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/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
/*
* Main authors:
* Christian Schulte <schulte@gecode.org>
* Guido Tack <tack@gecode.org>
*
* Copyright:
* Christian Schulte, 2009
* Guido Tack, 2010
*
* This file is part of Gecode, the generic constraint
* development environment:
* http://www.gecode.org
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
*/
#ifndef GECODE_INT_CUMULATIVE_HH
#define GECODE_INT_CUMULATIVE_HH
#include <gecode/int/task.hh>
#include <gecode/int/unary.hh>
/**
* \namespace Gecode::Int::Cumulative
*
* The edge-finding and overload-checking algorithms and data structures
* follow (mostly):
* Petr Vilím, Max Energy Filtering Algorithm for Discrete
* Cumulative Resources, CP-AI-OR, 2009.
* Petr Vilím, Edge Finding Filtering Algorithm for Discrete
* Cumulative Resources in O(kn log n), CP, 2009.
*
* \brief %Scheduling for cumulative resources
*/
namespace Gecode { namespace Int { namespace Cumulative {
/// Throw exception if multiplication of \a x and \a y overflows
void mul_check(long long int x, long long int y);
/// Throw exception if multiplication of \a x, \a y, and \a z overflows
void mul_check(long long int x, long long int y, long long int z);
}}}
#include <gecode/int/cumulative/limits.hpp>
namespace Gecode { namespace Int { namespace Cumulative {
/// Cumulative (mandatory) task with fixed processing time
class ManFixPTask : public Unary::ManFixPTask {
protected:
/// Required capacity
int _c;
public:
/// \name Constructors and initialization
//@{
/// Default constructor
ManFixPTask(void);
/// Initialize task with start time \a s, processing time \a p, and required resource \a c
ManFixPTask(IntVar s, int p, int c);
/// Initialize task with start time \a s, processing time \a p, and required resource \a c
void init(IntVar s, int p, int c);
/// Initialize from task \a t
void init(const ManFixPTask& t);
//@}
/// \name Value access
//@{
/// Return required capacity
int c(void) const;
/// Return required energy
long long int e(void) const;
//@}
/// \name Cloning
//@{
/// Update this task to be a clone of task \a t
void update(Space& home, ManFixPTask& t);
//@}
};
/**
* \brief Print task in format est:[p,c]:lct
* \relates ManFixPTask
*/
template<class Char, class Traits>
std::basic_ostream<Char,Traits>&
operator <<(std::basic_ostream<Char,Traits>& os, const ManFixPTask& t);
/// Cumulative (mandatory) task with fixed processing, start or end time
class ManFixPSETask : public Unary::ManFixPSETask {
protected:
/// Required capacity
int _c;
public:
/// \name Constructors and initialization
//@{
/// Default constructor
ManFixPSETask(void);
/**
* \brief Initialize task
*
* Depending on \a t, \a s is either the end time (if \a t is FIXS)
* or the start time of the task, \a p is the fixed parameter,
* and \a c is the required capacity.
*/
ManFixPSETask(TaskType t, IntVar s, int p, int c);
/**
* \brief Initialize task
*
* Depending on \a t, \a s is either the end time (if \a t is FIXS)
* or the start time of the task, \a p is the fixed parameter,
* and \a c is the required capacity.
*/
void init(TaskType t, IntVar s, int p, int c);
/// Initialize from task \a t
void init(const ManFixPSETask& t);
//@}
/// \name Value access
//@{
/// Return required capacity
int c(void) const;
/// Return required energy
long long int e(void) const;
//@}
/// \name Cloning
//@{
/// Update this task to be a clone of task \a t
void update(Space& home, ManFixPSETask& t);
//@}
};
/**
* \brief Print task in format est:[p,c]:lct
* \relates ManFixPSETask
*/
template<class Char, class Traits>
std::basic_ostream<Char,Traits>&
operator <<(std::basic_ostream<Char,Traits>& os, const ManFixPSETask& t);
/// Cumulative (mandatory) task with flexible processing time
class ManFlexTask : public Unary::ManFlexTask {
protected:
/// Required capacity
int _c;
public:
/// \name Constructors and initialization
//@{
/// Default constructor
ManFlexTask(void);
/// Initialize with start time \a s, processing time \a p, end time \a e
ManFlexTask(IntVar s, IntVar p, IntVar e, int c);
/// Initialize with start time \a s, processing time \a p, end time \a e
void init(IntVar s, IntVar p, IntVar e, int c);
/// Initialize from task \a t
void init(const ManFlexTask& t);
//@}
/// \name Value access
//@{
/// Return required capacity
int c(void) const;
/// Return required energy
long long int e(void) const;
//@}
/// \name Cloning
//@{
/// Update this task to be a clone of task \a t
void update(Space& home, ManFlexTask& t);
//@}
};
/**
* \brief Print task in format est:[p,c]:lct
* \relates ManFlexTask
*/
template<class Char, class Traits>
std::basic_ostream<Char,Traits>&
operator <<(std::basic_ostream<Char,Traits>& os, const ManFlexTask& t);
/// Cumulative optional task with fixed processing time
class OptFixPTask : public ManToOptTask<ManFixPTask> {
protected:
using ManToOptTask<ManFixPTask>::_m;
public:
/// \name Constructors and initialization
//@{
/// Default constructor
OptFixPTask(void);
/// Initialize with start time \a s, processing time \a p, required capacity \a c, and mandatory flag \a m
OptFixPTask(IntVar s, int p, int c, BoolVar m);
/// Initialize with start time \a s, processing time \a p, required capacity \a c, and mandatory flag \a m
void init(IntVar s, int p, int c, BoolVar m);
//@}
/// Cast to corresponding unary task
operator Unary::OptFixPTask (void);
};
/**
* \brief Print optional task in format est:[p,c]:lct:m
* \relates OptFixPTask
*/
template<class Char, class Traits>
std::basic_ostream<Char,Traits>&
operator <<(std::basic_ostream<Char,Traits>& os, const OptFixPTask& t);
/// Cumulative optional task with fixed processing, start or end time
class OptFixPSETask : public ManToOptTask<ManFixPSETask> {
protected:
using ManToOptTask<ManFixPSETask>::_m;
public:
/// \name Constructors and initialization
//@{
/// Default constructor
OptFixPSETask(void);
/// Initialize with start time \a s, processing time \a p, required capacity \a c, and mandatory flag \a m
OptFixPSETask(TaskType t, IntVar s, int p, int c, BoolVar m);
/// Initialize with start time \a s, processing time \a p, required capacity \a c, and mandatory flag \a m
void init(TaskType t, IntVar s, int p, int c, BoolVar m);
//@}
/// Cast to corresponding unary task
operator Unary::OptFixPSETask (void);
};
/**
* \brief Print optional task in format est:[p,c]:lct:m
* \relates OptFixPSETask
*/
template<class Char, class Traits>
std::basic_ostream<Char,Traits>&
operator <<(std::basic_ostream<Char,Traits>& os, const OptFixPSETask& t);
/// %Cumulative optional task with flexible processing time
class OptFlexTask : public ManToOptTask<ManFlexTask> {
protected:
using ManToOptTask<ManFlexTask>::_m;
public:
/// \name Constructors and initialization
//@{
/// Default constructor
OptFlexTask(void);
/// Initialize with start time \a s, processing time \a p, end time \a e, and mandatory flag \a m
OptFlexTask(IntVar s, IntVar p, IntVar e, int c, BoolVar m);
/// Initialize with start time \a s, processing time \a p, end time \a e, and mandatory flag \a m
void init(IntVar s, IntVar p, IntVar e, int c, BoolVar m);
//@}
/// Cast to corresponding unary task
operator Unary::OptFlexTask (void);
};
/**
* \brief Print optional task in format est:lst:pmin:pmax:c:ect:lct:m
* \relates OptFlexTask
*/
template<class Char, class Traits>
std::basic_ostream<Char,Traits>&
operator <<(std::basic_ostream<Char,Traits>& os, const OptFlexTask& t);
}}}
#include <gecode/int/cumulative/task.hpp>
namespace Gecode { namespace Int { namespace Cumulative {
/// Forward mandatory fixed task view
typedef ManFixPTask ManFixPTaskFwd;
/// Backward (dual) mandatory fixed task view
typedef FwdToBwd<ManFixPTaskFwd> ManFixPTaskBwd;
/// Forward mandatory fixed task view
typedef ManFixPSETask ManFixPSETaskFwd;
/// Backward (dual) mandatory fixed task view
typedef FwdToBwd<ManFixPSETaskFwd> ManFixPSETaskBwd;
/// Forward optional fixed task view
typedef OptFixPTask OptFixPTaskFwd;
/// Backward (dual) optional fixed task view
typedef FwdToBwd<OptFixPTaskFwd> OptFixPTaskBwd;
/// Forward optional fixed task view
typedef OptFixPSETask OptFixPSETaskFwd;
/// Backward (dual) optional fixed task view
typedef FwdToBwd<OptFixPSETaskFwd> OptFixPSETaskBwd;
/// Forward mandatory flexible task view
typedef ManFlexTask ManFlexTaskFwd;
/// Backward (dual) mandatory flexible task view
typedef FwdToBwd<ManFlexTaskFwd> ManFlexTaskBwd;
/// Forward optional flexible task view
typedef OptFlexTask OptFlexTaskFwd;
/// Backward (dual) optional flexible task view
typedef FwdToBwd<OptFlexTaskFwd> OptFlexTaskBwd;
/**
* \brief Print backward task view in format est:p:lct
* \relates ManFixPTaskBwd
*/
template<class Char, class Traits>
std::basic_ostream<Char,Traits>&
operator <<(std::basic_ostream<Char,Traits>& os, const ManFixPTaskBwd& t);
/**
* \brief Print backward task view in format est:p:lct
* \relates ManFixPSETaskBwd
*/
template<class Char, class Traits>
std::basic_ostream<Char,Traits>&
operator <<(std::basic_ostream<Char,Traits>& os, const ManFixPSETaskBwd& t);
/**
* \brief Print optional backward task view in format est:p:lct:m
* \relates OptFixPTaskBwd
*/
template<class Char, class Traits>
std::basic_ostream<Char,Traits>&
operator <<(std::basic_ostream<Char,Traits>& os, const OptFixPTaskBwd& t);
/**
* \brief Print optional backward task view in format est:p:lct:m
* \relates OptFixPSETaskBwd
*/
template<class Char, class Traits>
std::basic_ostream<Char,Traits>&
operator <<(std::basic_ostream<Char,Traits>& os, const OptFixPSETaskBwd& t);
}}}
#include <gecode/int/cumulative/task-view.hpp>
namespace Gecode { namespace Int {
/// Task view traits for forward task views
template<>
class TaskViewTraits<Cumulative::ManFixPTaskFwd> {
public:
/// The task type
typedef Cumulative::ManFixPTask Task;
};
/// Task view traits for backward task views
template<>
class TaskViewTraits<Cumulative::ManFixPTaskBwd> {
public:
/// The task type
typedef Cumulative::ManFixPTask Task;
};
/// Task view traits for forward task views
template<>
class TaskViewTraits<Cumulative::ManFixPSETaskFwd> {
public:
/// The task type
typedef Cumulative::ManFixPSETask Task;
};
/// Task view traits for backward task views
template<>
class TaskViewTraits<Cumulative::ManFixPSETaskBwd> {
public:
/// The task type
typedef Cumulative::ManFixPSETask Task;
};
/// Task view traits for forward optional task views
template<>
class TaskViewTraits<Cumulative::OptFixPTaskFwd> {
public:
/// The task type
typedef Cumulative::OptFixPTask Task;
};
/// Task view traits for backward task views
template<>
class TaskViewTraits<Cumulative::OptFixPTaskBwd> {
public:
/// The task type
typedef Cumulative::OptFixPTask Task;
};
/// Task view traits for forward optional task views
template<>
class TaskViewTraits<Cumulative::OptFixPSETaskFwd> {
public:
/// The task type
typedef Cumulative::OptFixPSETask Task;
};
/// Task view traits for backward task views
template<>
class TaskViewTraits<Cumulative::OptFixPSETaskBwd> {
public:
/// The task type
typedef Cumulative::OptFixPSETask Task;
};
/// Task view traits for forward task views
template<>
class TaskViewTraits<Cumulative::ManFlexTaskFwd> {
public:
/// The task type
typedef Cumulative::ManFlexTask Task;
};
/// Task view traits for backward task views
template<>
class TaskViewTraits<Cumulative::ManFlexTaskBwd> {
public:
/// The task type
typedef Cumulative::ManFlexTask Task;
};
/// Task view traits for forward optional task views
template<>
class TaskViewTraits<Cumulative::OptFlexTaskFwd> {
public:
/// The task type
typedef Cumulative::OptFlexTask Task;
};
/// Task view traits for backward task views
template<>
class TaskViewTraits<Cumulative::OptFlexTaskBwd> {
public:
/// The task type
typedef Cumulative::OptFlexTask Task;
};
/// Task traits for mandatory fixed tasks
template<>
class TaskTraits<Cumulative::ManFixPTask> {
public:
/// The forward task view type
typedef Cumulative::ManFixPTaskFwd TaskViewFwd;
/// The backward task view type
typedef Cumulative::ManFixPTaskBwd TaskViewBwd;
/// The corresponding unary task type
typedef Unary::ManFixPTask UnaryTask;
};
/// Task traits for mandatory fixed tasks
template<>
class TaskTraits<Cumulative::ManFixPSETask> {
public:
/// The forward task view type
typedef Cumulative::ManFixPSETaskFwd TaskViewFwd;
/// The backward task view type
typedef Cumulative::ManFixPSETaskBwd TaskViewBwd;
/// The corresponding unary task type
typedef Unary::ManFixPSETask UnaryTask;
};
/// Task traits for optional fixed tasks
template<>
class TaskTraits<Cumulative::OptFixPTask> {
public:
/// The forward task view type
typedef Cumulative::OptFixPTaskFwd TaskViewFwd;
/// The backward task view type
typedef Cumulative::OptFixPTaskBwd TaskViewBwd;
/// The corresponding mandatory task
typedef Cumulative::ManFixPTask ManTask;
/// The corresponding unary task type
typedef Unary::OptFixPTask UnaryTask;
};
/// Task traits for optional fixed tasks
template<>
class TaskTraits<Cumulative::OptFixPSETask> {
public:
/// The forward task view type
typedef Cumulative::OptFixPSETaskFwd TaskViewFwd;
/// The backward task view type
typedef Cumulative::OptFixPSETaskBwd TaskViewBwd;
/// The corresponding mandatory task
typedef Cumulative::ManFixPSETask ManTask;
/// The corresponding unary task type
typedef Unary::OptFixPSETask UnaryTask;
};
/// Task traits for mandatory flexible tasks
template<>
class TaskTraits<Cumulative::ManFlexTask> {
public:
/// The forward task view type
typedef Cumulative::ManFlexTaskFwd TaskViewFwd;
/// The backward task view type
typedef Cumulative::ManFlexTaskBwd TaskViewBwd;
/// The corresponding unary task type
typedef Unary::ManFlexTask UnaryTask;
};
/// Task traits for optional flexible tasks
template<>
class TaskTraits<Cumulative::OptFlexTask> {
public:
/// The forward task view type
typedef Cumulative::OptFlexTaskFwd TaskViewFwd;
/// The backward task view type
typedef Cumulative::OptFlexTaskBwd TaskViewBwd;
/// The corresponding mandatory task
typedef Cumulative::ManFlexTask ManTask;
/// The corresponding unary task type
typedef Unary::OptFlexTask UnaryTask;
};
}}
namespace Gecode { namespace Int { namespace Cumulative {
/// Node for an omega tree
class OmegaNode {
public:
/// Energy for subtree
long long int e;
/// Energy envelope for subtree
long long int env;
/// Initialize node from left child \a l and right child \a r
void init(const OmegaNode& l, const OmegaNode& r);
/// Update node from left child \a l and right child \a r
void update(const OmegaNode& l, const OmegaNode& r);
};
/// Omega trees for computing ect of task sets
template<class TaskView>
class OmegaTree : public TaskTree<TaskView,OmegaNode> {
protected:
using TaskTree<TaskView,OmegaNode>::tasks;
using TaskTree<TaskView,OmegaNode>::leaf;
using TaskTree<TaskView,OmegaNode>::root;
using TaskTree<TaskView,OmegaNode>::init;
using TaskTree<TaskView,OmegaNode>::update;
/// Capacity
int c;
public:
/// Initialize tree for tasks \a t and capacity \a c
OmegaTree(Region& r, int c, const TaskViewArray<TaskView>& t);
/// Insert task with index \a i
void insert(int i);
/// Remove task with index \a i
void remove(int i);
/// Return energy envelope of all tasks
long long int env(void) const;
};
/// Node for an extended omega tree
class ExtOmegaNode : public OmegaNode {
public:
/// Energy envelope for subtree
long long int cenv;
/// Initialize node from left child \a l and right child \a r
void init(const ExtOmegaNode& l, const ExtOmegaNode& r);
/// Update node from left child \a l and right child \a r
void update(const ExtOmegaNode& l, const ExtOmegaNode& r);
};
/// Omega trees for computing ect of task sets
template<class TaskView>
class ExtOmegaTree : public TaskTree<TaskView,ExtOmegaNode> {
protected:
using TaskTree<TaskView,ExtOmegaNode>::tasks;
using TaskTree<TaskView,ExtOmegaNode>::leaf;
using TaskTree<TaskView,ExtOmegaNode>::root;
using TaskTree<TaskView,ExtOmegaNode>::init;
using TaskTree<TaskView,ExtOmegaNode>::update;
using TaskTree<TaskView,ExtOmegaNode>::node;
using TaskTree<TaskView,ExtOmegaNode>::n_leaf;
using TaskTree<TaskView,ExtOmegaNode>::n_left;
using TaskTree<TaskView,ExtOmegaNode>::left;
using TaskTree<TaskView,ExtOmegaNode>::n_right;
using TaskTree<TaskView,ExtOmegaNode>::right;
using TaskTree<TaskView,ExtOmegaNode>::n_root;
using TaskTree<TaskView,ExtOmegaNode>::n_parent;
using TaskTree<TaskView,ExtOmegaNode>::n_nodes;
using TaskTree<TaskView,ExtOmegaNode>::_leaf;
/// Capacity
int c, ci;
public:
/// Initialize tree for tasks \a t and capacity \a c
template<class Node>
ExtOmegaTree(Region& r, int c, const TaskTree<TaskView,Node>& t);
/// Initialize tasks for current capacity \a ci
void init(int ci);
/// Compute update for task with index \a i
long long int env(int i);
};
/// Node for an omega lambda tree
class OmegaLambdaNode : public OmegaNode {
public:
/// Undefined task
static const int undef = -1;
/// Energy for subtree
long long int le;
/// Energy envelope for subtree
long long int lenv;
/// Node which is responsible for le
int resLe;
/// Node which is responsible for lenv
int resLenv;
/// Initialize node from left child \a l and right child \a r
void init(const OmegaLambdaNode& l, const OmegaLambdaNode& r);
/// Update node from left child \a l and right child \a r
void update(const OmegaLambdaNode& l, const OmegaLambdaNode& r);
};
/// Omega-lambda trees for computing ect of task sets
template<class TaskView>
class OmegaLambdaTree : public TaskTree<TaskView,OmegaLambdaNode> {
protected:
using TaskTree<TaskView,OmegaLambdaNode>::tasks;
using TaskTree<TaskView,OmegaLambdaNode>::leaf;
using TaskTree<TaskView,OmegaLambdaNode>::root;
using TaskTree<TaskView,OmegaLambdaNode>::init;
using TaskTree<TaskView,OmegaLambdaNode>::update;
/// Capacity
int c;
public:
/// Initialize tree for tasks \a t and capcity \a c with all tasks included in omega
OmegaLambdaTree(Region& r, int c, const TaskViewArray<TaskView>& t);
/// Shift task with index \a i from omega to lambda
void shift(int i);
/// Remove task with index \a i from lambda
void lremove(int i);
/// Whether has responsible task
bool lempty(void) const;
/// Return responsible task
int responsible(void) const;
/// Return energy envelope of all tasks
long long int env(void) const;
/// Return energy envelope of all tasks excluding lambda tasks
long long int lenv(void) const;
};
}}}
#include <gecode/int/cumulative/tree.hpp>
namespace Gecode { namespace Int { namespace Cumulative {
/// Check for subsumption (all tasks must be assigned)
template<class Task>
ExecStatus
subsumed(Space& home, Propagator& p, int c, TaskArray<Task>& t);
/// Check mandatory tasks \a t for overload
template<class ManTask>
ExecStatus overload(Space& home, int c, TaskArray<ManTask>& t);
/// Perform time-tabling propagation
template<class Task, class Cap>
ExecStatus timetabling(Space& home, Propagator& p, Cap c,
TaskArray<Task>& t);
/// Propagate by edge-finding
template<class Task>
ExecStatus edgefinding(Space& home, int c, TaskArray<Task>& t);
/**
* \brief Scheduling propagator for cumulative resource with mandatory tasks
*
* Requires \code #include <gecode/int/cumulative.hh> \endcode
* \ingroup FuncIntProp
*/
template<class ManTask, class Cap, class PL>
class ManProp : public TaskProp<ManTask,PL> {
protected:
using TaskProp<ManTask,PL>::t;
/// Resource capacity
Cap c;
/// Constructor for creation
ManProp(Home home, Cap c, TaskArray<ManTask>& t);
/// Constructor for cloning \a p
ManProp(Space& home, ManProp& p);
public:
/// Perform copying during cloning
virtual Actor* copy(Space& home);
/// Perform propagation
virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
/// Post propagator that schedules tasks on cumulative resource
static ExecStatus post(Home home, Cap c, TaskArray<ManTask>& t);
/// Delete propagator and return its size
virtual size_t dispose(Space& home);
};
/**
* \brief Scheduling propagator for cumulative resource with optional tasks
*
* Requires \code #include <gecode/int/cumulative.hh> \endcode
* \ingroup FuncIntProp
*/
template<class OptTask, class Cap, class PL>
class OptProp : public TaskProp<OptTask,PL> {
protected:
using TaskProp<OptTask,PL>::t;
/// Resource capacity
Cap c;
/// Constructor for creation
OptProp(Home home, Cap c, TaskArray<OptTask>& t);
/// Constructor for cloning \a p
OptProp(Space& home, OptProp& p);
public:
/// Perform copying during cloning
virtual Actor* copy(Space& home);
/// Perform propagation
virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
/// Post propagator that schedules tasks on cumulative resource
static ExecStatus post(Home home, Cap c, TaskArray<OptTask>& t);
/// Delete propagator and return its size
virtual size_t dispose(Space& home);
};
/// Post mandatory task propagator according to propagation level
template<class ManTask, class Cap>
ExecStatus
cmanpost(Home home, Cap c, TaskArray<ManTask>& t, IntPropLevel ipl);
/// Post optional task propagator according to propagation level
template<class OptTask, class Cap>
ExecStatus
coptpost(Home home, Cap c, TaskArray<OptTask>& t, IntPropLevel ipl);
}}}
#include <gecode/int/cumulative/time-tabling.hpp>
#include <gecode/int/cumulative/subsumption.hpp>
#include <gecode/int/cumulative/overload.hpp>
#include <gecode/int/cumulative/edge-finding.hpp>
#include <gecode/int/cumulative/man-prop.hpp>
#include <gecode/int/cumulative/opt-prop.hpp>
#include <gecode/int/cumulative/post.hpp>
#endif
// STATISTICS: int-prop