ortools-clone/src/constraint_solver/constraint_solver.h

// Copyright 2010-2013 Google
// 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.
//
// Declaration of the core objects for the constraint solver.
// The literature around constraint programming is extremelly dense but one
// can find some basic introductions in the following links:
//   http://en.wikipedia.org/wiki/Constraint_programming
//   http://kti.mff.cuni.cz/~bartak/constraints/index.html
//
//
// Here is a very simple Constraint Programming problem:
//   Knowing that we see 56 legs and 20 heads, how many pheasants and rabbits
//   are we looking at?
//
// Here is a simple Constraint Programming code to find out:
//   void pheasant() {
//     Solver s("pheasant");
//     IntVar* const p = s.MakeIntVar(0, 20, "pheasant"));
//     IntVar* const r = s.MakeIntVar(0, 20, "rabbit"));
//     IntExpr* const legs = s.MakeSum(s.MakeProd(p, 2), s.MakeProd(r, 4));
//     IntExpr* const heads = s.MakeSum(p, r);
//     Constraint* const ct_legs = s.MakeEquality(legs, 56);
//     Constraint* const ct_heads = s.MakeEquality(heads, 20);
//     s.AddConstraint(ct_legs);
//     s.AddConstraint(ct_heads);
//     DecisionBuilder* const db = s.MakePhase(p, r,
//                                             Solver::CHOOSE_FIRST_UNBOUND,
//                                             Solver::ASSIGN_MIN_VALUE);
//     s.NewSearch(db);
//     CHECK(s.NextSolution());
//     LG << "rabbits -> " << r->Value() << ", pheasants -> " << p->Value();
//     LG << s.DebugString();
//     s.EndSearch();
//   }
//
// which outputs:
//   rabbits -> 8, pheasants -> 12
//   Solver(name = "pheasant",
//          state = OUTSIDE_SEARCH,
//          branches = 0,
//          fails = 0,
//          decisions = 0
//          propagation loops = 11,
//          demons Run = 25,
//          Run time = 0 ms)
//
//
// TODO(user): Remove C-style API and update following comment.
// Global remark: many functions and methods in this file can take as argument
// either a const std::vector<IntVar>& or an IntVar* const* and a size; the two
// signatures are equivalent, size defining the number of variables.

#ifndef OR_TOOLS_CONSTRAINT_SOLVER_CONSTRAINT_SOLVER_H_
#define OR_TOOLS_CONSTRAINT_SOLVER_CONSTRAINT_SOLVER_H_

#include "base/hash.h"
#include "base/hash.h"
#include <iosfwd>
#include <string>
#include <utility>
#include <vector>

#include "base/callback.h"
#include "base/commandlineflags.h"
#include "base/integral_types.h"
#include "base/logging.h"
#include "base/macros.h"
#include "base/scoped_ptr.h"
#include "base/stringprintf.h"
#include "base/sysinfo.h"
#include "base/timer.h"
#include "base/concise_iterator.h"
#include "base/map-util.h"
#include "base/hash.h"
#include "base/random.h"
#include "util/tuple_set.h"

class Closure;
class File;
template <class A1, class A2, class A3> class Callback3;
template <typename R, typename T1, typename T2, typename T3>
class ResultCallback3;
template <typename R, typename T1, typename T2> class ResultCallback2;
template <typename R, typename T1> class ResultCallback1;
template <typename T1> class Callback1;
template <typename T> class ResultCallback;


using std::string;

namespace operations_research {

class Action;
class Assignment;
class AssignmentProto;
class BaseObject;
class CPArgumentProto;
class CPConstraintProto;
class CPIntegerExpressionProto;
class CPIntervalVariableProto;
class CPModelLoader;
class CPModelProto;
class CPSequenceVariableProto;
class CastConstraint;
class ConstIntArray;
class Constraint;
class Decision;
class DecisionBuilder;
class DecisionVisitor;
class Demon;
class DemonProfiler;
class DemonProfiler;
class DependencyGraph;
class Dimension;
class DisjunctiveConstraint;
class ExpressionCache;
class IntExpr;
class IntTupleSet;
class IntVar;
class IntVarAssignmentProto;
class IntVarElement;
class IntervalVar;
class IntervalVarAssignmentProto;
class IntervalVarElement;
class LocalSearchFilter;
class LocalSearchOperator;
class LocalSearchPhaseParameters;
class MPSolver;
class ModelCache;
class ModelVisitor;
class NoGoodManager;
class NoGoodTerm;
class OptimizeVar;
class Pack;
class PropagationBaseObject;
class PropagationMonitor;
class Queue;
class RevBitMatrix;
class RevBitSet;
class Search;
class SearchLimit;
class SearchLimitProto;
class SearchMonitor;
class SequenceVar;
class SequenceVarAssignmentProto;
class SolutionCollector;
class SolutionPool;
class Solver;
class SymmetryBreaker;
struct StateInfo;
struct Trail;
template <class T> class SimpleRevFIFO;

// This struct holds all parameters for the Solver object.
// SolverParameters is only used by the Solver constructor to define solving
// parameters such as the trail compression or the profile level.
// Note this is for advanced users only.
struct SolverParameters {
 public:
  enum TrailCompression {
    NO_COMPRESSION, COMPRESS_WITH_ZLIB
  };

  enum ProfileLevel {
    NO_PROFILING,
    NORMAL_PROFILING
  };

  enum TraceLevel {
    NO_TRACE,
    NORMAL_TRACE
  };

  static const TrailCompression kDefaultTrailCompression;
  static const int kDefaultTrailBlockSize;
  static const int kDefaultArraySplitSize;
  static const bool kDefaultNameStoring;
  static const ProfileLevel kDefaultProfileLevel;
  static const TraceLevel kDefaultTraceLevel;
  static const bool kDefaultNameAllVariables;

  SolverParameters();

  // This parameter indicates if the solver should compress the trail
  // during the search. No compression means that the solver will be faster,
  // but will use more memory.
  TrailCompression compress_trail;

  // This parameter indicates the default size of a block of the trail.
  // Compression applies at the block level.
  int trail_block_size;

  // When a sum/min/max operation is applied on a large array, this
  // array is recursively split into blocks of size 'array_split_size'.
  int array_split_size;

  // This parameters indicates if the solver should store the names of
  // the objets it manages.
  bool store_names;

  // Support for profiling propagation. LIGHT supports only a reduced
  // version of the summary. COMPLETE supports the full version of the
  // summary, as well as the csv export.
  ProfileLevel profile_level;

  // Support for full trace of propagation.
  TraceLevel trace_level;

  // Should anonymous variables be given a name.
  bool name_all_variables;
};

// This struct holds all parameters for the default search.
// DefaultPhaseParameters is only used by Solver::MakeDefaultPhase methods.
// Note this is for advanced users only.
struct DefaultPhaseParameters {
 public:
  enum VariableSelection {
    CHOOSE_MAX_SUM_IMPACT = 0,
    CHOOSE_MAX_AVERAGE_IMPACT = 1,
    CHOOSE_MAX_VALUE_IMPACT = 2,
  };

  enum ValueSelection {
    SELECT_MIN_IMPACT = 0,
    SELECT_MAX_IMPACT = 1,
  };

  enum DisplayLevel {
    NONE = 0,
    NORMAL = 1,
    VERBOSE = 2
  };

  static const int kDefaultNumberOfSplits;
  static const int kDefaultHeuristicPeriod;
  static const int kDefaultHeuristicNumFailuresLimit;
  static const int kDefaultSeed;
  static const double kDefaultRestartLogSize;
  static const bool kDefaultUseNoGoods;

  DefaultPhaseParameters()
      : var_selection_schema(CHOOSE_MAX_SUM_IMPACT),
        value_selection_schema(SELECT_MIN_IMPACT),
        initialization_splits(kDefaultNumberOfSplits),
        run_all_heuristics(true),
        heuristic_period(kDefaultHeuristicPeriod),
        heuristic_num_failures_limit(kDefaultHeuristicNumFailuresLimit),
        persistent_impact(true),
        random_seed(kDefaultSeed),
        restart_log_size(kDefaultRestartLogSize),
        display_level(NORMAL),
        use_no_goods(kDefaultUseNoGoods),
        decision_builder(nullptr) {}

  // This parameter describes how the next variable to instantiate
  // will be chosen.
  VariableSelection var_selection_schema;

  // This parameter describes which value to select for a given var.
  ValueSelection value_selection_schema;

  // Maximum number of intervals the initialization of impacts will scan
  // per variable.
  int initialization_splits;

  // The default phase will run heuristic periodically. This parameter
  // indicates if we should run all heuristics, or a randomly selected
  // one.
  bool run_all_heuristics;

  // The distance in nodes between each run of the heuristics. A
  // negative or null value will mean that we will not run heuristics
  // at all.
  int heuristic_period;

  // The failure limit for each heuristic that we run.
  int heuristic_num_failures_limit;

  // Whether to keep the impact from the first search for other searches
  // or to recompute the impact for each new search.
  bool persistent_impact;

  // Seed used to initialize the random part in some heuristics.
  int random_seed;

  // Automatic Restart Size. When diving down, the size of the search
  // space disminishes. We maintain the minimal log of the size of the search
  // space with the following behavior:
  //   - A failure is ignored (no null size).
  //   - A solution has a size of 1 (and a log of 0).
  // Then when backtracking, if the current log of the size of the search space
  // is greater than the minimizal log size recorded + 'restart_log_size', then
  // the search is restarted from scratch. A parameter < 0 means no restart.
  // A parameter of 0 indicates that we restart after each failure.
  double restart_log_size;

  // This represents the amount of information displayed by the default search.
  // NONE means no display, VERBOSE means extra information.
  DisplayLevel display_level;

  // Should we use Nogoods when restarting. The default is false.
  bool use_no_goods;

  // When defined, this override the default impact based decision builder.
  DecisionBuilder* decision_builder;
};


/////////////////////////////////////////////////////////////////////
//
// Solver Class
//
// A solver represent the main computation engine. It implements the whole
// range of Constraint Programming protocol:
//   - Reversibility
//   - Propagation
//   - Search
//
// Usually, a Constraint Programming code consists of
//   - the creation of the Solver,
//   - the creation of the decision variables of the model,
//   - the creation of the constraints of the model and their addition to the
//     solver() through the AddConstraint() method,
//   - the creation of the main DecisionBuilder class,
//   - the launch of the solve method with the above-created decision builder.
//
// For the time being, Solver is not MT_SAFE, nor MT_HOT.
/////////////////////////////////////////////////////////////////////

class Solver {
 public:
  // Callback typedefs
  typedef ResultCallback1<int64, int64> IndexEvaluator1;
  typedef ResultCallback2<int64, int64, int64> IndexEvaluator2;
  typedef ResultCallback3<int64, int64, int64, int64> IndexEvaluator3;
#ifndef SWIG
  typedef ResultCallback2<IntExpr*,
                          CPModelLoader*,
                          const CPIntegerExpressionProto&>
      IntegerExpressionBuilder;
  typedef ResultCallback2<Constraint*,
                          CPModelLoader*,
                          const CPConstraintProto&> ConstraintBuilder;
  typedef ResultCallback2<IntervalVar*,
                          CPModelLoader*,
                          const CPIntervalVariableProto&>
      IntervalVariableBuilder;
  typedef ResultCallback2<SequenceVar*,
                          CPModelLoader*,
                          const CPSequenceVariableProto&>
      SequenceVariableBuilder;
#endif  // SWIG

  // Holds semantic information stating that the 'expression' has been
  // cast into 'variable' using the Var() method, and that
  // 'maintainer' is responsible for maintaining the equality between
  // 'variable' and 'expression'.
  struct IntegerCastInfo {
    IntegerCastInfo() : variable(NULL), expression(NULL), maintainer(NULL) {}
    IntegerCastInfo(IntVar* const v, IntExpr* const e, Constraint* const c)
        : variable(v), expression(e), maintainer(c) {}
    IntVar* variable;
    IntExpr* expression;
    Constraint* maintainer;
  };

  // Number of priorities for demons.
  static const int kNumPriorities = 3;

  // This enum describes the strategy used to select the next branching
  // variable at each node during the search.
  enum IntVarStrategy {
    // The default behavior is CHOOSE_FIRST_UNBOUND.
    INT_VAR_DEFAULT,

    // The simple selection is CHOOSE_FIRST_UNBOUND.
    INT_VAR_SIMPLE,

    // Select the first unbound variable.
    // Variables are considered in the order of the vector of IntVars used
    // to create the selector.
    CHOOSE_FIRST_UNBOUND,

    // Randomly select one of the remaining unbound variables.
    CHOOSE_RANDOM,

    // Among unbound variables, select the variable with the smallest size,
    // i.e. the smallest number of possible values.
    // In case of tie, the selected variables is the one with the lowest min
    // value.
    // In case of tie, the first one is selected, first being defined by the
    // order in the vector of IntVars used to create the selector.
    CHOOSE_MIN_SIZE_LOWEST_MIN,

    // Among unbound variables, select the variable with the smallest size,
    // i.e. the smallest number of possible values.
    // In case of tie, the selected variables is the one with the highest min
    // value.
    // In case of tie, the first one is selected, first being defined by the
    // order in the vector of IntVars used to create the selector.
    CHOOSE_MIN_SIZE_HIGHEST_MIN,

    // Among unbound variables, select the variable with the smallest size,
    // i.e. the smallest number of possible values.
    // In case of tie, the selected variables is the one with the lowest max
    // value.
    // In case of tie, the first one is selected, first being defined by the
    // order in the vector of IntVars used to create the selector.
    CHOOSE_MIN_SIZE_LOWEST_MAX,

    // Among unbound variables, select the variable with the smallest size,
    // i.e. the smallest number of possible values.
    // In case of tie, the selected variables is the one with the highest max
    // value.
    // In case of tie, the first one is selected, first being defined by the
    // order in the vector of IntVars used to create the selector.
    CHOOSE_MIN_SIZE_HIGHEST_MAX,

    // Among unbound variables, select the variable with the smallest minimal
    // value.
    // In case of tie, the first one is selected, first being defined by the
    // order in the vector of IntVars used to create the selector.
    CHOOSE_LOWEST_MIN,

    // Among unbound variables, select the variable with the highest maximal
    // value.
    // In case of tie, the first one is selected, first being defined by the
    // order in the vector of IntVars used to create the selector.
    CHOOSE_HIGHEST_MAX,

    // Among unbound variables, select the variable with the smallest size.
    // In case of tie, the first one is selected, first being defined by the
    // order in the vector of IntVars used to create the selector.
    CHOOSE_MIN_SIZE,

    // Among unbound variables, select the variable with the highest size.
    // In case of tie, the first one is selected, first being defined by the
    // order in the vector of IntVars used to create the selector.
    CHOOSE_MAX_SIZE,

    // Among unbound variables, select the variable with the largest
    // gap between the first and the second values of the domain.
    CHOOSE_MAX_REGRET_ON_MIN,

    // Selects the next unbound variable on a path, the path being defined by
    // the variables: var[i] corresponds to the index of the next of i.
    CHOOSE_PATH,
  };
  // TODO(user): add HIGHEST_MIN and LOWEST_MAX.

  // This enum describes the strategy used to select the next variable value to
  // set.
  enum IntValueStrategy {
    // The default behavior is ASSIGN_MIN_VALUE.
    INT_VALUE_DEFAULT,

    // The simple selection is ASSIGN_MIN_VALUE.
    INT_VALUE_SIMPLE,

    // Selects the min value of the selected variable.
    ASSIGN_MIN_VALUE,

    // Selects the max value of the selected variable.
    ASSIGN_MAX_VALUE,

    // Selects randomly one of the possible values of the selected variable.
    ASSIGN_RANDOM_VALUE,

    // Selects the first possible value which is the closest to the center
    // of the domain of the selected variable.
    // The center is defined as (min + max) / 2.
    ASSIGN_CENTER_VALUE,

    // Split the domain in two around the center, and choose the lower
    // part first.
    SPLIT_LOWER_HALF,

    // Split the domain in two around the center, and choose the lower
    // part first.
    SPLIT_UPPER_HALF,
  };

  // This enum is used by Solver::MakePhase to specify how to select variables
  // and values during the search.
  // In Solver::MakePhase(const std::vector<IntVar*>&, IntVarStrategy,
  // IntValueStrategy), variables are selected first, and then the associated
  // value.
  // In Solver::MakePhase(const std::vector<IntVar*>& vars, IndexEvaluator2*,
  // EvaluatorStrategy), the selection is done scanning every pair
  // <variable, possible value>. The next selected pair is then the best among
  // all possibilities, i.e. the pair with the smallest evaluation.
  // As this is costly, two options are offered: static or dynamic evaluation.
  enum EvaluatorStrategy {
    // Pairs are compared at the first call of the selector, and results are
    // cached. Next calls to the selector use the previous computation, and so
    // are not up-to-date, e.g. some <variable, value> pairs may not be possible
    // anymore due to propagation since the first to call.
    CHOOSE_STATIC_GLOBAL_BEST,

    // Pairs are compared each time a variable is selected. That way all pairs
    // are relevant and evaluation is accurate.
    // This strategy runs in O(number-of-pairs) at each variable selection,
    // versus O(1) in the static version.
    CHOOSE_DYNAMIC_GLOBAL_BEST,
  };

  // Used for scheduling. Not yet implemented.
  enum SequenceStrategy {
    SEQUENCE_DEFAULT,
    SEQUENCE_SIMPLE,
    CHOOSE_MIN_SLACK_RANK_FORWARD,
    CHOOSE_RANDOM_RANK_FORWARD,
  };

  // Used for scheduling. Not yet implemented.
  enum IntervalStrategy {
    INTERVAL_DEFAULT,
    INTERVAL_SIMPLE,
    INTERVAL_SET_TIMES_FORWARD
  };

  // This enum is used in Solver::MakeOperator to specify the neighborhood to
  // create.
  enum LocalSearchOperators {
    // Operator which reverves a sub-chain of a path. It is called TwoOpt
    // because it breaks two arcs on the path; resulting paths are called
    // two-optimal.
    // Possible neighbors for the path 1 -> 2 -> 3 -> 4 -> 5
    // (where (1, 5) are first and last nodes of the path and can therefore not
    // be moved):
    //   1 -> [3 -> 2] -> 4  -> 5
    //   1 -> [4 -> 3  -> 2] -> 5
    //   1 ->  2 -> [4 -> 3] -> 5
    TWOOPT,

    // Relocate: OROPT and RELOCATE.
    // Operator which moves a sub-chain of a path to another position; the
    // specified chain length is the fixed length of the chains being moved.
    // When this length is 1, the operator simply moves a node to another
    // position.
    // Possible neighbors for the path 1 -> 2 -> 3 -> 4 -> 5, for a chain length
    // of 2 (where (1, 5) are first and last nodes of the path and can
    // therefore not be moved):
    //   1 ->  4 -> [2 -> 3] -> 5
    //   1 -> [3 -> 4] -> 2  -> 5
    //
    // Using Relocate with chain lengths of 1, 2 and 3 together is equivalent to
    // the OrOpt operator on a path. The OrOpt operator is a limited version of
    // 3Opt (breaks 3 arcs on a path).
    OROPT,

    // Relocate neighborhood with length of 1 (see OROPT comment).
    RELOCATE,

    // Operator which exchanges the positions of two nodes.
    // Possible neighbors for the path 1 -> 2 -> 3 -> 4 -> 5
    // (where (1, 5) are first and last nodes of the path and can therefore not
    // be moved):
    //   1 -> [3] -> [2] ->  4  -> 5
    //   1 -> [4] ->  3  -> [2] -> 5
    //   1 ->  2  -> [4] -> [3] -> 5
    EXCHANGE,

    // Operator which cross exchanges the starting chains of 2 paths, including
    // exchanging the whole paths.
    // First and last nodes are not moved.
    // Possible neighbors for the paths 1 -> 2 -> 3 -> 4 -> 5 and 6 -> 7 -> 8
    // (where (1, 5) and (6, 8) are first and last nodes of the paths and can
    // therefore not be moved):
    //   1 -> [7] -> 3 -> 4 -> 5  6 -> [2] -> 8
    //   1 -> [7] -> 4 -> 5       6 -> [2 -> 3] -> 8
    //   1 -> [7] -> 5            6 -> [2 -> 3 -> 4] -> 8
    CROSS,

    // Operator which inserts an inactive node into a path.
    // Possible neighbors for the path 1 -> 2 -> 3 -> 4 with 5 inactive
    // (where 1 and 4 are first and last nodes of the path) are:
    //   1 -> [5] ->  2  ->  3  -> 4
    //   1 ->  2  -> [5] ->  3  -> 4
    //   1 ->  2  ->  3  -> [5] -> 4
    MAKEACTIVE,

    // Operator which makes path nodes inactive.
    // Possible neighbors for the path 1 -> 2 -> 3 -> 4 (where 1 and 4 are first
    // and last nodes of the path) are:
    //   1 -> 3 -> 4 with 2 inactive
    //   1 -> 2 -> 4 with 3 inactive
    MAKEINACTIVE,

    // Operator which makes a "chain" of path nodes inactive.
    // Possible neighbors for the path 1 -> 2 -> 3 -> 4 (where 1 and 4 are first
    // and last nodes of the path) are:
    //   1 -> 3 -> 4 with 2 inactive
    //   1 -> 2 -> 4 with 3 inactive
    //   1 -> 4 with 2 and 3 inactive
    MAKECHAININACTIVE,

    // Operator which replaces an active node by an inactive one.
    // Possible neighbors for the path 1 -> 2 -> 3 -> 4 with 5 inactive
    // (where 1 and 4 are first and last nodes of the path) are:
    //   1 -> [5] ->  3  -> 4 with 2 inactive
    //   1 ->  2  -> [5] -> 4 with 3 inactive
    SWAPACTIVE,

    // Operator which makes an inactive node active and an active one inactive.
    // It is similar to SwapActiveOperator excepts that it tries to insert the
    // inactive node in all possible positions instead of just the position of
    // the node made inactive.
    // Possible neighbors for the path 1 -> 2 -> 3 -> 4 with 5 inactive
    // (where 1 and 4 are first and last nodes of the path) are:
    //   1 -> [5] ->  3  -> 4 with 2 inactive
    //   1 ->  3  -> [5] -> 4 with 2 inactive
    //   1 -> [5] ->  2  -> 4 with 3 inactive
    //   1 ->  2  -> [5] -> 4 with 3 inactive
    EXTENDEDSWAPACTIVE,

    // Operator which relaxes two sub-chains of three consecutive arcs each.
    // Each sub-chain is defined by a start node and the next three arcs. Those
    // six arcs are relaxed to build a new neighbor.
    // PATHLNS explores all possible pairs of starting nodes and so defines
    // n^2 neighbors, n being the number of nodes.
    // Note that the two sub-chains can be part of the same path; they even may
    // overlap.
    PATHLNS,

    // Operator which relaxes one entire path and all unactive nodes, thus
    // defining num_paths neighbors.
    FULLPATHLNS,

    // Operator which relaxes all inactive nodes and one sub-chain of six
    // consecutive arcs. That way the path can be improve by inserting inactive
    // nodes or swaping arcs.
    UNACTIVELNS,

    // Operator which defines one neighbor per variable. Each neighbor tries to
    // increment by one the value of the corresponding variable. When a new
    // solution is found the neighborhood is rebuilt from scratch, i.e. tries
    // to increment values in the variable order.
    // Consider for instance variables x and y. x is incremented 1 by 1 to its
    // max, and when it is not possible to increment x anymore, y is incremented
    // once. If this is a solution, then next neighbor tries to increment x.
    INCREMENT,

    // Operator which defines a neighborhood to decrement values.
    // The behavior is the same as INCREMENT, except values are decremented
    // instead of incremented.
    DECREMENT,

    // Operator which defines one neighbor per variable. Each neighbor relaxes
    // one variable.
    // When a new solution is found the neighborhood is rebuilt from scratch.
    // Consider for instance variables x and y. First x is relaxed and the
    // solver is looking for the best possible solution (with only x relaxed).
    // Then y is relaxed, and the solver is looking for a new solution.
    // If a new solution is found, then the next variable to be relaxed is x.
    SIMPLELNS
  };

  // This enum is used in Solver::MakeOperator associated with an evaluator
  // to specify the neighborhood to create.
  enum EvaluatorLocalSearchOperators {
    // Lin–Kernighan local search.
    // While the accumulated local gain is positive, perform a 2opt or a 3opt
    // move followed by a series of 2opt moves. Return a neighbor for which the
    // global gain is positive.
    LK,

    // Sliding TSP operator.
    // Uses an exact dynamic programming algorithm to solve the TSP
    // corresponding to path sub-chains.
    // For a subchain 1 -> 2 -> 3 -> 4 -> 5 -> 6, solves the TSP on
    // nodes A, 2, 3, 4, 5, where A is a merger of nodes 1 and 6 such that
    // cost(A,i) = cost(1,i) and cost(i,A) = cost(i,6).
    TSPOPT,

    // TSP-base LNS.
    // Randomly merge consecutive nodes until n "meta"-nodes remain and solve
    // the corresponding TSP.
    // This is an "unlimited" neighborhood which must be stopped by search
    // limits. To force diversification, the operator iteratively forces each
    // node to serve as base of a meta-node.
    TSPLNS
  };

  // This enum is used in Solver::MakeLocalSearchObjectiveFilter. It specifies
  // the behavior of the objective filter to create. The goal is to define
  // under which condition a move is accepted based on the current objective
  // value.
  enum LocalSearchFilterBound {
    // Move is accepted when the current objective value >= objective.Min.
    GE,
    // Move is accepted when the current objective value <= objective.Max.
    LE,
    // Move is accepted when the current objective value is in the interval
    // objective.Min .. objective.Max.
    EQ
  };

  // This enum is used in Solver::MakeLocalSearchObjectiveFilter. It specifies
  // the operation used in the objective to build the corresponding filter.
  enum LocalSearchOperation {
    // The objective is the sum of the variables defined in
    // Solver::MakeLocalSearchObjectiveFilter.
    SUM,

    // The objective is the product of the variables defined in
    // Solver::MakeLocalSearchObjectiveFilter.
    PROD,

    // The objective is the max of the variables defined in
    // Solver::MakeLocalSearchObjectiveFilter.
    MAX,

    // The objective is the min of the variables defined in
    // Solver::MakeLocalSearchObjectiveFilter.
    MIN
  };

  // This enum represents the three possible priorities for a demon in the
  // Solver queue.
  // Note this is for advanced users only.
  enum DemonPriority {
    // DELAYED_PRIORITY is the lowest priority: Demons will be processed after
    // VAR_PRIORITY and NORMAL_PRIORITY demons.
    DELAYED_PRIORITY = 0,

    // VAR_PRIORITY is between DELAYED_PRIORITY and NORMAL_PRIORITY.
    VAR_PRIORITY = 1,

    // NORMAL_PRIORITY is the highest priority: Demons will be processed first.
    NORMAL_PRIORITY = 2,
  };

  // This enum is used in Solver::MakeIntervalVarRelation to specify the
  // temporal relation between the two intervals t1 and t2.
  enum BinaryIntervalRelation {
    // t1 ends after t2 end, i.e. End(t1) >= End(t2).
    ENDS_AFTER_END,

    // t1 ends after t2 start, i.e. End(t1) >= Start(t2).
    ENDS_AFTER_START,

    // t1 ends at t2 end, i.e. End(t1) == End(t2).
    ENDS_AT_END,

    // t1 ends at t2 start, i.e. End(t1) == Start(t2).
    ENDS_AT_START,

    // t1 starts after t2 end, i.e. Start(t1) >= End(t2).
    STARTS_AFTER_END,

    // t1 starts after t2 start, i.e. Start(t1) >= Start(t2).
    STARTS_AFTER_START,

    // t1 starts at t2 end, i.e. Start(t1) == End(t2).
    STARTS_AT_END,

    // t1 starts at t2 start, i.e. Start(t1) == Start(t2).
    STARTS_AT_START,

    // STARTS_AT_START and ENDS_AT_END at the same time.
    // t1 starts at t2 start, i.e. Start(t1) == Start(t2).
    // t1 ends at t2 end, i.e. End(t1) == End(t2).
    STAYS_IN_SYNC
  };

  // This enum is used in Solver::MakeIntervalVarRelation to specify the
  // temporal relation between an interval t and an integer d.
  enum UnaryIntervalRelation {
    // t ends after d, i.e. End(t) >= d.
    ENDS_AFTER,

    // t ends at d, i.e. End(t) == d.
    ENDS_AT,

    // t ends before d, i.e. End(t) <= d.
    ENDS_BEFORE,

    // t starts after d, i.e. Start(t) >= d.
    STARTS_AFTER,

    // t starts at d, i.e. Start(t) == d.
    STARTS_AT,

    // t starts before d, i.e. Start(t) <= d.
    STARTS_BEFORE,

    // STARTS_BEFORE and ENDS_AFTER at the same time, i.e. d is in t.
    // t starts before d, i.e. Start(t) <= d.
    // t ends after d, i.e. End(t) >= d.
    CROSS_DATE,

    // STARTS_AFTER or ENDS_BEFORE, i.e. d is not in t.
    // t starts after d, i.e. Start(t) >= d.
    // t ends before d, i.e. End(t) <= d.
    AVOID_DATE
  };

  // The Solver is responsible for creating the search tree. Thanks to the
  // DecisionBuilder, it creates a new decision with two branches at each node:
  // left and right.
  // The DecisionModification enum is used to specify how the branch selector
  // should behave.
  enum DecisionModification {
    // Keeps the default behavior, i.e. apply left branch first, and then right
    // branch in case of backtracking.
    NO_CHANGE,

    // Right branches are ignored. This is used to make the code faster when
    // backtrack makes no sense or is not useful.
    // This is faster as there is no need to create one new node per decision.
    KEEP_LEFT,

    // Left branches are ignored. This is used to make the code faster when
    // backtrack makes no sense or is not useful.
    // This is faster as there is no need to create one new node per decision.
    KEEP_RIGHT,

    // Backtracks to the previous decisions, i.e. left and right branches are
    // not applied.
    KILL_BOTH,

    // Applies right branch first. Left branch will be applied in case of
    // backtracking.
    SWITCH_BRANCHES
  };

  // This enum is used internally in private methods Solver::PushState and
  // Solver::PopState to tag states in the search tree.
  enum MarkerType {
    SENTINEL,
    SIMPLE_MARKER,
    CHOICE_POINT,
    REVERSIBLE_ACTION
  };

  // This enum represents the state of the solver w.r.t. the search.
  enum SolverState {
    OUTSIDE_SEARCH,     // Before search, after search.
    IN_ROOT_NODE,       // Executing the root node.
    IN_SEARCH,          // Executing the search code.
    AT_SOLUTION,        // After successful NextSolution and before EndSearch.
    NO_MORE_SOLUTIONS,  // After failed NextSolution and before EndSearch.
    PROBLEM_INFEASIBLE  // After search, the model is infeasible.
  };

  explicit Solver(const string& modelname);
  Solver(const string& modelname, const SolverParameters& parameters);
  ~Solver();

  // Read-only Parameters.
  const SolverParameters& parameters() const { return parameters_; }

  // reversibility

  // SaveValue() will save the value of the corresponding object. It must be
  //   called before modifying the object. The value will be restored upon
  //   backtrack.
  template <class T> void SaveValue(T* o) {
    InternalSaveValue(o);
  }

  // Registers the given object as being reversible. By calling this method, the
  // caller gives ownership of the object to the solver, which will delete it
  // when there is a backtrack out of the current state.
  //
  // Returns the argument for convenience: this way, the caller may directly
  // invoke a constructor in the argument, without having to store the pointer
  // first.
  //
  // This function is only for users that define their own subclasses of
  // BaseObject: for all subclasses predefined in the library, the corresponding
  // factory methods (e.g., MakeIntVar(...), MakeAllDifferent(...) already take
  // care of the registration.
  template <typename T> T* RevAlloc(T* object) {
    return reinterpret_cast<T*>(SafeRevAlloc(object));
  }

  // Like RevAlloc() above, but for an array of objects: the array
  // must have been allocated with the new[] operator. The entire array
  // will be deleted when backtracking out of the current state.
  //
  // This method is valid for arrays of int, int64, uint64, bool,
  // BaseObject*, IntVar*, IntExpr*, and Constraint*.
  template <typename T> T* RevAllocArray(T* object) {
    return reinterpret_cast<T*>(SafeRevAllocArray(object));
  }

  // propagation

  // Adds the constraint 'c' to the model.
  //
  // After calling this method, and until there is a backtrack that undoes the
  // addition, any assignment of variables to values must satisfy the given
  // constraint in order to be considered feasible. There are two fairly
  // different use cases:
  //
  // - the most common use case is modeling: the given constraint is really part
  // of the problem that the user is trying to solve. In this use case,
  // AddConstraint is called outside of search (i.e., with <tt>state() ==
  // OUTSIDE_SEARCH</tt>). Most users should only use AddConstraint in this way.
  // In this case, the constraint will belong to the model forever: it cannot
  // not be removed by backtracking.
  //
  // - a rarer use case is that 'c' is not a real constraint of the model. It
  // may be a constraint generated by a branching decision (a constraint whose
  // goal is to restrict the search space), a symmetry breaking constraint (a
  // constraint that does restrict the search space, but in a way that cannot
  // have an impact on the quality of the solutions in the subtree), or an
  // inferred constraint that, while having no semantic value to the model (it
  // does not restrict the set of solutions), is worth having because we believe
  // it may strengthen the propagation. In these cases, it happens that the
  // constraint is added during the search (i.e., with <tt>state() ==
  // IN_SEARCH</tt> or <tt>state() == IN_ROOT_NODE</tt>). When a constraint is
  // added during a search, it applies only to the subtree of the search tree
  // rooted at the current node, and will be automatically removed by
  // bracktracking.
  //
  // This method does not take ownership of the constraint. If the constraint
  // has been created by any factory method (Solver::MakeXXX), it will
  // automatically be deleted. However, power users who implement their own
  // constraints should do: <tt>solver.AddConstraint(solver.RevAlloc(new
  // MyConstraint(...));</tt>
  void AddConstraint(Constraint* const c);
  // Adds the constraint 'c' to the solver and marks it as a cast
  // constraint, that is, a constraint created calling Var() on an
  // expression. This is used internally.
  void AddCastConstraint(CastConstraint* const c,
                         IntVar* const target_var,
                         IntExpr* const casted_expression);

  // @{
  // Solves the problem using the given DecisionBuilder and returns true if a
  // solution was found and accepted.
  //
  // These methods are the ones most users should use to search for a solution.
  // Note that the definition of 'solution' is subtle. A solution here is
  // defined as a leaf of the search tree with respect to the given decision
  // builder for which there is no failure. What this means is that, contrary to
  // intuition, a solution may not have all variables of the model bound. It is
  // the responsibility of the decision builder to keep returning decisions
  // until all variables are indeed bound. The most extreme counterexample is
  // calling Solve with a trivial decision builder whose Next() method always
  // returns NULL. In this case, Solve immediately returns 'true', since not
  // assigning any variable to any value is a solution, unless the root node
  // propagation discovers that the model is infeasible.
  //
  // This function must be called either from outside of search,
  // or from within the Next() method of a decision builder.
  //
  // Solve will terminate whenever any of the following event arise:
  // * A search monitor asks the solver to terminate the search by calling
  // SearchMonitor::FinishCurrentSearch().
  // * A solution is found that is accepted by all search monitors, and none of
  // the search monitors decides to search for another one.
  //
  // Upon search termination, there will be a series of backtracks all the way
  // to the top level. This means that a user cannot expect to inspect the
  // solution by querying variables after a call to Solve(): all the information
  // will be lost. In order to do something with the solution, the user must
  // either:
  // * Use a search monitor that can process such a leaf. See, in particular,
  //     the SolutionCollector class.
  // * Do not use Solve. Instead, use the more fine-grained approach using
  //     methods NewSearch(...), NextSolution(), and EndSearch().
  //
  // @param db The decision builder that will generate the search tree.
  // @param monitors A vector of search monitors that will be notified of
  // various events during the search. In their reaction to these events, such
  // monitors may influence the search.
  bool Solve(DecisionBuilder* const db, const std::vector<SearchMonitor*>& monitors);
  bool Solve(DecisionBuilder* const db);
  bool Solve(DecisionBuilder* const db, SearchMonitor* const m1);
  bool Solve(DecisionBuilder* const db,
             SearchMonitor* const m1,
             SearchMonitor* const m2);
  bool Solve(DecisionBuilder* const db,
             SearchMonitor* const m1,
             SearchMonitor* const m2,
             SearchMonitor* const m3);
  bool Solve(DecisionBuilder* const db,
             SearchMonitor* const m1,
             SearchMonitor* const m2,
             SearchMonitor* const m3,
             SearchMonitor* const m4);
  // @}

  // @{
  // Decomposed search.
  // The code for a top level search should look like
  // solver->NewSearch(db);
  // while (solver->NextSolution()) {
  //   //.. use the current solution
  // }
  // solver()->EndSearch();

  void NewSearch(DecisionBuilder* const db,
                 const std::vector<SearchMonitor*>& monitors);
  void NewSearch(DecisionBuilder* const db);
  void NewSearch(DecisionBuilder* const db, SearchMonitor* const m1);
  void NewSearch(DecisionBuilder* const db,
                 SearchMonitor* const m1,
                 SearchMonitor* const m2);
  void NewSearch(DecisionBuilder* const db,
                 SearchMonitor* const m1,
                 SearchMonitor* const m2,
                 SearchMonitor* const m3);
  void NewSearch(DecisionBuilder* const db,
                 SearchMonitor* const m1,
                 SearchMonitor* const m2,
                 SearchMonitor* const m3,
                 SearchMonitor* const m4);

  bool NextSolution();
  void RestartSearch();
  void EndSearch();
  // @}

  // SolveAndCommit using a decision builder and up to three
  //   search monitors, usually one for the objective, one for the limits
  //   and one to collect solutions.
  //
  // The difference between a SolveAndCommit() and a Solve() method
  // call is the fact that SolveAndCommit will not backtrack all
  // modifications at the end of the search. This method is only
  // usable during the Next() method of a decision builder.
  bool SolveAndCommit(DecisionBuilder* const db,
                      const std::vector<SearchMonitor*>& monitors);
  bool SolveAndCommit(DecisionBuilder* const db);
  bool SolveAndCommit(DecisionBuilder* const db,
                      SearchMonitor* const m1);
  bool SolveAndCommit(DecisionBuilder* const db,
                      SearchMonitor* const m1, SearchMonitor* const m2);
  bool SolveAndCommit(DecisionBuilder* const db,
                      SearchMonitor* const m1,
                      SearchMonitor* const m2,
                      SearchMonitor* const m3);

  // Checks whether the given assignment satisfies all the relevant constraints.
  bool CheckAssignment(Assignment* const assignment);

  // Checks whether adding this constraint will lead to an immediate
  // failure.  It will return false if the model is already
  // inconsistent, or if adding the constraint makes it inconsistent.
  bool CheckConstraint(Constraint* const constraint);

  // State of the solver.
  SolverState state() const { return state_; }

  // Abandon the current branch in the search tree. A backtrack will follow.
  void Fail();

  // Exports the model to protobuf. This code will be called
  // from inside the solver during the start of the search.
  void ExportModel(CPModelProto* const proto) const;
  // Exports the model to protobuf. Search monitors are useful to pass
  // the objective and limits to the protobuf.
  void ExportModel(const std::vector<SearchMonitor*>& monitors,
                   CPModelProto* const proto) const;
  // Exports the model to protobuf. Search monitors are useful to pass
  // the objective and limits to the protobuf.
  void ExportModel(const std::vector<SearchMonitor*>& monitors,
                   CPModelProto* const proto,
                   DecisionBuilder* const db) const;
  // Loads the model into the solver, and returns true upon success.
  bool LoadModel(const CPModelProto& proto);
  // Loads the model into the solver, appends search monitors to monitors,
  // and returns true upon success.
  bool LoadModel(const CPModelProto& proto, std::vector<SearchMonitor*>* monitors);
  // Upgrades the model to the latest version.
  static bool UpgradeModel(CPModelProto* const proto);

#if !defined(SWIG)
  // Collects decision variables.
  // All decision variables will be collected in 4 groups:
  //   - Main integer decision variables.
  //   - Secondary integer variables (that are derived integer variables that
  //     should be fixed like times of tasks after the order has been fixed).
  //   - Sequence variables.
  //   - Interval variables.
  //
  // From these 4 groups, one could write a decision builder:
  // solver.Compose(
  //     solver.MakeDefaultPhase(primary_integer_variables),
  //     solver.MakePhase(sequence_variables, Solver::SEQUENCE_DEFAULT),
  //     solver.MakePhase(interval_variables, Solver::INTERVAL_DEFAULT),
  //     solver.MakePhase(secondary_integer_variables, Solver::INT_VAR_DEFAULT);
  bool CollectDecisionVariables(
      std::vector<IntVar*>* const primary_integer_variables,
      std::vector<IntVar*>* const secondary_integer_variables,
      std::vector<SequenceVar*>* const sequence_variables,
      std::vector<IntervalVar*>* const interval_variables);

  // Registers a constraint builder. Ownership is passed to the solver.
  void RegisterBuilder(const string& tag,
                       ConstraintBuilder* const builder);
  // Registers an integer expression builder. Ownership is passed to the solver.
  void RegisterBuilder(const string& tag,
                       IntegerExpressionBuilder* const builder);
  // Registers an interval variable builder. Ownership is passed to the solver.
  void RegisterBuilder(const string& tag,
                       IntervalVariableBuilder* const builder);
  // Registers a sequence variable builder. Ownership is passed to the solver.
  void RegisterBuilder(const string& tag,
                       SequenceVariableBuilder* const builder);

  ConstraintBuilder* GetConstraintBuilder(const string& tag) const;
  IntegerExpressionBuilder*
      GetIntegerExpressionBuilder(const string& tag) const;
  IntervalVariableBuilder* GetIntervalVariableBuilder(const string& tag) const;
  SequenceVariableBuilder* GetSequenceVariableBuilder(const string& tag) const;
#endif  // SWIG

  // When SaveValue() is not the best way to go, one can create a reversible
  // action that will be called upon backtrack. The "fast" parameter
  // indicates whether we need restore all values saved through SaveValue()
  // before calling this method.
  void AddBacktrackAction(Action* a, bool fast);

  // misc debug string.
  string DebugString() const;

  // Current memory usage in bytes
  static int64 MemoryUsage();


  // wall_time() in ms since the creation of the solver.
  int64 wall_time() const;

  // number of branches explored since the creation of the solver.
  int64 branches() const { return branches_; }

  // number of solutions found since the start of the search.
  int64 solutions() const;

  // number of demons executed during search for a given priority.
  int64 demon_runs(DemonPriority p) const { return demon_runs_[p]; }

  // number of failures encountered since the creation of the solver.
  int64 failures() const { return fails_; }

  // number of neighbors created
  int64 neighbors() const { return neighbors_; }

  // number of filtered neighbors (neighbors accepted by filters)
  int64 filtered_neighbors() const { return filtered_neighbors_; }

  // number of accepted neighbors
  int64 accepted_neighbors() const { return accepted_neighbors_; }

  // The stamp indicates how many moves in the search tree we have performed.
  // It is useful to detect if we need to update same lazy structures.
  uint64 stamp() const;

  // The fail_stamp() is incremented after each backtrack.
  uint64 fail_stamp() const;

  // ---------- Make Factory ----------

  // All factories (MakeXXX methods) encapsulate creation of objects
  // through RevAlloc(). Hence, the Solver used for allocating the
  // returned object will retain ownership of the allocated memory.
  // Destructors are called upon backtrack, or when the Solver is
  // itself destructed.

  // ----- Int Variables and Constants -----

  // MakeIntVar will create the best range based int var for the bounds given.
  IntVar* MakeIntVar(int64 vmin, int64 vmax, const string& name);

  // MakeIntVar will create a variable with the given sparse domain.
  IntVar* MakeIntVar(const std::vector<int64>& values, const string& name);

  // MakeIntVar will create a variable with the given sparse domain.
  IntVar* MakeIntVar(const std::vector<int>& values, const string& name);

  // MakeIntVar will create the best range based int var for the bounds given.
  IntVar* MakeIntVar(int64 vmin, int64 vmax);

  // MakeIntVar will create a variable with the given sparse domain.
  IntVar* MakeIntVar(const std::vector<int64>& values);

  // MakeIntVar will create a variable with the given sparse domain.
  IntVar* MakeIntVar(const std::vector<int>& values);

  // MakeBoolVar will create a variable with a {0, 1} domain.
  IntVar* MakeBoolVar(const string& name);

  // MakeBoolVar will create a variable with a {0, 1} domain.
  IntVar* MakeBoolVar();

  // IntConst will create a constant expression.
  IntVar* MakeIntConst(int64 val, const string& name);

  // IntConst will create a constant expression.
  IntVar* MakeIntConst(int64 val);

  // This method will append the vector vars with 'var_count' variables
  // having bounds vmin and vmax and having name "name<i>" where <i> is
  // the index of the variable.
  void MakeIntVarArray(int var_count,
                       int64 vmin,
                       int64 vmax,
                       const string& name,
                       std::vector<IntVar*>* vars);
  // This method will append the vector vars with 'var_count' variables
  // having bounds vmin and vmax and having no names.
  void MakeIntVarArray(int var_count,
                       int64 vmin,
                       int64 vmax,
                       std::vector<IntVar*>* vars);
  // Same but allocates an array and returns it.
  IntVar** MakeIntVarArray(int var_count,
                           int64 vmin,
                           int64 vmax,
                           const string& name);


  // This method will append the vector vars with 'var_count' boolean
  // variables having name "name<i>" where <i> is the index of the
  // variable.
  void MakeBoolVarArray(int var_count,
                        const string& name,
                        std::vector<IntVar*>* vars);
  // This method will append the vector vars with 'var_count' boolean
  // variables having no names.
  void MakeBoolVarArray(int var_count,
                        std::vector<IntVar*>* vars);
  // Same but allocates an array and returns it.
  IntVar** MakeBoolVarArray(int var_count, const string& name);

  // ----- Integer Expressions -----

  // left + right.
  IntExpr* MakeSum(IntExpr* const left, IntExpr* const right);
  // expr + value.
  IntExpr* MakeSum(IntExpr* const expr, int64 value);
  // sum of all vars.
  IntExpr* MakeSum(const std::vector<IntVar*>& vars);

  // scalar product
  IntExpr* MakeScalProd(const std::vector<IntVar*>& vars,
                        const std::vector<int64>& coefs);
  // scalar product
  IntExpr* MakeScalProd(const std::vector<IntVar*>& vars,
                        const std::vector<int>& coefs);

  // left - right
  IntExpr* MakeDifference(IntExpr* const left, IntExpr* const right);
  // value - expr
  IntExpr* MakeDifference(int64 value, IntExpr* const expr);
  // -expr
  IntExpr* MakeOpposite(IntExpr* const expr);

  // left * right
  IntExpr* MakeProd(IntExpr* const left, IntExpr* const right);
  // expr * value
  IntExpr* MakeProd(IntExpr* const expr, int64 value);

  // expr / value (integer division)
  IntExpr* MakeDiv(IntExpr* const expr, int64 value);
  // numerator / denominator (integer division). Terms need to be positive.
  IntExpr* MakeDiv(IntExpr* const numerator, IntExpr* const denominator);

  // |expr|
  IntExpr* MakeAbs(IntExpr* const expr);
  // expr * expr
  IntExpr* MakeSquare(IntExpr* const expr);
  // expr ^ n (n > 0)
  IntExpr* MakePower(IntExpr* const expr, int64 n);

  // vals[expr]
  IntExpr* MakeElement(const std::vector<int64>& vals, IntVar* const index);
  // vals[expr]
  IntExpr* MakeElement(const std::vector<int>& vals, IntVar* const index);

  // Function-based element. The constraint takes ownership of
  // callback The callback must be able to cope with any possible
  // value in the domain of 'index' (potentially negative ones too).
  IntExpr* MakeElement(IndexEvaluator1* values, IntVar* const index);
  // Function based element. The constraint takes ownership of
  // callback.  The callback must be monotonic. It must be able to
  // cope with any possible value in the domain of 'index'
  // (potentially negative ones too). Furtermore, monotonicity is not
  // checked. Thus giving a non monotonic function, or specifying an
  // incorrect increasing parameter will result in undefined behavior.
  IntExpr* MakeMonotonicElement(IndexEvaluator1* values,
                                bool increasing,
                                IntVar* const index);
  // 2D version of function-based element expression, values(expr1, expr2).
  IntExpr* MakeElement(IndexEvaluator2* values,
                       IntVar* const index1,
                       IntVar* const index2);

  // vars[expr]
  IntExpr* MakeElement(const std::vector<IntVar*>& vars, IntVar* const index);

  // Returns the expression expr such that vars[expr] == value.
  // It assumes that vars are all different.
  IntExpr* MakeIndexExpression(const std::vector<IntVar*>& vars, int64 value);

  // min(vars)
  IntExpr* MakeMin(const std::vector<IntVar*>& vars);
  // min (left, right)
  IntExpr* MakeMin(IntExpr* const left, IntExpr* const right);
  // min(expr, val)
  IntExpr* MakeMin(IntExpr* const expr, int64 val);
  // min(expr, val)
  IntExpr* MakeMin(IntExpr* const expr, int val);

  // max(vars)
  IntExpr* MakeMax(const std::vector<IntVar*>& vars);
  // max(left, right)
  IntExpr* MakeMax(IntExpr* const left, IntExpr* const right);
  // max(expr, val)
  IntExpr* MakeMax(IntExpr* const expr, int64 val);
  // max(expr, val)
  IntExpr* MakeMax(IntExpr* const expr, int val);

  // convex piecewise function.
  IntExpr* MakeConvexPiecewiseExpr(IntExpr* e,
                                   int64 early_cost, int64 early_date,
                                   int64 late_date, int64 late_cost);

  // Semi continuous Expression (x <= 0 -> f(x) = 0; x > 0 -> f(x) = ax + b)
  // a >= 0 and b >= 0
  IntExpr* MakeSemiContinuousExpr(IntExpr* const e,
                                  int64 fixed_charge,
                                  int64 step);

  // Modulo expression x % mod (with the python convention for modulo).
  IntExpr* MakeModulo(IntExpr* const x, int64 mod);

  // Modulo expression x % mod (with the python convention for modulo).
  IntExpr* MakeModulo(IntExpr* const x, IntExpr* const mod);

  // ----- Constraints -----
  // This constraint always succeeds.
  Constraint* MakeTrueConstraint();
  // This constraint always fails.
  Constraint* MakeFalseConstraint();
  Constraint* MakeFalseConstraint(const string& explanation);

  // b == (v == c)
  Constraint* MakeIsEqualCstCt(IntExpr* const v, int64 c, IntVar* const b);
  // status var of (v == c)
  IntVar* MakeIsEqualCstVar(IntExpr* const var, int64 value);
  // b == (v1 == v2)
  Constraint* MakeIsEqualCt(IntExpr* const v1, IntExpr* v2, IntVar* const b);
  // status var of (v1 == v2)
  IntVar* MakeIsEqualVar(IntExpr* const var, IntExpr* v2);
  // left == right
  Constraint* MakeEquality(IntExpr* const left, IntExpr* const right);
  // expr == value
  Constraint* MakeEquality(IntExpr* const expr, int64 value);
  // expr == value
  Constraint* MakeEquality(IntExpr* const expr, int value);

  // b == (v != c)
  Constraint* MakeIsDifferentCstCt(IntExpr* const v, int64 c, IntVar* const b);
  // status var of (v != c)
  IntVar* MakeIsDifferentCstVar(IntExpr* const v, int64 c);
  // status var of (v1 != v2)
  IntVar* MakeIsDifferentVar(IntExpr* const v1, IntExpr* const v2);
  // b == (v1 != v2)
  Constraint* MakeIsDifferentCt(IntExpr* const v1, IntExpr* const v2,
                                IntVar* const b);
  // left != right
  Constraint* MakeNonEquality(IntExpr* const left, IntExpr* const right);
  // expr != value
  Constraint* MakeNonEquality(IntExpr* const expr, int64 value);
  // expr != value
  Constraint* MakeNonEquality(IntExpr* const expr, int value);

  // b == (v <= c)
  Constraint* MakeIsLessOrEqualCstCt(IntExpr* const v, int64 c,
                                     IntVar* const b);
  // status var of (v <= c)
  IntVar* MakeIsLessOrEqualCstVar(IntExpr* const v, int64 c);
  // status var of (left <= right)
  IntVar* MakeIsLessOrEqualVar(IntExpr* const left, IntExpr* const right);
  // b == (left <= right)
  Constraint* MakeIsLessOrEqualCt(IntExpr* const left, IntExpr* const right,
                                  IntVar* const b);
  // left <= right
  Constraint* MakeLessOrEqual(IntExpr* const left, IntExpr* const right);
  // expr <= value
  Constraint* MakeLessOrEqual(IntExpr* const expr, int64 value);
  // expr <= value
  Constraint* MakeLessOrEqual(IntExpr* const expr, int value);

  // b == (v >= c)
  Constraint* MakeIsGreaterOrEqualCstCt(IntExpr* const v, int64 c,
                                        IntVar* const b);
  // status var of (v >= c)
  IntVar* MakeIsGreaterOrEqualCstVar(IntExpr* const v, int64 c);
  // status var of (left >= right)
  IntVar* MakeIsGreaterOrEqualVar(IntExpr* const left, IntExpr* const right);
  // b == (left >= right)
  Constraint* MakeIsGreaterOrEqualCt(IntExpr* const left, IntExpr* const right,
                                     IntVar* const b);
  // left >= right
  Constraint* MakeGreaterOrEqual(IntExpr* const left, IntExpr* const right);
  // expr >= value
  Constraint* MakeGreaterOrEqual(IntExpr* const expr, int64 value);
  // expr >= value
  Constraint* MakeGreaterOrEqual(IntExpr* const expr, int value);

  // b == (v > c)
  Constraint* MakeIsGreaterCstCt(IntExpr* const v, int64 c, IntVar* const b);
  // status var of (v > c)
  IntVar* MakeIsGreaterCstVar(IntExpr* const v, int64 c);
  // status var of (left > right)
  IntVar* MakeIsGreaterVar(IntExpr* const left, IntExpr* const right);
  // b == (left > right)
  Constraint* MakeIsGreaterCt(IntExpr* const left, IntExpr* const right,
                              IntVar* const b);
  // left > right
  Constraint* MakeGreater(IntExpr* const left, IntExpr* const right);
  // expr > value
  Constraint* MakeGreater(IntExpr* const expr, int64 value);
  // expr > value
  Constraint* MakeGreater(IntExpr* const expr, int value);

  // b == (v < c)
  Constraint* MakeIsLessCstCt(IntExpr* const v, int64 c, IntVar* const b);
  // status var of (v < c)
  IntVar* MakeIsLessCstVar(IntExpr* const v, int64 c);
  // status var of (left < right)
  IntVar* MakeIsLessVar(IntExpr* const left, IntExpr* const right);
  // b == (left < right)
  Constraint* MakeIsLessCt(IntExpr* const left, IntExpr* const right,
                           IntVar* const b);
  // left < right
  Constraint* MakeLess(IntExpr* const left, IntExpr* const right);
  // expr < value
  Constraint* MakeLess(IntExpr* const expr, int64 value);
  // expr < value
  Constraint* MakeLess(IntExpr* const expr, int value);

  // Variation on arrays.
  Constraint* MakeSumLessOrEqual(const std::vector<IntVar*>& vars, int64 cst);
  Constraint* MakeSumGreaterOrEqual(const std::vector<IntVar*>& vars, int64 cst);
  Constraint* MakeSumEquality(const std::vector<IntVar*>& vars, int64 cst);
  Constraint* MakeSumEquality(const std::vector<IntVar*>& vars, IntVar* const var);
  Constraint* MakeScalProdEquality(const std::vector<IntVar*>& vars,
                                   const std::vector<int64>& coefficients,
                                   int64 cst);
  Constraint* MakeScalProdEquality(const std::vector<IntVar*>& vars,
                                   const std::vector<int>& coefficients,
                                   int64 cst);
  Constraint* MakeScalProdEquality(const std::vector<IntVar*>& vars,
                                   const std::vector<int64>& coefficients,
                                   IntVar* const target);
  Constraint* MakeScalProdEquality(const std::vector<IntVar*>& vars,
                                   const std::vector<int>& coefficients,
                                   IntVar* const target);
  Constraint* MakeScalProdGreaterOrEqual(const std::vector<IntVar*>& vars,
                                         const std::vector<int64>& coefficients,
                                         int64 cst);
  Constraint* MakeScalProdGreaterOrEqual(const std::vector<IntVar*>& vars,
                                         const std::vector<int>& coefficients,
                                         int64 cst);
  Constraint* MakeScalProdLessOrEqual(const std::vector<IntVar*>& vars,
                                      const std::vector<int64>& coefficients,
                                      int64 cst);
  Constraint* MakeScalProdLessOrEqual(const std::vector<IntVar*>& vars,
                                      const std::vector<int>& coefficients,
                                      int64 cst);

  Constraint* MakeMinEquality(const std::vector<IntVar*>& vars, IntVar* const var);
  Constraint* MakeMaxEquality(const std::vector<IntVar*>& vars, IntVar* const var);

  Constraint* MakeElementEquality(const std::vector<int64>& vals,
                                  IntVar* const index,
                                  IntVar* const target);
  Constraint* MakeElementEquality(const std::vector<int>& vals,
                                  IntVar* const index,
                                  IntVar* const target);
  Constraint* MakeElementEquality(const std::vector<IntVar*>& vars,
                                  IntVar* const index,
                                  IntVar* const target);
  Constraint* MakeElementEquality(const std::vector<IntVar*>& vars,
                                  IntVar* const index,
                                  int64 target);
  // Creates the constraint abs(var) == abs_var.
  Constraint* MakeAbsEquality(IntVar* const var, IntVar* const abs_var);
  // This constraint is a special case of the element constraint with
  // an array of integer variables where the variables are all
  // different and the index variable is constrained such that
  // vars[index] == target.
  Constraint* MakeIndexOfConstraint(const std::vector<IntVar*>& vars,
                                    IntVar* const index,
                                    int64 target);

  // This method is a specialized case of the MakeConstraintDemon
  // method to call the InitiatePropagate of the constraint 'ct'.
  Demon* MakeConstraintInitialPropagateCallback(Constraint* const ct);
  // This method is a specialized case of the MakeConstraintDemon
  // method to call the InitiatePropagate of the constraint 'ct' with
  // low priority.
  Demon* MakeDelayedConstraintInitialPropagateCallback(Constraint* const ct);
  // Creates a demon from a callback.
  Demon* MakeCallbackDemon(Callback1<Solver*>* const callback);
  // Creates a demon from a closure.
  Demon* MakeCallbackDemon(Closure* const closure);

  // (l <= b <= u)
  Constraint* MakeBetweenCt(IntVar* const v, int64 l, int64 u);

  // b == (l <= v <= u)
  Constraint* MakeIsBetweenCt(IntVar* const v,  int64 l, int64 u,
                              IntVar* const b);
  IntVar* MakeIsBetweenVar(IntVar* const v,  int64 l, int64 u);

  // b == (v in set)
  Constraint* MakeIsMemberCt(IntVar* const v, const std::vector<int64>& values,
                             IntVar* const b);
  Constraint* MakeIsMemberCt(IntVar* const v, const std::vector<int>& values,
                             IntVar* const b);
  IntVar* MakeIsMemberVar(IntVar* const v, const std::vector<int64>& values);
  IntVar* MakeIsMemberVar(IntVar* const v, const std::vector<int>& values);
  // v in set. Propagation is lazy, i.e. this constraint does not
  // creates holes in the domain of the variable.
  Constraint* MakeMemberCt(IntVar* const v, const std::vector<int64>& values);
  Constraint* MakeMemberCt(IntVar* const v, const std::vector<int>& values);


  // |{i | v[i] == value}| == count
  Constraint* MakeCount(const std::vector<IntVar*>& v, int64 value, int64 count);
  // |{i | v[i] == value}| == count
  Constraint* MakeCount(const std::vector<IntVar*>& v, int64 value,
                        IntVar* const count);

  // Aggregated version of count:  |{i | v[i] == values[j]}| == cards[j]
  Constraint* MakeDistribute(const std::vector<IntVar*>& vars,
                             const std::vector<int64>& values,
                             const std::vector<IntVar*>& cards);
  // Aggregated version of count:  |{i | v[i] == values[j]}| == cards[j]
  Constraint* MakeDistribute(const std::vector<IntVar*>& vars,
                             const std::vector<int>& values,
                             const std::vector<IntVar*>& cards);
  // Aggregated version of count:  |{i | v[i] == j}| == cards[j]
  Constraint* MakeDistribute(const std::vector<IntVar*>& vars,
                             const std::vector<IntVar*>& cards);
  // Aggregated version of count with bounded cardinalities:
  // forall j in 0 .. card_size - 1: card_min <= |{i | v[i] == j}| <= card_max
  Constraint* MakeDistribute(const std::vector<IntVar*>& vars,
                             int64 card_min,
                             int64 card_max,
                             int64 card_size);
  // Aggregated version of count with bounded cardinalities:
  // forall j in 0 .. card_size - 1:
  //    card_min[j] <= |{i | v[i] == j}| <= card_max[j]
  Constraint* MakeDistribute(const std::vector<IntVar*>& vars,
                             const std::vector<int64>& card_min,
                             const std::vector<int64>& card_max);
  // Aggregated version of count with bounded cardinalities:
  // forall j in 0 .. card_size - 1:
  //    card_min[j] <= |{i | v[i] == j}| <= card_max[j]
  Constraint* MakeDistribute(const std::vector<IntVar*>& vars,
                             const std::vector<int>& card_min,
                             const std::vector<int>& card_max);
  // Aggregated version of count with bounded cardinalities:
  // forall j in 0 .. card_size - 1:
  //    card_min[j] <= |{i | v[i] == values[j]}| <= card_max[j]
  Constraint* MakeDistribute(const std::vector<IntVar*>& vars,
                             const std::vector<int64>& values,
                             const std::vector<int64>& card_min,
                             const std::vector<int64>& card_max);
  // Aggregated version of count with bounded cardinalities:
  // forall j in 0 .. card_size - 1:
  //    card_min[j] <= |{i | v[i] == values[j]}| <= card_max[j]
  Constraint* MakeDistribute(const std::vector<IntVar*>& vars,
                             const std::vector<int>& values,
                             const std::vector<int>& card_min,
                             const std::vector<int>& card_max);

  // Deviation constraint:
  // sum_i |n * vars[i] - total_sum| <= deviation_var and
  // sum_i vars[i] == total_sum
  // n = #vars
  Constraint* MakeDeviation(const std::vector<IntVar*>& vars,
                            IntVar* const deviation_var,
                            int64 total_sum);

  // All variables are pairwise different. This corresponds to the
  // stronger version of the propagation algorithm.
  Constraint* MakeAllDifferent(const std::vector<IntVar*>& vars);

  // All variables are pairwise different.  If 'stronger_propagation'
  // is true, stronger, and potentially slower propagation will
  // occur. This API will be deprecated in the future.
  Constraint* MakeAllDifferent(const std::vector<IntVar*>& vars,
                               bool stronger_propagation);

  // All variables are pairwise different, unless they are assigned to
  // the escape value.
  Constraint* MakeAllDifferentExcept(const std::vector<IntVar*>& vars,
                                     int64 escape_value);
  // TODO(user): Do we need a version with an array of escape
  // values.

  // Creates a constraint binding the arrays of variables "vars" and
  // "sorted_vars": sorted_vars[0] must be equal to the minimum of all
  // variables in vars, and so on: the value of sorted_vars[i] must be
  // equal to the i-th value of variables invars.
  //
  // This constraint propagate in both directions: from "vars" to
  // "sorted_vars" and vice-versa.
  //
  // Behind the scenes, this constraint maintains that:
  //   - sorted is always increasing.
  //   - whatever the values of vars, there exists a permutation that
  //     injects its values into the sorted variables.
  //
  // For more info, please have a look at:
  //   https://mpi-inf.mpg.de/~mehlhorn/ftp/Mehlhorn-Thiel.pdf
  Constraint* MakeSortingConstraint(const std::vector<IntVar*>& vars,
                                    const std::vector<IntVar*>& sorted);
  // TODO(user): Add void MakeSortedArray(const std::vector<IntVar*>& vars,
  //                                         std::vector<IntVar*>* const sorted);

  // Creates a constraint that states that all variables in the first
  // vector are different from all variables from the second
  // group. Thus the set of values in the first vector does not
  // intersect the set of values in the second vector.
  Constraint* MakeNullIntersect(const std::vector<IntVar*>& first_vars,
                                const std::vector<IntVar*>& second_vars);

  // Creates a constraint that states that all variables in the first
  // vector are different from all variables from the second group,
  // unless they are assigned to the escape value. Thus the set of
  // values in the first vector minus the escape value does not
  // intersect the set of values in the second vector.
  Constraint* MakeNullIntersectExcept(const std::vector<IntVar*>& first_vars,
                                      const std::vector<IntVar*>& second_vars,
                                      int64 escape_value);

  // TODO(user): Implement MakeAllNullIntersect taking an array of
  // variable vectors.

  // Prevent cycles, nexts variables representing the next in the chain.
  // Active variables indicate if the corresponding next variable is active;
  // this could be useful to model unperformed nodes in a routing problem.
  // A callback can be added to specify sink values (by default sink values
  // are values >= vars.size()). Ownership of the callback is passed to the
  // constraint.
  // If assume_paths is either not specified or true, the constraint assumes the
  // 'next' variables represent paths (and performs a faster propagation);
  // otherwise the constraint assumes the 'next' variables represent a forest.
  Constraint* MakeNoCycle(const std::vector<IntVar*>& nexts,
                          const std::vector<IntVar*>& active,
                          ResultCallback1<bool, int64>* sink_handler = NULL);
  Constraint* MakeNoCycle(const std::vector<IntVar*>& nexts,
                          const std::vector<IntVar*>& active,
                          ResultCallback1<bool, int64>* sink_handler,
                          bool assume_paths);

  // Force the nexts() variable to create an complete hamiltonian path.
  Constraint* MakeCircuit(const std::vector<IntVar*>& nexts);


  // Force the nexts() variable to create an complete hamiltonian path
  // for those that do not loop upon themselves.
  Constraint* MakeSubCircuit(const std::vector<IntVar*>& nexts);

  // Creates a constraint which accumulates values along a path such that:
  // cumuls[next[i]] = cumuls[i] + transits[i].
  // Active variables indicate if the corresponding next variable is active;
  // this could be useful to model unperformed nodes in a routing problem.
  Constraint* MakePathCumul(const std::vector<IntVar*>& nexts,
                            const std::vector<IntVar*>& active,
                            const std::vector<IntVar*>& cumuls,
                            const std::vector<IntVar*>& transits);
  // Creates a constraint which accumulates values along a path such that:
  // cumuls[next[i]] = cumuls[i] + transit_evaluator(i, next[i]).
  // Active variables indicate if the corresponding next variable is active;
  // this could be useful to model unperformed nodes in a routing problem.
  // Ownership of transit_evaluator is taken and it must be a repeatable
  // callback.
  // TODO(user): Add a version taking slack variables.
  Constraint* MakePathCumul(const std::vector<IntVar*>& nexts,
                            const std::vector<IntVar*>& active,
                            const std::vector<IntVar*>& cumuls,
                            IndexEvaluator2* transit_evaluator);

  // This constraint maps the domain of 'var' onto the array of
  // variables 'vars'. That is
  // for all i in [0 .. size - 1]: vars[i] == 1 <=> var->Contains(i);
  Constraint* MakeMapDomain(IntVar* const var, const std::vector<IntVar*>& vars);

  // This method creates a constraint where the graph of the relation
  // between the variables is given in extension. There are 'arity'
  // variables involved in the relation and the graph is given by a
  // integer tuple set.
  Constraint* MakeAllowedAssignments(const std::vector<IntVar*>& vars,
                                     const IntTupleSet& tuples);

  // This constraint create a finite automaton that will check the
  // sequence of variables vars. It uses a transition table called
  // 'transitions'. Each transition is a triple
  //    (current_state, variable_value, new_state).
  // The initial state is given, and the set of accepted states is decribed
  // by 'final_states'. These states are hidden inside the constraint.
  // Only the transitions (i.e. the variables) are visible.
  Constraint* MakeTransitionConstraint(
      const std::vector<IntVar*>& vars,
      const IntTupleSet& transitions,
      int64 initial_state,
      const std::vector<int64>& final_states);

  // This constraint create a finite automaton that will check the
  // sequence of variables vars. It uses a transition table called
  // 'transitions'. Each transition is a triple
  //    (current_state, variable_value, new_state).
  // The initial state is given, and the set of accepted states is decribed
  // by 'final_states'. These states are hidden inside the constraint.
  // Only the transitions (i.e. the variables) are visible.
  Constraint* MakeTransitionConstraint(
      const std::vector<IntVar*>& vars,
      const IntTupleSet& transitions,
      int64 initial_state,
      const std::vector<int>& final_states);

#if defined(SWIGPYTHON)
  // Compatibility layer for python API.
  Constraint* MakeAllowedAssignments(const std::vector<IntVar*>& vars,
                                     const std::vector<std::vector<int64> >& raw_tuples) {
    IntTupleSet tuples(vars.size());
    tuples.InsertAll(raw_tuples);
    return MakeAllowedAssignments(vars, tuples);
  }

  Constraint* MakeTransitionConstraint(
      const std::vector<IntVar*>& vars,
      const std::vector<std::vector<int64> >& raw_transitions,
      int64 initial_state,
      const std::vector<int>& final_states) {
    IntTupleSet transitions(3);
    transitions.InsertAll(raw_transitions);
    return MakeTransitionConstraint(vars,
                                    transitions,
                                    initial_state,
                                    final_states);
  }
#endif

  // This constraint states that all the boxes must not overlap.
  // The coordinates of box i are :
  //   (x_vars[i], y_vars[i]),
  //   (x_vars[i], y_vars[i] + y_size[i]),
  //   (x_vars[i] + x_size[i], y_vars[i]),
  //   (x_vars[i] + x_size[i], y_vars[i] + y_size[i]).
  // The sizes must be strictly positive.
  Constraint* MakeNonOverlappingBoxesConstraint(
      const std::vector<IntVar*>& x_vars,
      const std::vector<IntVar*>& y_vars,
      const std::vector<IntVar*>& x_size,
      const std::vector<IntVar*>& y_size);
  Constraint* MakeNonOverlappingBoxesConstraint(
      const std::vector<IntVar*>& x_vars,
      const std::vector<IntVar*>& y_vars,
      const std::vector<int64>& x_size,
      const std::vector<int64>& y_size);
  Constraint* MakeNonOverlappingBoxesConstraint(
      const std::vector<IntVar*>& x_vars,
      const std::vector<IntVar*>& y_vars,
      const std::vector<int>& x_size,
      const std::vector<int>& y_size);

  // ----- Packing constraint -----

  // This constraint packs all variables onto 'number_of_bins'
  // variables.  For any given variable, a value of 'number_of_bins'
  // indicates that the variable is not assigned to any bin.
  // Dimensions, i.e. cumulative constraints on this packing can be
  // added directly from the pack class.
  Pack* MakePack(const std::vector<IntVar*>& vars, int number_of_bins);

  // ----- scheduling objects -----

  // Creates an interval var with a fixed duration. The duration must
  // be greater than 0. If optional is true, then the interval can be
  // performed or unperformed. If optional is false, then the interval
  // is always performed.
  IntervalVar* MakeFixedDurationIntervalVar(int64 start_min,
                                            int64 start_max,
                                            int64 duration,
                                            bool optional,
                                            const string& name);

  // This method fills the vector with 'count' interval var built with
  // the corresponding parameters.
  void MakeFixedDurationIntervalVarArray(int count,
                                         int64 start_min,
                                         int64 start_max,
                                         int64 duration,
                                         bool optional,
                                         const string& name,
                                         std::vector<IntervalVar*>* const array);

  // Creates an interval var with a fixed duration. The duration must
  // be greater than 0.
  IntervalVar* MakeFixedDurationIntervalVar(IntVar* const start_variable,
                                            int64 duration,
                                            const string& name);

  // This method fills the vector with 'count' interval var built with
  // the corresponding start variables.
  void MakeFixedDurationIntervalVarArray(
      const std::vector<IntVar*>& start_variables,
      int64 duration,
      const string& name,
      std::vector<IntervalVar*>* const array);

  // This method fills the vector with interval variables built with
  // the corresponding start variables.
  void MakeFixedDurationIntervalVarArray(
      const std::vector<IntVar*>& start_variables,
      const std::vector<int64>& durations,
      const string& name,
      std::vector<IntervalVar*>* const array);
  // This method fills the vector with interval variables built with
  // the corresponding start variables.
  void MakeFixedDurationIntervalVarArray(
      const std::vector<IntVar*>& start_variables,
      const std::vector<int>& durations,
      const string& name,
      std::vector<IntervalVar*>* const array);


  // Creates a fixed and performed interval.
  IntervalVar* MakeFixedInterval(int64 start,
                                 int64 duration,
                                 const string& name);

  // Creates an interval var by specifying the bounds on start,
  // duration, and end.
  IntervalVar* MakeIntervalVar(int64 start_min,
                               int64 start_max,
                               int64 duration_min,
                               int64 duration_max,
                               int64 end_min,
                               int64 end_max,
                               bool optional,
                               const string& name);

  // This method fills the vector with 'count' interval var built with
  // the corresponding parameters.
  void MakeIntervalVarArray(int count,
                            int64 start_min,
                            int64 start_max,
                            int64 duration_min,
                            int64 duration_max,
                            int64 end_min,
                            int64 end_max,
                            bool optional,
                            const string& name,
                            std::vector<IntervalVar*>* const array);

  // Creates an interval var that is the mirror image of the given one, that is,
  // the interval var obtained by reversing the axis.
  IntervalVar* MakeMirrorInterval(IntervalVar* const interval_var);

  // Creates an interval var with a fixed duration whose start is
  // synchronized with the start of another interval, with a given
  // offset. The performed status is also in sync with the performed
  // status of the given interval variable.
  IntervalVar* MakeFixedDurationStartSyncedOnStartIntervalVar(
      IntervalVar* const interval_var, int64 duration, int64 offset);

  // Creates an interval var with a fixed duration whose start is
  // synchronized with the end of another interval, with a given
  // offset. The performed status is also in sync with the performed
  // status of the given interval variable.
  IntervalVar* MakeFixedDurationStartSyncedOnEndIntervalVar(
      IntervalVar* const interval_var, int64 duration, int64 offset);

  // Creates an interval var with a fixed duration whose end is
  // synchronized with the start of another interval, with a given
  // offset. The performed status is also in sync with the performed
  // status of the given interval variable.
  IntervalVar* MakeFixedDurationEndSyncedOnStartIntervalVar(
      IntervalVar* const interval_var, int64 duration, int64 offset);

  // Creates an interval var with a fixed duration whose end is
  // synchronized with the end of another interval, with a given
  // offset. The performed status is also in sync with the performed
  // status of the given interval variable.
  IntervalVar* MakeFixedDurationEndSyncedOnEndIntervalVar(
      IntervalVar* const interval_var, int64 duration, int64 offset);

  // Creates and returns an interval variable that wraps around the given one,
  // relaxing the min start and end. Relaxing means making unbounded when
  // optional. If the variable is non optional, this methods returns
  // interval_var.
  //
  // More precisely, such an interval variable behaves as follows:
  // * When the underlying must be performed, the returned interval variable
  //     behaves exactly as the underlying;
  // * When the underlying may or may not be performed, the returned interval
  //     variable behaves like the underlying, except that it is unbounded on
  //     the min side;
  // * When the underlying cannot be performed, the returned interval variable
  //     is of duration 0 and must be performed in an interval unbounded on both
  //     sides.
  //
  // This is very useful to implement propagators that may only modify
  // the start max or end max.
  IntervalVar* MakeIntervalRelaxedMin(IntervalVar* const interval_var);

  // Creates and returns an interval variable that wraps around the given one,
  // relaxing the max start and end. Relaxing means making unbounded when
  // optional. If the variable is non optional, this methods returns
  // interval_var.
  //
  // More precisely, such an interval variable behaves as follows:
  // * When the underlying must be performed, the returned interval variable
  //     behaves exactly as the underlying;
  // * When the underlying may or may not be performed, the returned interval
  //     variable behaves like the underlying, except that it is unbounded on
  //     the max side;
  // * When the underlying cannot be performed, the returned interval variable
  //     is of duration 0 and must be performed in an interval unbounded on both
  //     sides.
  //
  // This is very useful to implement propagators that may only modify
  // the start min or end min.
  IntervalVar* MakeIntervalRelaxedMax(IntervalVar* const interval_var);

  // ----- scheduling constraints -----

  // This method creates a relation between an interval var and a
  // date.
  Constraint* MakeIntervalVarRelation(IntervalVar* const t,
                                      UnaryIntervalRelation r,
                                      int64 d);

  // This method creates a relation between two an interval vars.
  Constraint* MakeIntervalVarRelation(IntervalVar* const t1,
                                      BinaryIntervalRelation r,
                                      IntervalVar* const t2);

  // This constraint implements a temporal disjunction between two
  // interval vars t1 and t2. 'alt' indicates which alternative was
  // chosen (alt == 0 is equivalent to t1 before t2).
  Constraint* MakeTemporalDisjunction(IntervalVar* const t1,
                                      IntervalVar* const t2,
                                      IntVar* const alt);

  // This constraint implements a temporal disjunction between two
  // interval vars.
  Constraint* MakeTemporalDisjunction(IntervalVar* const t1,
                                      IntervalVar* const t2);

  // This constraint forces all interval vars into an non overlapping
  // sequence.
  DisjunctiveConstraint* MakeDisjunctiveConstraint(
      const std::vector<IntervalVar*>& intervals,
      const string& name);

  // This constraint forces that, for any integer t, the sum of the demands
  // corresponding to an interval containing t does not exceed the given
  // capacity.
  //
  // Intervals and demands should be vectors of equal size.
  //
  // Demands should only contain non-negative values. Zero values are supported,
  // and the corresponding intervals are filtered out, as they neither impact
  // nor are impacted by this constraint.
  Constraint* MakeCumulative(const std::vector<IntervalVar*>& intervals,
                             const std::vector<int64>& demands,
                             int64 capacity,
                             const string& name);

  // This constraint forces that, for any integer t, the sum of the demands
  // corresponding to an interval containing t does not exceed the given
  // capacity.
  //
  // Intervals and demands should be vectors of equal size.
  //
  // Demands should only contain non-negative values. Zero values are supported,
  // and the corresponding intervals are filtered out, as they neither impact
  // nor are impacted by this constraint.
  Constraint* MakeCumulative(const std::vector<IntervalVar*>& intervals,
                             const std::vector<int>& demands,
                             int64 capacity,
                             const string& name);

  // This constraint forces that, for any integer t, the sum of the demands
  // corresponding to an interval containing t does not exceed the given
  // capacity.
  //
  // Intervals and demands should be vectors of equal size.
  //
  // Demands should only contain non-negative values. Zero values are supported,
  // and the corresponding intervals are filtered out, as they neither impact
  // nor are impacted by this constraint.
  Constraint* MakeCumulative(const std::vector<IntervalVar*>& intervals,
                             const std::vector<int64>& demands,
                             IntVar* const capacity,
                             const string& name);

  // This constraint forces that, for any integer t, the sum of the demands
  // corresponding to an interval containing t does not exceed the given
  // capacity.
  //
  // Intervals and demands should be vectors of equal size.
  //
  // Demands should only contain non-negative values. Zero values are supported,
  // and the corresponding intervals are filtered out, as they neither impact
  // nor are impacted by this constraint.
  Constraint* MakeCumulative(const std::vector<IntervalVar*>& intervals,
                             const std::vector<int>& demands,
                             IntVar* const capacity,
                             const string& name);

  // This constraint states that the target_var is the convex hull of
  // the intervals. If none of the interval variables is performed,
  // then the target var is unperformed too. Also, if the target
  // variable is unperformed, then all the intervals variables are
  // unperformed too.
  Constraint* MakeCover(const std::vector<IntervalVar*>& intervals,
                        IntervalVar* const target_var);

  // This constraints states that the two interval variables are equal.
  Constraint* MakeEquality(IntervalVar* const left, IntervalVar* const right);

  // ----- Assignments -----

  // This method creates an empty assignment.
  Assignment* MakeAssignment();

  // This method creates an assignnment which is a copy of 'a'.
  Assignment* MakeAssignment(const Assignment* const a);

  // ----- Solution Collectors -----

  // Collect the first solution of the search.
  SolutionCollector* MakeFirstSolutionCollector(
      const Assignment* const assignment);
  // Collect the first solution of the search. The variables will need to
  // be added later.
  SolutionCollector* MakeFirstSolutionCollector();

  // Collect the last solution of the search.
  SolutionCollector* MakeLastSolutionCollector(
      const Assignment* const assignment);
  // Collect the last solution of the search. The variables will need to
  // be added later.
  SolutionCollector* MakeLastSolutionCollector();

  // Collect the solution corresponding to the optimal value of the objective
  // of 'a'; if 'a' does not have an objective no solution is collected. This
  // collector only collects one solution corresponding to the best objective
  // value (the first one found).
  SolutionCollector* MakeBestValueSolutionCollector(
      const Assignment* const assignment, bool maximize);
  // Collect the solution corresponding to the optimal value of the
  // objective of 'a'; if 'a' does not have an objective no solution
  // is collected. This collector only collects one solution
  // corresponding to the best objective value (the first one
  // found). The variables will need to be added later.
  SolutionCollector* MakeBestValueSolutionCollector(bool maximize);

  // Collect all solutions of the search.
  SolutionCollector* MakeAllSolutionCollector(
      const Assignment* const assignment);
  // Collect all solutions of the search. The variables will need to
  // be added later.
  SolutionCollector* MakeAllSolutionCollector();

  // ----- Objective -----

  // Creates a minimization objective.
  OptimizeVar* MakeMinimize(IntVar* const v, int64 step);

  // Creates a maximization objective.
  OptimizeVar* MakeMaximize(IntVar* const v, int64 step);

  // Creates a objective with a given sense (true = maximization).
  OptimizeVar* MakeOptimize(bool maximize, IntVar* const v, int64 step);

  // Creates a minimization weighted objective. The actual objective is
  // scalar_prod(vars, weights).
  OptimizeVar* MakeWeightedMinimize(const std::vector<IntVar*>& vars,
                                    const std::vector<int64>& weights,
                                    int64 step);

  // Creates a minimization weighted objective. The actual objective is
  // scalar_prod(vars, weights).
  OptimizeVar* MakeWeightedMinimize(const std::vector<IntVar*>& vars,
                                    const std::vector<int>& weights,
                                    int64 step);

  // Creates a maximization weigthed objective.
  OptimizeVar* MakeWeightedMaximize(const std::vector<IntVar*>& vars,
                                    const std::vector<int64>& weights,
                                    int64 step);

  // Creates a maximization weigthed objective.
  OptimizeVar* MakeWeightedMaximize(const std::vector<IntVar*>& vars,
                                    const std::vector<int>& weights,
                                    int64 step);

  // Creates a weighted objective with a given sense (true = maximization).
  OptimizeVar* MakeWeightedOptimize(bool maximize,
                                    const std::vector<IntVar*>& vars,
                                    const std::vector<int64>& weights,
                                    int64 step);

  // Creates a weighted objective with a given sense (true = maximization).
  OptimizeVar* MakeWeightedOptimize(bool maximize,
                                    const std::vector<IntVar*>& vars,
                                    const std::vector<int>& weights,
                                    int64 step);

  // ----- Meta-heuristics -----
  // Search monitors which try to get the search out of local optima.

  // Creates a Tabu Search monitor.
  // In the context of local search the behavior is similar to MakeOptimize(),
  // creating an objective in a given sense. The behavior differs once a local
  // optimum is reached: thereafter solutions which degrade the value of the
  // objective are allowed if they are not "tabu". A solution is "tabu" if it
  // doesn't respect the following rules:
  // - improving the best solution found so far
  // - variables in the "keep" list must keep their value, variables in the
  // "forbid" list must not take the value they have in the list.
  // Variables with new values enter the tabu lists after each new solution
  // found and leave the lists after a given number of iterations (called
  // tenure). Only the variables passed to the method can enter the lists.
  // The tabu criterion is softened by the tabu factor which gives the number
  // of "tabu" violations which is tolerated; a factor of 1 means no violations
  // allowed, a factor of 0 means all violations allowed.

  SearchMonitor* MakeTabuSearch(bool maximize,
                                IntVar* const v,
                                int64 step,
                                const std::vector<IntVar*>& vars,
                                int64 keep_tenure,
                                int64 forbid_tenure,
                                double tabu_factor);

  // Creates a Simulated Annealing monitor.
  // TODO(user): document behavior
  SearchMonitor* MakeSimulatedAnnealing(bool maximize,
                                        IntVar* const v,
                                        int64 step,
                                        int64 initial_temperature);

  // Creates a Guided Local Search monitor.
  // Description here: http://en.wikipedia.org/wiki/Guided_Local_Search
  SearchMonitor* MakeGuidedLocalSearch(bool maximize,
                                       IntVar* const objective,
                                       IndexEvaluator2* objective_function,
                                       int64 step,
                                       const std::vector<IntVar*>& vars,
                                       double penalty_factor);
  SearchMonitor* MakeGuidedLocalSearch(bool maximize,
                                       IntVar* const objective,
                                       IndexEvaluator3* objective_function,
                                       int64 step,
                                       const std::vector<IntVar*>& vars,
                                       const std::vector<IntVar*>& secondary_vars,
                                       double penalty_factor);

  // ----- Restart Search -----

  // This search monitor will restart the search periodically.
  // At the iteration n, it will restart after scale_factor * Luby(n) failures
  // where Luby is the Luby Strategy (i.e. 1 1 2 1 1 2 4 1 1 2 1 1 2 4 8...).
  SearchMonitor* MakeLubyRestart(int scale_factor);

  // This search monitor will restart the search periodically after 'frequency'
  // failures.
  SearchMonitor* MakeConstantRestart(int frequency);


  // ----- Search Limit -----

  // Creates a search limit that constrains the running time given in
  // milliseconds.
  SearchLimit* MakeTimeLimit(int64 time_in_ms);

  // Creates a search limit that constrains the number of branches
  // explored in the search tree.
  SearchLimit* MakeBranchesLimit(int64 branches);

  // Creates a search limit that constrains the number of failures
  // that can happen when exploring the search tree.
  SearchLimit* MakeFailuresLimit(int64 failures);

  // Creates a search limit that constrains the number of solutions found
  // during the search.
  SearchLimit* MakeSolutionsLimit(int64 solutions);

  // Limits the search with the 'time', 'branches', 'failures' and
  // 'solutions' limits.
  SearchLimit* MakeLimit(int64 time,
                         int64 branches,
                         int64 failures,
                         int64 solutions);
  // Version reducing calls to wall timer by estimating number of remaining
  // calls.
  SearchLimit* MakeLimit(int64 time,
                         int64 branches,
                         int64 failures,
                         int64 solutions,
                         bool smart_time_check);
  // Creates a search limit which can either apply cumulatively or
  // search-by-search.
  SearchLimit* MakeLimit(int64 time,
                         int64 branches,
                         int64 failures,
                         int64 solutions,
                         bool smart_time_check,
                         bool cumulative);
  // Creates a search limit from its protobuf description
  SearchLimit* MakeLimit(const SearchLimitProto& proto);

  // Creates a search limit that is reached when either of the underlying limit
  // is reached. That is, the returned limit is more stringent than both
  // argument limits.
  SearchLimit* MakeLimit(SearchLimit* const limit_1,
                         SearchLimit* const limit_2);

  void UpdateLimits(int64 time,
                    int64 branches,
                    int64 failures,
                    int64 solutions,
                    SearchLimit* limit);
  // Returns 'time' limit of search limit
  int64 GetTime(SearchLimit* limit);

  // Callback-based search limit. Search stops when limiter returns true; if
  // this happens at a leaf the corresponding solution will be rejected.
  SearchLimit* MakeCustomLimit(ResultCallback<bool>* limiter);

  // ----- No Goods -----

  // Creates a non-reversible nogood manager to store and use nogoods
  // during search. Nogoods are defined by the NoGood class. It can be
  // used during search with restart to avoid revisiting the same
  // portion of the search tree.
  NoGoodManager* MakeNoGoodManager();

  // ----- Tree Monitor -----
  // Creates a tree monitor that outputs a detailed overview of the
  // decision phase in cpviz format. The XML data is written to files
  // file_tree and file_visualization as the search finishes.
  SearchMonitor* MakeTreeMonitor(const std::vector<IntVar*>& vars,
                                 const string& file_tree,
                                 const string& file_visualization);

  // Creates a tree monitor that outputs a detailed overview of the
  // decision phase in cpviz format. The XML data is written to files
  // file_config, file_tree and file_visualization as the search
  // finishes.
  SearchMonitor* MakeTreeMonitor(const std::vector<IntVar*>& vars,
                                 const string& file_config,
                                 const string& file_tree,
                                 const string& file_visualization);

#if !defined(SWIG)
  // Creates a tree monitor that outputs a detailed overview of the
  // decision phase in cpviz format. The XML data is copied to tree_xml
  // and visualization_xml as the search finishes. The tree monitor does
  // not take ownership of either string.
  SearchMonitor* MakeTreeMonitor(const std::vector<IntVar*>& vars,
                                 string* const tree_xml,
                                 string* const visualization_xml);

  // Creates a tree monitor that outputs a detailed overview of the
  // decision phase in cpviz format. The XML data is copied to config_xml,
  // tree_xml and visualization_xml as the search finishes. The tree monitor
  // does not take ownership of these strings.
  SearchMonitor* MakeTreeMonitor(const std::vector<IntVar*>& vars,
                                 string* const config_xml,
                                 string* const tree_xml,
                                 string* const visualization_xml);

#endif  // #if !defined(SWIG)

  // TODO(user): DEPRECATE API of MakeSearchLog(.., IntVar* var,..).

  // ----- Search Log -----
  // The SearchMonitors below will display a periodic search log
  // on LOG(INFO) every branch_count branches explored.

  SearchMonitor* MakeSearchLog(int branch_count);

  // At each solution, this monitor also display the objective value.
  SearchMonitor* MakeSearchLog(int branch_count, IntVar* const objective);

  // At each solution, this monitor will also display result of @p
  // display_callback.
  SearchMonitor* MakeSearchLog(int branch_count,
                               ResultCallback<string>* display_callback);

  // At each solution, this monitor will display the objective value and the
  // result of @p display_callback.
  SearchMonitor* MakeSearchLog(int branch_count,
                               IntVar* objective,
                               ResultCallback<string>* display_callback);

  // OptimizeVar Search Logs
  // At each solution, this monitor will also display the objective->Print().

  SearchMonitor* MakeSearchLog(int branch_count, OptimizeVar* const objective);

  // Creates a search monitor that will also print the result of the
  // display callback.
  SearchMonitor* MakeSearchLog(int branch_count,
                               OptimizeVar* const objective,
                               ResultCallback<string>* display_callback);


  // ----- Search Trace ------

  // Creates a search monitor that will trace precisely the behavior of the
  // search. Use this only for low level debugging.
  SearchMonitor* MakeSearchTrace(const string& prefix);

  // ----- ModelVisitor -----

  // Prints the model.
  ModelVisitor* MakePrintModelVisitor();
  // Displays some nice statistics on the model.
  ModelVisitor* MakeStatisticsModelVisitor();
#if !defined(SWIG)
  // Compute the number of constraints a variable is attached to.
  ModelVisitor* MakeVariableDegreeVisitor(hash_map<IntVar*, int>* const map);
#endif

  // ----- Symmetry Breaking -----

  SearchMonitor* MakeSymmetryManager(const std::vector<SymmetryBreaker*>& visitors);
  SearchMonitor* MakeSymmetryManager(SymmetryBreaker* const v1);
  SearchMonitor* MakeSymmetryManager(SymmetryBreaker* const v1,
                                     SymmetryBreaker* const v2);
  SearchMonitor* MakeSymmetryManager(SymmetryBreaker* const v1,
                                     SymmetryBreaker* const v2,
                                     SymmetryBreaker* const v3);
  SearchMonitor* MakeSymmetryManager(SymmetryBreaker* const v1,
                                     SymmetryBreaker* const v2,
                                     SymmetryBreaker* const v3,
                                     SymmetryBreaker* const v4);

  // ----- Simplex Connection -----
#if !defined(SWIG)
  SearchMonitor* MakeSimplexConnection(Callback1<MPSolver*>* const builder,
                                       Callback1<MPSolver*>* const modifier,
                                       Callback1<MPSolver*>* const runner,
                                       int simplex_frequency);
#endif  // #if !defined(SWIG)

  // ----- Linear Relaxation Constraint -----

  // Creates a search monitor that will maintain a linear relaxation
  // of the problem. Every 'simplex_frequency' nodes explored in the
  // search tree, this linear relaxation will be called and the
  // resulting optimal solution found by the simplex will be used to
  // prune the objective of the constraint programming model.
  SearchMonitor* MakeSimplexConstraint(int simplex_frequency);

  // ----- Search Decicions and Decision Builders -----

  // ----- Decisions -----
  Decision* MakeAssignVariableValue(IntVar* const var, int64 value);
  Decision* MakeVariableLessOrEqualValue(IntVar* const var, int64 value);
  Decision* MakeVariableGreaterOrEqualValue(IntVar* const var, int64 value);
  Decision* MakeSplitVariableDomain(IntVar* const var,
                                    int64 value,
                                    bool start_with_lower_half);
  Decision* MakeAssignVariableValueOrFail(IntVar* const var, int64 value);
  Decision* MakeAssignVariablesValues(const std::vector<IntVar*>& vars,
                                      const std::vector<int64>& values);
  Decision* MakeFailDecision();

  // Creates a decision builder which sequentially composes decision builders.
  // At each leaf of a decision builder, the next decision builder is therefore
  // called. For instance Compose(db1, db2) will result in the following tree:
  //          d1 tree              |
  //         /   |   \             |
  //         db1 leaves            |
  //       /     |     \           |
  //  db2 tree db2 tree db2 tree   |
  DecisionBuilder* Compose(DecisionBuilder* const db1,
                           DecisionBuilder* const db2);
  DecisionBuilder* Compose(DecisionBuilder* const db1,
                           DecisionBuilder* const db2,
                           DecisionBuilder* const db3);
  DecisionBuilder* Compose(DecisionBuilder* const db1,
                           DecisionBuilder* const db2,
                           DecisionBuilder* const db3,
                           DecisionBuilder* const db4);
  DecisionBuilder* Compose(const std::vector<DecisionBuilder*>& dbs);

  // Creates a decision builder which will create a search tree where each
  // decision builder is called from the top of the search tree. For instance
  // the decision builder Try(db1, db2) will entirely explore the search tree
  // of db1 then the one of db2, resulting in the following search tree:
  //        Tree root            |
  //        /       \            |
  //  db1 tree     db2 tree      |
  //
  // This is very handy to try a decision builder which partially explores the
  // search space and if it fails to try another decision builder.
  //
  // TODO(user): The search tree can be balanced by using binary
  // "Try"-builders "recursively". For instance, Try(a,b,c,d) will give a tree
  // unbalanced to the right, whereas Try(Try(a,b), Try(b,c)) will give a
  // balanced tree. Investigate if we should only provide the binary version
  // and/or if we should balance automatically.
  DecisionBuilder* Try(DecisionBuilder* const db1,
                       DecisionBuilder* const db2);
  DecisionBuilder* Try(DecisionBuilder* const db1,
                       DecisionBuilder* const db2,
                       DecisionBuilder* const db3);
  DecisionBuilder* Try(DecisionBuilder* const db1,
                       DecisionBuilder* const db2,
                       DecisionBuilder* const db3,
                       DecisionBuilder* const db4);
  DecisionBuilder* Try(const std::vector<DecisionBuilder*>& dbs);


  // Phases on IntVar arrays.
  DecisionBuilder* MakePhase(const std::vector<IntVar*>& vars,
                             IntVarStrategy var_str,
                             IntValueStrategy val_str);
  DecisionBuilder* MakePhase(const std::vector<IntVar*>& vars,
                             IndexEvaluator1* var_evaluator,
                             IntValueStrategy val_str);

  DecisionBuilder* MakePhase(const std::vector<IntVar*>& vars,
                             IntVarStrategy var_str,
                             IndexEvaluator2* val_eval);

  DecisionBuilder* MakePhase(const std::vector<IntVar*>& vars,
                             IndexEvaluator1* var_evaluator,
                             IndexEvaluator2* val_eval);

  DecisionBuilder* MakePhase(const std::vector<IntVar*>& vars,
                             IntVarStrategy var_str,
                             IndexEvaluator2* val_eval,
                             IndexEvaluator1* tie_breaker);

  DecisionBuilder* MakePhase(const std::vector<IntVar*>& vars,
                             IndexEvaluator1* var_evaluator,
                             IndexEvaluator2* val_eval,
                             IndexEvaluator1* tie_breaker);

  DecisionBuilder* MakeDefaultPhase(const std::vector<IntVar*>& vars);
  DecisionBuilder* MakeDefaultPhase(const std::vector<IntVar*>& vars,
                                    const DefaultPhaseParameters& parameters);

  // shortcuts for small arrays.
  DecisionBuilder* MakePhase(IntVar* const v0,
                             IntVarStrategy var_str,
                             IntValueStrategy val_str);
  DecisionBuilder* MakePhase(IntVar* const v0,
                             IntVar* const v1,
                             IntVarStrategy var_str,
                             IntValueStrategy val_str);
  DecisionBuilder* MakePhase(IntVar* const v0,
                             IntVar* const v1,
                             IntVar* const v2,
                             IntVarStrategy var_str,
                             IntValueStrategy val_str);
  DecisionBuilder* MakePhase(IntVar* const v0,
                             IntVar* const v1,
                             IntVar* const v2,
                             IntVar* const v3,
                             IntVarStrategy var_str,
                             IntValueStrategy val_str);

  // ----- Scheduling Decisions -----

  // Returns a decision that tries to schedule a task at a given time.
  // On the Apply branch, it will set that interval var as performed and set
  // its start to 'est'. On the Refute branch, it will just update the
  // 'marker' to 'est' + 1. This decision is used in the
  // INTERVAL_SET_TIMES_FORWARD strategy.
  Decision* MakeScheduleOrPostpone(IntervalVar* const var,
                                   int64 est,
                                   int64* const marker);

  // Returns a decision that tries to rank first the ith interval var
  // in the sequence variable.
  Decision* MakeRankFirstInterval(SequenceVar* const sequence, int index);

  // Returns a decision that tries to rank last the ith interval var
  // in the sequence variable.
  Decision* MakeRankLastInterval(SequenceVar* const sequence, int index);

  // Returns a decision builder which assigns values to variables which
  // minimize the values returned by the evaluator. The arguments passed to the
  // evaluator callback are the indices of the variables in vars and the values
  // of these variables. Ownership of the callback is passed to the decision
  // builder.
  DecisionBuilder* MakePhase(const std::vector<IntVar*>& vars,
                             IndexEvaluator2* evaluator,
                             EvaluatorStrategy str);

  // Returns a decision builder which assigns values to variables
  // which minimize the values returned by the evaluator. In case of
  // tie breaks, the second callback is used to choose the best index
  // in the array of equivalent pairs with equivalent evaluations. The
  // arguments passed to the evaluator callback are the indices of the
  // variables in vars and the values of these variables. Ownership of
  // the callback is passed to the decision builder.
  DecisionBuilder* MakePhase(const std::vector<IntVar*>& vars,
                             IndexEvaluator2* evaluator,
                             IndexEvaluator1* tie_breaker,
                             EvaluatorStrategy str);

  // Scheduling phases.

  DecisionBuilder* MakePhase(const std::vector<IntervalVar*>& intervals,
                             IntervalStrategy str);

  DecisionBuilder* MakePhase(const std::vector<SequenceVar*>& sequences,
                             SequenceStrategy str);

  // Returns a decision builder for which the left-most leaf corresponds
  // to assignment, the rest of the tree being explored using 'db'.
  DecisionBuilder* MakeDecisionBuilderFromAssignment(
      Assignment* const assignment,
      DecisionBuilder* const db,
      const std::vector<IntVar*>& vars);

  // Returns a decision builder that will add the given constraint to
  // the model.
  DecisionBuilder* MakeConstraintAdder(Constraint* const ct);

  // SolveOnce will collapse a search tree described by a decision
  // builder 'db' and a set of monitors and wrap it into a single point.
  // If there are no solutions to this nested tree, then SolveOnce will
  // fail. If there is a solution, it will find it and returns NULL.
  DecisionBuilder* MakeSolveOnce(DecisionBuilder* const db);
  DecisionBuilder* MakeSolveOnce(DecisionBuilder* const db,
                                 SearchMonitor* const monitor1);
  DecisionBuilder* MakeSolveOnce(DecisionBuilder* const db,
                                 SearchMonitor* const monitor1,
                                 SearchMonitor* const monitor2);
  DecisionBuilder* MakeSolveOnce(DecisionBuilder* const db,
                                 SearchMonitor* const monitor1,
                                 SearchMonitor* const monitor2,
                                 SearchMonitor* const monitor3);
  DecisionBuilder* MakeSolveOnce(DecisionBuilder* const db,
                                 SearchMonitor* const monitor1,
                                 SearchMonitor* const monitor2,
                                 SearchMonitor* const monitor3,
                                 SearchMonitor* const monitor4);
  DecisionBuilder* MakeSolveOnce(DecisionBuilder* const db,
                                 const std::vector<SearchMonitor*>& monitors);

  // NestedOptimize will collapse a search tree described by a
  // decision builder 'db' and a set of monitors and wrap it into a
  // single point. If there are no solutions to this nested tree, then
  // NestedOptimize will fail. If there are solutions, it will find
  // the best as described by the mandatory objective in the solution,
  // as well as the optimization direction, instantiate all variables
  // to this solution, and returns NULL.
  DecisionBuilder* MakeNestedOptimize(DecisionBuilder* const db,
                                      Assignment* const solution,
                                      bool maximize,
                                      int64 step);
  DecisionBuilder* MakeNestedOptimize(DecisionBuilder* const db,
                                      Assignment* const solution,
                                      bool maximize,
                                      int64 step,
                                      SearchMonitor* const monitor1);
  DecisionBuilder* MakeNestedOptimize(DecisionBuilder* const db,
                                      Assignment* const solution,
                                      bool maximize,
                                      int64 step,
                                      SearchMonitor* const monitor1,
                                      SearchMonitor* const monitor2);
  DecisionBuilder* MakeNestedOptimize(DecisionBuilder* const db,
                                      Assignment* const solution,
                                      bool maximize,
                                      int64 step,
                                      SearchMonitor* const monitor1,
                                      SearchMonitor* const monitor2,
                                      SearchMonitor* const monitor3);
  DecisionBuilder* MakeNestedOptimize(DecisionBuilder* const db,
                                      Assignment* const solution,
                                      bool maximize,
                                      int64 step,
                                      SearchMonitor* const monitor1,
                                      SearchMonitor* const monitor2,
                                      SearchMonitor* const monitor3,
                                      SearchMonitor* const monitor4);
  DecisionBuilder* MakeNestedOptimize(DecisionBuilder* const db,
                                      Assignment* const solution,
                                      bool maximize,
                                      int64 step,
                                      const std::vector<SearchMonitor*>& monitors);

  // Returns a DecisionBuilder which restores an Assignment
  // (calls void Assignment::Restore())
  DecisionBuilder* MakeRestoreAssignment(Assignment* assignment);

  // Returns a DecisionBuilder which stores an Assignment
  // (calls void Assignment::Store())
  DecisionBuilder* MakeStoreAssignment(Assignment* assignment);

  // ----- Local Search Operators -----

  LocalSearchOperator* MakeOperator(const std::vector<IntVar*>& vars,
                                    LocalSearchOperators op);
  LocalSearchOperator* MakeOperator(const std::vector<IntVar*>& vars,
                                    const std::vector<IntVar*>& secondary_vars,
                                    LocalSearchOperators op);
  // TODO(user): Make the callback an IndexEvaluator2 when there are no
  // secondary variables.
  LocalSearchOperator* MakeOperator(const std::vector<IntVar*>& vars,
                                    IndexEvaluator3* const evaluator,
                                    EvaluatorLocalSearchOperators op);
  LocalSearchOperator* MakeOperator(const std::vector<IntVar*>& vars,
                                    const std::vector<IntVar*>& secondary_vars,
                                    IndexEvaluator3* const evaluator,
                                    EvaluatorLocalSearchOperators op);

  // Creates a large neighborhood search operator which creates fragments (set
  // of relaxed variables) with up to number_of_variables random variables
  // (sampling with replacement is performed meaning that at most
  // number_of_variables variables are selected). Warning: this operator will
  // always return neighbors; using it without a search limit will result in a
  // non-ending search.
  // Optionally a random seed can be specified.
  LocalSearchOperator* MakeRandomLNSOperator(const std::vector<IntVar*>& vars,
                                             int number_of_variables);
  LocalSearchOperator* MakeRandomLNSOperator(const std::vector<IntVar*>& vars,
                                             int number_of_variables,
                                             int32 seed);

  // Creates a local search operator that tries to move the assignment of some
  // variables toward a target. The target is given as an Assignment. This
  // operator generates neighbors in which the only difference compared to the
  // current state is that one variable that belongs to the target assignment is
  // set to its target value.
  LocalSearchOperator* MakeMoveTowardTargetOperator(const Assignment& target);

  // Creates a local search operator that tries to move the assignment of some
  // variables toward a target. The target is given either as two vectors: a
  // vector of variables and a vector of associated target values. The two
  // vectors should be of the same length. This operator generates neighbors in
  // which the only difference compared to the current state is that one
  // variable that belongs to the given vector is set to its target value.
  LocalSearchOperator* MakeMoveTowardTargetOperator(
      const std::vector<IntVar*>& variables,
      const std::vector<int64>& target_values);

  // Creates a local search operator which concatenates a vector of operators.
  // Each operator from the vector is called sequentially. By default, when a
  // neighbor is found the neighborhood exploration restarts from the last
  // active operator (the one which produced the neighbor).
  // This can be overriden by setting restart to true to force the exploration
  // to start from the first operator in the vector.
  // The default behavior can also be overriden using an evaluation callback to
  // set the order in which the operators are explored (the callback is called
  // in LocalSearchOperator::Start()). The first argument of the callback is
  // the index of the operator which produced the last move, the second
  // argument is the index of the operator to be evaluated.
  // Ownership of the callback is taken by ConcatenateOperators.
  //
  // Example:
  //
  //  const int kPriorities = {10, 100, 10, 0};
  //  int64 Evaluate(int active_operator, int current_operator) {
  //    return kPriorities[current_operator];
  //  }
  //
  //  LocalSearchOperator* concat =
  //    solver.ConcatenateOperators(operators,
  //                                NewPermanentCallback(&Evaluate));
  //
  // The elements of the vector operators will be sorted by increasing priority
  // and explored in that order (tie-breaks are handled by keeping the relative
  // operator order in the vector). This would result in the following order:
  // operators[3], operators[0], operators[2], operators[1].
  //
  LocalSearchOperator* ConcatenateOperators(
      const std::vector<LocalSearchOperator*>& ops);
  LocalSearchOperator* ConcatenateOperators(
      const std::vector<LocalSearchOperator*>& ops, bool restart);
  LocalSearchOperator* ConcatenateOperators(
      const std::vector<LocalSearchOperator*>& ops,
      ResultCallback2<int64, int, int>* const evaluator);
  // Randomized version of local search concatenator; calls a random operator at
  // each call to MakeNextNeighbor().
  LocalSearchOperator* RandomConcatenateOperators(
      const std::vector<LocalSearchOperator*>& ops);

  // Randomized version of local search concatenator; calls a random operator at
  // each call to MakeNextNeighbor(). The provided seed is used to init
  // the random number generator.
  LocalSearchOperator* RandomConcatenateOperators(
      const std::vector<LocalSearchOperator*>& ops, int32 seed);

  // Creates a local search operator that wraps another local search
  // operator and limits the number of neighbors explored (i.e. calls
  // to MakeNextNeighbor from the current solution (between two calls
  // to Start()). When this limit is reached, MakeNextNeighbor()
  // returns false. The counter is cleared when Start() is called.
  LocalSearchOperator* MakeNeighborhoodLimit(LocalSearchOperator* const op,
                                             int64 limit);

  // Local Search decision builders factories.
  // Local search is used to improve a given solution. This initial solution
  // can be specified either by an Assignment or by a DecisionBulder, and the
  // corresponding variables, the initial solution being the first solution
  // found by the DecisionBuilder.
  // The LocalSearchPhaseParameters parameter holds the actual definition of
  // the local search phase:
  // - a local search operator used to explore the neighborhood of the current
  //   solution,
  // - a decision builder to instantiate unbound variables once a neighbor has
  //   been defined; in the case of LNS-based operators instantiates fragment
  //   variables; search monitors can be added to this sub-search by wrapping
  //   the decision builder with MakeSolveOnce.
  // - a search limit specifying how long local search looks for neighbors
  //   before accepting one; the last neighbor is always taken and in the case
  //   of a greedy search, this corresponds to the best local neighbor;
  //   first-accept (which is the default behavior) can be modeled using a
  //    solution found limit of 1,
  // - a vector of local search filters used to speed up the search by pruning
  //   unfeasible neighbors.
  // Metaheuristics can be added by defining specialized search monitors;
  // currently down/up-hill climbing is available through OptimizeVar, as well
  // as Guided Local Search, Tabu Search and Simulated Annealing.
  //
  // TODO(user): Make a variant which runs a local search after each
  //                solution found in a dfs

  DecisionBuilder* MakeLocalSearchPhase(
      Assignment* const assignment,
      LocalSearchPhaseParameters* const parameters);
  DecisionBuilder* MakeLocalSearchPhase(
      const std::vector<IntVar*>& vars,
      DecisionBuilder* const first_solution,
      LocalSearchPhaseParameters* const parameters);

  // Solution Pool.
  SolutionPool* MakeDefaultSolutionPool();

  // Local Search Phase Parameters
  LocalSearchPhaseParameters* MakeLocalSearchPhaseParameters(
      LocalSearchOperator* const ls_operator,
      DecisionBuilder* const sub_decision_builder);
  LocalSearchPhaseParameters* MakeLocalSearchPhaseParameters(
      LocalSearchOperator* const ls_operator,
      DecisionBuilder* const sub_decision_builder,
      SearchLimit* const limit);
  LocalSearchPhaseParameters* MakeLocalSearchPhaseParameters(
      LocalSearchOperator* const ls_operator,
      DecisionBuilder* const sub_decision_builder,
      SearchLimit* const limit,
      const std::vector<LocalSearchFilter*>& filters);

  LocalSearchPhaseParameters* MakeLocalSearchPhaseParameters(
      SolutionPool* const pool,
      LocalSearchOperator* const ls_operator,
      DecisionBuilder* const sub_decision_builder);
  LocalSearchPhaseParameters* MakeLocalSearchPhaseParameters(
      SolutionPool* const pool,
      LocalSearchOperator* const ls_operator,
      DecisionBuilder* const sub_decision_builder,
      SearchLimit* const limit);
  LocalSearchPhaseParameters* MakeLocalSearchPhaseParameters(
      SolutionPool* const pool,
      LocalSearchOperator* const ls_operator,
      DecisionBuilder* const sub_decision_builder,
      SearchLimit* const limit,
      const std::vector<LocalSearchFilter*>& filters);

  // Local Search Filters
  LocalSearchFilter* MakeVariableDomainFilter();
  LocalSearchFilter* MakeLocalSearchObjectiveFilter(
      const std::vector<IntVar*>& vars,
      IndexEvaluator2* const values,
      const IntVar* const objective,
      Solver::LocalSearchFilterBound filter_enum,
      Solver::LocalSearchOperation op_enum);
  LocalSearchFilter* MakeLocalSearchObjectiveFilter(
      const std::vector<IntVar*>& vars,
      IndexEvaluator2* const values,
      Callback1<int64>* delta_objective_callback,
      const IntVar* const objective,
      Solver::LocalSearchFilterBound filter_enum,
      Solver::LocalSearchOperation op_enum);
  LocalSearchFilter* MakeLocalSearchObjectiveFilter(
      const std::vector<IntVar*>& vars,
      const std::vector<IntVar*>& secondary_vars,
      Solver::IndexEvaluator3* const values,
      const IntVar* const objective,
      Solver::LocalSearchFilterBound filter_enum,
      Solver::LocalSearchOperation op_enum);
  LocalSearchFilter* MakeLocalSearchObjectiveFilter(
      const std::vector<IntVar*>& vars,
      const std::vector<IntVar*>& secondary_vars,
      Solver::IndexEvaluator3* const values,
      Callback1<int64>* delta_objective_callback,
      const IntVar* const objective,
      Solver::LocalSearchFilterBound filter_enum,
      Solver::LocalSearchOperation op_enum);

  // Performs PeriodicCheck on the top-level search; can be called from a nested
  // solve to check top-level limits for instance.
  void TopPeriodicCheck();
  // Returns a percentage representing the propress of the search before
  // reaching the limits of the top-level search (can be called from a nested
  // solve).
  int TopProgressPercent();

  // The PushState and PopState methods manipulates the states
  // of the reversible objects. They are visible only because they
  // are useful to write unitary tests.
  void PushState();
  void PopState();

  // Gets the search depth of the current active search. Returns -1 in
  // case there are no active search opened.
  int SearchDepth() const;

  // Gets the search left depth of the current active search. Returns -1 in
  // case there are no active search opened.
  int SearchLeftDepth() const;

  // Gets the number of nested searches. It returns 0 outside search,
  // 1 during the top level search, 2 or more in case of nested searches.
  int SolveDepth() const;

  // Sets the given branch selector on the current active search.
  void SetBranchSelector(
      ResultCallback1<Solver::DecisionModification, Solver*>* const bs);

  // Creates a decision builder that will set the branch selector.
  DecisionBuilder* MakeApplyBranchSelector(
      ResultCallback1<Solver::DecisionModification, Solver*>* const bs);

  // All-in-one SaveAndSetValue.
  template <class T> void SaveAndSetValue(T* adr, T val) {
    if (*adr != val) {
      InternalSaveValue(adr);
      *adr = val;
    }
  }

  // All-in-one SaveAndAdd_value.
  template <class T> void SaveAndAdd(T* adr, T val) {
    if (val != 0) {
      InternalSaveValue(adr);
      (*adr) += val;
    }
  }

  // Returns a random value between 0 and 'size' - 1;
  int64 Rand64(int64 size) {
    return random_.Next64() % size;
  }

  // Returns a random value between 0 and 'size' - 1;
  int32 Rand32(int32 size) {
    return random_.Next() % size;
  }

  // Reseed the solver random generator.
  void ReSeed(int32 seed) {
    random_.Reset(seed);
  }

  // Adds a fail hook, that is an action that will be called after each failure.
  void AddFailHook(Action* a);

  // Exports the profiling information in a human readable overview.
  // The parameter profile_level used to create the solver must be
  // different from NO_PROFILING.
  void ExportProfilingOverview(const string& filename);

  // Returns true whether the current search has been
  // created using a Solve() call instead of a NewSearch 0ne. It
  // returns false if the solver is not is search at all.
  bool CurrentlyInSolve() const;

  // Counts the number of constraints that have been added
  // to the solver before the search,
  int constraints() const { return constraints_list_.size(); }

  // Accepts the given model visitor.
  void Accept(ModelVisitor* const visitor) const;
  // Accepts the given model visitor.
  void Accept(ModelVisitor* const visitor,
              const std::vector<SearchMonitor*>& monitors) const;
  void Accept(ModelVisitor* const visitor,
              const std::vector<SearchMonitor*>& monitors,
              DecisionBuilder* const db) const;


  Decision* balancing_decision() const { return balancing_decision_.get(); }

  // Internal
  // set_fail_intercept does not take ownership of the closure.
  void set_fail_intercept(Closure* const c) { fail_intercept_ = c; }
  void clear_fail_intercept() { fail_intercept_ = NULL; }
  // Access to demon profiler.
  DemonProfiler* demon_profiler() const { return demon_profiler_; }
  // Returns whether the object has been named or not.
  bool HasName(const PropagationBaseObject* object) const;
  // Adds a new demon and wraps it inside a DemonProfiler if necessary.
  Demon* RegisterDemon(Demon* const d);
  // Registers a new IntExpr and wraps it inside a TraceIntExpr if necessary.
  IntExpr* RegisterIntExpr(IntExpr* const expr);
  // Registers a new IntVar and wraps it inside a TraceIntVar if necessary.
  IntVar* RegisterIntVar(IntVar* const var);
  // Registers a new IntervalVar and wraps it inside a TraceIntervalVar
  // if necessary.
  IntervalVar* RegisterIntervalVar(IntervalVar* const var);

  // Returns the active search, NULL outside search.
  Search* ActiveSearch() const;
  // Returns the cache of the model.
  ModelCache* Cache() const;
  // Returns whether we are instrumenting demons.
  bool InstrumentsDemons() const;
  // Returns whether we are profiling the solver.
  bool IsProfilingEnabled() const;
  // Returns whether we are tracing variables.
  bool InstrumentsVariables() const;
  // Returns whether all variables should be named.
  bool NameAllVariables() const;
  // Returns the name of the model.
  string model_name() const;
  // Returns the dependency graph of the solver.
  DependencyGraph* Graph() const;
  // Returns the propagation monitor.
  PropagationMonitor* GetPropagationMonitor() const;
  // Adds the propagation monitor to the solver. This is called internally when
  // a propagation monitor is passed to the Solve() or NewSearch() method.
  void AddPropagationMonitor(PropagationMonitor* const monitor);

  friend class BaseIntExpr;
  friend class Constraint;
  friend class DemonProfiler;
  friend class FindOneNeighbor;
  friend class IntVar;
  friend class PropagationBaseObject;
  friend class Queue;
  friend class SearchMonitor;
  friend class SearchLimit;

#ifndef SWIG
  friend void InternalSaveBooleanVarValue(Solver* const, IntVar* const);
  friend void SetQueueCleanerOnFail(Solver* const, IntVar* const);
  template<class> friend class SimpleRevFIFO;
  template<class K, class V> friend class RevImmutableMultiMap;
#endif
  // Returns true if expr represents either boolean_var or 1 -
  // boolean_var.  In that case, it fills sub_var and is_negated to be
  // true if the expression is 1 - boolean_var -- equivalent to
  // not(boolean_var).
  bool IsBooleanVar(IntExpr* const expr,
                    IntVar** sub_var,
                    bool* is_negated) const;

  // Internal. If the variables is the result of expr->Var(), this
  // method returns expr, NULL otherwise.
  IntExpr* CastExpression(IntVar* const var) const;

 private:
  void Init();  // Initialization. To be called by the constructors only.
  void PushState(MarkerType t, const StateInfo& info);
  MarkerType PopState(StateInfo* info);
  void PushSentinel(int magic_code);
  void BacktrackToSentinel(int magic_code);
  void CallFailHooks();
  void ProcessConstraints();
  bool BacktrackOneLevel(Decision** fd);
  void JumpToSentinelWhenNested();
  void JumpToSentinel();
  void check_alloc_state();
  void FreezeQueue();
  void EnqueueVar(Demon* const d);
  void EnqueueDelayedDemon(Demon* const d);
  void Execute(Demon* const d);
  void ExecuteAll(const SimpleRevFIFO<Demon*>& demons);
  void EnqueueAll(const SimpleRevFIFO<Demon*>& demons);
  void UnfreezeQueue();
  void set_queue_action_on_fail(Action* a);
  void set_queue_cleaner_on_fail(IntVar* const var);
  void clear_queue_action_on_fail();

  void InternalSaveValue(int* valptr);
  void InternalSaveValue(int64* valptr);
  void InternalSaveValue(uint64* valptr);
  void InternalSaveValue(double* valptr);
  void InternalSaveValue(bool* valptr);
  void InternalSaveValue(void** valptr);
  void InternalSaveValue(int64** valptr) {
    InternalSaveValue(reinterpret_cast<void**>(valptr));
  }

  BaseObject* SafeRevAlloc(BaseObject* ptr);

  int* SafeRevAllocArray(int* ptr);
  int64* SafeRevAllocArray(int64* ptr);
  uint64* SafeRevAllocArray(uint64* ptr);
  double* SafeRevAllocArray(double* ptr);
  BaseObject** SafeRevAllocArray(BaseObject** ptr);
  IntVar** SafeRevAllocArray(IntVar** ptr);
  IntExpr** SafeRevAllocArray(IntExpr** ptr);
  Constraint** SafeRevAllocArray(Constraint** ptr);
  // UnsafeRevAlloc is used internally for cells in SimpleRevFIFO
  // and other structures like this.
  void* UnsafeRevAllocAux(void* ptr);
  template <class T> T* UnsafeRevAlloc(T* ptr) {
    return reinterpret_cast<T*>(
        UnsafeRevAllocAux(reinterpret_cast<void*>(ptr)));
  }
  void** UnsafeRevAllocArrayAux(void** ptr);
  template <class T> T** UnsafeRevAllocArray(T** ptr) {
    return reinterpret_cast<T**>(
        UnsafeRevAllocArrayAux(reinterpret_cast<void**>(ptr)));
  }

  void InitCachedIntConstants();
  void InitCachedConstraint();
  void InitBuilders();
  void DeleteBuilders();

  // Returns the Search object that is at the bottom of the search stack. This
  // is to be contrasted with ActiveSearch(), which returns the search at the
  // top of the stack.
  Search* TopLevelSearch() const {
    return searches_.at(1);
  }
  // Returns the Search object which is the parent of the active search, i.e.
  // the search below the top of the stack. If the active search is at the
  // bottom of the stack, returns the active search.
  Search* ParentSearch() const {
    const size_t search_size = searches_.size();
    DCHECK_GT(search_size, 1);
    return searches_[search_size - 2];
  }

  // Naming
  string GetName(const PropagationBaseObject* object);
  void SetName(const PropagationBaseObject* object, const string& name);

  // Internal.
  bool IsADifference(IntExpr* expr,
                     IntExpr** const left,
                     IntExpr** const right);

  const string name_;
  const SolverParameters parameters_;
  hash_map<const PropagationBaseObject*, string> propagation_object_names_;
  hash_map<const PropagationBaseObject*, IntegerCastInfo> cast_information_;
  hash_set<const Constraint*> cast_constraints_;
  const string empty_name_;
  scoped_ptr<Queue> queue_;
  scoped_ptr<Trail> trail_;
  std::vector<Constraint*> constraints_list_;
  std::vector<Constraint*> additional_constraints_list_;
  std::vector<int> additional_constraints_parent_list_;
  SolverState state_;
  int64 branches_;
  int64 fails_;
  int64 decisions_;
  int64 demon_runs_[kNumPriorities];
  int64 neighbors_;
  int64 filtered_neighbors_;
  int64 accepted_neighbors_;
  scoped_ptr<Action> variable_cleaner_;
  scoped_ptr<ClockTimer> timer_;
  std::vector<Search*> searches_;
  ACMRandom random_;
  SimpleRevFIFO<Action*>* fail_hooks_;
  uint64 fail_stamp_;
  scoped_ptr<Decision> balancing_decision_;
  // intercept failures
  Closure* fail_intercept_;
  // Demon monitor
  DemonProfiler* const demon_profiler_;

  // interval of constants cached, inclusive:
  enum { MIN_CACHED_INT_CONST = -8, MAX_CACHED_INT_CONST = 8 };
  IntVar* cached_constants_[MAX_CACHED_INT_CONST + 1 - MIN_CACHED_INT_CONST];

  // Cached constraints.
  Constraint* true_constraint_;
  Constraint* false_constraint_;

  scoped_ptr<Decision> fail_decision_;
  int constraint_index_;
  int additional_constraint_index_;

  // Support for model loading.
  hash_map<string, IntegerExpressionBuilder*> expression_builders_;
  hash_map<string, ConstraintBuilder*> constraint_builders_;
  hash_map<string, IntervalVariableBuilder*> interval_builders_;
  hash_map<string, SequenceVariableBuilder*> sequence_builders_;

  scoped_ptr<ModelCache> model_cache_;
  scoped_ptr<DependencyGraph> dependency_graph_;
  scoped_ptr<PropagationMonitor> propagation_monitor_;
  PropagationMonitor* print_trace_;
  int anonymous_variable_index_;

  DISALLOW_COPY_AND_ASSIGN(Solver);
};

std::ostream& operator << (std::ostream& out, const Solver* const s);  // NOLINT

// ---------- Misc ----------

// This method returns 0. It is useful when 0 can be cast either as
// a pointer or as an integer value and thus lead to an ambiguous
// function call.
inline int64 Zero() {
  return 0LL;
}

/////////////////////////////////////////////////////////////////////
//
// Useful Search and Modeling Objects
//
/////////////////////////////////////////////////////////////////////

// A BaseObject is the root of all reversibly allocated objects.
// A DebugString method and the associated << operator are implemented
// as a convenience.

class BaseObject {
 public:
  BaseObject() {}
  virtual ~BaseObject() {}
  virtual string DebugString() const { return "BaseObject"; }

 private:
  DISALLOW_COPY_AND_ASSIGN(BaseObject);
};

std::ostream& operator <<(std::ostream& out, const BaseObject* o);  // NOLINT

// The PropagationBaseObject is a subclass of BaseObject that is also
// friend to the Solver class. It allows accessing methods useful when
// writing new constraints or new expressions.
class PropagationBaseObject : public BaseObject {
 public:
  explicit PropagationBaseObject(Solver* const s) : solver_(s) {}
  virtual ~PropagationBaseObject() {}

  virtual string DebugString() const {
    if (name().empty()) {
      return "PropagationBaseObject";
    } else {
      return StringPrintf("PropagationBaseObject: %s", name().c_str());
    }
  }
  Solver* solver() const { return solver_; }
  // This method freezes the propagation queue. It is useful when you
  // need to apply multiple modifications at once.
  void FreezeQueue() { solver_->FreezeQueue(); }

  // This method unfreezes the propagation queue. All modifications
  // that happened when the queue was frozen will be processed.
  void UnfreezeQueue() { solver_->UnfreezeQueue(); }

  // This method pushes the demon onto the propagation queue. It will
  // be processed directly if the queue is empty. It will be enqueued
  // according to its priority otherwise.
  void EnqueueDelayedDemon(Demon* const d) { solver_->EnqueueDelayedDemon(d); }
  void EnqueueVar(Demon* const d) { solver_->EnqueueVar(d); }
  void Execute(Demon* const d) { solver_->Execute(d); }
  void ExecuteAll(const SimpleRevFIFO<Demon*>& demons);
  void EnqueueAll(const SimpleRevFIFO<Demon*>& demons);

  // This method sets a callback that will be called if a failure
  // happens during the propagation of the queue.
  void set_queue_action_on_fail(Action* a) {
    solver_->set_queue_action_on_fail(a);
  }

  // This methods clears the failure callback.
  void clear_queue_action_on_fail() {
    solver_->clear_queue_action_on_fail();
  }

  // Naming
  virtual string name() const;
  void set_name(const string& name);
  // Returns whether the object has been named or not.
  bool HasName() const;
  // Returns a base name for automatic naming.
  virtual string BaseName() const;


 private:
  Solver* const solver_;
  DISALLOW_COPY_AND_ASSIGN(PropagationBaseObject);
};

// A Decision represents a choice point in the search tree. The two main
// methods are Apply() to go left, or Refute() to go right.
class Decision : public BaseObject {
 public:
  Decision() {}
  virtual ~Decision() {}

  // Apply will be called first when the decision is executed.
  virtual void Apply(Solver* const s) = 0;

  // Refute will be called after a backtrack.
  virtual void Refute(Solver* const s) = 0;

  virtual string DebugString() const {
    return "Decision";
  }
  // Accepts the given visitor.
  virtual void Accept(DecisionVisitor* const visitor) const;

 private:
  DISALLOW_COPY_AND_ASSIGN(Decision);
};

// A DecisionVisitor is used to inspect a decision.
// It contains virtual methods for all type of 'declared' decisions.
class DecisionVisitor : public BaseObject {
 public:
  DecisionVisitor() {}
  virtual ~DecisionVisitor() {}
  virtual void VisitSetVariableValue(IntVar* const var, int64 value);
  virtual void VisitSplitVariableDomain(IntVar* const var,
                                        int64 value,
                                        bool start_with_lower_half);
  virtual void VisitScheduleOrPostpone(IntervalVar* const var, int64 est);
  virtual void VisitRankFirstInterval(SequenceVar* const sequence, int index);
  virtual void VisitRankLastInterval(SequenceVar* const sequence, int index);
  virtual void VisitUnknownDecision();

 private:
  DISALLOW_COPY_AND_ASSIGN(DecisionVisitor);
};

// A DecisionBuilder is responsible for creating the search tree. The
// important method is Next() that returns the next decision to execute.
class DecisionBuilder : public BaseObject {
 public:
  DecisionBuilder() {}
  virtual ~DecisionBuilder() {}
  // This is the main method of the decision builder class. It must
  // return a decision (an instance of the class Decision). If it
  // returns NULL, this means that the decision builder has finished
  // its work.
  virtual Decision* Next(Solver* const s) = 0;
  virtual string DebugString() const;
#if !defined(SWIG)
  // This method will be called at the start of the search.  It asks
  // the decision builder if it wants to append search monitors to the
  // list of active monitors for this search. Please note there are no
  // checks at this point for duplication.
  virtual void AppendMonitors(Solver* const solver,
                              std::vector<SearchMonitor*>* const extras);
  virtual void Accept(ModelVisitor* const visitor) const;
#endif

 private:
  DISALLOW_COPY_AND_ASSIGN(DecisionBuilder);
};

// A Demon is the base element of a propagation queue. It is the main
//   object responsible for implementing the actual propagation
//   of the constraint and pruning the inconsistent values in the domains
//   of the variables. The main concept is that demons are listeners that are
//   attached to the variables and listen to their modifications.
// There are two methods:
//  - Run() is the actual methods that is called when the demon is processed
//  - priority() returns its priority. Standart priorities are slow, normal
//    or fast. immediate is reserved for variables and are treated separately.
class Demon : public BaseObject {
 public:
  // This indicates the priority of a demon. Immediate demons are treated
  // separately and corresponds to variables.
  Demon() : stamp_(GG_ULONGLONG(0)) {}
  virtual ~Demon() {}

  // This is the main callback of the demon.
  virtual void Run(Solver* const s) = 0;

  // This method returns the priority of the demon. Usually a demon is
  // fast, slow or normal. Immediate demons are reserved for internal
  // use to maintain variables.
  virtual Solver::DemonPriority priority() const;

  virtual string DebugString() const;

  // This method inhibits the demon in the search tree below the
  // current position.
  void inhibit(Solver* const s);

  // This method un-inhibit the demon that was inhibited.
  void desinhibit(Solver* const s);

 private:
  friend class Queue;
  void set_stamp(int64 stamp) { stamp_ = stamp; }
  uint64 stamp() const { return stamp_; }
  uint64 stamp_;
  DISALLOW_COPY_AND_ASSIGN(Demon);
};

// An action is the base callback method. It is separated from the standard
// google callback class because of its specific memory management.
class Action : public BaseObject {
 public:
  Action() {}
  virtual ~Action() {}

  // The main callback of the class.
  virtual void Run(Solver* const s) = 0;
  virtual string DebugString() const;

 private:
  DISALLOW_COPY_AND_ASSIGN(Action);
};

// Model visitor.
class ModelVisitor : public BaseObject {
 public:
  // Constraint and Expression types.
  static const char kAbs[];
  static const char kAbsEqual[];
  static const char kAllDifferent[];
  static const char kAllowedAssignments[];
  static const char kIndexOf[];
  static const char kBetween[];
  static const char kCircuit[];
  static const char kConvexPiecewise[];
  static const char kCountEqual[];
  static const char kCover[];
  static const char kCumulative[];
  static const char kDeviation[];
  static const char kDifference[];
  static const char kDisjunctive[];
  static const char kDistribute[];
  static const char kDivide[];
  static const char kDurationExpr[];
  static const char kElement[];
  static const char kElementEqual[];
  static const char kEndExpr[];
  static const char kEquality[];
  static const char kFalseConstraint[];
  static const char kGlobalCardinality[];
  static const char kGreater[];
  static const char kGreaterOrEqual[];
  static const char kIntegerVariable[];
  static const char kIntervalBinaryRelation[];
  static const char kIntervalDisjunction[];
  static const char kIntervalUnaryRelation[];
  static const char kIntervalVariable[];
  static const char kIsBetween[];
  static const char kIsDifferent[];
  static const char kIsEqual[];
  static const char kIsGreater[];
  static const char kIsGreaterOrEqual[];
  static const char kIsLess[];
  static const char kIsLessOrEqual[];
  static const char kIsMember[];
  static const char kLess[];
  static const char kLessOrEqual[];
  static const char kLinkExprVar[];
  static const char kMapDomain[];
  static const char kMax[];
  static const char kMaxEqual[];
  static const char kMember[];
  static const char kMin[];
  static const char kMinEqual[];
  static const char kModulo[];
  static const char kNoCycle[];
  static const char kNonEqual[];
  static const char kNullIntersect[];
  static const char kOpposite[];
  static const char kPack[];
  static const char kPathCumul[];
  static const char kPerformedExpr[];
  static const char kPower[];
  static const char kProduct[];
  static const char kScalProd[];
  static const char kScalProdEqual[];
  static const char kScalProdGreaterOrEqual[];
  static const char kScalProdLessOrEqual[];
  static const char kSemiContinuous[];
  static const char kSequenceVariable[];
  static const char kSortingConstraint[];
  static const char kSquare[];
  static const char kStartExpr[];
  static const char kSum[];
  static const char kSumEqual[];
  static const char kSumGreaterOrEqual[];
  static const char kSumLessOrEqual[];
  static const char kTrace[];
  static const char kTransition[];
  static const char kTrueConstraint[];
  static const char kVarBoundWatcher[];
  static const char kVarValueWatcher[];

  // Extension names:
  static const char kCountAssignedItemsExtension[];
  static const char kCountUsedBinsExtension[];
  static const char kInt64ToBoolExtension[];
  static const char kInt64ToInt64Extension[];
  static const char kObjectiveExtension[];
  static const char kSearchLimitExtension[];
  static const char kUsageEqualVariableExtension[];

  static const char kUsageLessConstantExtension[];
  static const char kVariableGroupExtension[];
  static const char kVariableUsageLessConstantExtension[];
  static const char kWeightedSumOfAssignedEqualVariableExtension[];

  // argument names:
  static const char kActiveArgument[];
  static const char kAssumePathsArgument[];
  static const char kBranchesLimitArgument[];
  static const char kCapacityArgument[];
  static const char kCardsArgument[];
  static const char kCoefficientsArgument[];
  static const char kCountArgument[];
  static const char kCumulativeArgument[];
  static const char kCumulsArgument[];
  static const char kDemandsArgument[];
  static const char kDurationMaxArgument[];
  static const char kDurationMinArgument[];
  static const char kEarlyCostArgument[];
  static const char kEarlyDateArgument[];
  static const char kEndMaxArgument[];
  static const char kEndMinArgument[];
  static const char kExpressionArgument[];
  static const char kFailuresLimitArgument[];
  static const char kFinalStatesArgument[];
  static const char kFixedChargeArgument[];
  static const char kIndex2Argument[];
  static const char kIndexArgument[];
  static const char kInitialState[];
  static const char kIntervalArgument[];
  static const char kIntervalsArgument[];
  static const char kLateCostArgument[];
  static const char kLateDateArgument[];
  static const char kLeftArgument[];
  static const char kMaxArgument[];
  static const char kMaximizeArgument[];
  static const char kMinArgument[];
  static const char kModuloArgument[];
  static const char kNextsArgument[];
  static const char kOptionalArgument[];
  static const char kPositionXArgument[];
  static const char kPositionYArgument[];
  static const char kRangeArgument[];
  static const char kRelationArgument[];
  static const char kRightArgument[];
  static const char kSequenceArgument[];
  static const char kSequencesArgument[];
  static const char kSizeArgument[];
  static const char kSizeXArgument[];
  static const char kSizeYArgument[];
  static const char kSmartTimeCheckArgument[];
  static const char kSolutionLimitArgument[];
  static const char kStartMaxArgument[];
  static const char kStartMinArgument[];
  static const char kStepArgument[];
  static const char kTargetArgument[];
  static const char kTimeLimitArgument[];
  static const char kTransitsArgument[];
  static const char kTuplesArgument[];
  static const char kValueArgument[];
  static const char kValuesArgument[];
  static const char kVariableArgument[];
  static const char kVarsArgument[];

  // Operations.
  static const char kMirrorOperation[];
  static const char kRelaxedMaxOperation[];
  static const char kRelaxedMinOperation[];
  static const char kSumOperation[];
  static const char kDifferenceOperation[];
  static const char kProductOperation[];
  static const char kStartSyncOnStartOperation[];
  static const char kStartSyncOnEndOperation[];
  static const char kTraceOperation[];

  virtual ~ModelVisitor();

  // ----- Virtual methods for visitors -----

  // Begin/End visit element.
  virtual void BeginVisitModel(const string& solver_name);
  virtual void EndVisitModel(const string& solver_name);
  virtual void BeginVisitConstraint(const string& type_name,
                                    const Constraint* const constraint);
  virtual void EndVisitConstraint(const string& type_name,
                                  const Constraint* const constraint);
  virtual void BeginVisitExtension(const string& type);
  virtual void EndVisitExtension(const string& type);
  virtual void BeginVisitIntegerExpression(const string& type_name,
                                           const IntExpr* const expr);
  virtual void EndVisitIntegerExpression(const string& type_name,
                                         const IntExpr* const expr);
  virtual void VisitIntegerVariable(const IntVar* const variable,
                                    const IntExpr* const delegate);
  virtual void VisitIntegerVariable(const IntVar* const variable,
                                    const string& operation,
                                    int64 value,
                                    const IntVar* const delegate);
  virtual void VisitIntervalVariable(const IntervalVar* const variable,
                                     const string& operation,
                                     int64 value,
                                     const IntervalVar* const delegate);
  virtual void VisitIntervalVariable(const IntervalVar* const variable,
                                     const string& operation,
                                     const IntervalVar* const * delegate,
                                     int size);
  virtual void VisitSequenceVariable(const SequenceVar* const sequence);


  // Visit integer arguments.
  virtual void VisitIntegerArgument(const string& arg_name, int64 value);

  virtual void VisitIntegerArrayArgument(const string& arg_name,
                                         const int64* const values,
                                         int size);
  virtual void VisitIntegerMatrixArgument(const string& arg_name,
                                          const IntTupleSet& tuples);

  // Visit integer expression argument.
  virtual void VisitIntegerExpressionArgument(
      const string& arg_name,
      const IntExpr* const argument);

  virtual void VisitIntegerVariableArrayArgument(
      const string& arg_name,
      const IntVar* const * arguments,
      int size);

  // Visit interval argument.
  virtual void VisitIntervalArgument(const string& arg_name,
                                     const IntervalVar* const argument);

  virtual void VisitIntervalArrayArgument(const string& arg_name,
                                          const IntervalVar* const * argument,
                                          int size);
  // Visit sequence argument.
  virtual void VisitSequenceArgument(const string& arg_name,
                                     const SequenceVar* const argument);

  virtual void VisitSequenceArrayArgument(const string& arg_name,
                                          const SequenceVar* const * argument,
                                          int size);
  // Helpers.
#if !defined(SWIG)
  // Using SWIG on calbacks is troublesome, let's hide these methods during
  // the wrapping.
  virtual void VisitIntegerVectorArgument(const string& arg_name,
                                          const std::vector<int64>& values);
  void VisitConstIntArrayArgument(const string& arg_name,
                                  const ConstIntArray& argument);
  void VisitInt64ToBoolExtension(ResultCallback1<bool, int64>* const callback,
                                 int64 index_min,
                                 int64 index_max);
  void VisitInt64ToInt64Extension(ResultCallback1<int64, int64>* const callback,
                                  int64 index_min,
                                  int64 index_max);
  // Expands function as array when index min is 0.
  void VisitInt64ToInt64AsArray(ResultCallback1<int64, int64>* const callback,
                                const string& arg_name,
                                int64 index_max);
  void VisitIntegerVariableArrayArgument(const string& arg_name,
                                         const std::vector<IntVar*>& arguments);
#endif  // #if !defined(SWIG)
};

// A constraint is the main modeling object. It proposes two methods:
//   - Post() is responsible for creating the demons and attaching them to
//     immediate demons()
//   - InitialPropagate() is called once just after the Post and performs
//     the initial propagation. The subsequent propagations will be performed
//     by the demons Posted during the post() method.
class Constraint : public PropagationBaseObject {
 public:
  explicit Constraint(Solver* const solver) : PropagationBaseObject(solver) {}
  virtual ~Constraint() {}

  // This method is called when the constraint is processed by the
  // solver. Its main usage is to attach demons to variables.
  virtual void Post() = 0;

  // This method performs the initial propagation of the
  // constraint. It is called just after the post.
  virtual void InitialPropagate() = 0;
  virtual string DebugString() const;

  // Calls Post and then Propagate to initialize the constraints. This
  // is usually done in the root node.
  void PostAndPropagate();

  // Accepts the given visitor.
  virtual void Accept(ModelVisitor* const visitor) const;

  // Is the constraint created by a cast from expression to integer variable?
  bool IsCastConstraint() const;

  // Creates an boolean variable representing the status of the
  // variable (false = constraint is violated, true constraint is
  // satisfied). It returns NULL if the constraint does not support his API.
  virtual IntVar* Var();

 private:
  DISALLOW_COPY_AND_ASSIGN(Constraint);
};

// Cast constraints are special channeling constraints the goal of
// which is to keep a variable in sync with an expression.  They are
// created internally when Var() is called on a subclass of IntExpr.
class CastConstraint : public Constraint {
 public:
  CastConstraint(Solver* const solver, IntVar* const target_var)
      : Constraint(solver), target_var_(target_var) {
    CHECK_NOTNULL(target_var);
  }
  virtual ~CastConstraint() {}

  IntVar* target_var() const { return target_var_; }

 protected:
  IntVar* const target_var_;
};

// A search monitor is a simple set of callbacks to monitor all search events
class SearchMonitor : public BaseObject {
 public:
  static const int kNoProgress = -1;

  explicit SearchMonitor(Solver* const s) : solver_(s) {}
  virtual ~SearchMonitor() {}
  // Beginning of the search.
  virtual void EnterSearch();

  // Restart the search.
  virtual void RestartSearch();

  // End of the search.
  virtual void ExitSearch();

  // Before calling DecisionBuilder::Next
  virtual void BeginNextDecision(DecisionBuilder* const b);

  // After calling DecisionBuilder::Next, along with the returned decision.
  virtual void EndNextDecision(DecisionBuilder* const b, Decision* const d);

  // Before applying the decision
  virtual void ApplyDecision(Decision* const d);

  // Before refuting the Decision
  virtual void RefuteDecision(Decision* const d);

  // Just after refuting or applying the decision, apply is true after Apply.
  // This is called only if the Apply() or Refute() methods have not failed.
  virtual void AfterDecision(Decision* const d, bool apply);

  // Just when the failure occurs.
  virtual void BeginFail();

  // After completing the backtrack.
  virtual void EndFail();

  // Before the initial propagation.
  virtual void BeginInitialPropagation();

  // After the initial propagation.
  virtual void EndInitialPropagation();

  // This method is called when a solution is found. It asserts of the
  // solution is valid. A value of false indicate that the solution
  // should be discarded.
  virtual bool AcceptSolution();

  // This method is called when a valid solution is found. If the
  // return value is true, then search will resume after. If the result
  // is false, then search will stop there.
  virtual bool AtSolution();

  // When the search tree is finished.
  virtual void NoMoreSolutions();

  // When a local optimum is reached. If 'true' is returned, the last solution
  // is discarded and the search proceeds with the next one.
  virtual bool LocalOptimum();

  //
  virtual bool AcceptDelta(Assignment* delta, Assignment* deltadelta);

  // After accepting a neighbor during local search.
  virtual void AcceptNeighbor();

  Solver* solver() const { return solver_; }

  // Tells the solver to kill the current search.
  void FinishCurrentSearch();

  // Tells the solver to restart the current search.
  void RestartCurrentSearch();

  // Periodic call to check limits in long running methods.
  virtual void PeriodicCheck();

  // Returns a percentage representing the propress of the search before
  // reaching limits.
  virtual int ProgressPercent() { return kNoProgress; }

  // Accepts the given model visitor.
  virtual void Accept(ModelVisitor* const visitor) const;

  // Registers itself on the solver such that it gets notified of the search
  // and propagation events.
  virtual void Install();

 private:
  Solver* const solver_;
  DISALLOW_COPY_AND_ASSIGN(SearchMonitor);
};

// This class adds reversibility to a POD type.
// It contains the stamp optimization. i.e. the SaveValue call is done
// only once per node of the search tree.  Please note that actual
// stamps always starts at 1, thus an initial value of 0 will always
// trigger the first SaveValue.
template <class T> class Rev {
 public:
  explicit Rev(const T& val) : stamp_(0), value_(val) {}

  const T& Value() const { return value_; }

  void SetValue(Solver* const s, const T& val) {
    if (val != value_) {
      if (stamp_ < s->stamp()) {
        s->SaveValue(&value_);
        stamp_ = s->stamp();
      }
      value_ = val;
    }
  }

 private:
  uint64 stamp_;
  T value_;
};

// Subclass of Rev<T> which adds numerical operations.
template <class T> class NumericalRev : public Rev<T> {
 public:
  explicit NumericalRev(const T& val) : Rev<T>(val) {}

  void Add(Solver* const s, const T& to_add) {
    this->SetValue(s, this->Value() + to_add);
  }

  void Incr(Solver* const s) {
    Add(s, 1);
  }

  void Decr(Solver* const s) {
    Add(s, -1);
  }
};

// Reversible array of POD types.
// It Contains the stamp optimization. i.e. the SaveValue call is done only
// once per node of the search tree.
// Please note that actual stamps always starts at 1, thus an initial value of
// 0 will always trigger the first SaveValue.
template <class T> class RevArray {
 public:
  RevArray(int size, const T& val)
      : stamps_(new uint64[size]), values_(new T[size]), size_(size) {
    for (int i = 0; i < size; ++i) {
      stamps_[i] = 0;
      values_[i] = val;
    }
  }

  ~RevArray() {}

  int size() const { return size_; }

  const T& Value(int index) const { return values_[index]; }

#if !defined(SWIG)
  const T& operator[](int index) const { return values_[index]; }
#endif

  void SetValue(Solver* const s, int index, const T& val) {
    if (val != values_[index]) {
      if (stamps_[index] < s->stamp()) {
        s->SaveValue(&values_[index]);
        stamps_[index] = s->stamp();
      }
      values_[index] = val;
    }
  }

 private:
  scoped_array<uint64> stamps_;
  scoped_array<T> values_;
  const int size_;
};

// Subclass of RevArray<T> which adds numerical operations.
template <class T> class NumericalRevArray : public RevArray<T> {
 public:
  NumericalRevArray(int size, const T& val) : RevArray<T>(size, val) {}

  void Add(Solver* const s, int index, const T& to_add) {
    this->SetValue(s, index, this->Value(index) + to_add);
  }

  void Incr(Solver* const s, int index) {
    Add(s, index, 1);
  }

  void Decr(Solver* const s, int index) {
    Add(s, index, -1);
  }
};


// The class IntExpr is the base of all integer expressions in
// constraint programming.
// It Contains the basic protocol for an expression:
//   - setting and modifying its bound
//   - querying if it is bound
//   - listening to events modifying its bounds
//   - casting it into a variable (instance of IntVar)
class IntExpr : public PropagationBaseObject {
 public:
  explicit IntExpr(Solver* const s) : PropagationBaseObject(s) {}
  virtual ~IntExpr() {}

  virtual int64 Min() const = 0;
  virtual void SetMin(int64 m) = 0;
  virtual int64 Max() const = 0;
  virtual void SetMax(int64 m) = 0;

  // By default calls Min() and Max(), but can be redefined when Min and Max
  // code can be factorized.
  virtual void Range(int64* l, int64* u) {
    *l = Min();
    *u = Max();
  }
  // This method sets both the min and the max of the expression.
  virtual void SetRange(int64 l, int64 u) {
    SetMin(l);
    SetMax(u);
  }

  // This method sets the value of the expression.
  virtual void SetValue(int64 v) { SetRange(v, v); }

  // Returns true if the min and the max of the expression are equal.
  virtual bool Bound() const { return (Min() == Max()); }

  // Returns true if the expression is indeed a variable.
  virtual bool IsVar() const { return false; }

  // Creates a variable from the expression.
  virtual IntVar* Var() = 0;

  // Creates a variable from the expression and set the name of the
  // resulting var. If the expression is already a variable, then it
  // will set the name of the expression, possibly overwriting it.
  // This is just a shortcut to Var() followed by set_name().
  IntVar* VarWithName(const string& name);

  // Attach a demon that will watch the min or the max of the expression.
  virtual void WhenRange(Demon* d) = 0;

  // Accepts the given visitor.
  virtual void Accept(ModelVisitor* const visitor) const;

 private:
  DISALLOW_COPY_AND_ASSIGN(IntExpr);
};

// The class Iterator has two direct subclasses. HoleIterators
// iterates over all holes, that is value removed between the
// current min and max of the variable since the last time the
// variable was processed in the queue. DomainIterators iterates
// over all elements of the variable domain. Both iterators are not
// robust to domain changes. Hole iterators can also report values outside
// the current min and max of the variable.

// HoleIterators should only be called from a demon attached to the
// variable that has created this iterator.

// IntVar* current_var;
// scoped_ptr<IntVarIterator> it(current_var->MakeHoleIterator(false));
// for (it->Init(); it->Ok(); it->Next()) {
//   const int64 hole = it->Value();
//   // use the hole
// }

class IntVarIterator : public BaseObject {
 public:
  virtual ~IntVarIterator() {}

  // This method must be called before each loop.
  virtual void Init() = 0;

  // This method indicates if we can call Value() or not.
  virtual bool Ok() const = 0;

  // This method returns the value of the hole.
  virtual int64 Value() const = 0;

  // This method moves the iterator to the next value.
  virtual void Next() = 0;

  // Pretty Print.
  virtual string DebugString() const {
    return "IntVar::Iterator";
  }
};

// The class IntVar is a subset of IntExpr. In addition to the
// IntExpr protocol, it offers persistance,
// removing values from the domains and a finer model for events
class IntVar : public IntExpr {
 public:
  explicit IntVar(Solver* const s);
  IntVar(Solver* const s, const string& name);
  virtual ~IntVar() {}

  virtual bool IsVar() const { return true; }
  virtual IntVar* Var() { return this; }

  // This method returns the value of the variable. This method checks
  // before that the variable is bound.
  virtual int64 Value() const = 0;

  // This method removes the value 'v' from the domain of the variable.
  virtual void RemoveValue(int64 v) = 0;

  // This method removes the interval 'l' .. 'u' from the domain of
  // the variable. It assumes that 'l' <= 'u'.
  virtual void RemoveInterval(int64 l, int64 u) = 0;

  // This method remove the values from the domain of the variable.
  virtual void RemoveValues(const int64* const values, int size);

  // This method remove the values from the domain of the variable.
  void RemoveValues(const std::vector<int64>& values) {
    RemoveValues(values.data(), values.size());
  }

  // This method intersects the current domain with the values in the array.
  virtual void SetValues(const int64* const values, int size);

  // This method intersects the current domain with the values in the array.
  void SetValues(const std::vector<int64>& values) {
    SetValues(values.data(), values.size());
  }

  void SetValues(const std::vector<int>& values);

  // This method attaches a demon that will be awakened when the
  // variable is bound.
  virtual void WhenBound(Demon* d) = 0;

  // This method attaches a demon that will watch any domain
  // modification of the domain of the variable.
  virtual void WhenDomain(Demon* d) = 0;

  // This method returns the number of values in the domain of the variable.
  virtual uint64 Size() const = 0;

  // This method returns whether the value 'v' is in the domain of the variable.
  virtual bool Contains(int64 v) const = 0;

  // Creates a hole iterator. The object is created on the normal C++
  // heap and the solver does NOT take ownership of the object.
  virtual IntVarIterator* MakeHoleIterator(bool reversible) const = 0;

  // Creates a domain iterator. The object is created on the normal C++
  // heap and the solver does NOT take ownership of the object.
  virtual IntVarIterator* MakeDomainIterator(bool reversible) const = 0;

  // Returns the previous min.
  virtual int64 OldMin() const = 0;

  // Returns the previous max.
  virtual int64 OldMax() const = 0;

  virtual int VarType() const;

  // Accepts the given visitor.
  virtual void Accept(ModelVisitor* const visitor) const;

  // IsEqual
  virtual IntVar* IsEqual(int64 constant) = 0;
  virtual IntVar* IsDifferent(int64 constant) = 0;
  virtual IntVar* IsGreaterOrEqual(int64 constant) = 0;
  virtual IntVar* IsLessOrEqual(int64 constant) = 0;

 private:
  DISALLOW_COPY_AND_ASSIGN(IntVar);
};

// ---------- Solution Collectors ----------

// This class is the root class of all solution collectors
// It implements a basic query API to be used independently
// from the collector used.
class SolutionCollector : public SearchMonitor {
 public:
  SolutionCollector(Solver* const s, const Assignment* assignment);
  explicit SolutionCollector(Solver* const s);
  virtual ~SolutionCollector();

  // Add API
  void Add(IntVar* const var);
  void Add(const std::vector<IntVar*>& vars);
  void Add(IntervalVar* const var);
  void Add(const std::vector<IntervalVar*>& vars);
  void Add(SequenceVar* const var);
  void Add(const std::vector<SequenceVar*>& vars);
  void AddObjective(IntVar* const objective);

  // Beginning of the search.
  virtual void EnterSearch();

  // Returns how many solutions were stored during the search.
  int solution_count() const;

  // Returns the nth solution.
  Assignment* solution(int n) const;

  // Returns the wall time in ms for the nth solution.
  int64 wall_time(int n) const;

  // Returns the number of branches when the nth solution was found.
  int64 branches(int n) const;

  // Returns the number of failures encountered at the time of the nth
  // solution.
  int64 failures(int n) const;

  // Returns the objective value of the nth solution.
  int64 objective_value(int n) const;

  // This is a short-cut to get the Value of 'var' in the nth solution.
  int64 Value(int n, IntVar* const var) const;

  // This is a short-cut to get the StartValue of 'var' in the nth solution.
  int64 StartValue(int n, IntervalVar* const var) const;

  // This is a short-cut to get the EndValue of 'var' in the nth solution.
  int64 EndValue(int n, IntervalVar* const var) const;

  // This is a short-cut to get the DurationValue of 'var' in the nth solution.
  int64 DurationValue(int n, IntervalVar* const var) const;

  // This is a short-cut to get the PerformedValue of 'var' in the nth solution.
  int64 PerformedValue(int n, IntervalVar* const var) const;

#if !defined(SWIG)
  // This is a short-cut to get the ForwardSequence of 'var' in the
  // nth solution. The forward sequence is the list of ranked interval
  // variables starting from the start of the sequence.
  const std::vector<int>& ForwardSequence(int n, SequenceVar* const var) const;
  // This is a short-cut to get the BackwardSequence of 'var' in the
  // nth solution. The backward sequence is the list of ranked interval
  // variables starting from the end of the sequence.
  const std::vector<int>& BackwardSequence(int n, SequenceVar* const var) const;
  // This is a short-cut to get the list of unperformed of 'var' in the
  // nth solution.
  const std::vector<int>& Unperformed(int n, SequenceVar* const var) const;
#endif

 protected:
  // Push the current state as a new solution.
  void PushSolution();
  // Remove and delete the last popped solution.
  void PopSolution();

  void check_index(int n) const;
  scoped_ptr<Assignment> prototype_;
  std::vector<Assignment*> solutions_;
  std::vector<Assignment*> recycle_solutions_;
  std::vector<int64> times_;
  std::vector<int64> branches_;
  std::vector<int64> failures_;
  std::vector<int64> objective_values_;

 private:
  DISALLOW_COPY_AND_ASSIGN(SolutionCollector);
};

// TODO(user): Refactor this into an Objective class:
//   - print methods for AtNode and AtSolution.
//   - support for weighted objective and lexicographical objective.

// ---------- Objective Management ----------

// This class encapsulate an objective. It requires the direction
// (minimize or maximize), the variable to optimize and the
// improvement step.
class OptimizeVar : public SearchMonitor {
 public:
  OptimizeVar(Solver* const s, bool maximize, IntVar* const a, int64 step);
  virtual ~OptimizeVar();

  // Returns the best value found during search.
  int64 best() const { return best_; }

  // Returns the variable that is optimized.
  IntVar* Var() const { return var_; }
  // Internal methods
  virtual void EnterSearch();
  virtual void BeginNextDecision(DecisionBuilder* const db);
  virtual void RefuteDecision(Decision* const d);
  virtual bool AtSolution();
  virtual bool AcceptSolution();
  virtual string Print() const;
  virtual string DebugString() const;
  virtual void Accept(ModelVisitor* const visitor) const;

  void ApplyBound();

 protected:
  IntVar* const var_;
  int64 step_;
  int64 best_;
  bool maximize_;
  bool found_initial_solution_;

 private:
  DISALLOW_COPY_AND_ASSIGN(OptimizeVar);
};

// ---------- Search Limits ----------

// Base class of all search limits.
class SearchLimit : public SearchMonitor {
 public:
  explicit SearchLimit(Solver* const s) : SearchMonitor(s), crossed_(false) { }
  virtual ~SearchLimit();

  // Returns true if the limit has been crossed.
  bool crossed() const { return crossed_; }

  // This method is called to check the status of the limit. A return
  // value of true indicates that we have indeed crossed the limit. In
  // that case, this method will not be called again and the remaining
  // search will be discarded.
  virtual bool Check() = 0;

  // This method is called when the search limit is initialized.
  virtual void Init() = 0;

  // Copy a limit. Warning: leads to a direct (no check) downcasting of 'limit'
  // so one needs to be sure both SearchLimits are of the same type.
  virtual void Copy(const SearchLimit* const limit) = 0;

  // Allocates a clone of the limit
  virtual SearchLimit* MakeClone() const = 0;

  // Internal methods
  virtual void EnterSearch();
  virtual void BeginNextDecision(DecisionBuilder* const b);
  virtual void PeriodicCheck();
  virtual void RefuteDecision(Decision* const d);
  virtual string DebugString() const {
    return StringPrintf("SearchLimit(crossed = %i)", crossed_);
  }

 private:
  void TopPeriodicCheck();

  bool crossed_;
  DISALLOW_COPY_AND_ASSIGN(SearchLimit);
};

// ---------- NoGood Recorder ------

// Nogoods are used to store negative information collected during
// search. They are by definition non reversible.

// ----- No Good ----

// A nogood is a conjunction of unary constraints that represents a
// state that must not be visited during search.  For instance if X
// and Y are variables, (X == 5) && (Y != 3) is a nogood that forbid
// all part of the search tree where X is 5 and Y is not 3.
class NoGood {
 public:
  ~NoGood();
  // Creates a term var == value.
  void AddIntegerVariableEqualValueTerm(IntVar* const var, int64 value);
  // Creates a term var != value.
  void AddIntegerVariableNotEqualValueTerm(IntVar* const var, int64 value);
  // Applies the nogood. That is if there is only one undecided term and
  // all remaining terms are always true, then the opposite of this
  // term is added to the solver. It returns true if the nogood is
  // still active and needs to be reevaluated.
  bool Apply(Solver* const solver);
  // Pretty print.
  string DebugString() const;
  // TODO(user) : support interval variables and more types of constraints.

 private:
  std::vector<NoGoodTerm*> terms_;
};

// ----- Base class of no good manager -----

// A no good recorder is used to store a set of no goods in a non
// reversible way during search. It will actively propagate nogoods,
// that is if all its terms minus one are always true, then it will
// apply the reverse of this term during the search.
class NoGoodManager : public SearchMonitor {
 public:
  explicit NoGoodManager(Solver* const s) : SearchMonitor(s) {}
  virtual ~NoGoodManager() {}

  // ----- User API -----

  // Clear all stored nogoods.
  virtual void Clear() = 0;
  // NoGood factory. Create an empty nogood.
  NoGood* MakeNoGood();
  // Add one nogood to the recorder. Ownership is transfered to the recorder.
  virtual void AddNoGood(NoGood* const nogood) = 0;
  // Returns the number of nogoods added to the recorder.
  virtual int NoGoodCount() const = 0;
  // Pretty Print.
  virtual string DebugString() const = 0;


  // ----- Internal methods that links search events to the recorder API -----
  virtual void EnterSearch();
  virtual void BeginNextDecision(DecisionBuilder* const db);
  virtual bool AcceptSolution();

 private:
  // ----- Implementor API -----

  // Initialize data structures.
  virtual void Init() = 0;
  // Applies the nogood.
  virtual void Apply() = 0;

  DISALLOW_COPY_AND_ASSIGN(NoGoodManager);
};

// ---------- Interval Var ----------

// An interval var is often used in scheduling. Its main
// characteristics are its start position, its duration and its end
// date. All these characteristics can be queried, set and demons can
// be posted on their modifications.  An important aspect is
// optionality. An interval var can be performed or not. If
// unperformed, then it simply does not exist. Its characteristics
// cannot be accessed anymore. An interval var is automatically marked
// as unperformed when it is not consistent anymore (start greater
// than end, duration < 0...)
class IntervalVar : public PropagationBaseObject {
 public:
  // The smallest acceptable value to be returned by StartMin()
  static const int64 kMinValidValue;
  // The largest acceptable value to be returned by EndMax()
  static const int64 kMaxValidValue;
  IntervalVar(Solver* const solver, const string& name)
      : PropagationBaseObject(solver),
        start_expr_(NULL), duration_expr_(NULL), end_expr_(NULL),
        performed_expr_(NULL) {
    set_name(name);
  }
  virtual ~IntervalVar() {}

  // These methods query, set and watch the start position of the
  // interval var.
  virtual int64 StartMin() const = 0;
  virtual int64 StartMax() const = 0;
  virtual void SetStartMin(int64 m) = 0;
  virtual void SetStartMax(int64 m) = 0;
  virtual void SetStartRange(int64 mi, int64 ma) = 0;
  virtual int64 OldStartMin() const = 0;
  virtual int64 OldStartMax() const = 0;
  virtual void WhenStartRange(Demon* const d) = 0;
  virtual void WhenStartBound(Demon* const d) = 0;

  // These methods query, set and watch the duration of the interval var.
  virtual int64 DurationMin() const = 0;
  virtual int64 DurationMax() const = 0;
  virtual void SetDurationMin(int64 m) = 0;
  virtual void SetDurationMax(int64 m) = 0;
  virtual void SetDurationRange(int64 mi, int64 ma) = 0;
  virtual int64 OldDurationMin() const = 0;
  virtual int64 OldDurationMax() const = 0;
  virtual void WhenDurationRange(Demon* const d) = 0;
  virtual void WhenDurationBound(Demon* const d) = 0;

  // These methods query, set and watch the end position of the interval var.
  virtual int64 EndMin() const = 0;
  virtual int64 EndMax() const = 0;
  virtual void SetEndMin(int64 m) = 0;
  virtual void SetEndMax(int64 m) = 0;
  virtual void SetEndRange(int64 mi, int64 ma) = 0;
  virtual int64 OldEndMin() const = 0;
  virtual int64 OldEndMax() const = 0;
  virtual void WhenEndRange(Demon* const d) = 0;
  virtual void WhenEndBound(Demon* const d) = 0;

  // These methods query, set and watches the performed status of the
  // interval var.
  virtual bool MustBePerformed() const = 0;
  virtual bool MayBePerformed() const = 0;
  bool CannotBePerformed() const { return !MayBePerformed(); }
  bool IsPerformedBound() const {
    return MustBePerformed() == MayBePerformed();
  }
  virtual void SetPerformed(bool val) = 0;
  virtual bool WasPerformedBound() const = 0;
  virtual void WhenPerformedBound(Demon* const d) = 0;

  // Attaches a demon awakened when anything about this interval changes.
  void WhenAnything(Demon* const d);

  // These methods create expressions encapsulating the start, end
  // and duration of the interval var. Please note that these must not
  // be used if the interval var is unperformed.
  IntExpr* StartExpr();
  IntExpr* DurationExpr();
  IntExpr* EndExpr();
  IntExpr* PerformedExpr();
  // These methods create expressions encapsulating the start, end
  // and duration of the interval var. If the interval var is
  // unperformed, they will return the unperformed_value.
  IntExpr* SafeStartExpr(int64 unperformed_value);
  IntExpr* SafeDurationExpr(int64 unperformed_value);
  IntExpr* SafeEndExpr(int64 unperformed_value);

  // Accepts the given visitor.
  virtual void Accept(ModelVisitor* const visitor) const = 0;

 private:
  IntExpr* start_expr_;
  IntExpr* duration_expr_;
  IntExpr* end_expr_;
  IntExpr* performed_expr_;
  DISALLOW_COPY_AND_ASSIGN(IntervalVar);
};

// ----- SequenceVar -----

// A sequence variable is a variable which domain is a set of possible
// orderings of the interval variables. It allows ordering tasks.  It
// has two sets of methods: ComputePossibleFirstsAndLasts() which
// returns the list of interval variables thant can be ranked first or
// lasts, and RankFirst/RankNotFirst/RankLast/RankNotLast which can be
// used to create the search decision.
class SequenceVar : public PropagationBaseObject {
 public:
  SequenceVar(Solver* const s,
              const IntervalVar* const * intervals,
              const IntVar* const * nexts,
              int size,
              const string& name);

  virtual ~SequenceVar();

  virtual string DebugString() const;

  // Returns the minimum and maximum duration of combined interval
  // vars in the sequence.
  void DurationRange(int64* const dmin, int64* const dmax) const;

  // Returns the minimum start min and the maximum end max of all
  // interval vars in the sequence.
  void HorizonRange(int64* const hmin, int64* const hmax) const;

  // Returns the minimum start min and the maximum end max of all
  // unranked interval vars in the sequence.
  void ActiveHorizonRange(int64* const hmin, int64* const hmax) const;

  // Compute statistics on the sequence.
  void ComputeStatistics(int* const ranked,
                         int* const not_ranked,
                         int* const unperformed) const;

  // Ranks the index_th interval var first of all unranked interval
  // vars. After that, it will no longer be considered ranked.
  void RankFirst(int index);

  // Indicates that the index_th interval var will not be ranked first
  // of all currently unranked interval vars.
  void RankNotFirst(int index);

  // Ranks the index_th interval var first of all unranked interval
  // vars. After that, it will no longer be considered ranked.
  void RankLast(int index);

  // Indicates that the index_th interval var will not be ranked first
  // of all currently unranked interval vars.
  void RankNotLast(int index);

  // Computes the set of indices of interval variables that can be
  // ranked first in the set of unranked activities.
  void ComputePossibleFirstsAndLasts(std::vector<int>* const possible_firsts,
                                     std::vector<int>* const possible_lasts);

  // Applies the following sequence of ranks, ranks first, then rank
  // last.  rank_first and rank_last represents different directions.
  // rank_first[0] corresponds to the first interval of the sequence.
  // rank_last[0] corresponds to the last interval of the sequence.
  // All intervals in the unperformed vector will be marked as such.
  void RankSequence(const std::vector<int>& rank_firsts,
                    const std::vector<int>& rank_lasts,
                    const std::vector<int>& unperformed);

  // Clears 'rank_first' and 'rank_last', and fills them with the
  // intervals in the order of the ranks. If all variables are ranked,
  // 'rank_first' will contain all variables, and 'rank_last' will
  // contain none.
  // 'unperformed' will contains all such interval variables.
  // rank_first and rank_last represents different directions.
  // rank_first[0] corresponds to the first interval of the sequence.
  // rank_last[0] corresponds to the last interval of the sequence.
  void FillSequence(std::vector<int>* const rank_first,
                    std::vector<int>* const rank_lasts,
                    std::vector<int>* const unperformed) const;

  // Returns the index_th interval of the sequence.
  IntervalVar* Interval(int index) const;

  // Returns the next of the index_th interval of the sequence.
  IntVar* Next(int index) const;

  // Returns the number of interval vars in the sequence.
  int size() const { return size_; }

  // Accepts the given visitor.
  virtual void Accept(ModelVisitor* const visitor) const;

 private:
  int ComputeForwardFrontier();
  int ComputeBackwardFrontier();
  void UpdatePrevious() const;

  scoped_array<IntervalVar*> intervals_;
  scoped_array<IntVar*> nexts_;
  const int size_;
  const int next_size_;
  mutable std::vector<int> previous_;
};

// --------- Assignments ----------------------------

// ---------- Assignment Elements ----------

// ----- AssignmentElement -----

class AssignmentElement {
 public:
  AssignmentElement() : activated_(true) {}

  void Activate() { activated_ = true; }
  void Deactivate() { activated_ = false; }
  bool Activated() const { return activated_; }

 private:
  bool activated_;
};

// ----- IntVarElement -----

class IntVarElement : public AssignmentElement {
 public:
  IntVarElement();
  explicit IntVarElement(IntVar* const var);
  void Reset(IntVar* const var);
  IntVarElement* Clone();
  void Copy(const IntVarElement& element);
  IntVar* Var() const { return var_; }
  void Store() {
    min_ = var_->Min();
    max_ = var_->Max();
  }
  void Restore() { var_->SetRange(min_, max_); }
  void LoadFromProto(const IntVarAssignmentProto& int_var_assignment_proto);
  void WriteToProto(IntVarAssignmentProto* int_var_assignment_proto) const;

  int64 Min() const { return min_; }
  void SetMin(int64 m) { min_ = m; }
  int64 Max() const { return max_; }
  void SetMax(int64 m) { max_ = m; }
  int64 Value() const {
    DCHECK_EQ(min_, max_);
    // Getting the value from an unbound int var assignment element.
    return min_;
  }
  bool Bound() const { return (max_ == min_); }
  void SetRange(int64 l, int64 u) {
    min_ = l;
    max_ = u;
  }
  void SetValue(int64 v) {
    min_ = v;
    max_ = v;
  }
  string DebugString() const;

  bool operator==(const IntVarElement& element) const;
  bool operator!=(const IntVarElement& element) const {
    return !(*this == element);
  }

 private:
  IntVar* var_;
  int64 min_;
  int64 max_;
};

// ----- IntervalVarElement -----

class IntervalVarElement : public AssignmentElement {
 public:
  IntervalVarElement();
  explicit IntervalVarElement(IntervalVar* const var);
  void Reset(IntervalVar* const var);
  IntervalVarElement* Clone();
  void Copy(const IntervalVarElement& element);
  IntervalVar* Var() const { return var_; }
  void Store();
  void Restore();
  void LoadFromProto(
      const IntervalVarAssignmentProto& interval_var_assignment_proto);
  void WriteToProto(
      IntervalVarAssignmentProto* interval_var_assignment_proto) const;

  int64 StartMin() const { return start_min_; }
  int64 StartMax() const { return start_max_; }
  int64 StartValue() const {
    CHECK_EQ(start_max_, start_min_);
    return start_max_;
  }
  int64 DurationMin() const { return duration_min_; }
  int64 DurationMax() const { return duration_max_; }
  int64 DurationValue() const {
    CHECK_EQ(duration_max_, duration_min_);
    return duration_max_;
  }
  int64 EndMin() const { return end_min_; }
  int64 EndMax() const { return end_max_; }
  int64 EndValue() const {
    CHECK_EQ(end_max_, end_min_);
    return end_max_;
  }
  int64 PerformedMin() const { return performed_min_; }
  int64 PerformedMax() const { return performed_max_; }
  int64 PerformedValue() const {
    CHECK_EQ(performed_max_, performed_min_);
    return performed_max_;
  }
  void SetStartMin(int64 m) { start_min_ = m; }
  void SetStartMax(int64 m) { start_max_ = m; }
  void SetStartRange(int64 mi, int64 ma) {
    start_min_ = mi;
    start_max_ = ma;
  }
  void SetStartValue(int64 v) {
    start_min_ = v;
    start_max_ = v;
  }
  void SetDurationMin(int64 m) { duration_min_ = m; }
  void SetDurationMax(int64 m) { duration_max_ = m; }
  void SetDurationRange(int64 mi, int64 ma) {
    duration_min_ = mi;
    duration_max_ = ma;
  }
  void SetDurationValue(int64 v) {
    duration_min_ = v;
    duration_max_ = v;
  }
  void SetEndMin(int64 m) { end_min_ = m; }
  void SetEndMax(int64 m) { end_max_ = m; }
  void SetEndRange(int64 mi, int64 ma) {
    end_min_ = mi;
    end_max_ = ma;
  }
  void SetEndValue(int64 v) {
    end_min_ = v;
    end_max_ = v;
  }
  void SetPerformedMin(int64 m) { performed_min_ = m; }
  void SetPerformedMax(int64 m) { performed_max_ = m; }
  void SetPerformedRange(int64 mi, int64 ma) {
    performed_min_ = mi;
    performed_max_ = ma;
  }
  void SetPerformedValue(int64 v) {
    performed_min_ = v;
    performed_max_ = v;
  }
  string DebugString() const;
  bool operator==(const IntervalVarElement& element) const;
  bool operator!=(const IntervalVarElement& element) const {
    return !(*this == element);
  }

 private:
  int64 start_min_;
  int64 start_max_;
  int64 duration_min_;
  int64 duration_max_;
  int64 end_min_;
  int64 end_max_;
  int64 performed_min_;
  int64 performed_max_;
  IntervalVar* var_;
};

// ----- SequenceVarElement -----

// The sequence var element stores a partial representation of ranked
// interval variables in the underlying sequence variable.
// This representation consists of three vectors:
//   - the forward sequence. That is the list of interval variables
//     ranked first in the sequence.  The first element of the backward
//     sequence is the first interval in the sequence variable.
//   - the backward sequence. That is the list of interval variables
//     ranked last in the sequence. The first element of the backward
//     sequence is the last interval in the sequence variable.
//   - The list of unperformed interval variables.
//  Furthermore, if all performed variables are ranked, then by
//  convention, the forward_sequence will contains all such variables
//  and the backward_sequence will be empty.
class SequenceVarElement : public AssignmentElement {
 public:
  SequenceVarElement();
  explicit SequenceVarElement(SequenceVar* const var);
  void Reset(SequenceVar* const var);
  SequenceVarElement* Clone();
  void Copy(const SequenceVarElement& element);
  SequenceVar* Var() const { return var_; }
  void Store();
  void Restore();
  void LoadFromProto(
      const SequenceVarAssignmentProto& sequence_var_assignment_proto);
  void WriteToProto(
      SequenceVarAssignmentProto* sequence_var_assignment_proto) const;

#if !defined(SWIG)
  const std::vector<int>& ForwardSequence() const;
  const std::vector<int>& BackwardSequence() const;
  const std::vector<int>& Unperformed() const;
#endif
  void SetSequence(const std::vector<int>& forward_sequence,
                   const std::vector<int>& backward_sequence,
                   const std::vector<int>& unperformed);
  void SetForwardSequence(const std::vector<int>& forward_sequence);
  void SetBackwardSequence(const std::vector<int>& backward_sequence);
  void SetUnperformed(const std::vector<int>& unperformed);

  string DebugString() const;

  bool operator==(const SequenceVarElement& element) const;
  bool operator!=(const SequenceVarElement& element) const {
    return !(*this == element);
  }

 private:
  bool CheckClassInvariants();

  SequenceVar* var_;
  std::vector<int> forward_sequence_;
  std::vector<int> backward_sequence_;
  std::vector<int> unperformed_;
};

// ----- Assignment element container -----

template <class V, class E> class AssignmentContainer {
 public:
  AssignmentContainer() {}
  E& Add(V* const var) {
    CHECK_NOTNULL(var);
    int index = -1;
    if (!Find(var, &index)) {
      return FastAdd(var);
    } else {
      return elements_[index];
    }
  }
  // Adds element without checking its presence in the container.
  E& FastAdd(V* const var) {
    DCHECK(var != NULL);
    E e(var);
    elements_.push_back(e);
    return elements_.back();
  }
  void Clear() {
    elements_.clear();
    if (!elements_map_.empty()) {  // 2x speedup on or-tools.
      elements_map_.clear();
    }
  }
  bool Empty() const {
    return elements_.empty();
  }
  // Copies intersection of containers.
  void Copy(const AssignmentContainer<V, E>& container) {
    for (int i = 0; i < container.elements_.size(); ++i) {
      const E& element = container.elements_[i];
      const V* const var = element.Var();
      int index = -1;
      if (i < elements_.size() && elements_[i].Var() == var) {
        index = i;
      } else if (!Find(var, &index)) {
        continue;
      }
      DCHECK_GE(index, 0);
      E& local_element(elements_[index]);
      local_element.Copy(element);
      if (element.Activated()) {
        local_element.Activate();
      } else {
        local_element.Deactivate();
      }
    }
  }
  bool Contains(const V* const var) const {
    int index;
    return Find(var, &index);
  }
  E& MutableElement(const V* const var) {
    int index = -1;
    const bool found = Find(var, &index);
    CHECK(found) << "Unknown variable " << var->DebugString() << " in solution";
    return MutableElement(index);
  }
  const E& Element(const V* const var) const {
    int index = -1;
    const bool found = Find(var, &index);
    CHECK(found) << "Unknown variable " << var->DebugString() << " in solution";
    return Element(index);
  }
  const std::vector<E>& elements() const { return elements_; }
  E& MutableElement(int index) { return elements_[index]; }
  const E& Element(int index) const { return elements_[index]; }
  int Size() const { return elements_.size(); }
  void Store() {
    for (int i = 0; i < elements_.size(); ++i) {
      elements_[i].Store();
    }
  }
  void Restore() {
    for (int i = 0; i < elements_.size(); ++i) {
      E& element = elements_[i];
      if (element.Activated()) {
        element.Restore();
      }
    }
  }

  // Returns true if this and 'container' both represent the same V* -> E map.
  // Runs in linear time; requires that the == operator on the type E is well
  // defined.
  bool operator==(const AssignmentContainer<V, E>& container) const {
    // We may not have any work to do
    if (Size() != container.Size()) {
      return false;
    }
    // The == should be order-independent
    EnsureMapIsUpToDate();
    // Do not use the hash_map::== operator! It does not just compare content,
    // but also how the map is hashed (e.g., number of buckets). This is not
    // what we want.
    typedef ConstIter<std::vector<E> > Iterator;
    for (Iterator it(container.elements_); !it.at_end(); ++it) {
      const int position = FindWithDefault(elements_map_, it->Var(), -1);
      if (position < 0 || elements_[position] != *it) {
        return false;
      }
    }
    return true;
  }
  bool operator!=(const AssignmentContainer<V, E>& container) const {
    return !(*this == container);
  }

 private:
  void EnsureMapIsUpToDate() const {
    hash_map<const V*, int>* map =
        const_cast<hash_map<const V*, int>* >(&elements_map_);
    for (int i = map->size(); i < elements_.size(); ++i) {
      (*map)[elements_[i].Var()] = i;
    }
  }
  bool Find(const V* const var, int* index) const {
    EnsureMapIsUpToDate();
    DCHECK_EQ(elements_map_.size(), elements_.size());
    return FindCopy(elements_map_, var, index);
  }

  std::vector<E> elements_;
  hash_map<const V*, int> elements_map_;
};

// ----- Assignment -----

// An Assignment is a variable -> domains mapping
// It is used to report solutions to the user
class Assignment : public PropagationBaseObject {
 public:
  typedef AssignmentContainer<IntVar, IntVarElement> IntContainer;
  typedef AssignmentContainer<IntervalVar, IntervalVarElement>
  IntervalContainer;
  typedef AssignmentContainer<SequenceVar, SequenceVarElement>
  SequenceContainer;

  explicit Assignment(Solver* const s);
  explicit Assignment(const Assignment* const copy);
  virtual ~Assignment();

  void Clear();
  bool Empty() const {
    return int_var_container_.Empty() &&
        interval_var_container_.Empty() &&
        sequence_var_container_.Empty();
  }
  int Size() const {
    return NumIntVars() + NumIntervalVars() + NumSequenceVars();
  }
  int NumIntVars() const {
    return int_var_container_.Size();
  }
  int NumIntervalVars() const {
    return interval_var_container_.Size();
  }
  int NumSequenceVars() const {
    return sequence_var_container_.Size();
  }
  void Store();
  void Restore();

  // Loads an assignment from a file; does not add variables to the
  // assignment (only the variables contained in the assignment are modified).
  bool Load(const string& filename);
#if !defined(SWIG)
  bool Load(File* file);
#endif  // #if !defined(SWIG)
  void Load(const AssignmentProto& proto);
  // Saves the assignment to a file.
  bool Save(const string& filename) const;
#if !defined(SWIG)
  bool Save(File* file) const;
#endif  // #if !defined(SWIG)
  void Save(AssignmentProto* const proto) const;

  void AddObjective(IntVar* const v);
  IntVar* Objective() const;
  bool HasObjective() const { return (objective_element_.Var() != NULL); }
  int64 ObjectiveMin() const;
  int64 ObjectiveMax() const;
  int64 ObjectiveValue() const;
  bool ObjectiveBound() const;
  void SetObjectiveMin(int64 m);
  void SetObjectiveMax(int64 m);
  void SetObjectiveValue(int64 value);
  void SetObjectiveRange(int64 l, int64 u);

  IntVarElement& Add(IntVar* const v);
  void Add(IntVar* const* vars, int size);
  void Add(const std::vector<IntVar*>& v);
  // Adds without checking if variable has been previously added.
  IntVarElement& FastAdd(IntVar* const v);
  int64 Min(const IntVar* const v) const;
  int64 Max(const IntVar* const v) const;
  int64 Value(const IntVar* const v) const;
  bool Bound(const IntVar* const v) const;
  void SetMin(const IntVar* const v, int64 m);
  void SetMax(const IntVar* const v, int64 m);
  void SetRange(const IntVar* const v, int64 l, int64 u);
  void SetValue(const IntVar* const v, int64 value);

  IntervalVarElement& Add(IntervalVar* const v);
  void Add(IntervalVar* const * vars, int size);
  void Add(const std::vector<IntervalVar*>& vars);
  // Adds without checking if variable has been previously added.
  IntervalVarElement& FastAdd(IntervalVar* const v);
  int64 StartMin(const IntervalVar* const v) const;
  int64 StartMax(const IntervalVar* const v) const;
  int64 StartValue(const IntervalVar* const v) const;
  int64 DurationMin(const IntervalVar* const v) const;
  int64 DurationMax(const IntervalVar* const v) const;
  int64 DurationValue(const IntervalVar* const c) const;
  int64 EndMin(const IntervalVar* const v) const;
  int64 EndMax(const IntervalVar* const v) const;
  int64 EndValue(const IntervalVar* const v) const;
  int64 PerformedMin(const IntervalVar* const v) const;
  int64 PerformedMax(const IntervalVar* const v) const;
  int64 PerformedValue(const IntervalVar* const v) const;
  void SetStartMin(const IntervalVar* const v, int64 m);
  void SetStartMax(const IntervalVar* const v, int64 m);
  void SetStartRange(const IntervalVar* const v, int64 mi, int64 ma);
  void SetStartValue(const IntervalVar* const v, int64 value);
  void SetDurationMin(const IntervalVar* const v, int64 m);
  void SetDurationMax(const IntervalVar* const v, int64 m);
  void SetDurationRange(const IntervalVar* const v, int64 mi, int64 ma);
  void SetDurationValue(const IntervalVar* const v, int64 value);
  void SetEndMin(const IntervalVar* const v, int64 m);
  void SetEndMax(const IntervalVar* const v, int64 m);
  void SetEndRange(const IntervalVar* const v, int64 mi, int64 ma);
  void SetEndValue(const IntervalVar* const v, int64 value);
  void SetPerformedMin(const IntervalVar* const v, int64 m);
  void SetPerformedMax(const IntervalVar* const v, int64 m);
  void SetPerformedRange(const IntervalVar* const v, int64 mi, int64 ma);
  void SetPerformedValue(const IntervalVar* const v, int64 value);

  SequenceVarElement& Add(SequenceVar* const v);
  void Add(SequenceVar* const * vars, int size);
  void Add(const std::vector<SequenceVar*>& vars);
  // Adds without checking if variable has been previously added.
  SequenceVarElement& FastAdd(SequenceVar* const v);
#if !defined(SWIG)
  const std::vector<int>& ForwardSequence(const SequenceVar* const v) const;
  const std::vector<int>& BackwardSequence(const SequenceVar* const v) const;
  const std::vector<int>& Unperformed(const SequenceVar* const v) const;
#endif
  void SetSequence(const SequenceVar* const v,
                   const std::vector<int>& forward_sequence,
                   const std::vector<int>& backward_sequence,
                   const std::vector<int>& unperformed);
  void SetForwardSequence(const SequenceVar* const v,
                          const std::vector<int>& forward_sequence);
  void SetBackwardSequence(const SequenceVar* const v,
                           const std::vector<int>& backward_sequence);
  void SetUnperformed(const SequenceVar* const v,
                      const std::vector<int>& unperformed);

  void Activate(const IntVar* const v);
  void Deactivate(const IntVar* const v);
  bool Activated(const IntVar* const v) const;

  void Activate(const IntervalVar* const v);
  void Deactivate(const IntervalVar* const v);
  bool Activated(const IntervalVar* const v) const;

  void Activate(const SequenceVar* const v);
  void Deactivate(const SequenceVar* const v);
  bool Activated(const SequenceVar* const v) const;

  void ActivateObjective();
  void DeactivateObjective();
  bool ActivatedObjective() const;

  virtual string DebugString() const;

  bool Contains(const IntVar* const var) const;
  bool Contains(const IntervalVar* const var) const;
  bool Contains(const SequenceVar* const var) const;
  // Copies the intersection of the 2 assignments to the current assignment.
  void Copy(const Assignment* assignment);

  // TODO(user): Add iterators on elements to avoid exposing container class.
  const IntContainer& IntVarContainer() const {
    return int_var_container_;
  }
  IntContainer& MutableIntVarContainer() {
    return int_var_container_;
  }
  const IntervalContainer& IntervalVarContainer() const {
    return interval_var_container_;
  }
  IntervalContainer& MutableIntervalVarContainer() {
    return interval_var_container_;
  }
  const SequenceContainer& SequenceVarContainer() const {
    return sequence_var_container_;
  }
  SequenceContainer& MutableSequenceVarContainer() {
    return sequence_var_container_;
  }
  bool operator==(const Assignment& assignment) const {
    return int_var_container_ == assignment.int_var_container_
        && interval_var_container_ == assignment.interval_var_container_
        && sequence_var_container_ == assignment.sequence_var_container_
        && objective_element_ == assignment.objective_element_;
  }
  bool operator!=(const Assignment& assignment) const {
    return !(*this == assignment);
  }

 private:
  IntContainer int_var_container_;
  IntervalContainer interval_var_container_;
  SequenceContainer sequence_var_container_;
  IntVarElement objective_element_;
  DISALLOW_COPY_AND_ASSIGN(Assignment);
};

std::ostream& operator<<(std::ostream& out, const Assignment& assignment);  // NOLINT

// ---------- Pack Constraint ----------

class Pack : public Constraint {
 public:
  typedef ResultCallback1<int64, int> ItemUsageEvaluator;
  typedef ResultCallback2<int64, int, int> ItemUsagePerBinEvaluator;

  Pack(Solver* const s,
       const IntVar* const * vars,
       int vsize,
       int number_of_bins);

  virtual ~Pack();

  // ----- Public API -----

  // Dimensions are additional constraints than can restrict what is
  // possible with the pack constraint. It can be used to set capacity
  // limits, to count objects per bin, to compute unassigned
  // penalties...


  // This dimension imposes that for all bins b, the weighted sum
  // (weights[i]) of all objects i assigned to 'b' is less or equal
  // 'bounds[b]'.
  void AddWeightedSumLessOrEqualConstantDimension(const std::vector<int64>& weights,
                                                  const std::vector<int64>& bounds);

  // This dimension imposes that for all bins b, the weighted sum
  // (weights->Run(i)) of all objects i assigned to 'b' is less or
  // equal to 'bounds[b]'. Ownership of the callback is transfered to
  // the pack constraint.
  void AddWeightedSumLessOrEqualConstantDimension(ItemUsageEvaluator* weights,
                                                  const std::vector<int64>& bounds);

  // This dimension imposes that for all bins b, the weighted sum
  // (weights->Run(i, b) of all objects i assigned to 'b' is less or
  // equal to 'bounds[b]'. Ownership of the callback is transfered to
  // the pack constraint.
  void AddWeightedSumLessOrEqualConstantDimension(
      ItemUsagePerBinEvaluator* weights,
      const std::vector<int64>& bounds);


  // This dimension imposes that for all bins b, the weighted sum
  // (weights[i]) of all objects i assigned to 'b' is equal to loads[b].
  void AddWeightedSumEqualVarDimension(const std::vector<int64>& weights,
                                       const std::vector<IntVar*>& loads);


  // This dimension imposes that for all bins b, the weighted sum
  // (weights->Run(i, b)) of all objects i assigned to 'b' is equal to loads[b].
  void AddWeightedSumEqualVarDimension(ItemUsagePerBinEvaluator* weights,
                                       const std::vector<IntVar*>& loads);


  // This dimension imposes:
  // forall b in bins,
  //    sum (i in items: weight[i] * is_assigned(i, b)) <= capacities[b]
  // where is_assigned(i, b) is true if and only if item i is assigned
  // to the bin b.
  //
  // This can be used to model shapes of items by linking variables of
  // the same item on parallel dimensions with an allowed assignment
  // constraint.
  void AddSumVariableWeightsLessOrEqualConstantDimension(
      const std::vector<IntVar*>& weights,
      const std::vector<int64>& capacities);

  // This dimension enforces that cost_var == sum of weights[i] for
  // all objects 'i' assigned to a bin.
  void AddWeightedSumOfAssignedDimension(const std::vector<int64>& weights,
                                         IntVar* const cost_var);

  // This dimension links 'count_var' to the actual number of bins used in the
  // pack.
  void AddCountUsedBinDimension(IntVar* const count_var);

  // This dimension links 'count_var' to the actual number of items
  // assigned to a bin in the pack.
  void AddCountAssignedItemsDimension(IntVar* const count_var);
  // ----- Internal API -----

  virtual void Post();
  void ClearAll();
  void PropagateDelayed();
  virtual void InitialPropagate();
  void Propagate();
  void OneDomain(int var_index);
  virtual string DebugString() const;
  bool IsUndecided(int var_index, int bin_index) const;
  void SetImpossible(int var_index, int bin_index);
  void Assign(int var_index, int bin_index);
  bool IsAssignedStatusKnown(int var_index) const;
  bool IsPossible(int var_index, int bin_index) const;
  IntVar* AssignVar(int var_index, int bin_index) const;
  void SetAssigned(int var_index);
  void SetUnassigned(int var_index);
  void RemoveAllPossibleFromBin(int bin_index);
  void AssignAllPossibleToBin(int bin_index);
  void AssignFirstPossibleToBin(int bin_index);
  void AssignAllRemainingItems();
  void UnassignAllRemainingItems();
  // Accepts the given visitor.
  virtual void Accept(ModelVisitor* const visitor) const;

 private:
  bool IsInProcess() const;
  scoped_array<IntVar*> vars_;
  const int vsize_;
  const int bins_;
  std::vector<Dimension*> dims_;
  scoped_ptr<RevBitMatrix> unprocessed_;
  std::vector<std::vector<int> > forced_;
  std::vector<std::vector<int> > removed_;
  scoped_array<IntVarIterator*> holes_;
  uint64 stamp_;
  Demon* demon_;
  std::vector<std::pair<int, int> > to_set_;
  std::vector<std::pair<int, int> > to_unset_;
  bool in_process_;
};

// ----- Disjunctive Constraint -----

class DisjunctiveConstraint : public Constraint {
 public:
  DisjunctiveConstraint(Solver* const s,
                        IntervalVar* const * intervals,
                        int size,
                        const string& name);
  virtual ~DisjunctiveConstraint();

  // Creates a sequence variable from the constraint.
  virtual SequenceVar* MakeSequenceVar() = 0;

 protected:
  scoped_array<IntervalVar*> intervals_;
  const int size_;

 private:
  DISALLOW_COPY_AND_ASSIGN(DisjunctiveConstraint);
};

// ----- SolutionPool -----

// This class is used to manage a pool of solutions. It can transform
// a single point local search into a multi point local search.
class SolutionPool : public BaseObject {
 public:
  SolutionPool() {}
  virtual ~SolutionPool() {}

  // This method is called to initialize the solution pool with the assignment
  // from the local search.
  virtual void Initialize(Assignment* const assignment) = 0;

  // This method is called when a new solution has been accepted by the local
  // search.
  virtual void RegisterNewSolution(Assignment* const assignment) = 0;

  // This method is called when the local search starts a new neighborhood to
  // initialize the default assignment.
  virtual void GetNextSolution(Assignment* const assignment) = 0;

  // This method checks if the local solution needs to be updated with
  // an external one.
  virtual bool SyncNeeded(Assignment* const local_assignment) = 0;
};

#if !defined(SWIG)
// ----- MultiThread and distributed LNS -----

// This class acts as a glue between the master and different workers
// in a multi thread or distributed environment. It offers
// synchronization services and help creates the different objects
// needed by the searches.

class ParallelSolveSupport {
 public:
  typedef Callback3<ParallelSolveSupport*, bool, int> ModelBuilder;

  ParallelSolveSupport(bool maximize, ModelBuilder* const run_model);

  virtual ~ParallelSolveSupport();

  // This method is used by workers to wait for the initial solution to
  // be found by the master. If the return value is false, then no
  // solution has been found and the worker should exit gracefully.
  virtual bool WaitForInitialSolution(Assignment* const to_fill,
                                      int worker) = 0;

  // This method is used be the master to signal the initial solution
  // to workers.
  virtual void RegisterInitialSolution(Assignment* const to_save) = 0;

  // This method is used by the master to signal that no initial
  // solution has been found.
  virtual void RegisterNoInitialSolution() = 0;

  // Creates a decision builder for the master. This decision builder
  // will print out each solutions found by the workers.
  virtual DecisionBuilder* MakeReplayDecisionBuilder(
      Solver* const s, const Assignment* const solution) = 0;

  // A simple shortcut to create the search log only on the master.
  virtual SearchMonitor* MakeSearchLog(Solver* const s,
                                       bool master,
                                       int64 freq,
                                       IntVar* const objective) = 0;

  // A simple shortcut to create the limit only on the workers and not
  // on the master.
  virtual SearchMonitor* MakeLimit(Solver* const s,
                                   bool master,
                                   int64 time_limit,
                                   int64 branch_limit,
                                   int64 fail_limit,
                                   int64 solution_limit) = 0;

  // Creates a search monitor that communicates solutions found by the
  // workers to the master. Both master and workers should use this.
  virtual SearchMonitor* MakeCommunicationMonitor(
      Solver* const s,
      const Assignment* const solution,
      bool master,
      int worker) = 0;

  // Creates a solution pool to be used in the Local Search for each
  // worker. This solution pool is responsible for pulling improved
  // solution from the master.
  virtual SolutionPool* MakeSolutionPool(Solver* const s, int worker) = 0;

  // This method launches the computation that will itself call the run_model
  // callback given to the constructor.
  virtual void Run() {}

  // Are we maximizing the search.
  bool maximize() const { return maximize_; }
  // Returns the best stored solution.
  AssignmentProto* solution() const { return local_solution_.get(); }

 protected:
  // Best solution found so far.
  scoped_ptr<AssignmentProto> local_solution_;
  // Are we maximizing.
  const bool maximize_;
  // Callback to run the model
  scoped_ptr<ModelBuilder> run_model_;
};

// This method creates an instance of ParallelSolveSupport suited for
// multi-threaded computation.  In the callback, the first argument
// will be the instance of the ParallelSolveSupport class, the second
// one will be a bool true for the master and the last one will be the index of
// the slave.
ParallelSolveSupport* MakeMtSolveSupport(
    int workers,
    bool maximize,
    ParallelSolveSupport::ModelBuilder* const model_builder);

#endif  // SWIG

}  // namespace operations_research
#endif  // OR_TOOLS_CONSTRAINT_SOLVER_CONSTRAINT_SOLVER_H_