index =
        GetSiblingAlternativeIndex(BaseNode(i));
    return sibling_alternative_index >= 0
               ? alternative_sets_[sibling_alternative_index]
                                  [base_sibling_alternatives_[i]]
               : BaseNode(i);
  }
  int64_t StartNode(int i) const { return path_starts_[base_paths_[i]]; }
  int64_t EndNode(int i) const { return path_ends_[base_paths_[i]]; }
  const std::vector<int64_t>& path_starts() const { return path_starts_; }
  int PathClass(int i) const { return PathClassFromStartNode(StartNode(i)); }
  int PathClassFromStartNode(int64_t start_node) const {
    return iteration_parameters_.start_empty_path_class != nullptr
               ? iteration_parameters_.start_empty_path_class(start_node)
               : start_node;
  }
 
  // TODO(user): remove this when automatic detection of such cases in done.
  virtual bool RestartAtPathStartOnSynchronize() { return false; }
  // TODO(user): ideally this should be OnSamePath(int64_t node1, int64_t
  // node2);
  virtual bool OnSamePathAsPreviousBase(int64_t base_index) { return false; }
  virtual int64_t GetBaseNodeRestartPosition(int base_index) {
    return StartNode(base_index);
  }
  virtual void SetNextBaseToIncrement(int64_t base_index) {
    next_base_to_increment_ = base_index;
  }
  virtual bool ConsiderAlternatives(int64_t base_index) const { return false; }
 
  int64_t OldNext(int64_t node) const {
    DCHECK(!IsPathEnd(node));
    return OldValue(node);
  }
 
  int64_t PrevNext(int64_t node) const {
    DCHECK(!IsPathEnd(node));
    return PrevValue(node);
  }
 
  int64_t OldPrev(int64_t node) const {
    DCHECK(!IsPathStart(node));
    return OldInverseValue(node);
  }
 
  int64_t OldPath(int64_t node) const {
    return ignore_path_vars_ ? 0LL : OldValue(node + number_of_nexts_);
  }
 
  int CurrentNodePathStart(int64_t node) const {
    return node_path_starts_[node];
  }
 
  int CurrentNodePathEnd(int64_t node) const { return node_path_ends_[node]; }
 
  bool MoveChain(int64_t before_chain, int64_t chain_end, int64_t destination);
 
  bool ReverseChain(int64_t before_chain, int64_t after_chain,
                    int64_t* chain_last);
 
  bool MakeActive(int64_t node, int64_t destination);
  bool MakeChainInactive(int64_t before_chain, int64_t chain_end);
  bool SwapActiveAndInactive(int64_t active, int64_t inactive);
 
  void SetNext(int64_t from, int64_t to, int64_t path) {
    DCHECK_LT(from, number_of_nexts_);
    SetValue(from, to);
    if (!ignore_path_vars_) {
      DCHECK_LT(from + number_of_nexts_, Size());
      SetValue(from + number_of_nexts_, path);
    }
  }
 
  bool IsPathEnd(int64_t node) const { return node >= number_of_nexts_; }
 
  bool IsPathStart(int64_t node) const { return OldInverseValue(node) == -1; }
 
  bool IsInactive(int64_t node) const {
    return !IsPathEnd(node) && inactives_[node];
  }
 
  virtual bool InitPosition() const { return false; }
  void ResetPosition() { just_started_ = true; }
 
  int AddAlternativeSet(const std::vector<int64_t>& alternative_set) {
    const int alternative = alternative_sets_.size();
    for (int64_t node : alternative_set) {
      DCHECK_EQ(-1, alternative_index_[node]);
      alternative_index_[node] = alternative;
    }
    alternative_sets_.push_back(alternative_set);
    sibling_alternative_.push_back(-1);
    return alternative;
  }
#ifndef SWIG
  template <typename PairType>
  void AddPairAlternativeSets(
      const std::vector<PairType>& pair_alternative_sets) {
    for (const auto& [alternative_set, sibling_alternative_set] :
         pair_alternative_sets) {
      sibling_alternative_.back() = AddAlternativeSet(alternative_set) + 1;
      AddAlternativeSet(sibling_alternative_set);
    }
  }
#endif  // SWIG
  int64_t GetActiveInAlternativeSet(int alternative_index) const {
    return alternative_index >= 0
               ? active_in_alternative_set_[alternative_index]
               : -1;
  }
  int64_t GetActiveAlternativeNode(int node) const {
    return GetActiveInAlternativeSet(alternative_index_[node]);
  }
  int GetSiblingAlternativeIndex(int node) const {
    if (node >= alternative_index_.size()) return -1;
    const int alternative = alternative_index_[node];
    return alternative >= 0 ? sibling_alternative_[alternative] : -1;
  }
  int64_t GetActiveAlternativeSibling(int node) const {
    if (node >= alternative_index_.size()) return -1;
    const int alternative = alternative_index_[node];
    const int sibling_alternative =
        alternative >= 0 ? sibling_alternative_[alternative] : -1;
    return GetActiveInAlternativeSet(sibling_alternative);
  }
  bool CheckChainValidity(int64_t before_chain, int64_t chain_end,
                          int64_t exclude) const;
 
  bool HasNeighbors() const {
    return iteration_parameters_.get_neighbors != nullptr;
  }
 
  int GetNeighborForBaseNode(int64_t base_index) const {
    DCHECK(HasNeighbors());
    return iteration_parameters_.get_neighbors(
        BaseNode(base_index),
        StartNode(base_index))[calls_per_base_node_[base_index]];
  }
 
  const int number_of_nexts_;
  const bool ignore_path_vars_;
 
 private:
  void OnStart() override;
  bool OnSamePath(int64_t node1, int64_t node2) const;
 
  bool CheckEnds() const {
    const int base_node_size = base_nodes_.size();
    for (int i = base_node_size - 1; i >= 0; --i) {
      if (base_nodes_[i] != end_nodes_[i] || calls_per_base_node_[0] > 0) {
        return true;
      }
    }
    return false;
  }
  bool IncrementPosition();
  void InitializePathStarts();
  void InitializeInactives();
  void InitializeBaseNodes();
  void InitializeAlternatives();
  void Synchronize();
 
  class ActivePaths {
   public:
    explicit ActivePaths(int num_nodes) : start_to_path_(num_nodes, -1) {}
    void Clear() { is_path_pair_active_.clear(); }
    template <typename T>
    void Initialize(T is_start) {
      if (is_path_pair_active_.empty()) {
        num_paths_ = 0;
        absl::c_fill(start_to_path_, -1);
        for (int i = 0; i < start_to_path_.size(); ++i) {
          if (is_start(i)) {
            start_to_path_[i] = num_paths_;
            ++num_paths_;
          }
        }
        is_path_pair_active_.resize(num_paths_ * num_paths_, true);
      }
    }
    void DeactivatePathPair(int start1, int start2) {
      is_path_pair_active_[start_to_path_[start1] * num_paths_ +
                           start_to_path_[start2]] = false;
    }
    void ActivatePath(int start) {
      const int p1 = start_to_path_[start];
      const int p1_block = num_paths_ * p1;
      for (int p2 = 0; p2 < num_paths_; ++p2) {
        is_path_pair_active_[p1_block + p2] = true;
      }
      for (int p2_block = 0; p2_block < is_path_pair_active_.size();
           p2_block += num_paths_) {
        is_path_pair_active_[p2_block + p1] = true;
      }
    }
    bool IsPathPairActive(int start1, int start2) const {
      return is_path_pair_active_[start_to_path_[start1] * num_paths_ +
                                  start_to_path_[start2]];
    }
 
   private:
    int num_paths_ = 0;
    std::vector<int64_t> start_to_path_;
    std::vector<bool> is_path_pair_active_;
  };
 
  std::vector<int> base_nodes_;
  std::vector<int> base_alternatives_;
  std::vector<int> base_sibling_alternatives_;
  std::vector<int> end_nodes_;
  std::vector<int> base_paths_;
  std::vector<int> node_path_starts_;
  std::vector<int> node_path_ends_;
  std::vector<int> calls_per_base_node_;
  std::vector<int64_t> path_starts_;
  std::vector<int64_t> path_ends_;
  std::vector<bool> inactives_;
  bool just_started_;
  bool first_start_;
  int next_base_to_increment_;
  IterationParameters iteration_parameters_;
  bool optimal_paths_enabled_;
  std::vector<int> path_basis_;
  ActivePaths active_paths_;
#ifndef SWIG
  std::vector<std::vector<int64_t>> alternative_sets_;
#endif  // SWIG
  std::vector<int> alternative_index_;
  std::vector<int64_t> active_in_alternative_set_;
  std::vector<int> sibling_alternative_;
};
 
template <class T>
LocalSearchOperator* MakeLocalSearchOperator(
    Solver* solver, const std::vector<IntVar*>& vars,
    const std::vector<IntVar*>& secondary_vars,
    std::function<int(int64_t)> start_empty_path_class);
 
template <class T>
LocalSearchOperator* MakeLocalSearchOperatorWithNeighbors(
    Solver* solver, const std::vector<IntVar*>& vars,
    const std::vector<IntVar*>& secondary_vars,
    std::function<int(int64_t)> start_empty_path_class,
    std::function<const std::vector<int>&(int, int)> get_neighbors);
 
 
#if !defined(SWIG)
// After building a Directed Acyclic Graph, allows to generate sub-DAGs
// reachable from a node.
// Workflow:
// - Call AddArc() repeatedly to add arcs describing a DAG. Nodes are allocated
//   on the user side, they must be nonnegative, and it is better but not
//   mandatory for the set of nodes to be dense.
// - Call BuildGraph(). This precomputes all the information needed to make
//   subsequent requests for sub-DAGs.
// - Call ComputeSortedSubDagArcs(node). This returns a view to arcs reachable
//   from node, in topological order.
// All arcs must be added before calling BuildGraph(),
// and ComputeSortedSubDagArcs() can only be called after BuildGraph().
// If the arcs form a graph that has directed cycles,
// - in debug mode, BuildGraph() will crash.
// - otherwise, BuildGraph() will not crash, but ComputeSortedSubDagArcs()
//   will only return a subset of arcs reachable by the given node.
class SubDagComputer {
 public:
  DEFINE_STRONG_INT_TYPE(ArcId, int);
  DEFINE_STRONG_INT_TYPE(NodeId, int);
  SubDagComputer() = default;
  // Adds an arc between node 'tail' and node 'head'. Nodes must be nonnegative.
  // Returns the index of the new arc, those are used to identify arcs when
  // calling ComputeSortedSubDagArcs().
  ArcId AddArc(NodeId tail, NodeId head) {
    DCHECK(!graph_was_built_);
    num_nodes_ = std::max(num_nodes_, std::max(tail.value(), head.value()) + 1);
    const ArcId arc_id(arcs_.size());
    arcs_.push_back({.tail = tail, .head = head, .arc_id = arc_id});
    return arc_id;
  }
  // Finishes the construction of the DAG.  'num_nodes' is the number of nodes
  // in the DAG and must be greater than all node indices passed to AddArc().
  void BuildGraph(int num_nodes);
  // Computes the arcs of the sub-DAG reachable from node returns a view of
  // those arcs in topological order.
  const std::vector<ArcId>& ComputeSortedSubDagArcs(NodeId node);
 
 private:
  // Checks whether the underlying graph has a directed cycle.
  // Should be called after the graph has been built.
  bool HasDirectedCycle() const;
 
  struct Arc {
    NodeId tail;
    NodeId head;
    ArcId arc_id;
    bool operator<(const Arc& other) const {
      return std::tie(tail, arc_id) < std::tie(other.tail, other.arc_id);
    }
  };
  int num_nodes_ = 0;
  std::vector<Arc> arcs_;
  // Initialized by BuildGraph(), after which the outgoing arcs of node n are
  // the range from arcs_[arcs_of_node_[n]] included to
  // arcs_[arcs_of_node_[n+1]] excluded.
  util_intops::StrongVector<NodeId, int> arcs_of_node_;
  // Must be false before BuildGraph() is called, true afterwards.
  bool graph_was_built_ = false;
  // Used by ComputeSortedSubDagArcs.
  util_intops::StrongVector<NodeId, int> indegree_of_node_;
  // Used by ComputeSortedSubDagArcs.
  std::vector<NodeId> nodes_to_visit_;
  // Used as output, set up as a member to allow reuse.
  std::vector<ArcId> sorted_arcs_;
};
 
// A LocalSearchState is a container for variables with domains that can be
// relaxed and tightened, saved and restored. It represents the solution state
// of a local search engine, and allows it to go from solution to solution by
// relaxing some variables to form a new subproblem, then tightening those
// variables to move to a new solution representation. That state may be saved
// to an internal copy, or reverted to the last saved internal copy.
// Relaxing a variable returns its bounds to their initial state.
// Tightening a variable's bounds may make its min larger than its max,
// in that case, the tightening function will return false, and the state will
// be marked as invalid. No other operations than Revert() can be called on an
// invalid state: in particular, an invalid state cannot be saved.
class LocalSearchState {
 public:
  class Variable;
  DEFINE_STRONG_INT_TYPE(VariableDomainId, int);
  DEFINE_STRONG_INT_TYPE(ConstraintId, int);
  // Adds a variable domain to this state, returns a handler to the new domain.
  VariableDomainId AddVariableDomain(int64_t relaxed_min, int64_t relaxed_max);
  void RelaxVariableDomain(VariableDomainId domain_id);
  bool TightenVariableDomainMin(VariableDomainId domain_id, int64_t value);
  bool TightenVariableDomainMax(VariableDomainId domain_id, int64_t value);
  int64_t VariableDomainMin(VariableDomainId domain_id) const;
  int64_t VariableDomainMax(VariableDomainId domain_id) const;
  void ChangeRelaxedVariableDomain(VariableDomainId domain_id, int64_t min,
                                   int64_t max);
 
  // Propagation of all events.
  void PropagateRelax(VariableDomainId domain_id);
  bool PropagateTighten(VariableDomainId domain_id);
  // Makes a variable, an object with restricted operations on the underlying
  // domain identified by domain_id: only Relax, Tighten and Min/Max read
  // operations are available.
  Variable MakeVariable(VariableDomainId domain_id);
  void Commit();
  void Revert();
  bool StateIsFeasible() const {
    return state_domains_are_all_nonempty_ && num_committed_empty_domains_ == 0;
  }
  // Adds a constraint that output = input_offset + sum_i weight_i * input_i.
  void AddWeightedSumConstraint(
      const std::vector<VariableDomainId>& input_domain_ids,
      const std::vector<int64_t>& input_weights, int64_t input_offset,
      VariableDomainId output_domain_id);
  // Precomputes which domain change triggers which constraint(s).
  // Should be run after adding all constraints, before any Relax()/Tighten().
  void CompileConstraints();
 
 private:
  // VariableDomains implement the domain of Variables.
  // Those are trailed, meaning they are saved on their first modification,
  // and can be reverted or committed in O(1) per modification.
  struct VariableDomain {
    int64_t min;
    int64_t max;
  };
  bool IntersectionIsEmpty(const VariableDomain& d1,
                           const VariableDomain& d2) const {
    return d1.max < d2.min || d2.max < d1.min;
  }
  util_intops::StrongVector<VariableDomainId, VariableDomain> relaxed_domains_;
  util_intops::StrongVector<VariableDomainId, VariableDomain> current_domains_;
  struct TrailedVariableDomain {
    VariableDomain committed_domain;
    VariableDomainId domain_id;
  };
  std::vector<TrailedVariableDomain> trailed_domains_;
  util_intops::StrongVector<VariableDomainId, bool> domain_is_trailed_;
  // True iff all domains have their min <= max.
  bool state_domains_are_all_nonempty_ = true;
  bool state_has_relaxed_domains_ = false;
  // Number of domains d for which the intersection of
  // current_domains_[d] and relaxed_domains_[d] is empty.
  int num_committed_empty_domains_ = 0;
  int trailed_num_committed_empty_domains_ = 0;
 
  // Constraints may be trailed too, they decide how to track their internal
  // structure.
  class Constraint;
  void TrailConstraint(Constraint* constraint) {
    trailed_constraints_.push_back(constraint);
  }
  std::vector<Constraint*> trailed_constraints_;
 
  // Stores domain-constraint dependencies, allows to generate topological
  // orderings of dependency arcs reachable from nodes.
  class DependencyGraph {
   public:
    DependencyGraph() {}
    // There are two kinds of domain-constraint dependencies:
    // - domain -> constraint when the domain is an input to the constraint.
    //   Then the label is the index of the domain in the input tuple.
    // - constraint -> domain when the domain is the output of the constraint.
    //   Then, the label is -1.
    struct Dependency {
      VariableDomainId domain_id;
      int input_index;
      ConstraintId constraint_id;
    };
    // Adds all dependencies domains[i] -> constraint labelled by i.
    void AddDomainsConstraintDependencies(
        const std::vector<VariableDomainId>& domain_ids,
        ConstraintId constraint_id);
    // Adds a dependency domain -> constraint labelled by -1.
    void AddConstraintDomainDependency(ConstraintId constraint_id,
                                       VariableDomainId domain_id);
    // After all dependencies have been added,
    // builds the DAG representation that allows to compute sorted dependencies.
    void BuildDependencyDAG(int num_domains);
    // Returns a view on the list of arc dependencies reachable by given domain,
    // in some topological order of the overall DAG. Modifying the graph or
    // calling ComputeSortedDependencies() again invalidates the view.
    const std::vector<Dependency>& ComputeSortedDependencies(
        VariableDomainId domain_id);
 
   private:
    using ArcId = SubDagComputer::ArcId;
    using NodeId = SubDagComputer::NodeId;
    // Returns dag_node_of_domain_[domain_id] if already defined,
    // or makes a node for domain_id, possibly extending dag_node_of_domain_.
    NodeId GetOrCreateNodeOfDomainId(VariableDomainId domain_id);
    // Returns dag_node_of_constraint_[constraint_id] if already defined,
    // or makes a node for constraint_id, possibly extending
    // dag_node_of_constraint_.
    NodeId GetOrCreateNodeOfConstraintId(ConstraintId constraint_id);
    // Structure of the expression DAG, used to buffer propagation storage.
    SubDagComputer dag_;
    // Maps arcs of dag_ to domain/constraint dependencies.
    util_intops::StrongVector<ArcId, Dependency> dependency_of_dag_arc_;
    // Maps domain ids to dag_ nodes.
    util_intops::StrongVector<VariableDomainId, NodeId> dag_node_of_domain_;
    // Maps constraint ids to dag_ nodes.
    util_intops::StrongVector<ConstraintId, NodeId> dag_node_of_constraint_;
    // Number of nodes currently allocated in dag_.
    // Reserve node 0 as a default dummy node with no dependencies.
    int num_dag_nodes_ = 1;
    // Used as reusable output of ComputeSortedDependencies().
    std::vector<Dependency> sorted_dependencies_;
  };
  DependencyGraph dependency_graph_;
 
  // Propagation order storage: each domain change triggers constraints.
  // Each trigger tells a constraint that a domain changed, and identifies
  // the domain by the index in the list of the constraint's inputs.
  struct Trigger {
    Constraint* constraint;
    int input_index;
  };
  // Triggers of all constraints, concatenated.
  // The triggers of domain i are stored from triggers_of_domain_[i]
  // to triggers_of_domain_[i+1] excluded.
  std::vector<Trigger> triggers_;
  util_intops::StrongVector<VariableDomainId, int> triggers_of_domain_;
 
  // Constraints are used to form expressions that make up the objective.
  // Constraints are directed: they have inputs and an output, moreover the
  // constraint-domain graph must not have directed cycles.
  class Constraint {
   public:
    virtual ~Constraint() = default;
    virtual LocalSearchState::VariableDomain Propagate(int input_index) = 0;
    virtual VariableDomainId Output() const = 0;
    virtual void Commit() = 0;
    virtual void Revert() = 0;
  };
  // WeightedSum constraints enforces the equation:
  //   output = offset + sum_i input_weights[i] * input_domain_ids[i]
  class WeightedSum final : public Constraint {
   public:
    WeightedSum(LocalSearchState* state,
                const std::vector<VariableDomainId>& input_domain_ids,
                const std::vector<int64_t>& input_weights, int64_t input_offset,
                VariableDomainId output);
    ~WeightedSum() override = default;
    LocalSearchState::VariableDomain Propagate(int input_index) override;
    void Commit() override;
    void Revert() override;
    VariableDomainId Output() const override { return output_; }
 
   private:
    // Weighted variable holds a variable's domain, an associated weight,
    // and the variable's last known min and max.
    struct WeightedVariable {
      int64_t min;
      int64_t max;
      int64_t committed_min;
      int64_t committed_max;
      int64_t weight;
      VariableDomainId domain;
      bool is_trailed;
      void Commit() {
        committed_min = min;
        committed_max = max;
        is_trailed = false;
      }
      void Revert() {
        min = committed_min;
        max = committed_max;
        is_trailed = false;
      }
    };
    std::vector<WeightedVariable> inputs_;
    std::vector<WeightedVariable*> trailed_inputs_;
    // Invariants held by this constraint to allow O(1) propagation.
    struct Invariants {
      // Number of inputs_[i].min equal to kint64min.
      int64_t num_neg_inf;
      // Sum of inputs_[i].min that are different from kint64min.
      int64_t wsum_mins;
      // Number of inputs_[i].max equal to kint64max.
      int64_t num_pos_inf;
      // Sum of inputs_[i].max that are different from kint64max.
      int64_t wsum_maxs;
    };
    Invariants invariants_;
    Invariants committed_invariants_;
 
    const VariableDomainId output_;
    LocalSearchState* const state_;
    bool constraint_is_trailed_ = false;
  };
  // Used to identify constraints and hold ownership.
  util_intops::StrongVector<ConstraintId, std::unique_ptr<Constraint>> constraints_;
};
 
// A LocalSearchState Variable can only be created by a LocalSearchState,
// then it is meant to be passed by copy. If at some point the duplication of
// LocalSearchState pointers is too expensive, we could switch to index only,
// and the user would have to know the relevant state. The present setup allows
// to ensure that variable users will not misuse the state.
class LocalSearchState::Variable {
 public:
  int64_t Min() const { return state_->VariableDomainMin(domain_id_); }
  int64_t Max() const { return state_->VariableDomainMax(domain_id_); }
  bool SetMin(int64_t new_min) {
    return state_->TightenVariableDomainMin(domain_id_, new_min) &&
           state_->PropagateTighten(domain_id_);
  }
  bool SetMax(int64_t new_max) {
    return state_->TightenVariableDomainMax(domain_id_, new_max) &&
           state_->PropagateTighten(domain_id_);
  }
  void Relax() {
    state_->RelaxVariableDomain(domain_id_);
    state_->PropagateRelax(domain_id_);
  }
 
 private:
  // Only LocalSearchState can construct LocalSearchVariables.
  friend class LocalSearchState;
 
  Variable(LocalSearchState* state, VariableDomainId domain_id)
      : state_(state), domain_id_(domain_id) {}
 
  LocalSearchState* const state_;
  const VariableDomainId domain_id_;
};
#endif  // !defined(SWIG)
 
class LocalSearchFilter : public BaseObject {
 public:
  virtual void Relax(const Assignment* delta, const Assignment* deltadelta) {}
  virtual void Commit(const Assignment* delta, const Assignment* deltadelta) {}
 
  virtual bool Accept(const Assignment* delta, const Assignment* deltadelta,
                      int64_t objective_min, int64_t objective_max) = 0;
  virtual bool IsIncremental() const { return false; }
 
  virtual void Synchronize(const Assignment* assignment,
                           const Assignment* delta) = 0;
  virtual void Revert() {}
 
  virtual void Reset() {}
 
  virtual int64_t GetSynchronizedObjectiveValue() const { return 0LL; }
  // If the last Accept() call returned false, returns an undefined value.
  virtual int64_t GetAcceptedObjectiveValue() const { return 0LL; }
};
 
class LocalSearchFilterManager : public BaseObject {
 public:
  // This class is responsible for calling filters methods in a correct order.
  // For now, an order is specified explicitly by the user.
  enum FilterEventType { kAccept, kRelax };
  struct FilterEvent {
    LocalSearchFilter* filter;
    FilterEventType event_type;
    int priority;
  };
 
  std::string DebugString() const override {
    return "LocalSearchFilterManager";
  }
  // Builds a manager that calls filter methods ordered by increasing priority.
  // Note that some filters might appear only once, if their Relax() or Accept()
  // are trivial.
  explicit LocalSearchFilterManager(std::vector<FilterEvent> filter_events);
  // Builds a manager that calls filter methods using the following ordering:
  // first Relax() in vector order, then Accept() in vector order.
  explicit LocalSearchFilterManager(std::vector<LocalSearchFilter*> filters);
 
  // Calls Revert() of filters, in reverse order of Relax events.
  void Revert();
  bool Accept(LocalSearchMonitor* monitor, const Assignment* delta,
              const Assignment* deltadelta, int64_t objective_min,
              int64_t objective_max);
  void Synchronize(const Assignment* assignment, const Assignment* delta);
  int64_t GetSynchronizedObjectiveValue() const { return synchronized_value_; }
  int64_t GetAcceptedObjectiveValue() const { return accepted_value_; }
 
 private:
  // Finds the last event (incremental -itself- or not) with the same priority
  // as the last incremental event.
  void FindIncrementalEventEnd();
 
  std::vector<FilterEvent> events_;
  int last_event_called_ = -1;
  // If a filter is incremental, its Relax() and Accept() must be called for
  // every candidate, even if the Accept() of a prior filter rejected it.
  // To ensure that those incremental filters have consistent inputs, all
  // intermediate events with Relax() must also be called.
  int incremental_events_end_ = 0;
  int64_t synchronized_value_;
  int64_t accepted_value_;
};
 
class IntVarLocalSearchFilter : public LocalSearchFilter {
 public:
  explicit IntVarLocalSearchFilter(const std::vector<IntVar*>& vars);
  ~IntVarLocalSearchFilter() override;
  void Synchronize(const Assignment* assignment,
                   const Assignment* delta) override;
 
  bool FindIndex(IntVar* const var, int64_t* index) const {
    DCHECK(index != nullptr);
    const int var_index = var->index();
    *index = (var_index < var_index_to_index_.size())
                 ? var_index_to_index_[var_index]
                 : kUnassigned;
    return *index != kUnassigned;
  }
 
  void AddVars(const std::vector<IntVar*>& vars);
  int Size() const { return vars_.size(); }
  IntVar* Var(int index) const { return vars_[index]; }
  int64_t Value(int index) const {
    DCHECK(IsVarSynced(index));
    return values_[index];
  }
  bool IsVarSynced(int index) const { return var_synced_[index]; }
 
 protected:
  virtual void OnSynchronize(const Assignment* delta) {}
  void SynchronizeOnAssignment(const Assignment* assignment);
 
 private:
  std::vector<IntVar*> vars_;
  std::vector<int64_t> values_;
  std::vector<bool> var_synced_;
  std::vector<int> var_index_to_index_;
  static const int kUnassigned;
};
 
class PropagationMonitor : public SearchMonitor {
 public:
  explicit PropagationMonitor(Solver* solver);
  ~PropagationMonitor() override;
  std::string DebugString() const override { return "PropagationMonitor"; }
 
  virtual void BeginConstraintInitialPropagation(Constraint* constraint) = 0;
  virtual void EndConstraintInitialPropagation(Constraint* constraint) = 0;
  virtual void BeginNestedConstraintInitialPropagation(Constraint* parent,
                                                       Constraint* nested) = 0;
  virtual void EndNestedConstraintInitialPropagation(Constraint* parent,
                                                     Constraint* nested) = 0;
  virtual void RegisterDemon(Demon* demon) = 0;
  virtual void BeginDemonRun(Demon* demon) = 0;
  virtual void EndDemonRun(Demon* demon) = 0;
  virtual void StartProcessingIntegerVariable(IntVar* var) = 0;
  virtual void EndProcessingIntegerVariable(IntVar* var) = 0;
  virtual void PushContext(const std::string& context) = 0;
  virtual void PopContext() = 0;
  virtual void SetMin(IntExpr* expr, int64_t new_min) = 0;
  virtual void SetMax(IntExpr* expr, int64_t new_max) = 0;
  virtual void SetRange(IntExpr* expr, int64_t new_min, int64_t new_max) = 0;
  virtual void SetMin(IntVar* var, int64_t new_min) = 0;
  virtual void SetMax(IntVar* var, int64_t new_max) = 0;
  virtual void SetRange(IntVar* var, int64_t new_min, int64_t new_max) = 0;
  virtual void RemoveValue(IntVar* var, int64_t value) = 0;
  virtual void SetValue(IntVar* var, int64_t value) = 0;
  virtual void RemoveInterval(IntVar* var, int64_t imin, int64_t imax) = 0;
  virtual void SetValues(IntVar* var, const std::vector<int64_t>& values) = 0;
  virtual void RemoveValues(IntVar* var,
                            const std::vector<int64_t>& values) = 0;
  virtual void SetStartMin(IntervalVar* var, int64_t new_min) = 0;
  virtual void SetStartMax(IntervalVar* var, int64_t new_max) = 0;
  virtual void SetStartRange(IntervalVar* var, int64_t new_min,
                             int64_t new_max) = 0;
  virtual void SetEndMin(IntervalVar* var, int64_t new_min) = 0;
  virtual void SetEndMax(IntervalVar* var, int64_t new_max) = 0;
  virtual void SetEndRange(IntervalVar* var, int64_t new_min,
                           int64_t new_max) = 0;
  virtual void SetDurationMin(IntervalVar* var, int64_t new_min) = 0;
  virtual void SetDurationMax(IntervalVar* var, int64_t new_max) = 0;
  virtual void SetDurationRange(IntervalVar* var, int64_t new_min,
                                int64_t new_max) = 0;
  virtual void SetPerformed(IntervalVar* var, bool value) = 0;
  virtual void RankFirst(SequenceVar* var, int index) = 0;
  virtual void RankNotFirst(SequenceVar* var, int index) = 0;
  virtual void RankLast(SequenceVar* var, int index) = 0;
  virtual void RankNotLast(SequenceVar* var, int index) = 0;
  virtual void RankSequence(SequenceVar* var,
                            const std::vector<int>& rank_first,
                            const std::vector<int>& rank_last,
                            const std::vector<int>& unperformed) = 0;
  void Install() override;
};
 
class LocalSearchMonitor : public SearchMonitor {
  // TODO(user): Add monitoring of local search filters.
 public:
  explicit LocalSearchMonitor(Solver* solver);
  ~LocalSearchMonitor() override;
  std::string DebugString() const override { return "LocalSearchMonitor"; }
 
  virtual void BeginOperatorStart() = 0;
  virtual void EndOperatorStart() = 0;
  virtual void BeginMakeNextNeighbor(const LocalSearchOperator* op) = 0;
  virtual void EndMakeNextNeighbor(const LocalSearchOperator* op,
                                   bool neighbor_found, const Assignment* delta,
                                   const Assignment* deltadelta) = 0;
  virtual void BeginFilterNeighbor(const LocalSearchOperator* op) = 0;
  virtual void EndFilterNeighbor(const LocalSearchOperator* op,
                                 bool neighbor_found) = 0;
  virtual void BeginAcceptNeighbor(const LocalSearchOperator* op) = 0;
  virtual void EndAcceptNeighbor(const LocalSearchOperator* op,
                                 bool neighbor_found) = 0;
  virtual void BeginFiltering(const LocalSearchFilter* filter) = 0;
  virtual void EndFiltering(const LocalSearchFilter* filter, bool reject) = 0;
 
  virtual bool IsActive() const = 0;
 
  void Install() override;
};
 
class BooleanVar : public IntVar {
 public:
  static const int kUnboundBooleanVarValue;
 
  explicit BooleanVar(Solver* const s, const std::string& name = "")
      : IntVar(s, name), value_(kUnboundBooleanVarValue) {}
 
  ~BooleanVar() override {}
 
  int64_t Min() const override { return (value_ == 1); }
  void SetMin(int64_t m) override;
  int64_t Max() const override { return (value_ != 0); }
  void SetMax(int64_t m) override;
  void SetRange(int64_t mi, int64_t ma) override;
  bool Bound() const override { return (value_ != kUnboundBooleanVarValue); }
  int64_t Value() const override {
    CHECK_NE(value_, kUnboundBooleanVarValue) << "variable is not bound";
    return value_;
  }
  void RemoveValue(int64_t v) override;
  void RemoveInterval(int64_t l, int64_t u) override;
  void WhenBound(Demon* d) override;
  void WhenRange(Demon* d) override { WhenBound(d); }
  void WhenDomain(Demon* d) override { WhenBound(d); }
  uint64_t Size() const override;
  bool Contains(int64_t v) const override;
  IntVarIterator* MakeHoleIterator(bool reversible) const override;
  IntVarIterator* MakeDomainIterator(bool reversible) const override;
  std::string DebugString() const override;
  int VarType() const override { return BOOLEAN_VAR; }
 
  IntVar* IsEqual(int64_t constant) override;
  IntVar* IsDifferent(int64_t constant) override;
  IntVar* IsGreaterOrEqual(int64_t constant) override;
  IntVar* IsLessOrEqual(int64_t constant) override;
 
  virtual void RestoreValue() = 0;
  std::string BaseName() const override { return "BooleanVar"; }
 
  int RawValue() const { return value_; }
 
 protected:
  int value_;
  SimpleRevFIFO<Demon*> bound_demons_;
  SimpleRevFIFO<Demon*> delayed_bound_demons_;
};
 
class SymmetryManager;
 
class SymmetryBreaker : public DecisionVisitor {
 public:
  SymmetryBreaker()
      : symmetry_manager_(nullptr), index_in_symmetry_manager_(-1) {}
  ~SymmetryBreaker() override {}
 
  void AddIntegerVariableEqualValueClause(IntVar* var, int64_t value);
  void AddIntegerVariableGreaterOrEqualValueClause(IntVar* var, int64_t value);
  void AddIntegerVariableLessOrEqualValueClause(IntVar* var, int64_t value);
 
 private:
  friend class SymmetryManager;
  void set_symmetry_manager_and_index(SymmetryManager* manager, int index) {
    CHECK(symmetry_manager_ == nullptr);
    CHECK_EQ(-1, index_in_symmetry_manager_);
    symmetry_manager_ = manager;
    index_in_symmetry_manager_ = index;
  }
  SymmetryManager* symmetry_manager() const { return symmetry_manager_; }
  int index_in_symmetry_manager() const { return index_in_symmetry_manager_; }
 
  SymmetryManager* symmetry_manager_;
  int index_in_symmetry_manager_;
};
 
class SearchLog : public SearchMonitor {
 public:
  SearchLog(Solver* solver, std::vector<IntVar*> vars, std::string vars_name,
            std::vector<double> scaling_factors, std::vector<double> offsets,
            std::function<std::string()> display_callback,
            bool display_on_new_solutions_only, int period);
  ~SearchLog() override;
  void EnterSearch() override;
  void ExitSearch() override;
  bool AtSolution() override;
  void BeginFail() override;
  void NoMoreSolutions() override;
  void AcceptUncheckedNeighbor() override;
  void ApplyDecision(Decision* decision) override;
  void RefuteDecision(Decision* decision) override;
  void OutputDecision();
  void Maintain();
  void BeginInitialPropagation() override;
  void EndInitialPropagation() override;
  std::string DebugString() const override;
 
 protected:
  /* Bottleneck function used for all UI related output. */
  virtual void OutputLine(const std::string& line);
 
 private:
  static std::string MemoryUsage();
 
  const int period_;
  std::unique_ptr<WallTimer> timer_;
  const std::vector<IntVar*> vars_;
  const std::string vars_name_;
  const std::vector<double> scaling_factors_;
  const std::vector<double> offsets_;
  std::function<std::string()> display_callback_;
  const bool display_on_new_solutions_only_;
  int nsol_;
  int64_t tick_;
  std::vector<int64_t> objective_min_;
  std::vector<int64_t> objective_max_;
  int min_right_depth_;
  int max_depth_;
  int sliding_min_depth_;
  int sliding_max_depth_;
  int neighbors_offset_ = 0;
};
 
class ModelCache {
 public:
  enum VoidConstraintType {
    VOID_FALSE_CONSTRAINT = 0,
    VOID_TRUE_CONSTRAINT,
    VOID_CONSTRAINT_MAX,
  };
 
  enum VarConstantConstraintType {
    VAR_CONSTANT_EQUALITY = 0,
    VAR_CONSTANT_GREATER_OR_EQUAL,
    VAR_CONSTANT_LESS_OR_EQUAL,
    VAR_CONSTANT_NON_EQUALITY,
    VAR_CONSTANT_CONSTRAINT_MAX,
  };
 
  enum VarConstantConstantConstraintType {
    VAR_CONSTANT_CONSTANT_BETWEEN = 0,
    VAR_CONSTANT_CONSTANT_CONSTRAINT_MAX,
  };
 
  enum ExprExprConstraintType {
    EXPR_EXPR_EQUALITY = 0,
    EXPR_EXPR_GREATER,
    EXPR_EXPR_GREATER_OR_EQUAL,
    EXPR_EXPR_LESS,
    EXPR_EXPR_LESS_OR_EQUAL,
    EXPR_EXPR_NON_EQUALITY,
    EXPR_EXPR_CONSTRAINT_MAX,
  };
 
  enum ExprExpressionType {
    EXPR_OPPOSITE = 0,
    EXPR_ABS,
    EXPR_SQUARE,
    EXPR_EXPRESSION_MAX,
  };
 
  enum ExprExprExpressionType {
    EXPR_EXPR_DIFFERENCE = 0,
    EXPR_EXPR_PROD,
    EXPR_EXPR_DIV,
    EXPR_EXPR_MAX,
    EXPR_EXPR_MIN,
    EXPR_EXPR_SUM,
    EXPR_EXPR_IS_LESS,
    EXPR_EXPR_IS_LESS_OR_EQUAL,
    EXPR_EXPR_IS_EQUAL,
    EXPR_EXPR_IS_NOT_EQUAL,
    EXPR_EXPR_EXPRESSION_MAX,
  };
 
  enum ExprExprConstantExpressionType {
    EXPR_EXPR_CONSTANT_CONDITIONAL = 0,
    EXPR_EXPR_CONSTANT_EXPRESSION_MAX,
  };
 
  enum ExprConstantExpressionType {
    EXPR_CONSTANT_DIFFERENCE = 0,
    EXPR_CONSTANT_DIVIDE,
    EXPR_CONSTANT_PROD,
    EXPR_CONSTANT_MAX,
    EXPR_CONSTANT_MIN,
    EXPR_CONSTANT_SUM,
    EXPR_CONSTANT_IS_EQUAL,
    EXPR_CONSTANT_IS_NOT_EQUAL,
    EXPR_CONSTANT_IS_GREATER_OR_EQUAL,
    EXPR_CONSTANT_IS_LESS_OR_EQUAL,
    EXPR_CONSTANT_EXPRESSION_MAX,
  };
  enum VarConstantConstantExpressionType {
    VAR_CONSTANT_CONSTANT_SEMI_CONTINUOUS = 0,
    VAR_CONSTANT_CONSTANT_EXPRESSION_MAX,
  };
 
  enum VarConstantArrayExpressionType {
    VAR_CONSTANT_ARRAY_ELEMENT = 0,
    VAR_CONSTANT_ARRAY_EXPRESSION_MAX,
  };
 
  enum VarArrayConstantArrayExpressionType {
    VAR_ARRAY_CONSTANT_ARRAY_SCAL_PROD = 0,
    VAR_ARRAY_CONSTANT_ARRAY_EXPRESSION_MAX,
  };
 
  enum VarArrayExpressionType {
    VAR_ARRAY_MAX = 0,
    VAR_ARRAY_MIN,
    VAR_ARRAY_SUM,
    VAR_ARRAY_EXPRESSION_MAX,
  };
 
  enum VarArrayConstantExpressionType {
    VAR_ARRAY_CONSTANT_INDEX = 0,
    VAR_ARRAY_CONSTANT_EXPRESSION_MAX,
  };
 
  explicit ModelCache(Solver* solver);
  virtual ~ModelCache();
 
  virtual void Clear() = 0;
 
 
  virtual Constraint* FindVoidConstraint(VoidConstraintType type) const = 0;
 
  virtual void InsertVoidConstraint(Constraint* ct,
                                    VoidConstraintType type) = 0;
 
  virtual Constraint* FindVarConstantConstraint(
      IntVar* var, int64_t value, VarConstantConstraintType type) const = 0;
 
  virtual void InsertVarConstantConstraint(Constraint* ct, IntVar* var,
                                           int64_t value,
                                           VarConstantConstraintType type) = 0;
 
 
  virtual Constraint* FindVarConstantConstantConstraint(
      IntVar* var, int64_t value1, int64_t value2,
      VarConstantConstantConstraintType type) const = 0;
 
  virtual void InsertVarConstantConstantConstraint(
      Constraint* ct, IntVar* var, int64_t value1, int64_t value2,
      VarConstantConstantConstraintType type) = 0;
 
 
  virtual Constraint* FindExprExprConstraint(
      IntExpr* expr1, IntExpr* expr2, ExprExprConstraintType type) const = 0;
 
  virtual void InsertExprExprConstraint(Constraint* ct, IntExpr* expr1,
                                        IntExpr* expr2,
                                        ExprExprConstraintType type) = 0;
 
 
  virtual IntExpr* FindExprExpression(IntExpr* expr,
                                      ExprExpressionType type) const = 0;
 
  virtual void InsertExprExpression(IntExpr* expression, IntExpr* expr,
                                    ExprExpressionType type) = 0;
 
 
  virtual IntExpr* FindExprConstantExpression(
      IntExpr* expr, int64_t value, ExprConstantExpressionType type) const = 0;
 
  virtual void InsertExprConstantExpression(
      IntExpr* expression, IntExpr* var, int64_t value,
      ExprConstantExpressionType type) = 0;
 
 
  virtual IntExpr* FindExprExprExpression(
      IntExpr* var1, IntExpr* var2, ExprExprExpressionType type) const = 0;
 
  virtual void InsertExprExprExpression(IntExpr* expression, IntExpr* var1,
                                        IntExpr* var2,
                                        ExprExprExpressionType type) = 0;
 
 
  virtual IntExpr* FindExprExprConstantExpression(
      IntExpr* var1, IntExpr* var2, int64_t constant,
      ExprExprConstantExpressionType type) const = 0;
 
  virtual void InsertExprExprConstantExpression(
      IntExpr* expression, IntExpr* var1, IntExpr* var2, int64_t constant,
      ExprExprConstantExpressionType type) = 0;
 
 
  virtual IntExpr* FindVarConstantConstantExpression(
      IntVar* var, int64_t value1, int64_t value2,
      VarConstantConstantExpressionType type) const = 0;
 
  virtual void InsertVarConstantConstantExpression(
      IntExpr* expression, IntVar* var, int64_t value1, int64_t value2,
      VarConstantConstantExpressionType type) = 0;
 
 
  virtual IntExpr* FindVarConstantArrayExpression(
      IntVar* var, const std::vector<int64_t>& values,
      VarConstantArrayExpressionType type) const = 0;
 
  virtual void InsertVarConstantArrayExpression(
      IntExpr* expression, IntVar* var, const std::vector<int64_t>& values,
      VarConstantArrayExpressionType type) = 0;
 
 
  virtual IntExpr* FindVarArrayExpression(
      const std::vector<IntVar*>& vars, VarArrayExpressionType type) const = 0;
 
  virtual void InsertVarArrayExpression(IntExpr* expression,
                                        const std::vector<IntVar*>& vars,
                                        VarArrayExpressionType type) = 0;
 
 
  virtual IntExpr* FindVarArrayConstantArrayExpression(
      const std::vector<IntVar*>& vars, const std::vector<int64_t>& values,
      VarArrayConstantArrayExpressionType type) const = 0;
 
  virtual void InsertVarArrayConstantArrayExpression(
      IntExpr* expression, const std::vector<IntVar*>& var,
      const std::vector<int64_t>& values,
      VarArrayConstantArrayExpressionType type) = 0;
 
 
  virtual IntExpr* FindVarArrayConstantExpression(
      const std::vector<IntVar*>& vars, int64_t value,
      VarArrayConstantExpressionType type) const = 0;
 
  virtual void InsertVarArrayConstantExpression(
      IntExpr* expression, const std::vector<IntVar*>& var, int64_t value,
      VarArrayConstantExpressionType type) = 0;
 
  Solver* solver() const;
 
 private:
  Solver* const solver_;
};
 
#if !defined(SWIG)
class ArgumentHolder {
 public:
  const std::string& TypeName() const;
  void SetTypeName(const std::string& type_name);
 
  void SetIntegerArgument(const std::string& arg_name, int64_t value);
  void SetIntegerArrayArgument(const std::string& arg_name,
                               const std::vector<int64_t>& values);
  void SetIntegerMatrixArgument(const std::string& arg_name,
                                const IntTupleSet& values);
  void SetIntegerExpressionArgument(const std::string& arg_name, IntExpr* expr);
  void SetIntegerVariableArrayArgument(const std::string& arg_name,
                                       const std::vector<IntVar*>& vars);
  void SetIntervalArgument(const std::string& arg_name, IntervalVar* var);
  void SetIntervalArrayArgument(const std::string& arg_name,
                                const std::vector<IntervalVar*>& vars);
  void SetSequenceArgument(const std::string& arg_name, SequenceVar* var);
  void SetSequenceArrayArgument(const std::string& arg_name,
                                const std::vector<SequenceVar*>& vars);
 
  bool HasIntegerExpressionArgument(const std::string& arg_name) const;
  bool HasIntegerVariableArrayArgument(const std::string& arg_name) const;
 
  int64_t FindIntegerArgumentWithDefault(const std::string& arg_name,
                                         int64_t def) const;
  int64_t FindIntegerArgumentOrDie(const std::string& arg_name) const;
  const std::vector<int64_t>& FindIntegerArrayArgumentOrDie(
      const std::string& arg_name) const;
  const IntTupleSet& FindIntegerMatrixArgumentOrDie(
      const std::string& arg_name) const;
 
  IntExpr* FindIntegerExpressionArgumentOrDie(
      const std::string& arg_name) const;
  const std::vector<IntVar*>& FindIntegerVariableArrayArgumentOrDie(
      const std::string& arg_name) const;
 
 private:
  std::string type_name_;
  absl::flat_hash_map<std::string, int64_t> integer_argument_;
  absl::flat_hash_map<std::string, std::vector<int64_t>>
      integer_array_argument_;
  absl::flat_hash_map<std::string, IntTupleSet> matrix_argument_;
  absl::flat_hash_map<std::string, IntExpr*> integer_expression_argument_;
  absl::flat_hash_map<std::string, IntervalVar*> interval_argument_;
  absl::flat_hash_map<std::string, SequenceVar*> sequence_argument_;
  absl::flat_hash_map<std::string, std::vector<IntVar*>>
      integer_variable_array_argument_;
  absl::flat_hash_map<std::string, std::vector<IntervalVar*>>
      interval_array_argument_;
  absl::flat_hash_map<std::string, std::vector<SequenceVar*>>
      sequence_array_argument_;
};
 
class ModelParser : public ModelVisitor {
 public:
  ModelParser();
 
  ~ModelParser() override;
 
  void BeginVisitModel(const std::string& solver_name) override;
  void EndVisitModel(const std::string& solver_name) override;
  void BeginVisitConstraint(const std::string& type_name,
                            const Constraint* constraint) override;
  void EndVisitConstraint(const std::string& type_name,
                          const Constraint* constraint) override;
  void BeginVisitIntegerExpression(const std::string& type_name,
                                   const IntExpr* expr) override;
  void EndVisitIntegerExpression(const std::string& type_name,
                                 const IntExpr* expr) override;
  void VisitIntegerVariable(const IntVar* variable, IntExpr* delegate) override;
  void VisitIntegerVariable(const IntVar* variable,
                            const std::string& operation, int64_t value,
                            IntVar* delegate) override;
  void VisitIntervalVariable(const IntervalVar* variable,
                             const std::string& operation, int64_t value,
                             IntervalVar* delegate) override;
  void VisitSequenceVariable(const SequenceVar* variable) override;
  void VisitIntegerArgument(const std::string& arg_name,
                            int64_t value) override;
  void VisitIntegerArrayArgument(const std::string& arg_name,
                                 const std::vector<int64_t>& values) override;
  void VisitIntegerMatrixArgument(const std::string& arg_name,
                                  const IntTupleSet& values) override;
  void VisitIntegerExpressionArgument(const std::string& arg_name,
                                      IntExpr* argument) override;
  void VisitIntegerVariableArrayArgument(
      const std::string& arg_name,
      const std::vector<IntVar*>& arguments) override;
  void VisitIntervalArgument(const std::string& arg_name,
                             IntervalVar* argument) override;
  void VisitIntervalArrayArgument(
      const std::string& arg_name,
      const std::vector<IntervalVar*>& arguments) override;
  void VisitSequenceArgument(const std::string& arg_name,
                             SequenceVar* argument) override;
  void VisitSequenceArrayArgument(
      const std::string& arg_name,
      const std::vector<SequenceVar*>& arguments) override;
 
 protected:
  void PushArgumentHolder();
  void PopArgumentHolder();
  ArgumentHolder* Top() const;
 
 private:
  std::vector<ArgumentHolder*> holders_;
};
 
template <class T>
class ArrayWithOffset : public BaseObject {
 public:
  ArrayWithOffset(int64_t index_min, int64_t index_max)
      : index_min_(index_min),
        index_max_(index_max),
        values_(new T[index_max - index_min + 1]) {
    DCHECK_LE(index_min, index_max);
  }
 
  ~ArrayWithOffset() override {}
 
  virtual T Evaluate(int64_t index) const {
    DCHECK_GE(index, index_min_);
    DCHECK_LE(index, index_max_);
    return values_[index - index_min_];
  }
 
  void SetValue(int64_t index, T value) {
    DCHECK_GE(index, index_min_);
    DCHECK_LE(index, index_max_);
    values_[index - index_min_] = value;
  }
 
  std::string DebugString() const override { return "ArrayWithOffset"; }
 
 private:
  const int64_t index_min_;
  const int64_t index_max_;
  std::unique_ptr<T[]> values_;
};
#endif  // SWIG
 
template <class T, class C>
class RevGrowingArray {
 public:
  explicit RevGrowingArray(int64_t block_size)
      : block_size_(block_size), block_offset_(0) {
    CHECK_GT(block_size, 0);
  }
 
  ~RevGrowingArray() {
    for (int i = 0; i < elements_.size(); ++i) {
      delete[] elements_[i];
    }
  }
 
  T At(int64_t index) const {
    const int64_t block_index = ComputeBlockIndex(index);
    const int64_t relative_index = block_index - block_offset_;
    if (relative_index < 0 || relative_index >= elements_.size()) {
      return T();
    }
    const T* block = elements_[relative_index];
    return block != nullptr ? block[index - block_index * block_size_] : T();
  }
 
  void RevInsert(Solver* const solver, int64_t index, T value) {
    const int64_t block_index = ComputeBlockIndex(index);
    T* const block = GetOrCreateBlock(block_index);
    const int64_t residual = index - block_index * block_size_;
    solver->SaveAndSetValue(reinterpret_cast<C*>(&block[residual]),
                            reinterpret_cast<C>(value));
  }
 
 private:
  T* NewBlock() const {
    T* const result = new T[block_size_];
    for (int i = 0; i < block_size_; ++i) {
      result[i] = T();
    }
    return result;
  }
 
  T* GetOrCreateBlock(int block_index) {
    if (elements_.size() == 0) {
      block_offset_ = block_index;
      GrowUp(block_index);
    } else if (block_index < block_offset_) {
      GrowDown(block_index);
    } else if (block_index - block_offset_ >= elements_.size()) {
      GrowUp(block_index);
    }
    T* block = elements_[block_index - block_offset_];
    if (block == nullptr) {
      block = NewBlock();
      elements_[block_index - block_offset_] = block;
    }
    return block;
  }
 
  int64_t ComputeBlockIndex(int64_t value) const {
    return value >= 0 ? value / block_size_
                      : (value - block_size_ + 1) / block_size_;
  }
 
  void GrowUp(int64_t block_index) {
    elements_.resize(block_index - block_offset_ + 1);
  }
 
  void GrowDown(int64_t block_index) {
    const int64_t delta = block_offset_ - block_index;
    block_offset_ = block_index;
    DCHECK_GT(delta, 0);
    elements_.insert(elements_.begin(), delta, nullptr);
  }
 
  const int64_t block_size_;
  std::vector<T*> elements_;
  int block_offset_;
};
 
template <class T>
class RevIntSet {
 public:
  static constexpr int kNoInserted = -1;
 
  explicit RevIntSet(int capacity)
      : elements_(new T[capacity]),
        num_elements_(0),
        capacity_(capacity),
        position_(new int[capacity]),
        delete_position_(true) {
    for (int i = 0; i < capacity; ++i) {
      position_[i] = kNoInserted;
    }
  }
 
  RevIntSet(int capacity, int* shared_positions, int shared_positions_size)
      : elements_(new T[capacity]),
        num_elements_(0),
        capacity_(capacity),
        position_(shared_positions),
        delete_position_(false) {
    for (int i = 0; i < shared_positions_size; ++i) {
      position_[i] = kNoInserted;
    }
  }
 
  ~RevIntSet() {
    if (delete_position_) {
      delete[] position_;
    }
  }
 
  int Size() const { return num_elements_.Value(); }
 
  int Capacity() const { return capacity_; }
 
  T Element(int i) const {
    DCHECK_GE(i, 0);
    DCHECK_LT(i, num_elements_.Value());
    return elements_[i];
  }
 
  T RemovedElement(int i) const {
    DCHECK_GE(i, 0);
    DCHECK_LT(i + num_elements_.Value(), capacity_);
    return elements_[i + num_elements_.Value()];
  }
 
  void Insert(Solver* const solver, const T& elt) {
    const int position = num_elements_.Value();
    DCHECK_LT(position, capacity_);  
    DCHECK(NotAlreadyInserted(elt));
    elements_[position] = elt;
    position_[elt] = position;
    num_elements_.Incr(solver);
  }
 
  void Remove(Solver* const solver, const T& value_index) {
    num_elements_.Decr(solver);
    SwapTo(value_index, num_elements_.Value());
  }
 
  void Restore(Solver* const solver, const T& value_index) {
    SwapTo(value_index, num_elements_.Value());
    num_elements_.Incr(solver);
  }
 
  void Clear(Solver* const solver) { num_elements_.SetValue(solver, 0); }
 
  typedef const T* const_iterator;
  const_iterator begin() const { return elements_.get(); }
  const_iterator end() const { return elements_.get() + num_elements_.Value(); }
 
 private:
  bool NotAlreadyInserted(const T& elt) {
    for (int i = 0; i < num_elements_.Value(); ++i) {
      if (elt == elements_[i]) {
        return false;
      }
    }
    return true;
  }
 
  void SwapTo(T value_index, int next_position) {
    const int current_position = position_[value_index];
    if (current_position != next_position) {
      const T next_value_index = elements_[next_position];
      elements_[current_position] = next_value_index;
      elements_[next_position] = value_index;
      position_[value_index] = next_position;
      position_[next_value_index] = current_position;
    }
  }
 
  std::unique_ptr<T[]> elements_;
  NumericalRev<int> num_elements_;
  const int capacity_;
  int* position_;
  const bool delete_position_;
};
 
 
class RevPartialSequence {
 public:
  explicit RevPartialSequence(const std::vector<int>& items)
      : elements_(items),
        first_ranked_(0),
        last_ranked_(items.size() - 1),
        size_(items.size()),
        position_(new int[size_]) {
    for (int i = 0; i < size_; ++i) {
      elements_[i] = items[i];
      position_[i] = i;
    }
  }
 
  explicit RevPartialSequence(int size)
      : elements_(size),
        first_ranked_(0),
        last_ranked_(size - 1),
        size_(size),
        position_(new int[size_]) {
    for (int i = 0; i < size_; ++i) {
      elements_[i] = i;
      position_[i] = i;
    }
  }
 
  ~RevPartialSequence() {}
 
  int NumFirstRanked() const { return first_ranked_.Value(); }
 
  int NumLastRanked() const { return size_ - 1 - last_ranked_.Value(); }
 
  int Size() const { return size_; }
 
#if !defined(SWIG)
  const int& operator[](int index) const {
    DCHECK_GE(index, 0);
    DCHECK_LT(index, size_);
    return elements_[index];
  }
#endif
 
  void RankFirst(Solver* const solver, int elt) {
    DCHECK_LE(first_ranked_.Value(), last_ranked_.Value());
    SwapTo(elt, first_ranked_.Value());
    first_ranked_.Incr(solver);
  }
 
  void RankLast(Solver* const solver, int elt) {
    DCHECK_LE(first_ranked_.Value(), last_ranked_.Value());
    SwapTo(elt, last_ranked_.Value());
    last_ranked_.Decr(solver);
  }
 
  bool IsRanked(int elt) const {
    const int position = position_[elt];
    return (position < first_ranked_.Value() ||
            position > last_ranked_.Value());
  }
 
  std::string DebugString() const {
    std::string result = "[";
    for (int i = 0; i < first_ranked_.Value(); ++i) {
      absl::StrAppend(&result, elements_[i]);
      if (i != first_ranked_.Value() - 1) {
        result.append("-");
      }
    }
    result.append("|");
    for (int i = first_ranked_.Value(); i <= last_ranked_.Value(); ++i) {
      absl::StrAppend(&result, elements_[i]);
      if (i != last_ranked_.Value()) {
        result.append("-");
      }
    }
    result.append("|");
    for (int i = last_ranked_.Value() + 1; i < size_; ++i) {
      absl::StrAppend(&result, elements_[i]);
      if (i != size_ - 1) {
        result.append("-");
      }
    }
    result.append("]");
    return result;
  }
 
 private:
  void SwapTo(int elt, int next_position) {
    const int current_position = position_[elt];
    if (current_position != next_position) {
      const int next_elt = elements_[next_position];
      elements_[current_position] = next_elt;
      elements_[next_position] = elt;
      position_[elt] = next_position;
      position_[next_elt] = current_position;
    }
  }
 
  std::vector<int> elements_;
  NumericalRev<int> first_ranked_;
  NumericalRev<int> last_ranked_;
  const int size_;
  std::unique_ptr<int[]> position_;
};
 
class UnsortedNullableRevBitset {
 public:
  explicit UnsortedNullableRevBitset(int bit_size);
 
  ~UnsortedNullableRevBitset() {}
 
  void Init(Solver* solver, const std::vector<uint64_t>& mask);
 
  bool RevSubtract(Solver* solver, const std::vector<uint64_t>& mask);
 
  bool RevAnd(Solver* solver, const std::vector<uint64_t>& mask);
 
  int ActiveWordSize() const { return active_words_.Size(); }
 
  bool Empty() const { return active_words_.Size() == 0; }
 
  bool Intersects(const std::vector<uint64_t>& mask, int* support_index);
 
  int64_t bit_size() const { return bit_size_; }
  int64_t word_size() const { return word_size_; }
  const RevIntSet<int>& active_words() const { return active_words_; }
 
 private:
  void CleanUpActives(Solver* solver);
 
  const int64_t bit_size_;
  const int64_t word_size_;
  RevArray<uint64_t> bits_;
  RevIntSet<int> active_words_;
  std::vector<int> to_remove_;
};
 
template <class T>
bool IsArrayConstant(const std::vector<T>& values, const T& value) {
  for (int i = 0; i < values.size(); ++i) {
    if (values[i] != value) {
      return false;
    }
  }
  return true;
}
 
template <class T>
bool IsArrayBoolean(const std::vector<T>& values) {
  for (int i = 0; i < values.size(); ++i) {
    if (values[i] != 0 && values[i] != 1) {
      return false;
    }
  }
  return true;
}
 
template <class T>
bool AreAllOnes(const std::vector<T>& values) {
  return IsArrayConstant(values, T(1));
}
 
template <class T>
bool AreAllNull(const std::vector<T>& values) {
  return IsArrayConstant(values, T(0));
}
 
template <class T>
bool AreAllGreaterOrEqual(const std::vector<T>& values, const T& value) {
  for (const T& current_value : values) {
    if (current_value < value) {
      return false;
    }
  }
  return true;
}
 
template <class T>
bool AreAllLessOrEqual(const std::vector<T>& values, const T& value) {
  for (const T& current_value : values) {
    if (current_value > value) {
      return false;
    }
  }
  return true;
}
 
template <class T>
bool AreAllPositive(const std::vector<T>& values) {
  return AreAllGreaterOrEqual(values, T(0));
}
 
template <class T>
bool AreAllNegative(const std::vector<T>& values) {
  return AreAllLessOrEqual(values, T(0));
}
 
template <class T>
bool AreAllStrictlyPositive(const std::vector<T>& values) {
  return AreAllGreaterOrEqual(values, T(1));
}
 
template <class T>
bool AreAllStrictlyNegative(const std::vector<T>& values) {
  return AreAllLessOrEqual(values, T(-1));
}
 
template <class T>
bool IsIncreasingContiguous(const std::vector<T>& values) {
  for (int i = 0; i < values.size() - 1; ++i) {
    if (values[i + 1] != values[i] + 1) {
      return false;
    }
  }
  return true;
}
 
template <class T>
bool IsIncreasing(const std::vector<T>& values) {
  for (int i = 0; i < values.size() - 1; ++i) {
    if (values[i + 1] < values[i]) {
      return false;
    }
  }
  return true;
}
 
template <class T>
bool IsArrayInRange(const std::vector<IntVar*>& vars, T range_min,
                    T range_max) {
  for (int i = 0; i < vars.size(); ++i) {
    if (vars[i]->Min() < range_min || vars[i]->Max() > range_max) {
      return false;
    }
  }
  return true;
}
 
inline bool AreAllBound(const std::vector<IntVar*>& vars) {
  for (int i = 0; i < vars.size(); ++i) {
    if (!vars[i]->Bound()) {
      return false;
    }
  }
  return true;
}
 
inline bool AreAllBooleans(const std::vector<IntVar*>& vars) {
  return IsArrayInRange(vars, 0, 1);
}
 
template <class T>
bool AreAllBoundOrNull(const std::vector<IntVar*>& vars,
                       const std::vector<T>& values) {
  for (int i = 0; i < vars.size(); ++i) {
    if (values[i] != 0 && !vars[i]->Bound()) {
      return false;
    }
  }
  return true;
}
 
inline bool AreAllBoundTo(const std::vector<IntVar*>& vars, int64_t value) {
  for (int i = 0; i < vars.size(); ++i) {
    if (!vars[i]->Bound() || vars[i]->Min() != value) {
      return false;
    }
  }
  return true;
}
 
inline int64_t MaxVarArray(const std::vector<IntVar*>& vars) {
  DCHECK(!vars.empty());
  int64_t result = kint64min;
  for (int i = 0; i < vars.size(); ++i) {
    result = std::max<int64_t>(result, vars[i]->Max());
  }
  return result;
}
 
inline int64_t MinVarArray(const std::vector<IntVar*>& vars) {
  DCHECK(!vars.empty());
  int64_t result = kint64max;
  for (int i = 0; i < vars.size(); ++i) {
    result = std::min<int64_t>(result, vars[i]->Min());
  }
  return result;
}
 
inline void FillValues(const std::vector<IntVar*>& vars,
                       std::vector<int64_t>* const values) {
  values->clear();
  values->resize(vars.size());
  for (int i = 0; i < vars.size(); ++i) {
    (*values)[i] = vars[i]->Value();
  }
}
 
inline int64_t PosIntDivUp(int64_t e, int64_t v) {
  DCHECK_GT(v, 0);
  return (e < 0 || e % v == 0) ? e / v : e / v + 1;
}
 
inline int64_t PosIntDivDown(int64_t e, int64_t v) {
  DCHECK_GT(v, 0);
  return (e >= 0 || e % v == 0) ? e / v : e / v - 1;
}
 
std::vector<int64_t> ToInt64Vector(const std::vector<int>& input);
 
#if !defined(SWIG)
// A PathState represents a set of paths and changes made on it.
//
// More accurately, let us define P_{num_nodes, starts, ends}-graphs the set of
// directed graphs with nodes [0, num_nodes) whose connected components are
// paths from starts[i] to ends[i] (for the same i) and loops.
// Let us fix num_nodes, starts and ends, so we call these P-graphs.
//
// A P-graph can be described by the sequence of nodes of each of its paths,
// and its set of loops. To describe a change made on a given P-graph G0 that
// yields another P-graph G1, we choose to describe G1 in terms of G0. When
// the difference between G0 and G1 is small, as is almost always the case in a
// local search setting, the description is compact, allowing for incremental
// filters to be efficient.
//
// In order to describe G1 in terms of G0 succintly, we describe each path of
// G1 as a sequence of chains of G0. A chain of G0 is either a nonempty sequence
// of consecutive nodes of a path of G0, or a node that was a loop in G0.
// For instance, a path that was not modified from G0 to G1 has one chain,
// the sequence of all nodes in the path. Typically, local search operators
// modify one or two paths, and the resulting paths can described as sequences
// of two to four chains of G0. Paths that were modified are listed explicitly,
// allowing to iterate only on changed paths.
// The loops of G1 are described more implicitly: the loops of G1 not in G0
// are listed explicitly, but those in both G1 and G0 are not listed.
//
// A PathState object can be in two states: committed or changed.
// At construction, the object is committed, G0.
// To enter a changed state G1, one can pass modifications with ChangePath() and
// ChangeLoops(). For reasons of efficiency, a chain is described as a range of
// node indices in the representation of the committed graph G0. To that effect,
// the nodes of a path of G0 are guaranteed to have consecutive indices.
//
// Filters can then browse the change efficiently using ChangedPaths(),
// Chains(), Nodes() and ChangedLoops().
//
// Then Commit() or Revert() can be called: Commit() sets the changed state G1
// as the new committed state, Revert() erases all changes.
class PathState {
 public:
  // A Chain allows to iterate on all nodes of a chain, and access some data:
  // first node, last node, number of nodes in the chain.
  // Chain is a range, its iterator ChainNodeIterator, its value type int.
  // Chains are returned by PathChainIterator's operator*().
  class Chain;
  // A ChainRange allows to iterate on all chains of a path.
  // ChainRange is a range, its iterator Chain*, its value type Chain.
  class ChainRange;
  // A NodeRange allows to iterate on all nodes of a path.
  // NodeRange is a range, its iterator PathNodeIterator, its value type int.
  class NodeRange;
 
  struct ChainBounds {
    ChainBounds() {}
    ChainBounds(int begin_index, int end_index)
        : begin_index(begin_index), end_index(end_index) {}
    int begin_index;
    int end_index;
  };
  int CommittedIndex(int node) const { return committed_index_[node]; }
  ChainBounds CommittedPathRange(int path) const { return chains_[path]; }
 
  // Path constructor: path_start and path_end must be disjoint,
  // their values in [0, num_nodes).
  PathState(int num_nodes, std::vector<int> path_start,
            std::vector<int> path_end);
 
  // Instance-constant accessors.
 
  // Returns the number of nodes in the underlying graph.
  int NumNodes() const { return num_nodes_; }
  // Returns the number of paths (empty paths included).
  int NumPaths() const { return num_paths_; }
  // Returns the start of a path.
  int Start(int path) const { return path_start_end_[path].start; }
  // Returns the end of a path.
  int End(int path) const { return path_start_end_[path].end; }
 
  // State-dependent accessors.
 
  // Returns the committed path of a given node, -1 if it is a loop.
  int Path(int node) const { return committed_paths_[node]; }
  // Returns the set of paths that actually changed,
  // i.e. that have more than one chain.
  const std::vector<int>& ChangedPaths() const { return changed_paths_; }
  // Returns the set of loops that were added by the change.
  const std::vector<int>& ChangedLoops() const { return changed_loops_; }
  // Returns the current range of chains of path.
  ChainRange Chains(int path) const;
  // Returns the current range of nodes of path.
  NodeRange Nodes(int path) const;
 
  // State modifiers.
 
  // Changes the path to the given sequence of chains of the committed state.
  // Chains are described by semi-open intervals. No optimization is made in
  // case two consecutive chains are actually already consecutive in the
  // committed state: they are not merged into one chain, and Chains(path) will
  // report the two chains.
  void ChangePath(int path, const std::vector<ChainBounds>& chains);
  // Same as above, but the initializer_list interface avoids the need to pass
  // a vector.
  void ChangePath(int path, const std::initializer_list<ChainBounds>& chains) {
    changed_paths_.push_back(path);
    const int path_begin_index = chains_.size();
    chains_.insert(chains_.end(), chains.begin(), chains.end());
    const int path_end_index = chains_.size();
    paths_[path] = {path_begin_index, path_end_index};
    // Always add sentinel, in case this is the last path change.
    chains_.emplace_back(0, 0);
  }
 
  // Describes the nodes that are newly loops in this change.
  void ChangeLoops(const std::vector<int>& new_loops);
 
  // Set the current state G1 as committed. See class comment for details.
  void Commit();
  // Erase incremental changes. See class comment for details.
  void Revert();
 
  // LNS Operators may not fix variables,
  // in which case we mark the candidate invalid.
  void SetInvalid() { is_invalid_ = true; }
  bool IsInvalid() const { return is_invalid_; }
 
 private:
  // Most structs below are named pairs of ints, for typing purposes.
 
  // Start and end are stored together to optimize (likely) simultaneous access.
  struct PathStartEnd {
    PathStartEnd(int start, int end) : start(start), end(end) {}
    int start;
    int end;
  };
  // Paths are ranges of chains, which are ranges of committed nodes, see below.
  struct PathBounds {
    int begin_index;
    int end_index;
  };
 
  // Copies nodes in chains of path at the end of nodes,
  // and sets those nodes' path member to value path.
  void CopyNewPathAtEndOfNodes(int path);
  // Commits paths in O(#{changed paths' nodes}) time,
  // increasing this object's space usage by O(|changed path nodes|).
  void IncrementalCommit();
  // Commits paths in O(num_nodes + num_paths) time,
  // reducing this object's space usage to O(num_nodes + num_paths).
  void FullCommit();
 
  // Instance-constant data.
  const int num_nodes_;
  const int num_paths_;
  std::vector<PathStartEnd> path_start_end_;
 
  // Representation of the committed and changed paths.
  // A path is a range of chains, which is a range of nodes.
  // Ranges are represented internally by indices in vectors:
  // ChainBounds are indices in committed_nodes_. PathBounds are indices in
  // chains_. When committed (after construction, Revert() or Commit()):
  // - path ranges are [path, path+1): they have one chain.
  // - chain ranges don't overlap, chains_ has an empty sentinel at the end.
  //   The sentinel allows the Nodes() iterator to maintain its current pointer
  //   to committed nodes on NodeRange::operator++().
  // - committed_nodes_ contains all nodes, both paths and loops.
  //   Actually, old duplicates will likely appear,
  //   the current version of a node is at the index given by
  //   committed_index_[node]. A Commit() can add nodes at the end of
  //   committed_nodes_ in a space/time tradeoff, but if committed_nodes_' size
  //   is above num_nodes_threshold_, Commit() must reclaim useless duplicates'
  //   space by rewriting the path/chain/nodes structure.
  // When changed (after ChangePaths() and ChangeLoops()),
  // the structure is updated accordingly:
  // - path ranges that were changed have nonoverlapping values [begin, end)
  //   where begin is >= num_paths_ + 1, i.e. new chains are stored after
  //   the committed state.
  // - additional chain ranges are stored after the committed chains and its
  //   sentinel to represent the new chains resulting from the changes.
  //   Those chains do not overlap with one another or with committed chains.
  // - committed_nodes_ are not modified, and still represent the committed
  //   paths. committed_index_ is not modified either.
  std::vector<int> committed_nodes_;
  // Maps nodes to their path in the latest committed state.
  std::vector<int> committed_paths_;
  // Maps nodes to their index in the latest committed state.
  std::vector<int> committed_index_;
  const int num_nodes_threshold_;
  std::vector<ChainBounds> chains_;
  std::vector<PathBounds> paths_;
 
  // Incremental information.
  std::vector<int> changed_paths_;
  std::vector<int> changed_loops_;
 
  // See IsInvalid() and SetInvalid().
  bool is_invalid_ = false;
};
 
// A Chain is a range of committed nodes.
class PathState::Chain {
 public:
  class Iterator {
   public:
    Iterator& operator++() {
      ++current_node_;
      return *this;
    }
    int operator*() const { return *current_node_; }
    bool operator!=(Iterator other) const {
      return current_node_ != other.current_node_;
    }
 
   private:
    // Only a Chain can construct its iterator.
    friend class PathState::Chain;
    explicit Iterator(const int* node) : current_node_(node) {}
    const int* current_node_;
  };
 
  // Chains hold CommittedNode* values, a Chain may be invalidated
  // if the underlying vector is modified.
  Chain(const int* begin_node, const int* end_node)
      : begin_(begin_node), end_(end_node) {}
 
  int NumNodes() const { return end_ - begin_; }
  int First() const { return *begin_; }
  int Last() const { return *(end_ - 1); }
  Iterator begin() const { return Iterator(begin_); }
  Iterator end() const { return Iterator(end_); }
 
  Chain WithoutFirstNode() const { return Chain(begin_ + 1, end_); }
 
 private:
  const int* const begin_;
  const int* const end_;
};
 
// A ChainRange is a range of Chains, committed or not.
class PathState::ChainRange {
 public:
  class Iterator {
   public:
    Iterator& operator++() {
      ++current_chain_;
      return *this;
    }
    Chain operator*() const {
      return {first_node_ + current_chain_->begin_index,
              first_node_ + current_chain_->end_index};
    }
    bool operator!=(Iterator other) const {
      return current_chain_ != other.current_chain_;
    }
 
   private:
    // Only a ChainRange can construct its Iterator.
    friend class ChainRange;
    Iterator(const ChainBounds* chain, const int* const first_node)
        : current_chain_(chain), first_node_(first_node) {}
    const ChainBounds* current_chain_;
    const int* const first_node_;
  };
 
  // ChainRanges hold ChainBounds* and CommittedNode*,
  // a ChainRange may be invalidated if on of the underlying vector is modified.
  ChainRange(const ChainBounds* const begin_chain,
             const ChainBounds* const end_chain, const int* const first_node)
      : begin_(begin_chain), end_(end_chain), first_node_(first_node) {}
 
  Iterator begin() const { return {begin_, first_node_}; }
  Iterator end() const { return {end_, first_node_}; }
 
 private:
  const ChainBounds* const begin_;
  const ChainBounds* const end_;
  const int* const first_node_;
};
 
// A NodeRange allows to iterate on all nodes of a path,
// by a two-level iteration on ChainBounds* and CommittedNode* of a PathState.
class PathState::NodeRange {
 public:
  class Iterator {
   public:
    Iterator& operator++() {
      ++current_node_;
      if (current_node_ == end_node_) {
        ++current_chain_;
        // Note: dereferencing bounds is valid because there is a sentinel
        // value at the end of PathState::chains_ to that intent.
        const ChainBounds bounds = *current_chain_;
        current_node_ = first_node_ + bounds.begin_index;
        end_node_ = first_node_ + bounds.end_index;
      }
      return *this;
    }
    int operator*() const { return *current_node_; }
    bool operator!=(Iterator other) const {
      return current_chain_ != other.current_chain_;
    }
 
   private:
    // Only a NodeRange can construct its Iterator.
    friend class NodeRange;
    Iterator(const ChainBounds* current_chain, const int* const first_node)
        : current_node_(first_node + current_chain->begin_index),
          end_node_(first_node + current_chain->end_index),
          current_chain_(current_chain),
          first_node_(first_node) {}
    const int* current_node_;
    const int* end_node_;
    const ChainBounds* current_chain_;
    const int* const first_node_;
  };
 
  // NodeRanges hold ChainBounds* and int* (first committed node),
  // a NodeRange may be invalidated if on of the underlying vector is modified.
  NodeRange(const ChainBounds* begin_chain, const ChainBounds* end_chain,
            const int* first_node)
      : begin_chain_(begin_chain),
        end_chain_(end_chain),
        first_node_(first_node) {}
  Iterator begin() const { return {begin_chain_, first_node_}; }
  // Note: there is a sentinel value at the end of PathState::chains_,
  // so dereferencing chain_range_.end()->begin_ is always valid.
  Iterator end() const { return {end_chain_, first_node_}; }
 
 private:
  const ChainBounds* begin_chain_;
  const ChainBounds* end_chain_;
  const int* const first_node_;
};
 
// This checker enforces dimension requirements.
// A dimension requires that there is some valuation of
// cumul and demand such that for all paths:
// - cumul[A] is in interval node_capacity[A]
// - if arc A -> B is on a path of path_class p,
//   then cumul[A] + demand[p](A, B) = cumul[B].
// - if A is on a path of class p, then
//   cumul[A] must be inside interval path_capacity[path].
class DimensionChecker {
 public:
  struct Interval {
    int64_t min;
    int64_t max;
  };
 
  struct ExtendedInterval {
    int64_t min;
    int64_t max;
    int64_t num_negative_infinity;
    int64_t num_positive_infinity;
  };
 
  // TODO(user): the addition of kMinRangeSizeForRIQ slowed down Check().
  // See if using a template parameter makes it faster.
  DimensionChecker(const PathState* path_state,
                   std::vector<Interval> path_capacity,
                   std::vector<int> path_class,
                   std::vector<std::function<Interval(int64_t, int64_t)>>
                       demand_per_path_class,
                   std::vector<Interval> node_capacity,
                   int min_range_size_for_riq = kOptimalMinRangeSizeForRIQ);
 
  // Given the change made in PathState, checks that the dimension
  // constraint is still feasible.
  bool Check() const;
 
  // Commits to the changes made in PathState,
  // must be called before PathState::Commit().
  void Commit();
 
  static constexpr int kOptimalMinRangeSizeForRIQ = 4;
 
 private:
  inline void UpdateCumulUsingChainRIQ(int first_index, int last_index,
                                       const ExtendedInterval& path_capacity,
                                       ExtendedInterval& cumul) const;
 
  // Commits to the current solution and rebuilds structures from scratch.
  void FullCommit();
  // Commits to the current solution and only build structures for paths that
  // changed, using additional space to do so in a time-memory tradeoff.
  void IncrementalCommit();
  // Adds sums of given path to the bottom layer of the Range Intersection Query
  // structure, updates index_ and previous_nontrivial_index_.
  void AppendPathDemandsToSums(int path);
  // Updates the Range Intersection Query structure from its bottom layer,
  // with [begin_index, end_index) the range of the change,
  // which must be at the end of the bottom layer.
  // Supposes that requests overlapping the range will be inside the range,
  // to avoid updating all layers.
  void UpdateRIQStructure(int begin_index, int end_index);
 
  const PathState* const path_state_;
  const std::vector<ExtendedInterval> path_capacity_;
  const std::vector<int> path_class_;
  const std::vector<std::function<Interval(int64_t, int64_t)>>
      demand_per_path_class_;
  std::vector<ExtendedInterval> cached_demand_;
  const std::vector<ExtendedInterval> node_capacity_;
 
  // Precomputed data.
  // Maps nodes to their pre-computed data, except for isolated nodes,
  // which do not have precomputed data.
  // Only valid for nodes that are in some path in the committed state.
  std::vector<int> index_;
  // Range intersection query in <O(n log n), O(1)>, with n = #nodes.
  // Let node be in a path, i = index_[node], start the start of node's path.
  // Let l such that index_[start] <= i - 2**l.
  // - riq_[l][i].tsum_at_lst contains the sum of demands from start to node.
  // - riq_[l][i].tsum_at_fst contains the sum of demands from start to the
  //   node at i - 2**l.
  // - riq_[l][i].tightest_tsum contains the intersection of
  //   riq_[0][j].tsum_at_lst for all j in (i - 2**l, i].
  // - riq_[0][i].cumuls_to_lst and riq_[0][i].cumuls_to_fst contain
  //   the node's capacity.
  // - riq_[l][i].cumuls_to_lst is the intersection, for j in (i - 2**l, i], of
  //   riq_[0][j].cumuls_to_lst + sum_{k in [j, i)} demand(k, k+1)
  // - riq_[l][i].cumuls_to_fst is the intersection, for j in (i - 2**l, i], of
  //   riq_[0][j].cumuls_to_fst - sum_{k in (i-2**l, j)} demand(k, k+1)
  struct RIQNode {
    ExtendedInterval cumuls_to_fst;
    ExtendedInterval tightest_tsum;
    ExtendedInterval cumuls_to_lst;
    ExtendedInterval tsum_at_fst;
    ExtendedInterval tsum_at_lst;
  };
  std::vector<std::vector<RIQNode>> riq_;
  // The incremental branch of Commit() may waste space in the layers of the
  // RIQ structure. This is the upper limit of a layer's size.
  const int maximum_riq_layer_size_;
  // Range queries are used on a chain only if the range is larger than this.
  const int min_range_size_for_riq_;
};
 
// Make a filter that takes ownership of a PathState and synchronizes it with
// solver events. The solver represents a graph with array of variables 'nexts'.
// Solver events are embodied by Assignment* deltas, that are translated to node
// changes during Relax(), committed during Synchronize(), and reverted on
// Revert().
LocalSearchFilter* MakePathStateFilter(Solver* solver,
                                       std::unique_ptr<PathState> path_state,
                                       const std::vector<IntVar*>& nexts);
 
// Make a filter that translates solver events to the input checker's interface.
// Since DimensionChecker has a PathState, the filter returned by this
// must be synchronized to the corresponding PathStateFilter:
// - Relax() must be called after the PathStateFilter's.
// - Accept() must be called after.
// - Synchronize() must be called before.
// - Revert() must be called before.
LocalSearchFilter* MakeDimensionFilter(
    Solver* solver, std::unique_ptr<DimensionChecker> checker,
    const std::string& dimension_name);
 
#endif  // !defined(SWIG)
 
}  // namespace operations_research
 
#endif  // OR_TOOLS_CONSTRAINT_SOLVER_CONSTRAINT_SOLVERI_H_