#include <chuffed/core/propagator.h>
#include <list>
#include <queue>
#include <set>
#include <iostream>

using namespace std;

#define CUMUVERB 0

	// Data types for the Chuffed solver
#define CUMU_ARR_INTVAR vec<IntVar*>
#define CUMU_MATRIX_INT vec<vec<int> >
#define CUMU_ARR_INT vec<int>
#define CUMU_INTVAR IntVar*
#define CUMU_INT int
#define CUMU_BOOL bool
#define CUMU_GETMIN(x) x.getMin()
#define CUMU_GETMAX(x) x.getMax()
#define CUMU_GETMAX0(x) x.getMax()
#define CUMU_PT_GETMIN(x) x->getMin()
#define CUMU_PT_GETMAX(x) x->getMax()
#define CUMU_PT_GETMIN0(x) x->getMin0()
#define CUMU_PT_GETMAX0(x) x->getMax0()
#define CUMU_PT_ISFIXED(x) x->isFixed()

#define CUMU_MEMCHECK(ptr) do { if (ptr == NULL) CHUFFED_ERROR("Out of memory!\n"); } while(0)


class CumulativeCalProp : public Propagator {
	enum ExplDeg {
		ED_NAIVE,
		ED_NORMAL,
		ED_LIFT
	};
	// Task-Duration tuple
	struct TaskDur {
		int task;
		int dur_in;
		TaskDur(int _task, int _dur_in) : task(_task), dur_in(_dur_in) {}
	};
	// TTEF Update Structure
	struct TTEFUpdate {
		int task;
		int bound_new;
		int tw_begin;
		int tw_end;
		bool is_lb_update;
		TTEFUpdate(int _t, int _n, int _b, int _e, int _l) : task(_t), bound_new(_n), 
			tw_begin(_b), tw_end(_e), is_lb_update(_l) {}
	};
	// Compulsory Part of a Task
	struct CompPart {
		CUMU_INT begin;
		CUMU_INT end;
		CUMU_INT level;
		CUMU_INT task;
		CompPart(CUMU_INT b, CUMU_INT e, CUMU_INT l, CUMU_INT t)
		: begin(b), end(e), level(l), task(t) {}
	};

	// Resource profile of the resource
	struct ProfilePart {
		CUMU_INT begin;
		CUMU_INT end;
		CUMU_INT level;
		set<CUMU_INT> tasks;
		ProfilePart(CUMU_INT b, CUMU_INT e, CUMU_INT l, CUMU_INT t)
		: begin(b), end(e), level(l) { tasks.insert(t); };
		ProfilePart() : begin(0), end(0), level(0) {}
	};

	enum ProfileChange { PROFINC, PROFDEC };
	struct ProfileChangePt {
		CUMU_INT time;
		ProfileChange change;
		ProfileChangePt(CUMU_INT t, ProfileChange c) : time(t), change(c) {}
	};

	Tint last_unfixed;

public:
    string name; // Name of the cumulative constraint for printing statistics

	// Constant Data
	CUMU_ARR_INTVAR	start;	// Start time variables of the tasks
	CUMU_ARR_INTVAR	dur;	// Durations of the tasks
	CUMU_ARR_INTVAR	usage;	// Resource usage of the tasks
	CUMU_INTVAR	    limit;	// Resource capacity of the resource
	CUMU_MATRIX_INT calendar2; //Different calendars of the project
	CUMU_ARR_INT taskCalendar; //Number of calendar that task depends on
	CUMU_INT rho; //=1 if resource stays engaged, =0 otherwise
	CUMU_INT resCalendar; //TTEF_cal: Number of calendar that resource depends on
	int ** calendar;
	int ** workingPeriods;

	const int minTime;		// Minimal time in the calendar
	const int maxTime;		// Maximal time in the calendar


	// Options
	const CUMU_BOOL	idem;	// Whether the cumulative propagator should be idempotent
	const CUMU_BOOL	tt_check;
	CUMU_BOOL	tt_filt;	// Timetabling bounds filtering of the start times
	CUMU_BOOL	ttef_check;	// Timetabling-edge-finding consistency check
	CUMU_BOOL	ttef_filt;	// Timetabling-edge-finding filtering of the start times
	const CUMU_BOOL	tteef_filt;	// Opportunistic timetabling-extended-edge-finding filtering of the start times
	long ttef_prop_factor;

	ExplDeg     ttef_expl_deg;

    // Counters
    long nb_tt_incons;      // Number of timetabling inconsistencies
    long nb_tt_filt;        // Number of timetabling propagations
    long nb_ttef_incons;    // Number of timetabling-edge-finding inconsistencies
    long nb_ttef_filt;      // Number of timetabling-edge-finding propagations
	long nb_prop_calls;
	long nb_ttefc_calls;
	long nb_ttefc_steps;
	long nb_ttef_lb_calls;
	long nb_ttef_ub_calls;

	// Parameters
	CUMU_BOOL	bound_update;

	// Structures
	CUMU_ARR_INT task_id;		// Unfixed tasks on the left-hand side and fixed tasks on the right-hand size
	int * task_id_est;
	int * task_id_lct;
	int * tt_after_est;
	int * tt_after_lct;
	int * new_est;
	int * new_lct;
	int tt_profile_size;
	struct ProfilePart * tt_profile;

	int * est_2;
	int * lst_2;
	int * ect_2;
	int * lct_2;
	int * min_energy2;
	Tint * min_energy2_global;
	int * free_energy2;

	// Inline functions
	struct SortEstAsc {
		CumulativeCalProp *p;
		bool operator() (int i, int j) { return p->est_2[i] < p->est_2[j]; }
		SortEstAsc(CumulativeCalProp *_p) : p(_p) {}
	} sort_est_asc;

	struct SortLctAsc {
		CumulativeCalProp *p;
		bool operator() (int i, int j) { return p->lct_2[i] < p->lct_2[j]; }
		SortLctAsc(CumulativeCalProp *_p) : p(_p) {}
	} sort_lct_asc;

	// Constructor
	CumulativeCalProp(CUMU_ARR_INTVAR & _start, CUMU_ARR_INTVAR & _dur, CUMU_ARR_INTVAR & _usage, 
			CUMU_INTVAR _limit, CUMU_MATRIX_INT & _cal, CUMU_ARR_INT & _taskCal, CUMU_INT _rho, CUMU_INT _resCalendar,
            list<string> opt)
	: name(""), start(_start), dur(_dur), usage(_usage), limit(_limit), 
		calendar2(_cal), taskCalendar(_taskCal), rho(_rho), resCalendar(_resCalendar),
		minTime(0), maxTime(calendar2[0].size() - 1),
		idem(false), tt_check(true), tt_filt(true), ttef_check(true), ttef_filt(true), tteef_filt(false),
		ttef_prop_factor(100),
        nb_tt_incons(0), nb_tt_filt(0), nb_ttef_incons(0), nb_ttef_filt(0), 
		nb_prop_calls(0), nb_ttefc_calls(0), nb_ttefc_steps(0), nb_ttef_lb_calls(0), nb_ttef_ub_calls(0),
		bound_update(false),
		sort_est_asc(this), sort_lct_asc(this)
	{
		// Some checks
		rassert(!tteef_filt || ttef_filt);
        
        // Overriding option defaults
        for (list<string>::iterator it = opt.begin(); it != opt.end(); it++) {
            if (!(*it).compare("tt_filt_on")) 
                tt_filt = true;
            else if (!(*it).compare("tt_filt_off")) 
                tt_filt = false;
            if (!(*it).compare("ttef_check_on"))
                ttef_check = true;
            else if (!(*it).compare("ttef_check_off"))
                ttef_check = false;
            if (!(*it).compare("ttef_filt_on"))
                ttef_filt = true;
            else if (!(*it).compare("ttef_filt_off"))
                ttef_filt = false;
            else if ((*it).find("__name__") == 0)
                name = (*it).substr(8);
        }

		// Creating a copy of the calendars
		calendar = (int **) malloc(calendar2.size() * sizeof(int *));
		for(int i = 0; i < calendar2.size(); i++){
			calendar[i] = (int *) malloc(calendar2[0].size() * sizeof(int));
		}
		
		for(int i = 0; i < calendar2.size(); i++){
			for(int j = 0; j < calendar2[0].size(); j++){
				calendar[i][j]=calendar2[i][j];
			}
		}

		// Memory allocation for the working periods
		workingPeriods = (int **) malloc(calendar2.size() * sizeof(int *));
		CUMU_MEMCHECK(workingPeriods);
		for(int i = 0; i < calendar2.size(); i++){
			workingPeriods[i] = (int *) malloc(calendar2[0].size() * sizeof(int));
			CUMU_MEMCHECK(workingPeriods[i]);
		}
	
		// Initialisation of the working periods
		for(int i = 0; i < calendar2.size(); i++){
			workingPeriods[i][calendar2[0].size()-1] = calendar[i][calendar2[0].size()-1];
			for(int j = calendar2[0].size()-2; j >= 0; j--){
				workingPeriods[i][j] = workingPeriods[i][j+1] + calendar[i][j];
			}
		}

		// Explanation options
		//ttef_expl_deg = ED_NAIVE;
		//ttef_expl_deg = ED_NORMAL;	// TODO Not adjusted to calendars yet
		ttef_expl_deg = ED_LIFT;

		// Allocation of the memory
		tt_profile = new ProfilePart[calendar2[0].size()];                     //[2 * start.size()];
		tt_profile_size = 0;

		// Memory allocation of the core structures
		est_2 = (int *) malloc(start.size() * sizeof(int));
		lst_2 = (int *) malloc(start.size() * sizeof(int));
		ect_2 = (int *) malloc(start.size() * sizeof(int));
		lct_2 = (int *) malloc(start.size() * sizeof(int));
		
		// Memory check
		CUMU_MEMCHECK(est_2);
		CUMU_MEMCHECK(lst_2);
		CUMU_MEMCHECK(ect_2);
		CUMU_MEMCHECK(lct_2);
		
		// Allocating memory required by the TTEF inconsistency check or
		// filtering algorithm
		if (ttef_check || ttef_filt) {
			// Memory allocation
			task_id_est  = (int *) malloc(start.size() * sizeof(int));
			task_id_lct  = (int *) malloc(start.size() * sizeof(int));
			tt_after_est = (int *) malloc(start.size() * sizeof(int));
			tt_after_lct = (int *) malloc(start.size() * sizeof(int));
			min_energy2   = (int *) malloc(start.size() * sizeof(int));
			min_energy2_global = (Tint *) malloc(start.size() * sizeof(Tint));
			free_energy2  = (int *) malloc(start.size() * sizeof(int));
			
			// Memory check
			CUMU_MEMCHECK(task_id_est);
			CUMU_MEMCHECK(task_id_lct);
			CUMU_MEMCHECK(tt_after_est);
			CUMU_MEMCHECK(tt_after_lct);
			CUMU_MEMCHECK(min_energy2);
			CUMU_MEMCHECK(min_energy2_global);
			CUMU_MEMCHECK(free_energy2);

			// Allocating memory only required by the TTEF filtering
			// algorithms
			if (ttef_filt) {
				// Memory allocation
				new_est = (int *) malloc(start.size() * sizeof(int));
				new_lct = (int *) malloc(start.size() * sizeof(int));
				
				// Memory check
				CUMU_MEMCHECK(new_est);
				CUMU_MEMCHECK(new_lct);
			} else {
				new_est = NULL;
				new_lct = NULL;
			}

			// Initialisation of some arrays
			for (int i = 0; i < start.size(); i++)
				min_energy2_global[i] = min_dur(i);
		} else {
			task_id_est  = NULL;
			task_id_lct  = NULL;
			tt_after_est = NULL;
			tt_after_lct = NULL;
			min_energy2   = NULL;
			min_energy2_global = NULL;
			free_energy2  = NULL;
		}
		
		// Priority of the propagator
		priority = 3;

#if CUMUVERB>1
		fprintf(stderr, "\tCumulative with n = %d\n", start.size());
#endif
        // Attach to var events
		for (int i = 0; i < start.size(); i++) {
#if CUMUVERB>1
			fprintf(stderr, "\t%d: %p\n", i, start[i]);
#endif
			start[i]->attach(this, i, EVENT_LU);
			if (min_dur(i) < max_dur(i)) dur[i]->attach(this, i, EVENT_LF);
            if (min_usage(i) < max_usage(i)) usage[i]->attach(this, i, EVENT_LF);
		}
		limit->attach(this, start.size(), EVENT_UF);
	
		for (int i = 0; i < start.size(); i++) {
			task_id.push(i);
		}
		last_unfixed = start.size() - 1;
	}

	// Statistics
	void printStats() {
        fprintf(stderr, "%% Cumulative propagator with calendars statistics");
        if (name != "")
            cerr << " for " << name;
        fprintf(stderr, ":\n");
        fprintf(stderr, "%%\t#TT incons.: %ld\n", nb_tt_incons);
        if (tt_filt) 
            fprintf(stderr, "%%\t#TT prop.: %ld\n", nb_tt_filt);
        if (ttef_check || ttef_filt)
            fprintf(stderr, "%%\t#TTEF incons.: %ld\n", nb_ttef_incons);
		if (ttef_check && !ttef_filt) {
			fprintf(stderr, "%%\t#TTEF calls: %ld\n", nb_ttefc_calls);
			fprintf(stderr, "%%\t#TTEF cons. steps: %ld\n", nb_ttefc_steps);
		}
        if (ttef_filt) {
            fprintf(stderr, "%%\t#TTEF prop.: %ld\n", nb_ttef_filt);
			fprintf(stderr, "%%\t#TTEF LB calls: %ld\n", nb_ttef_lb_calls);
			fprintf(stderr, "%%\t#TTEF UB calls: %ld\n", nb_ttef_ub_calls);
		}
    }


	/**
	 * Retrieval of parameters
	 **/

	int
	getEndTimeForStartTime(const int i, const int start, const int duration) {
		const int cal_idx = taskCalendar[i] - 1;
		int end = start + duration;
		if (end <= maxTime) {
			int workDays;
			do {
				workDays = workingPeriods[cal_idx][start] - workingPeriods[cal_idx][end];
				end += duration - workDays;
			} while (workDays < duration && end <= maxTime);
			assert(workDays == duration || end > maxTime);
		}
		if (end > maxTime) {
			end = maxTime + duration - (workingPeriods[cal_idx][start] - workingPeriods[cal_idx][maxTime]);
		}
		return end;
	}

	int
	getStartTimeForEndTime(const int i, const int end, const int duration) {
		const int cal_idx = taskCalendar[i] - 1;
		int start = end - duration;
		if (start >= minTime) {
			int workDays;
			do {
				workDays = workingPeriods[cal_idx][start] - workingPeriods[cal_idx][end];
				start -= duration - workDays;
			} while (workDays < duration && start >= minTime);
			assert(workDays == duration || start < minTime);
		}
		if (start < minTime) {
			start = minTime - duration + (workingPeriods[cal_idx][minTime] - workingPeriods[cal_idx][end]);
		}
		return start;
	}

	void
	retrieveCoreParameters(int i) {
		// Earliest start time
		est_2[i] = CUMU_PT_GETMIN(start[i]);
		// Latest start time
		lst_2[i] = CUMU_PT_GETMAX(start[i]);
		// Earliest completion time
		const int duration = CUMU_PT_GETMIN(dur[i]);
		ect_2[i] = getEndTimeForStartTime(i, est_2[i], duration);
		// Latest completion time
		lct_2[i] = getEndTimeForStartTime(i, lst_2[i], duration);
	}

	int
	retrieveMinEnergy(const int i) {
		int minEn = 0;
		if (rho == 0) {
			// Resource is released
			return minEn = min_usage(i) * min_dur(i);
		} 
		assert(rho == 1);
		// Resource stays engaged
		const int duration = min_dur(i);
		const int cal_idx = taskCalendar[i] - 1;
		const int ls = lst_2[i];
		// Calculate distance when task starts as earliest as possible
		int end = est_2[i] + duration;
		int workDays;
		int distance;
		do {
			workDays = workingPeriods[cal_idx][est_2[i]] - workingPeriods[cal_idx][end];
			end += duration - workDays;
		} while (workDays < duration);
		assert(workDays == duration);
		distance = end - est_2[i];
		// Calculate minimal distance
		for (int time = est_2[i] + 1; time <= ls && distance > min_energy2_global[i]; time++) {
			if (calendar[cal_idx][time - 1] == 1)
				workDays--;
			while (workDays < duration) {
				if (calendar[cal_idx][end] == 1)
					workDays++;
				end++;
			}
			assert(workDays == duration);
			distance = min(distance, end - time);
		}
		if (distance > min_energy2_global[i])
			min_energy2_global[i] = distance;
		return min_usage(i) * distance;
	}

	int
	retrieveFreeEnergy(const int i) {
		if (rho == 1) { 
			// Resource stays engaged
			return (min_energy2[i] - min_usage(i) * max(0, ect_2[i] - lst_2[i])); 
		} else { 
			// Resource is released
			int workDays = workingPeriods[taskCalendar[i]-1][lst_2[i]] - workingPeriods[taskCalendar[i]-1][ect_2[i]];
			return (min_energy2[i] - min_usage(i) * max(0, workDays)); 
		}
	}

	void
	retrieveEnergyParameters(const int i) {
		// NOTE it is assumpted that the arrays est_2, lst_2, ect_2, and lct_2 are up to date!
		// Minimal required energy for executing the task
		min_energy2[i] = retrieveMinEnergy(i);
		// Free energy
		free_energy2[i] = retrieveFreeEnergy(i);
	}

	/**
	 * Inline function for parameters of tasks
	 **/
		// Earliest start time of task i
	inline CUMU_INT 
	est(CUMU_INT i) { return CUMU_PT_GETMIN(start[i]); }
		// Latest start time of task i
	inline CUMU_INT 
	lst(CUMU_INT i) { return CUMU_PT_GETMAX(start[i]); }
		// Earliest completion time of task i
	inline CUMU_INT 
	ect(CUMU_INT i) { 
		int t = CUMU_PT_GETMIN(start[i]);
		int j = 0;
		while(j < CUMU_PT_GETMIN(dur[i])){
			if(calendar[taskCalendar[i]-1][t]==1) { j++;  }
			t++;
		}
		return t; }
		// Latest completion time of task i
	inline CUMU_INT 
	lct(CUMU_INT i) { 
		int t = CUMU_PT_GETMAX(start[i]);
		int j = 0;
		while(j < CUMU_PT_GETMIN(dur[i])){
			if(calendar[taskCalendar[i]-1][t]==1) { j++;  }
			t++;
		}
		return t; }
		// Minimal resource usage of task i
	inline CUMU_INT
	min_usage(CUMU_INT i) { return CUMU_PT_GETMIN(usage[i]); }
		// Minimal energy of task i
		// TTEF_cal: We could consider min_execution_time here, but computation is expensive
	inline CUMU_INT
	min_energy(CUMU_INT i) { 
		if(rho == 0) {  // TTEF_cal: resource is used exactly for p_i time units
			return min_usage(i) * min_dur(i); 
		}else{ // TTEF_cal: resource stays engaged during breaks / could be used more than p_i time units 
			int duration = min_dur(i);
			int t = est(i);
			int ls = lst(i);
			int distance = lct(i) - t;
			int j, tau, next;
			while(t <= ls) {
				tau = t;
				j = 0;
				next = ls+1;
				while(j < duration){
					if(calendar[taskCalendar[i]-1][t]==1) { 
						j++; 
					}else if(calendar[taskCalendar[i]-1][t+1]==1) {
						next = min(next, t+1);
					}
					t++;
				}
				distance = min(distance, t - tau);
				if(distance == duration) return min_usage(i) * duration;
				t = next;
			}
			return min_usage(i) * distance;
		}
	} 
		// Free Energy
	inline CUMU_INT
	free_energy(CUMU_INT i) {
		if (rho == 1) { 
			return (min_energy(i) - min_usage(i) * max(0, ect(i) - lst(i))); 
		} else { 
			int breaks = ect(i) - lst(i) - (workingPeriods[taskCalendar[i]-1][lst(i)] - workingPeriods[taskCalendar[i]-1][ect(i)]);
			return (min_energy(i) - min_usage(i) * max(0, ect(i) - lst(i) - breaks)); 
		}
	}

	/**
	 * Inline functions for receiving the minimum and maximum of integer
	 * variables
	 **/
	inline CUMU_INT
	min_start0(CUMU_INT i) { return CUMU_PT_GETMIN0(start[i]); }
	inline CUMU_INT
	max_start0(CUMU_INT i) { return CUMU_PT_GETMAX0(start[i]); }
	inline CUMU_INT
	min_dur(CUMU_INT i) { return CUMU_PT_GETMIN(dur[i]); }
	inline CUMU_INT
	max_dur(CUMU_INT i) { return CUMU_PT_GETMAX(dur[i]); }
	inline CUMU_INT
	min_dur0(CUMU_INT i) { return CUMU_PT_GETMIN0(dur[i]); }
	inline CUMU_INT
	max_usage(CUMU_INT i) { return CUMU_PT_GETMAX(usage[i]); }
	inline CUMU_INT
	min_usage0(CUMU_INT i) { return CUMU_PT_GETMIN0(usage[i]); }

	inline CUMU_INT
	min_limit() { return CUMU_PT_GETMIN(limit); }
	inline CUMU_INT
	max_limit() { return CUMU_PT_GETMAX(limit); }
	inline CUMU_INT
	max_limit0() { return CUMU_PT_GETMAX0(limit); }

	// TTEF Propagator
	// TTEF_cal: errors occurred when using shift_in function etc.; realized it with an integer shift_in
	//           if shift_in == 1 right shift is used; if shift_in == 2 left shift is used
	void 
	ttef_initialise_parameters();
	bool 
	ttef_consistency_check(int shift_in);
	bool 
	ttef_bounds_propagation(int shift_in1, int shift_in2);
	bool 
	ttef_bounds_propagation_lb(int shift_in, std::queue<TTEFUpdate> & update_queue);
	bool 
	ttef_bounds_propagation_ub(int shift_in, std::queue<TTEFUpdate> & update_queue);
	void
	tteef_bounds_propagation_lb(const int begin, const int end, const int en_avail, const int j,
		std::queue<TTEFUpdate> & update_queue);
	void
	tteef_bounds_propagation_ub(const int begin, const int end, const int en_avail, const int j,
		std::queue<TTEFUpdate> & update_queue);
	int
	ttef_get_new_start_time(const int begin, const int end, const int task, const int min_wdays_in);
	int
	ttef_get_new_end_time(const int begin, const int end, const int task, const int min_wdays_in);
	bool 
	ttef_update_bounds(int shift_in, 
			std::queue<TTEFUpdate> & queue_update);
	void
	ttef_explanation_for_update_lb(int shift_in, const int begin, const int end, const int task, 
		int & bound, vec<Lit> & expl);
	void
	ttef_explanation_for_update_ub(int shift_in, const int begin, const int end, const int task, 
		int & bound, vec<Lit> & expl);

	int
	ttef_retrieve_tasks(int shift_in, 
		int begin, int end, int fb_id, list<TaskDur> & tasks_tw, list<TaskDur> & tasks_cp);

		// TTEF Generation of explanations
		// TTEF_cal: consider breaks between begin and end
	void
	ttef_analyse_limit_and_tasks(const int begin, const int end, const int breaks, list<TaskDur> & tasks_tw,
		list<TaskDur> & tasks_cp, int & en_lift, vec<Lit> & expl);
	void
	ttef_analyse_tasks(const int begin, const int end, list<TaskDur> & tasks, int & en_lift, vec<Lit> & expl);
	int 
	ttef_analyse_tasks_left_shift(const int begin, const int end, const int dur_in, const int task, const int max_dur_lift, int & last_dur);
	int
	ttef_analyse_tasks_right_shift(const int begin, const int end, const int dur_in, const int task, const int max_dur_lift, int & last_dur);
	bool
	ttef_analyse_tasks_check_expl_lb(const int begin, const int end, const int task, const int dur_in, const int expl_ub);
	bool
	ttef_analyse_tasks_check_expl_ub(const int begin, const int end, const int task, const int dur_in, const int expl_ub);

	inline bool
	is_intersecting(const int begin1, const int end1, const int begin2, const int end2);


	inline int
	get_free_dur_right_shift2(const int tw_begin, const int tw_end, const int task)
	{
		if (tw_begin > est_2[task] || tw_end <= lst_2[task] || tw_end <= ect_2[task])
			return 0;
		const int free_lst = (lst_2[task] < ect_2[task] ? ect_2[task] : lst_2[task]);
		if (rho == 0) {
			// Resource is released
			const int cal_idx = taskCalendar[task] - 1;
			const int workingDays = workingPeriods[cal_idx][free_lst] - workingPeriods[cal_idx][tw_end];
			return workingDays;
		} else {
			// Resource stays engaged
			return (tw_end - free_lst);
		}
	}

	inline int
	get_free_dur_left_shift2(const int tw_begin, const int tw_end, const int task)
	{
		if (tw_end < lct_2[task] || tw_begin >= ect_2[task] || tw_begin >= lst_2[task])
			return 0;
		const int free_ect = (lst_2[task] < ect_2[task] ? lst_2[task] : ect_2[task]);
		if (rho == 0) {
			// Resource is released
			const int * wPeriods = workingPeriods[taskCalendar[task] - 1];
			const int workingDays = wPeriods[tw_begin] - wPeriods[free_ect];
			return workingDays;
		} else {
			// Resource stays engaged
			return (free_ect - tw_begin);
		}
	}

	inline int
	get_no_shift(const int tw_begin, const int tw_end, const int est, const int ect, 
		const int lst, const int lct, const int dur_fixed_in, const int task)
	{ 
		return 0;
	}

	// Cumulative Propagator
	CUMU_BOOL 
	propagate() {
#if CUMUVERB>1
		fprintf(stderr, "Entering cumulative propagation\n");
#endif
		assert(last_unfixed >= 0);
		// Retrieval of the task's core data and updating
		// the fixed-task array
		int new_unfixed = last_unfixed;
		int tw_begin = maxTime;
		int tw_end = minTime;
		for (int ii = new_unfixed; ii >= 0; ii--) {
			const int i = task_id[ii];
			// Retrieve core data (est, lst, ect, lct)
			if (min_dur(i) > 0 && min_usage(i) > 0)
				retrieveCoreParameters(i);
			// Compute the time window for consideration
			tw_begin = min(tw_begin, est_2[i]);
			tw_end   = max(tw_end, lct_2[i]);
			// Check whether the task 'i' is fixed
			if ((CUMU_PT_ISFIXED(start[i]) && CUMU_PT_ISFIXED(dur[i]) && CUMU_PT_ISFIXED(usage[i])) || max_dur(i) <= 0 || max_usage(i) <= 0) {
				// Swaping the id's
				task_id[ii] = task_id[new_unfixed];
				task_id[new_unfixed] = i;
				new_unfixed--;
				if (min_energy2 != NULL && min_dur(i) > 0 && min_usage(i) > 0) {
					free_energy2[i] = 0;
					if (rho == 1) {
						// Resource stays engaged
						min_energy2[i] = min_usage(i) * (lct_2[i] - est_2[i]);
					} else {
						// Resource is released
						min_energy2[i] = min_usage(i) * min_dur(i);
					}
				}
			}
		}
		tw_begin = minTime;
		tw_end = maxTime;
		// Trailing the index of the last unfixed task
		last_unfixed = new_unfixed;
#if CUMUVERB>1
		fprintf(stderr, "\tEntering cumulative propagation loop\n");
#endif
		// idempotent
		do {
			bound_update = false;
			// Reseting the profile size
			tt_profile_size = 0;
			// Time-table propagators
			if (tt_check || tt_filt) {
				// Time-table propagation
				if (! time_table_propagation(task_id, tw_begin, tw_end) ) {
					// Inconsistency was detected
#if CUMUVERB > 1
					fprintf(stderr, "Leaving cumulative propagation with failure\n");
#endif
					return false;
				}
			}
			//if (!bound_update)
			//	nb_prop_calls++;
			// Time-table-edge-finding propagation
			if (!bound_update && last_unfixed > 0 && (ttef_check || ttef_filt)) { // && nb_prop_calls % 100 == 0) {
				nb_prop_calls++;	
				if (ttef_prop_factor != 0 && nb_prop_calls % ttef_prop_factor != 0)
					continue;
#if CUMUVERB > 0
		fprintf(stderr, "Entering TTEF\n");
#endif
				// Retrieval of the data required for the TTEF propagation
				for (int ii = 0; ii <= last_unfixed; ii++) {
					const int i = task_id[ii];
					retrieveEnergyParameters(i);
				}
				// Initialisation of necessary structures
				// - Unfixed tasks sorted according earliest start time
				// - Unfixed tasks sorted according latest completion time
				// - Energy of the compulsory parts after the latest completion 
				// 	 time of unfixed tasks
				// - Energy of the compulsory parts after the earliest start
				//   time of unfixed tasks
				ttef_initialise_parameters();
				
				// TTEF filtering algorithm
				if (ttef_filt) {
					if (!ttef_bounds_propagation(1, 2)) {
						// Inconsistency was detected
						return false;
					}
				} else {
#if CUMUVERB > 0
		fprintf(stderr, "Entering TTEF Consistency\n");
#endif
					if (!ttef_consistency_check(1)) {
						// Inconsistency was detected
						return false;
					}
#if CUMUVERB > 0
		fprintf(stderr, "Leaving TTEF Consistency\n");
#endif
				}
#if CUMUVERB > 0
		fprintf(stderr, "Leaving TTEF\n");
#endif
			}
		} while (idem && bound_update);
#if CUMUVERB > 0
		fprintf(stderr, "\tLeaving cumulative propagation loop\n");
		fprintf(stderr, "Leaving cumulative propagation without failure\n");
#endif
		return true;
	}

	// Comparison between two compulsory parts
	static bool
	compare_CompParts(CompPart cp1, CompPart cp2) {
		if (cp1.begin < cp2.begin) return true;
		if (cp1.begin > cp2.begin) return false;
		// ASSUMPTION
		// - cp1.begin == cp2.begin
		if (cp1.end < cp2.end) return true;
		if (cp1.end > cp2.end) return false;
		// ASSUMPTION
		// - cp1.end == cp2.end
		if (cp1.task < cp2.task) return true;
		return false;
	}


	// Creation of the resource profile for the time-table consistency check
	// and propagator
	CUMU_BOOL
	time_table_propagation(CUMU_ARR_INT & task, const int tw_begin, const int tw_end) {
		list<ProfileChangePt> changes;
		list<CUMU_INT> comp_task;
		//int size_profile = 0;
#if CUMUVERB>10
		fprintf(stderr, "\tCompulsory Parts ...\n");
#endif
		get_compulsory_parts2(changes, comp_task, task, 0, task.size(), tw_begin, tw_end);
		// Proceed if there are compulsory parts
		if (!changes.empty()) {
#if CUMUVERB>1
			fprintf(stderr, "\tSorting (size %d)...\n", (int) changes.size());
#endif
			// Sorting the start and end points of all the profile
			changes.sort(compare_ProfileChangePt);
#if CUMUVERB>1
			fprintf(stderr, "\tSorting (size %d)...\n", (int) changes.size());
#endif
			// Counting the number of different profiles
			tt_profile_size = count_profile(changes);
#if CUMUVERB>1
			fprintf(stderr, "\t#profile parts = %d\n", tt_profile_size);
#endif
#if CUMUVERB>1
			fprintf(stderr, "\tProfile Parts ...\n");
#endif
			// Creating the different profile parts
			create_profile(changes);
			int i_max_usage = 0;
#if CUMUVERB>1
			fprintf(stderr, "\tFilling of Profile Parts ...\n");
#endif
			// Filling the profile parts with tasks
			if (!fill_in_profile_parts(tt_profile, tt_profile_size, comp_task, i_max_usage)) {
				return false;
			}
#if CUMUVERB>10
			fprintf(stderr, "\tFiltering Resource Limit ...\n");
#endif
			// Filtering of resource limit variable
			if (!filter_limit(tt_profile, i_max_usage)) {
				return false;
			}
			if (tt_filt) {
#if CUMUVERB>10
				fprintf(stderr, "\tFiltering Start Times ...\n");
#endif
				// Time-table filtering
				if (!time_table_filtering(tt_profile, tt_profile_size, task, 0, last_unfixed, tt_profile[i_max_usage].level)) {
					return false;
				}
			}
		}
#if CUMUVERB>10
		fprintf(stderr, "\tEnd of time-table propagation ...\n");
#endif
		return true;
	}

	void
	get_compulsory_parts2(
		list<ProfileChangePt> &changes, list<CUMU_INT> &comp_task, CUMU_ARR_INT & task, 
		CUMU_INT i_start, CUMU_INT i_end, const int tw_begin, const int tw_end
	);

	// Sets for each profile part its begin and end time in chronological order
	// Runtime complexity: O(n)
	//
	void
	create_profile(list<ProfileChangePt> &changes) {
		list<ProfileChangePt>::iterator iter = changes.begin();
		int cur_profile = 0;
		int cur_time = iter->time;
		ProfileChange cur_change = iter->change;
		int no_starts = 1;
		for (; iter != changes.end(); iter++) {
			if (iter->time > cur_time && no_starts > 1) {
#if CUMUVERB>20
				fprintf(stderr, "Set times for profile part %d = [%d, %d)\n", cur_profile, cur_time, iter->time);
				fprintf(stderr, "\t%p; %p; %d\n", tt_profile, this, start.size());
#endif
				set_times_for_profile(cur_profile, cur_time, iter->time);
				cur_profile++;
			}
			no_starts += (iter->change == PROFINC ? 1 : -1);
			cur_change = iter->change;
			cur_time = iter->time;
		}
	}
	
	inline void
	set_times_for_profile(int i, CUMU_INT begin, CUMU_INT end) {
		tt_profile[i].begin = begin;
		tt_profile[i].end = end;
		tt_profile[i].level = 0;
		tt_profile[i].tasks.clear();
	}

	// Filling the profile parts with compulsory parts and checking for a resource
	// overload
	CUMU_BOOL
	fill_in_profile_parts(ProfilePart * profile, int size, list<CUMU_INT> comp_task, int & i_max_usage) {
		list<CUMU_INT>::iterator iter;
		int i = 0;
		CUMU_INT lst_i, ect_i;
		
#if CUMUVERB>2
		fprintf(stderr, "\t\tstart filling profiles (size %d)\n", size);
#endif
		for (iter = comp_task.begin(); iter != comp_task.end(); iter++) {
#if CUMUVERB>2
			fprintf(stderr, "\t\tcomp part = %d\n", *iter);
#endif
			lst_i = lst_2[*iter];
			ect_i = ect_2[*iter];
#if CUMUVERB>2
			fprintf(stderr, "\t\tFinding first profile part ; est: %d ; lst: %d ; ect: %d ; dur: %d\n",est_2[*iter],lst_i, ect_i, min_dur(*iter));
#endif
			// Find first profile
			i = find_first_profile(profile, 0, size - 1, lst_i);
#if CUMUVERB>2
			fprintf(stderr, "\t\tAdding comp parts of level %d\n", min_usage(*iter));
#endif
			// Add compulsory part to the profile
			while (i < size && profile[i].begin < ect_i) {
				
				if (calendar[taskCalendar[*iter]-1][profile[i].begin] == 1 || rho == 1) {
							
#if CUMUVERB>2
				fprintf(stderr, "\t\t\tAdding comp parts in profile part %d\n", i);
#endif
				profile[i].level += min_usage(*iter);
				profile[i].tasks.insert(*iter);
				// Checking if the profile part i is the part with the maximal level
				//
				if (profile[i].level > profile[i_max_usage].level) {
					i_max_usage = i;
				}
				// Time-table consistency check
				//
				if (profile[i].level > max_limit()) {
#if CUMUVERB > 20
					fprintf(stderr, "\t\t\tResource overload (%d > %d) in profile part %d\n", profile[i].level, max_limit(), i);
#endif
                    // Increment the inconsistency counter
                    nb_tt_incons++;

					// The resource is overloaded in this part
					vec<Lit> expl;
					if (so.lazy) {
						CUMU_INT lift_usage = profile[i].level - max_limit() - 1;
						CUMU_INT begin1, end1;
						// TODO Different choices to pick the interval
						// Pointwise explanation
						begin1 = profile[i].begin + ((profile[i].end - profile[i].begin) / 2);
						end1 = begin1 + 1;
						// Generation of the explanation
						analyse_limit_and_tasks(
							expl, profile[i].tasks, lift_usage, begin1, end1
						);
					}
					// Submitting of the conflict explanation
					submit_conflict_explanation(expl);
#if CUMUVERB > 20
					fprintf(stderr, "\texpl size: %d\n",expl.size());
					fprintf(stderr, "\t\tend filling (conflict)\n");
#endif
					return false;
				}
				}
				i++;
			}
		}
#if CUMUVERB>2
		fprintf(stderr, "\t\tend filling (successful)\n");
#endif
		return true;
	}

	// Finds the profile part that begins at the time unit "lst"
	// Complexity: O(log(high - low + 1))
	//
	int
	find_first_profile(ProfilePart * profile, int low, int high, CUMU_INT lst) {
		int median = 0;
		while (profile[low].begin != lst) {
			median = low + (high - low + 1) / 2;
			if (profile[median].begin > lst) {
				high = median;
			} else {
				low = median;
			}
		}
		return low;
	}

	// Counting the number of profiles
	//
	int
	count_profile(list<ProfileChangePt> &changes) {
		list<ProfileChangePt>::iterator iter = changes.begin();
		int cur_time = iter->time;
		int next_time;
		ProfileChange cur_change = iter->change;
		int no_starts = ( iter->change == PROFINC ? 1 : 0 );
		int no_profile = no_starts;
		iter++;

#if CUMUVERB>2
		fprintf( stderr, "\t\t\ttime = %d; change = %d; no_starts = %d; no_profile = %d;\n", cur_time, cur_change, no_starts, no_profile);
#endif
		for (; iter != changes.end(); iter++) {
			if (iter->change == PROFINC) {
				if (cur_time < iter->time || cur_change == PROFDEC) {
					no_profile++;
				}
				no_starts++;
			} else {
				// ASSUMPTION
				// - iter->change = PROFDEC
				no_starts--;
				next_time = iter->time;
				iter++;
				if (iter != changes.end() && no_starts > 0 && iter->time > next_time) {
					no_profile++;
				}
				iter--;
			}
			cur_time = iter->time;
			cur_change = iter->change;
#if CUMUVERB>2
			fprintf( stderr, "\t\t\ttime = %d; change = %d; no_starts = %d; no_profile = %d;\n", cur_time, cur_change, no_starts, no_profile);
#endif
		}
		return no_profile;
	}

	static bool
	compare_ProfileChangePt(ProfileChangePt & pt1, ProfileChangePt & pt2) {
		if (pt1.time == pt2.time && pt1.change == PROFDEC && pt2.change == PROFINC) return true;
		return pt1.time < pt2.time;
	}

	// Time-table filtering on the lower bound of the resource limit variable
	// Complexity:
	CUMU_BOOL
	filter_limit(ProfilePart * profile, int & i_max_usage);

	// Time-table filtering on the start time variables
	// Complexity:
	CUMU_BOOL
	time_table_filtering(ProfilePart profile[], int size, CUMU_ARR_INT & task, int start, int end, CUMU_INT max_usage);
	CUMU_BOOL
	time_table_filtering_lb(ProfilePart profile[], int low, int high, int task);
	CUMU_BOOL
	time_table_filtering_ub(ProfilePart profile[], int low, int high, int task);
	
	int
	find_first_profile_for_lb(ProfilePart profile[], int low, int high, CUMU_INT t);
	int
	find_first_profile_for_ub(ProfilePart profile[], int low, int high, CUMU_INT t);

	// Analysing the conflict and generation of the explanations
	// NOTE: Fixed durations and resource usages are assumed!!!
	// 
	// Explanation is created for the time interval [begin, end), i.e., exluding end.
	//
	void
	analyse_limit_and_tasks(vec<Lit> & expl, set<CUMU_INT> & tasks, CUMU_INT lift_usage, CUMU_INT begin, CUMU_INT end);
	void
	analyse_tasks(vec<Lit> & expl, set<CUMU_INT> & tasks, CUMU_INT lift_usage, CUMU_INT begin, CUMU_INT end);
	void
	submit_conflict_explanation(vec<Lit> & expl);
	Clause *
	get_reason_for_update(vec<Lit> & expl);

	// TODO Disentailment check
	//CUMU_INT 
	//checkSatisfied() {
	//	// XXX Until no cumulative propagator is implemented the constraint
	//	// is always ?satisfied?
	//	return 1;
	//}

	// Wrapper to get the negated literal -[[v <= val]] = [[v >= val + 1]]
	inline Lit
	getNegLeqLit(CUMU_INTVAR v, CUMU_INT val) { 
		//return v->getLit(val + 1, 2); 
		return (INT_VAR_LL == v->getType() ? v->getMaxLit() : v->getLit(val + 1, 2));
	}
	// Wrapper to get the negated literal -[[v >= val]] = [[ v <= val - 1]]
	inline Lit
	getNegGeqLit(CUMU_INTVAR v, CUMU_INT val) { 
		//return v->getLit(val - 1, 3); 
		return (INT_VAR_LL == v->getType() ? v->getMinLit() : v->getLit(val - 1, 3));
	}

};

/****
 * Functions related to the Time-Table Consistency Check and Propagation
 ****/

void
CumulativeCalProp::get_compulsory_parts2(
	list<ProfileChangePt> &changes, list<CUMU_INT> &comp_task, CUMU_ARR_INT & task, CUMU_INT i_start, CUMU_INT i_end,
	const int tw_begin, const int tw_end
) {
#if CUMUVERB>2
	fprintf(stderr, "\tstart get_compulsory_part from %d to %d\n", i_start, i_end);
#endif
	for (int ii = i_start; ii < i_end; ii++) {
		const int i = task[ii];
#if CUMUVERB>2
		fprintf(stderr, "\t\tii = %d; task[ii] = %d; est %d; dur %d\n", ii, i, est_2[i], min_dur(i));
#endif
		// Check whether the task creates a compulsory part and if it falls into
		// the considered time window
		if (min_dur(i) > 0 && min_usage(i) > 0 && lst_2[i] < ect_2[i] && tw_begin < lct_2[i] && est_2[i] < tw_end) {
#if CUMUVERB>2
			fprintf(stderr, "\t\ttask[ii] = %d, comp part [%d, %d)\n", i, lst_2[i], ect_2[i]);
#endif
			// Add task to the list
			comp_task.push_back(i);
			// Add time points to change lists
			int t;
			changes.push_back( ProfileChangePt(lst_2[i], PROFINC) );
			changes.push_back( ProfileChangePt(ect_2[i], PROFDEC) );
			if (rho == 0){
				// Resource is released
				// Calculating the breaks of the task 'i'
				for	(t = lst_2[i] + 1; t < ect_2[i]; t++){
					const int tCal = taskCalendar[i] - 1;
					if (calendar[tCal][t] == 1 && calendar[tCal][t-1] == 0) {
						changes.push_back( ProfileChangePt(t, PROFINC) );
					}
					if (calendar[tCal][t] == 0 && calendar[tCal][t-1] == 1) {
						changes.push_back( ProfileChangePt(t, PROFDEC) );
					}
				}
			}
		}
	}
#if CUMUVERB>2
	fprintf(stderr, "\tend get_compulsory_part\n");
#endif
}


/***************************************************************************************
 * Function for time-table filtering on the lower bound of the resource limit variable *
 ***************************************************************************************/

CUMU_BOOL
CumulativeCalProp::filter_limit(ProfilePart * profile, int & i) {
	if (min_limit() < profile[i].level) {
		Clause * reason = NULL;
        nb_tt_filt++;
		if (so.lazy) {
			// Lower bound can be updated
			// XXX Determining what time period is the best
			int expl_begin = profile[i].begin + ((profile[i].end - profile[i].begin - 1)/2);
			int expl_end = expl_begin + 1;
			vec<Lit> expl;
			// Get the negated literals for the tasks in the profile
			analyse_tasks(expl, profile[i].tasks, 0, expl_begin, expl_end);
			// Transform literals to a clause
			reason = get_reason_for_update(expl);
		}
		if (! limit->setMin(profile[i].level, reason)) {
			// Conflict occurred
			return false;
		}
		// Set bound_update to true
		bound_update = true;
	}
	return true;
}

/******************************************************************
 * Functions for Time-Table Filtering on the start time variables *
 ******************************************************************/

CUMU_BOOL
CumulativeCalProp::time_table_filtering(ProfilePart profile[], int size, CUMU_ARR_INT & task, int i_start, int i_end, CUMU_INT max_usage) {
	for (int ii = i_start; ii <= i_end; ii++) {
		const int i = task[ii];
        // Skipping tasks with zero duration or usage
        if (min_dur(i) <= 0 || min_usage(i) <= 0)
            continue;
#if CUMUVERB>2
		fprintf(stderr, "TT Filtering of task %d\n", i);
#endif
		// Check if the sum of max_usage and the task's usage are greater then the upper bound
		// on the resource limit
		if (min_usage(i) + max_usage > max_limit()) {
			int index;
#if CUMUVERB>2
			fprintf(stderr, "Finding the first index for LB ...\n");
#endif
				// Find initial profile part for lower bound propagation
				//
			index = find_first_profile_for_lb(profile, 0, size - 1, est_2[i]);
#if CUMUVERB>2
			fprintf(stderr, "Lower bound starting from index %d\n", index);
#endif
			// Update the lower bound if possible
			if (! time_table_filtering_lb(profile, index, size - 1, i)) {
				return false;
			}
#if CUMUVERB>2
			fprintf(stderr, "Finding the first index for UB ...\n");
#endif
			// Find initial profile part for upper bound propagation
			index = find_first_profile_for_ub(profile, 0, size - 1, lct_2[task[i]]);
#if CUMUVERB>2
			fprintf(stderr, "Upper bound starting from index %d\n", index);
#endif
			// Update the upper bound if possible
			if (! time_table_filtering_ub(profile, 0, index, i)) {
				return false;
			}
		}
	}
	return true;
}

	// Time-Table Filtering on the Lower Bound of Start Times Variables
	//
CUMU_BOOL
CumulativeCalProp::time_table_filtering_lb(ProfilePart profile[], int low, int high, int task) {
	int i;
	for (i = low; i <= high; i++) {
		if (ect_2[task] <= profile[i].begin) {
			// No lower bound update possible
			break;
		}
		// ASSUMPTION
		// - ect_2[task] > profile[i].begin
		if (est_2[task] < profile[i].end && profile[i].level + min_usage(task) > max_limit() ) {
			// Possibly a lower bound update if "task" as no compulsory part in the profile
			if (lst_2[task] < ect_2[task] && lst_2[task] <= profile[i].begin && profile[i].end <= ect_2[task]) {
				// No lower bound update possible for this profile part, because 
				// "task" has a compulsory part in it
				continue ;
			}
			const int cal_idx = taskCalendar[task] - 1;
			const int * wPeriods = workingPeriods[cal_idx];
			const int end = min(ect_2[task], profile[i].end);
			if (rho == 0 && wPeriods[profile[i].begin] == wPeriods[end])
				continue;
#if CUMUVERB>1
			fprintf(stderr, "\n----\n");
			fprintf(stderr, "setMin of task %d in profile part [%d, %d)\n", task, profile[i].begin, profile[i].end);
			fprintf(stderr, "task %d: lst = %d; ect = %d; dur = %d;\n", task, lst_2[task], ect_2[task], min_dur(task));
#endif
			int expl_end = profile[i].end;
			Clause * reason = NULL;
			if (so.lazy) {
				// XXX Assumption for the remaining if-statement
				//   No compulsory part of task in profile[i]!
				int lift_usage = profile[i].level + min_usage(task) - max_limit() - 1;
				// TODO Choices of different explanation
				// Pointwise explanation
				expl_end = end;
				int expl_begin = expl_end - 1;
				
				vec<Lit> expl;
				const int wdays = min_dur(task) - (calendar[cal_idx][expl_end - 1] == 1 ? 0 : 1);
				int k = getStartTimeForEndTime(task, end, wdays);
				// Get the negated literal for [[start[task] >= ex_end - min_dur(task)]]

#if CUMUVERB>1
				fprintf(stderr, "start[%d] => %d ", task, k);
#endif
				//expl.push(getNegGeqLit(start[task], expl_end - min_dur(task)));
				expl.push(getNegGeqLit(start[task], k));
                // Get the negated literal for [[dur[task] >= min_dur(task)]]
                if (min_dur0(task) < min_dur(task)) 
                    expl.push(getNegGeqLit(dur[task], min_dur(task)));
                // Get the negated literal for [[usage[task] >= min_usage(task)]]
                if (min_usage0(task) < min_usage(task)) 
                    expl.push(getNegGeqLit(usage[task], min_usage(task)));
				// Get the negated literals for the tasks in the profile and the resource limit
				analyse_limit_and_tasks(expl, profile[i].tasks, lift_usage, expl_begin, expl_end);
#if CUMUVERB>1
				fprintf(stderr, " -> start[%d] => %d\n", task, expl_end);
#endif
				// Transform literals to a clause
				reason = get_reason_for_update(expl);
			}
            nb_tt_filt++;
			// Impose the new lower bound on start[task]
			if (! start[task]->setMin(expl_end, reason)) {
				// Conflict occurred
				return false;
			}
			// Update task's parameters
			retrieveCoreParameters(task);
			// Set bound_update to true
			bound_update = true;
			// Check for the next profile
			if (expl_end < profile[i].end) {
				i--;
			}
		}
	}
	return true;
}

	// Time-table filtering on the upper bound of start times variables
	//
CUMU_BOOL
CumulativeCalProp::time_table_filtering_ub(ProfilePart profile[], int low, int high, int task) {
	int i;
	for (i = high; i >= low; i--) {
		if (profile[i].end <= lst_2[task]) {
			// No upper bound update possible
			break;
		}
		// ASSUMPTION for the remaining for-loop
		// - profile[i].end > lst_2[task]
		if (profile[i].begin < lct_2[task] && profile[i].level + min_usage(task) > max_limit()) {
			// Possibly a upper bound update possible if "task" has no compulsory part 
			// in this profile part
			if (lst_2[task] < ect_2[task] && lst_2[task] <= profile[i].begin && profile[i].end <= ect_2[task]) {
				// No lower bound update possible for this profile part, because 
				// "task" has a compulsory part in it
				continue ;
			}
			// Check whether the task has a working period in the profile part
			// if the resource is released
			const int cal_idx = taskCalendar[task] - 1;
			const int begin = max(lst_2[task], profile[i].begin);
			if (rho == 0 && workingPeriods[cal_idx][begin] == workingPeriods[cal_idx][profile[i].end])
				continue;

			int expl_begin = profile[i].begin;
			Clause * reason = NULL;
			if (so.lazy) {
				// ASSUMPTION for the remaining if-statement
				// - No compulsory part of task in profile[i]
				int lift_usage = profile[i].level + min_usage(task) - max_limit() - 1;
				// TODO Choices of different explanations
				// Pointwise explanation
				expl_begin = begin;
				//expl_begin = max(profile[i].begin, lst_2[task]);
				int expl_end = expl_begin + 1;
				vec<Lit> expl;
				// Get the negated literal for [[start[task] <= expl_begin]]
				expl.push(getNegLeqLit(start[task], expl_begin));
                // Get the negated literal for [[dur[task] >= min_dur(task)]]
                if (min_dur0(task) < min_dur(task)) 
                    expl.push(getNegGeqLit(dur[task], min_dur(task)));
                // Get the negated literal for [[usage[task] >= min_usage(task)]]
                if (min_usage0(task) < min_usage(task)) 
                    expl.push(getNegGeqLit(usage[task], min_usage(task)));
				// Get the negated literals for the tasks in the profile and the resource limit
				analyse_limit_and_tasks(expl, profile[i].tasks, lift_usage, expl_begin, expl_end);
				// Transform literals to a clause
				reason = get_reason_for_update(expl);
			}
			int new_lst = expl_begin;
			int j = 0;
			while (j < min_dur(task)) {
				new_lst--;
				if (calendar[taskCalendar[task]-1][new_lst] == 1) { 
					j++;  
				}
			}

            nb_tt_filt++;
			// Impose the new lower bound on start[task]
			//if (! start[task]->setMax(expl_begin - min_dur(task), reason)) {
			if (! start[task]->setMax(new_lst, reason)) {
				// Conflict occurred
				return false;
			}
			// Update task's core parameters
			retrieveCoreParameters(task);
			// Set bound_update to true
			bound_update = true;
			// Check for the next profile
			if (profile[i].begin < expl_begin) {
				i++;
			}
		}
	}
	return true;
}


int
CumulativeCalProp::find_first_profile_for_lb(ProfilePart profile[], int low, int high, CUMU_INT t) {
	int median;
	if (profile[low].end > t || low == high) {
		return low;
	}
	if (profile[high].begin <= t) {
		return high;
	}
#if CUMUVERB>2
	fprintf(stderr, "time = %d\n", t);
	fprintf(stderr, "profile[low = %d] = [%d, %d); ", low, profile[low].begin, profile[low].end);
	fprintf(stderr, "profile[high = %d] = [%d, %d);\n", high, profile[high].begin, profile[high].end);
#endif
	// ASSUMPTIONS:
	// - profile[low].end <= t
	// - profile[high].begin > t
	// - low < high
	//
	while (!(profile[low].end <= t && t <= profile[low + 1].end)) {
		median = low + (high - low + 1) / 2;
#if CUMUVERB>2
		fprintf(stderr, "profile[lo = %d] = [%d, %d); ", low, profile[low].begin, profile[low].end);
		fprintf(stderr, "profile[me = %d] = [%d, %d); ", median, profile[median].begin, profile[median].end);
		fprintf(stderr, "profile[hi = %d] = [%d, %d);\n", high, profile[high].begin, profile[high].end);
#endif
		if (t < profile[median].end) {
			high = median;
			//high = median - 1;
			low++;
		} else {
			low = median;
		}
	}
	return low;
}

int
CumulativeCalProp::find_first_profile_for_ub(ProfilePart profile[], int low, int high, CUMU_INT t) {
	int median;
	if (profile[high].begin <= t || low == high) {
		return high;
	}
	if (t < profile[low].end) {
		return low;
	}
	// ASSUMPTIONS:
	// - profile[high].begin > t
	// - profile[low].end <= t
	// - low < high
	//
	while (!(profile[high - 1].begin <= t && t < profile[high].begin)) {
		median = low + (high - low + 1) / 2;
		if (t < profile[median].begin) {
			high = median;
		} else {
			low = median;
			high--;
		}
	}
	return high;
}


/************************************************************************
 * Functions for Analysing Conflicts or Bound Updates and Generation of *
 * their explanations                                                   *
 ************************************************************************/

void
CumulativeCalProp::analyse_limit_and_tasks(vec<Lit> & expl, set<CUMU_INT> & tasks, CUMU_INT lift_usage, CUMU_INT begin, CUMU_INT end) {
	CUMU_INT diff_limit = max_limit0() - max_limit();
	if (diff_limit > 0) {
		// Lifting of limit variable if possible
		if (diff_limit <= lift_usage) {
			// No explanation literal is needed
			lift_usage -= diff_limit;
		} else {
			lift_usage = 0;
			// Get explanation for [[limit <= max_limit() + lift_usage]]
#if CUMUVERB > 10
			fprintf(stderr, "/\\ limit <= %d ", max_limit() + lift_usage);
#endif
			expl.push(getNegLeqLit(limit, max_limit() + lift_usage));
		}
	}
	analyse_tasks(expl, tasks, lift_usage, begin, end);
}

void
CumulativeCalProp::analyse_tasks(vec<Lit> & expl, set<CUMU_INT> & tasks, CUMU_INT lift_usage, CUMU_INT begin, CUMU_INT end) {
	set<CUMU_INT>::iterator iter;
	for (iter = tasks.begin(); iter != tasks.end(); iter++) {
		const int i = *iter;
#if CUMUVERB > 10
		fprintf(stderr, "\ns[%d] in [%d..%d]\n", i, start[i]->getMin(), start[i]->getMax());
#endif
		if (min_usage(i) <= lift_usage) {
			// Task is not relevant for the resource overload
			lift_usage -= min_usage(i);
		} else {
			const int duration = min_dur(i) - (calendar[taskCalendar[i]-1][end-1] ? 0 : 1);
			const int t = getStartTimeForEndTime(i, end, duration);

			// Lower bound of the start time variable matters
			if(t > min_start0(i)){
			// Get explanation for [[start[i] >= end - min_dur(i)]]

#if CUMUVERB > 10
				fprintf(stderr, "/\\ start[%d] => %d ",  i, t);
#endif
				expl.push(getNegGeqLit(start[i], t));
			}
			if (begin < max_start0(i)) {
				// Upper bound of the start time variable matters
				// Get explanation for [[start[i] <= begin]]
#if CUMUVERB > 10
				fprintf(stderr, "/\\ start[%d] <= %d ", i, begin);
#endif
				expl.push(getNegLeqLit(start[i], begin));
			}
            // Get the negated literal for [[dur[i] >= min_dur(i)]]
            if (min_dur0(i) < min_dur(i)) 
                expl.push(getNegGeqLit(dur[i], min_dur(i)));
            // Get the negated literal for [[usage[i] >= min_usage(i)]]
            const int usage_diff = min_usage(i) - min_usage0(i);
            if (usage_diff > 0) { 
                if (usage_diff <= lift_usage)
                    lift_usage -= usage_diff;
                else
                    expl.push(getNegGeqLit(usage[i], min_usage(i)));
            }
		}
	}
}

void
CumulativeCalProp::submit_conflict_explanation(vec<Lit> & expl) {
	Clause * reason = NULL;
	if (so.lazy) {
		reason = Reason_new(expl.size());
		int i = 0;
		for (; i < expl.size(); i++) { (*reason)[i] = expl[i]; }
	}
	sat.confl = reason;
}

Clause *
CumulativeCalProp::get_reason_for_update(vec<Lit> & expl) {
	Clause* reason = Reason_new(expl.size() + 1);
	for (int i = 1; i <= expl.size(); i++) {
		(*reason)[i] = expl[i-1];
	}
	return reason;
}


void cumulative_cal(vec<IntVar*>& s, vec<IntVar*>& d, vec<IntVar*>& r, IntVar* limit, vec<vec<int> >& cal, vec<int>& taskCal, int rho_in, int resCal_in) {
    list<string> opt;
    cumulative_cal(s, d, r, limit, cal, taskCal, rho_in, resCal_in);
}

void cumulative_cal(vec<IntVar*>& s, vec<IntVar*>& d, vec<IntVar*>& r, IntVar* limit, vec<vec<int> >& cal, vec<int>& taskCal, int rho_in, int resCal_in, list<string> opt) {
	rassert(s.size() == d.size() && s.size() == r.size());
	// ASSUMPTION
	// - s, d, and r contain the same number of elements
    
    vec<IntVar*> s_new, d_new, r_new;
	vec<int> taskCal_new;
    int r_sum = 0;
	
    for (int i = 0; i < s.size(); i++) {
		if (r[i]->getMax() > 0 && d[i]->getMax() > 0) {
			s_new.push(s[i]);
			d_new.push(d[i]);
			r_new.push(r[i]);
			r_sum += r[i]->getMax();
			taskCal_new.push(taskCal[i]);
		}
    }
	
	

    if (r_sum <= limit->getMin()) return;

    // Global cumulative constraint
    new CumulativeCalProp(s_new, d_new, r_new, limit, cal, taskCal_new, rho_in, resCal_in, opt);
}

/********************************************
 * Functions related to the TTEF propagator
 *******************************************/

	// Initialisation of various parameters
	//
void
CumulativeCalProp::ttef_initialise_parameters() {
	int energy = 0;
	int p_idx = tt_profile_size - 1;

		// Initialisation of the task id's arrays
		//
	for (int ii = 0; ii <= last_unfixed; ii++) {
		task_id_est[ii] = task_id[ii];
		task_id_lct[ii] = task_id[ii];
	}
	if (ttef_filt) {
		for (int ii = 0; ii <= last_unfixed; ii++) {
			const int i = task_id[ii];
			new_est[i] = est_2[i];
			new_lct[i] = lct_2[i];
		}
	}
		// Sorting of the task id's arrays
		//
	sort(task_id_est, task_id_est + last_unfixed + 1, sort_est_asc);
	sort(task_id_lct, task_id_lct + last_unfixed + 1, sort_lct_asc);
		// Calculation of 'tt_after_est'
		//
	for (int ii = last_unfixed; ii >= 0; ii--) {
		const int i = task_id_est[ii];
		if (p_idx < 0 || tt_profile[p_idx].end <= est_2[i]) {
			tt_after_est[ii] = energy;
		} else if (tt_profile[p_idx].begin <= est_2[i]) {
			tt_after_est[ii] = energy + tt_profile[p_idx].level * (tt_profile[p_idx].end - est_2[i]);
		} else {
			assert(tt_profile[p_idx].begin > est_2[i]);
			energy += tt_profile[p_idx].level * (tt_profile[p_idx].end - tt_profile[p_idx].begin);
			p_idx--;
			ii++;
		} 
	}  
		// Calculation of 'tt_after_lct'
		//
    p_idx = tt_profile_size - 1;
	energy = 0;
	for (int ii = last_unfixed; ii >= 0; ii--) {
		unsigned i = task_id_lct[ii];
		if (p_idx < 0 || tt_profile[p_idx].end <= lct_2[i]) {
			tt_after_lct[ii] = energy;
		} else if (tt_profile[p_idx].begin <= lct_2[i]) {
			tt_after_lct[ii] = energy + tt_profile[p_idx].level * (tt_profile[p_idx].end - lct_2[i]);
		} else {
			assert(tt_profile[p_idx].begin > lct_2[i]);
			energy += tt_profile[p_idx].level * (tt_profile[p_idx].end - tt_profile[p_idx].begin);
			p_idx--;
			ii++;
		}
	}
}

	// TTEF Consistency Check
	//	Assumptions:
	//	- task_id_est sorted in non-decreasing order of est's
	//	- task_id_lct sorted in non-decreasing order of lct's
bool
CumulativeCalProp::ttef_consistency_check(
	int shift_in
) {
	assert(last_unfixed > 0);
	assert(shift_in == 0 || shift_in == 1);
	nb_ttefc_calls++;
	
	// Some constants
	const int * rPeriods = workingPeriods[resCalendar - 1];
	const int maxLimit = max_limit();

	// Some variables
	int begin, end, workingDays, dur_shift;		
	int est_idx_last = last_unfixed;
	int i, j, en_req, en_avail;
	int en_req_free;
	int min_en_avail = -1, lct_idx_last = last_unfixed, i_last = task_id_lct[lct_idx_last];
	bool consistent = true;
	
	int dom_jj_last = -1;
	int* sumFreeEnergy = new int[last_unfixed + 1];
	for (int ii = 0; ii <= last_unfixed; ii++) {
		const int i = task_id_est[ii];
		sumFreeEnergy[ii] = (ii > 0 ? sumFreeEnergy[ii - 1] : 0) + free_energy2[i];
	}
	
	end = lct_2[task_id_lct[last_unfixed]] + 1;

		// Outer Loop: iterating over lct in non-increasing order
		//
	for (int ii = last_unfixed; ii >= 0; ii--) {
		i = task_id_lct[ii];
		if (end == lct_2[i]) continue;

		assert(lct_2[i] < lct_2[i_last] || i == i_last);
			
			// Check whether the current latest completion time have to be considered
		// Dominance rule for skipping time intervals
		workingDays = lct_2[i_last] - lct_2[i];
		if(rho == 0) {
			// Resource is released
			workingDays = (rPeriods[lct_2[i]] - rPeriods[lct_2[i_last]]);
		} 
		const int free = maxLimit * workingDays - (tt_after_lct[ii] - tt_after_lct[lct_idx_last]);
		if (min_en_avail >= free) continue;

		lct_idx_last = ii;
		i_last = i;
		min_en_avail = maxLimit * (lct_2[task_id_lct[last_unfixed]] - est_2[task_id_est[0]]);
		
		end = lct_2[i];
		while (est_2[task_id_est[est_idx_last]] >= end) est_idx_last--;
		en_req_free = 0;

		dom_jj_last = -1;
			// Inner Loop: iterating over est in non-increasing order
			//
		for (int jj = est_idx_last; jj >= 0; jj--) {
			nb_ttefc_steps++;
			j = task_id_est[jj];
			
			// Dominance rule for skipping time intervals
			if (dom_jj_last >= 0) {
				// Computing an over-approximation of the required energy in the time
				// interval [est_2[j], end)
				const int dom_begin = est_2[j];
				const int dom_en_comp = tt_after_est[0] - tt_after_est[jj + 1];
				const int dom_en_free = sumFreeEnergy[jj] + en_req;
				const int dom_wdays = (rho == 1 ? end - dom_begin : rPeriods[dom_begin] - rPeriods[end]);
				const int dom_en_avail = maxLimit * dom_wdays - dom_en_comp - dom_en_free;
				if (dom_en_avail >= min_en_avail)
					break;
			}


			assert(est_2[j] < end);
			begin = est_2[j];
			if (lct_2[j] <= end) {
				// Task lies in the considered time interval	
				en_req_free += free_energy2[j];
			} else if (shift_in == 1) {
				// Task might partially lie in the considered time interval
				dur_shift = get_free_dur_right_shift2(begin, end, j);
				// Adjusting dur_shift if resource stays engaged
				if (rho == 1) {
					const int dur_fixed = max(0, ect_2[j] - lst_2[j]);
					dur_shift = min(min_energy2[j] / min_usage(j) - dur_fixed, dur_shift);
				}
				en_req_free += min_usage(j) * dur_shift;
			}
			en_req = en_req_free + tt_after_est[jj] - tt_after_lct[ii];
			// TTEF_cal: Consider resource calendar
			workingDays = end - begin;
			if (rho == 0) {
				// Resource is released
				workingDays = rPeriods[begin] - rPeriods[end];
			} 
			en_avail = maxLimit * workingDays - en_req;

			if (min_en_avail > en_avail) {
				min_en_avail = en_avail;
				dom_jj_last = jj;
			}

				// Check for resource overload
				//
			if (en_avail < 0) {
				consistent = false;
				ii = -1;
				break;
			}
		}
	}

	delete[] sumFreeEnergy;

	if (!consistent) {
		vec<Lit> expl;
        // Increment the inconsistency counter
        nb_ttef_incons++;
		if (so.lazy) {
#if CUMUVERB > 0
		fprintf(stderr, "Entering TTEF Inconsistent\n");
#endif
			list<TaskDur> tasks_tw;
			list<TaskDur> tasks_cp;
			int en_req1 = 0;
			// Retrieve tasks involved
			en_req1 = ttef_retrieve_tasks(shift_in, begin, end, -1, tasks_tw, tasks_cp);
			assert(en_req1 >= en_req);
			// Calculate the lifting TTEF_cal: added breaks
			int en_lift = en_req1 - 1 - maxLimit * workingDays;
			int breaks = end - begin - workingDays;
			assert(en_lift >= 0);
			// Explaining the overload
#if CUMUVERB > 0
		fprintf(stderr, "Explaining TTEF Overload\n");
#endif
			ttef_analyse_limit_and_tasks(begin, end, breaks, tasks_tw, tasks_cp, en_lift, expl);
		    assert(expl.size() > 0);
		}
#if CUMUVERB > 0
		fprintf(stderr, "TTEF Submitting Explanation\n");
#endif
		// Submitting of the conflict explanation
		submit_conflict_explanation(expl);
#if CUMUVERB > 0
		fprintf(stderr, "TTEF END Submitting Explanation: %d\n", consistent);
#endif
	}
	return consistent;
}

	// TTEF bounds propagation
	//
bool
CumulativeCalProp::ttef_bounds_propagation(
	int shift_in1,
	int shift_in2
) {
	std::queue<TTEFUpdate> update1;
	std::queue<TTEFUpdate> update2;
	// TODO LB bound on the limit
	// LB bounds on the start times
#if CUMUVERB > 0
		fprintf(stderr, "Entering TTEF Bounds Propagtion\n");
#endif
	if (!ttef_bounds_propagation_lb(shift_in1, update1)) {
		// Inconsistency
		return false;
	}
	// UB bounds on the start times
	if (!ttef_bounds_propagation_ub(shift_in2, update2)) {
		// Inconsistency
		return false;
	}
#if CUMUVERB > 0
		fprintf(stderr, "TTEF Bounds Propagtion\n");
#endif
	// Updating the bounds
	if (!ttef_update_bounds(shift_in1, update1)) {
		return false;
	}
	if (!ttef_update_bounds(shift_in2, update2)) {
		return false;
	}
#if CUMUVERB > 0
		fprintf(stderr, "Leaving TTEF Bounds Propagtion\n");
#endif
	return true;
}

bool
CumulativeCalProp::ttef_bounds_propagation_lb(
	int shift_in, std::queue<TTEFUpdate> & update_queue
) {
	assert(last_unfixed > 0);
	assert(shift_in == 0 || shift_in == 1);
	// Begin and end of the time interval [begin, end)
	
	// Some constants
	const int maxLimit = max_limit();
	const int * rPeriods = workingPeriods[resCalendar - 1];

	// Some variables
	int begin, end, dur_shift;
	int est_idx_last = last_unfixed;
	int i, j, en_req, en_avail;
	int en_req_free;
	int update_en_req_start, update_idx, update_workDays_req_in;
	int min_en_avail = -1, min_begin = minTime - 1;
	int workingDays = 0;
	bool consistent = true;
	
	int maxEnergy = 0, lct_idx_last = -1;
	int* sumFreeEnergy = new int[last_unfixed + 1];
	for (int ii = 0; ii <= last_unfixed; ii++) {
		const int i = task_id_est[ii];
		maxEnergy = max(maxEnergy, min_usage(i) * (rho == 1 ? ect_2[i] - est_2[i] : min_dur(i)));
		sumFreeEnergy[ii] = (ii == 0 ? 0 : sumFreeEnergy[ii - 1]) + free_energy2[i];
	}
	
	end = lct_2[task_id_lct[last_unfixed]] + 1;

		// Outer Loop: iterating over lct in non-increasing order
		//
	for (int ii = last_unfixed; ii >= 0; ii--) {
		i = task_id_lct[ii];
		if (end == lct_2[i]) continue;
			
		// Dominance rule for skipping time intervals
		if (min_en_avail >= 0) {
			const int dom_wdays = (rho == 1 ? end - lct_2[i] : rPeriods[lct_2[i]] - rPeriods[end]);
			const int dom_en_comp = tt_after_lct[ii] - tt_after_lct[lct_idx_last];
			const int dom_en_avail = maxLimit * dom_wdays - dom_en_comp;
			if (min_en_avail - dom_en_avail >= maxEnergy)
				continue;
		}
		lct_idx_last = ii;
			// Check whether the current latest completion time have to be considered
		min_en_avail = maxLimit * (lct_2[task_id_lct[last_unfixed]] - est_2[task_id_est[0]]);
		min_begin = minTime - 1;
		
		end = lct_2[i];
		while (est_2[task_id_est[est_idx_last]] >= end) est_idx_last--;
		
		// Initialisations for the inner loop
		en_req_free = 0;
		en_req = 0;
		update_idx = -1;
		update_en_req_start = -1;
		update_workDays_req_in = -1;

			// Inner Loop: iterating over est in non-increasing order
			//
		for (int jj = est_idx_last; jj >= 0; jj--) {
			nb_ttef_lb_calls++;
			j = task_id_est[jj];

			assert(est_2[j] < end);
			
			// Check for TTEEF propagation in the time interval [min_begin, end)
			if (minTime <= min_begin && tteef_filt)
				tteef_bounds_propagation_ub(min_begin, end, min_en_avail, j, update_queue);
			
			// TTEF Dominance rule for skipping time intervals
			// NOTE this rule can cut off TTEEF propagation
			if (jj < est_idx_last) {
				// Computing an over-estimate of the energy in the time interval [est_2[j], end)
				const int dom_wdays = (rho == 1 ? end - est_2[j] : rPeriods[est_2[j]] - rPeriods[end]);
				const int dom_en_comp = tt_after_est[0] - tt_after_est[jj + 1];
				const int dom_en_free = sumFreeEnergy[jj] + en_req;
				const int dom_en_avail = maxLimit * dom_wdays - dom_en_comp - dom_en_free;
				if (dom_en_avail >= min_en_avail && dom_en_avail >= maxEnergy)
					break;
			}

			begin = est_2[j];

			// Computing the required free energy of task 'j' in the
			// time interval [begin, end)
			if (lct_2[j] <= end) {
				// Task 'j' lies in the considered time interval	
				en_req_free += free_energy2[j];
			} else {
				// Task might partially lie in the considered time interval
				const int cal_idx = taskCalendar[j] - 1;
				const int * wPeriods = workingPeriods[cal_idx];
				const int ect_in = min(end, ect_2[j]);
				int workDays_req_in = 0;
				// Add the compulsory part of 'j' to the required energy in the time interval [begin, end)
				if (lst_2[j] < ect_2[j]) {
					const int begin_comp = min(end, lst_2[j]);
					workDays_req_in += (rho == 1 ? ect_in - begin_comp : wPeriods[begin_comp] - wPeriods[ect_in]);
				}
				
				// Computing the required energy in the time interval [begin, end) 
				// considering the right shift
				if (shift_in == 1) {
					dur_shift = get_free_dur_right_shift2(begin, end, j);
					// Adjusting dur_shift if resource stays engaged
					if (rho == 1) {
						const int dur_fixed = max(0, ect_2[j] - lst_2[j]);
						dur_shift = min(min_energy2[j] / min_usage(j) - dur_fixed, dur_shift);
					}
					workDays_req_in += dur_shift;
					en_req_free += min_usage(j) * dur_shift;
				}
				
				// Calculation of the additional required energy for starting at est_2[j]
				// in time window [begin, end)
				const int workDays_start = (rho == 1 ? ect_in - est_2[j] : wPeriods[est_2[j]] - wPeriods[ect_in]);
				const int en_req_start = min_usage(j) * (workDays_start - workDays_req_in);
				assert(workDays_start >= workDays_req_in);
				if (en_req_start > update_en_req_start) {
					update_en_req_start = en_req_start;
					update_workDays_req_in = workDays_req_in;
					update_idx = jj;
				}
			}

			// Adding the energy from the time table profile (compulsory parts)
			en_req = en_req_free + tt_after_est[jj] - tt_after_lct[ii];

			// Calculate the available energy in the time window [begin, end)
			workingDays = (rho == 1 ? end - begin : rPeriods[begin] - rPeriods[end]);
			en_avail = maxLimit * workingDays - en_req;

			// Update the time window [., end) with the minimal available energy
			// Note is required for the TTEEF propagation
			if (min_en_avail > en_avail) {
				min_en_avail = en_avail;
				min_begin = begin;
			}

			// Check for resource overload
			if (en_avail < 0) {
				consistent = false;
				ii = -1;
				break;
			}

			// Check for a lower bound update for the start time
			if (en_avail < update_en_req_start) {
				// Reset 'j' to the task to be updated
				j = task_id_est[update_idx];
				// Calculation of the possible new lower bound wrt. 
				// the current time interval [begin, end)
				const int en_avail_new = en_avail + update_workDays_req_in * min_usage(j);
				const int wdays_avail = en_avail_new / min_usage(j);
				const int start_new = ttef_get_new_start_time(begin, end, j, wdays_avail);
				// Check whether a new lower bound was found
				// - nfnl-rule TODO
				if (start_new > new_est[j]) {
					// Push possible update into the queue
					update_queue.push(TTEFUpdate(j, start_new, begin, end, true));
					new_est[j] = start_new;
				}
			}
		}
	}

	delete[] sumFreeEnergy;

	if (!consistent) {
		vec<Lit> expl;
        // Increment the inconsistency counter
        nb_ttef_incons++;
		if (so.lazy) {
			list<TaskDur> tasks_tw;
			list<TaskDur> tasks_cp;
			int en_req1 = 0;
			// Retrieve tasks involved
			en_req1 = ttef_retrieve_tasks(shift_in, begin, end, -1, tasks_tw, tasks_cp);
			assert(en_req1 >= en_req);
			// Calculate the lifting
			int breaks = end - begin - workingDays;
			int en_lift = en_req1 - 1 - maxLimit * (end - begin - breaks);
			assert(en_lift >= 0);
			// Explaining the overload
			ttef_analyse_limit_and_tasks(begin, end, breaks, tasks_tw, tasks_cp, en_lift, expl);
			assert(expl.size() > 0);
		}
		// Submitting of the conflict explanation
		submit_conflict_explanation(expl);
#if CUMUVERB > 0
		fprintf(stderr, "TTEF Inconsistency detected LB");
#endif
	}
	return consistent;
}

bool
CumulativeCalProp::ttef_bounds_propagation_ub(
	int shift_in,
	std::queue<TTEFUpdate> & update_queue
) {
	assert(last_unfixed > 0);
	assert(shift_in == 0 || shift_in == 2);

	// Some constants
	const int maxLimit = max_limit();
	const int * rPeriods = workingPeriods[resCalendar - 1];
	
	// Some variables
	// Begin and end of the time interval [begin, end)
	int begin, end = -1, dur_shift;
	int lct_idx_last = 0;
	int i, j, en_req, en_avail;
	int en_req_free;
	int update_en_req_end, update_idx, update_workDays_req_in;
	int min_en_avail = -1, min_end = minTime - 1;
	int workingDays = 0;
	bool consistent = true;

	int maxEnergy = 0, est_idx_last = -1;
	int maxLength = 0;
        int* sumFreeEnergy = new int[last_unfixed + 2];
        sumFreeEnergy[last_unfixed + 1] = 0;
	for (int ii = last_unfixed; ii >= 0; ii--) {
		const int i = task_id_lct[ii];
		maxLength = (rho == 1 ? max(lct_2[i] - lst_2[i], ect_2[i] - est_2[i]) : min_dur(i));
		maxEnergy = max(maxEnergy, min_usage(i) * maxLength);
		sumFreeEnergy[ii] = sumFreeEnergy[ii + 1] + free_energy2[i];
	}
	
	begin = est_2[task_id_est[0]] - 1;

		// Outer Loop: iterating over est in non-decreasing order
		//
	for (int ii = 0; ii <= last_unfixed; ii++) {
		i = task_id_est[ii];
		if (begin == est_2[i]) continue;
		
		// Dominance rule for skipping time intervals
		if (min_en_avail >= 0) {
			const int dom_wdays = (rho == 1 ? est_2[i] - begin : rPeriods[begin] - rPeriods[est_2[i]]);
			const int dom_en_comp = tt_after_est[est_idx_last] - tt_after_est[ii];
			const int dom_en_avail = maxLimit * dom_wdays - dom_en_comp;
			if (min_en_avail - dom_en_avail >= maxEnergy)
				continue;
		}
		est_idx_last = ii;

		// Intialisation for the minimal avaible energy of a time interval starting
		// at begin
		min_en_avail = maxLimit * (lct_2[task_id_lct[last_unfixed]] - est_2[task_id_est[0]]);
		min_end = minTime - 1;

		begin = est_2[i];
		while (lct_2[task_id_lct[lct_idx_last]] <= begin) lct_idx_last++;
		
		// Initialisations for the inner loop
		en_req = 0;
		en_req_free = 0;
		en_avail = -1;
		update_idx = -1;
		update_en_req_end = -1;
		update_workDays_req_in = -1;
		
			// Inner Loop: iterating over lct in non-decreasing order
			//
		for (int jj = lct_idx_last; jj <= last_unfixed; jj++) {
			nb_ttef_ub_calls++;
			j = task_id_lct[jj];

			assert(lct_2[j] > begin);

			// Check for TTEEF propagation in the time interval [begin, min_end)
			if (minTime <= min_end && tteef_filt)
				tteef_bounds_propagation_lb(begin, min_end, min_en_avail, j, update_queue);

			// TTEF Dominance rule for skipping time intervals
			// NOTE this rule can cut off TTEEF propagation
			if (jj > lct_idx_last) {
				// Computing an over-estimate of the energy in the time interval [begin, lct_2[j])
				const int dom_wdays = (rho == 1 ? lct_2[j] - begin : rPeriods[begin] - rPeriods[lct_2[j]]);
				const int dom_en_comp = tt_after_lct[jj - 1];
				const int dom_en_free = sumFreeEnergy[jj] + en_req;
				const int dom_en_avail =  maxLimit * dom_wdays - dom_en_comp - dom_en_free;
				if (dom_en_avail >= min_en_avail && dom_en_avail >= maxEnergy)
					break;
			}

			// Update end
			end = lct_2[j];

			// Computing the required free energy of task 'j' in the 
			// time interval [begin, end)
			if (begin <= est_2[j]) {
				// Task lies in the considered time interval [begin, end)
				en_req_free += free_energy2[j];
			} else {
				// Task might partially lie in the considered time interval
				const int cal_idx = taskCalendar[j] - 1;
				const int * wPeriods = workingPeriods[cal_idx];
				const int lst_in = max(begin, lst_2[j]);
				int workDays_req_in = 0;
				// Add the compulsory part of 'j' to the required energy in the time interval [begin, end)
				if (lst_2[j] < ect_2[j]) {
					const int end_comp = max(begin, ect_2[j]);
					workDays_req_in += (rho == 1 ? end_comp - lst_in : wPeriods[lst_in] - wPeriods[end_comp]);
				}

				// Computing the required energy in the time interval [begin, end) 
				// considering the lef shift
				if (shift_in == 2) {
					dur_shift = get_free_dur_left_shift2(begin, end, j);
					// Adjusting dur_shift if resource stays engaged
					if (rho == 1) {
						const int dur_fixed = max(0, ect_2[j] - lst_2[j]);
						dur_shift = min(min_energy2[j] / min_usage(j) - dur_fixed, dur_shift);
					}
					workDays_req_in += dur_shift;
					en_req_free += min_usage(j) * dur_shift;
				}

				// Calculation of the additional required energy for ending at lct_2[j]
				// in time window [begin, end)
				const int workDays_end = (rho == 1 ? lct_2[j] - lst_in : wPeriods[lst_in] - wPeriods[lct_2[j]]);
				const int en_req_end = min_usage(j) * (workDays_end - workDays_req_in);
				assert(workDays_end >= workDays_req_in);
				if (en_req_end > update_en_req_end) {
					update_en_req_end = en_req_end;
					update_workDays_req_in = workDays_req_in;
					update_idx = jj;
				}
			}

			// Adding the energy from the time table profile (compulsory parts)
			en_req = en_req_free + tt_after_est[ii] - tt_after_lct[jj];

			// Calculate the available energy in the time interval [begin, end)
			workingDays = (rho == 1 ? end - begin : rPeriods[begin] - rPeriods[end]);
			en_avail = maxLimit * workingDays - en_req;

			// Update the time window [begin, .) with the minimal available energy
			// Note is required for the TTEEF propagation
			if (min_en_avail > en_avail) {
				min_en_avail = en_avail;
				min_end = end;
			}

			// Check for resource overload
			if (en_avail < 0) {
				consistent = false;
				ii = last_unfixed + 1;
				break;
			}

			// Check for an upper bound update for the start time
			if (en_avail < update_en_req_end) {
				// Reset 'j' to the task to be updated
				j = task_id_lct[update_idx];
				// Calculation of the possible upper bound wrt.
				// the current time interval [begin , end)
				const int en_avail_new = en_avail + update_workDays_req_in * min_usage(j);
				const int wdays_avail = en_avail_new / min_usage(j);
				const int end_new = ttef_get_new_end_time(begin, end, j, wdays_avail);
				// Check whether a new upper bound was found
				// - nfnl-rule TODO
				if (end_new < new_lct[j]) {
					// Push possible update into queue
					update_queue.push(TTEFUpdate(j, end_new, begin, end, false));
					new_lct[j] = end_new;
				}
			}
		}
	}

	delete[] sumFreeEnergy;

	if (!consistent) {
		vec<Lit> expl;
        // Increment the inconsistency counter
        nb_ttef_incons++;
		if (so.lazy) {
			list<TaskDur> tasks_tw;
			list<TaskDur> tasks_cp;
			int en_req1 = 0;
			// Retrieve tasks involved
			en_req1 = ttef_retrieve_tasks(shift_in, begin, end, -1, tasks_tw, tasks_cp);
			assert(en_req1 >= en_req);
			// Calculate the lifting
			int breaks = end - begin - workingDays;
			int en_lift = en_req1 - 1 - maxLimit * (end - begin - breaks);
			assert(en_lift >= 0);
			// Explaining the overload
			ttef_analyse_limit_and_tasks(begin, end, breaks, tasks_tw, tasks_cp, en_lift, expl);
			assert(expl.size() > 0);
		}
		// Submitting of the conflict explanation
		submit_conflict_explanation(expl);
#if CUMUVERB > 0
		fprintf(stderr, "TTEF Inconsistency detected UB");
#endif
	}
	return consistent;
}

// Checking for TTEEF propagation on lower bound in the 
// time window [begin, end)
void
CumulativeCalProp::tteef_bounds_propagation_lb(
	const int begin, const int end, const int en_avail, const int j,
	std::queue<TTEFUpdate> & update_queue
) {
	if (begin <= est_2[j] || ect_2[j] <= begin)
		return ;

	// Some useful constants
	const int * wPeriods = workingPeriods[taskCalendar[j] - 1];
	const int est_in = max(begin, est_2[j]);
	const int ect_in = min(end, ect_2[j]);
	assert(est_in <= ect_in);

	// Computing the compulsory part in the time interval [begin, end)
	int wdays_in = 0;
	if (lst_2[j] < ect_2[j]) {
		const int end_comp_in = max(begin, ect_in);
		wdays_in += (rho == 1 ? end_comp_in - est_in : wPeriods[est_in] - wPeriods[end_comp_in]);
	}

	// Computing the working days in the time interval [begin, end) when
	// task 'j' is executed to its earliest start time
	const int wdays_start_in = (rho == 1 ? ect_in - est_in : wPeriods[est_in] - wPeriods[ect_in]);
	assert(wdays_start_in >= wdays_in);

	// Checking for lower bound propagation
	if (en_avail < min_usage(j) * (wdays_start_in - wdays_in)) {
		// Calculate new lower bound
		const int wdays_avail = (en_avail / min_usage(j)) + wdays_in;
		const int est_new = ttef_get_new_start_time(begin, end, j, wdays_avail);
		// Check whether a new lower bound was found
		if (est_new > new_est[j]) {
			// Push possible update into the queue
			update_queue.push(TTEFUpdate(j, est_new, begin, end, true));
			new_est[j] = est_new;
		}
	}
}

// Checking for TTEEF propagation on upper bound in the 
// time window [begin, end)
void
CumulativeCalProp::tteef_bounds_propagation_ub(
	const int begin, const int end, const int en_avail, const int j,
	std::queue<TTEFUpdate> & update_queue
) {
	if (lst_2[j] >= end || lct_2[j] <= begin || est_2[j] >= begin)
		return ;

	// Some useful constants
	const int * wPeriods = workingPeriods[taskCalendar[j] - 1];
	const int lst_in = max(begin, lst_2[j]);
	const int lct_in = min(end, lct_2[j]);
	
	// Computing the compulsory part in time interval [begin, end)
	int wdays_in = 0;
	if (lst_2[j] < ect_2[j]) {
		const int end_comp_in = max(begin, lct_in);
		wdays_in += (rho == 1 ? end_comp_in - lst_in : wPeriods[lst_in] - wPeriods[end_comp_in]);
	}
	
	// Computing the working days in the time interval [begin, end) when
	// task 'j' is executed to its latest start time
	const int wdays_end_in = (rho == 1 ? lct_in - lst_in : wPeriods[lst_in] - wPeriods[lct_in]);
	assert(wdays_end_in >= wdays_in);

	// Checking for upper bound propagation
	if (en_avail < min_usage(j) * (wdays_end_in - wdays_in)) {
		// Calculate new upper bound
		const int wdays_avail = (en_avail / min_usage(j)) + wdays_in;
		const int lct_new = ttef_get_new_end_time(begin, end, j, wdays_avail);
		// Check whether a new upper bound was found
		if (lct_new < new_lct[j]) {
			// Push possible update into the queue
			update_queue.push(TTEFUpdate(j, lct_new, begin, end, false));
			new_lct[j] = lct_new;
		}
	}
}

int
CumulativeCalProp::ttef_get_new_start_time(
	const int begin, const int end, const int task, const int min_wdays_in
) {
	assert(min_wdays_in >= 0);
	if (min_wdays_in == 0) {
		const int * cal = calendar[taskCalendar[task] - 1];
		int est = end;
		while (est <= maxTime && cal[est] == 0)
			est++;
		return est;
	}
	if (rho == 0) {
		// Resource is released
		return getStartTimeForEndTime(task, end, min_wdays_in);
	}
	// Resource stays engaged
	const int * cal = calendar[taskCalendar[task] - 1];
	const int begin_in = max(begin, est_2[task]);
	const int end_in = min(end, ect_2[task]);
	assert(begin_in < end_in);
	int wdays_in = end_in - begin_in;
	assert(wdays_in > min_wdays_in);
	//const int max_est = min(max_start0(task), end - min_wdays_in);
	const int max_est = max_start0(task);
	int last_est = est_2[task];
	int last_wdays_in = wdays_in;
	int est = est_2[task] + 1;
	int ect = ect_2[task] + 1;

	for (; est <= max_est; est++, ect++) {
		// Updating the working days
		assert(cal[est - 1] == 1);
		if (begin <= last_est)
			wdays_in--;
		// Computing the new start time and updating the working days
		while (cal[est] == 0 && est <= max_est) {
			if (begin <= est)
				wdays_in--;
			est++;
		}
		if (est > max_est)
			return last_est;
		// Computing the new end time and updating the working days
		assert(cal[ect - 2] == 1);
		while (cal[ect - 1] == 0) {
			if (ect <= end)
				wdays_in++;
			ect++;
		}
		// Updating the working days
		if (ect <= end)
			wdays_in++;
		// Checking working days
		if (wdays_in == min_wdays_in || (last_wdays_in > min_wdays_in && wdays_in < min_wdays_in))
			return est;
		else if (wdays_in < min_wdays_in)
			return last_est;
		// Updating last valid earliest start time
		last_est = est;
		last_wdays_in = wdays_in;
	}

	return last_est;
}

int
CumulativeCalProp::ttef_get_new_end_time(
	const int begin, const int end, const int task, const int min_wdays_in
) {
	assert(min_wdays_in >= 0);
	if (min_wdays_in == 0) {
		const int * cal = calendar[taskCalendar[task] - 1];
		int lct = begin;
		while (minTime < lct && cal[lct - 1] == 0)
			lct--;
		return lct;
	}
	if (rho == 0) {
		// Resource is released
		return getEndTimeForStartTime(task, begin, min_wdays_in);
	}
	// Resource stays engaged
	const int * cal = calendar[taskCalendar[task] - 1];
	const int begin_in = max(begin, lst_2[task]);
	const int end_in = min(end, lct_2[task]);
	assert(begin_in < end_in);
	int wdays_in = end_in - begin_in;
	assert(wdays_in > min_wdays_in);
	const int lst0 = min_start0(task);
	int last_lct = lct_2[task];
	int last_wdays_in = wdays_in;
	int lst = lst_2[task] - 1;
	int lct = lct_2[task] - 1;

	for (; lst <= lst0; lst--, lct--) {
		assert(cal[lst + 1] == 1);
		// Computing the new start time and updating the working days
		while (cal[lst] == 0 && lst0 <= lst) {
			if (begin <= lst)
				wdays_in++;
			lst++;
		}
		if (lst < lst0)
			return last_lct;
		// Updating the working days
		if (begin <= lst)
			wdays_in++;
		// Updating the working days
		if (lct < end)
			wdays_in--;
		// Computing the new end time and updating the working days
		assert(cal[lct] == 1);
		while (cal[lct - 1] == 0) {
			if (lct <= end)
				wdays_in--;
			lct--;
		}
		// Checking the working days
		if (wdays_in == min_wdays_in  || (last_wdays_in > min_wdays_in && wdays_in < min_wdays_in)) {
			return lct;
		} else if (wdays_in < min_wdays_in)
			return last_lct;
		// Updating the last valid latest completion time
		last_lct = lct;
		last_wdays_in = wdays_in;
	}
	return last_lct;
}

void
CumulativeCalProp::ttef_explanation_for_update_lb(
	int shift_in, const int begin, const int end, const int task, int & bound, vec<Lit> & expl
) {
	// Some constants
	const int maxLimit = max_limit();
	const int * rPeriods = workingPeriods[resCalendar - 1];
	const int * wPeriods = workingPeriods[taskCalendar[task] - 1];

	// Some variables
	list<TaskDur> tasks_tw;
	list<TaskDur> tasks_cp;
	
	// Retrieving tasks involved in the time interval [begin, end) excluding task 'task'
	const int en_req = ttef_retrieve_tasks(shift_in, begin, end, task, tasks_tw, tasks_cp);

	// Calculating the available energy in the time interval [begin, end)
	const int wdays = (rho == 1 ? end - begin : rPeriods[begin] - rPeriods[end]);
	const int en_avail = maxLimit * wdays - en_req;
	const int breaks = end - begin - wdays;

	// Calculating the working days available for the task 'task' in the considered time interval
	const int wdays_avail = en_avail / min_usage(task);
	const int min_wdays_in = wdays_avail + 1;

	// Determining the new lower bound on the start time
	const int new_lb = ttef_get_new_start_time(begin, end, task, wdays_avail);
	
	// Some consistency checks
	assert(new_lb >= bound);
	assert(rho == 0 || en_avail < min_usage(task) * (min(end, ect_2[task]) - max(begin, est_2[task])));
	assert(rho == 1 || en_avail < min_usage(task) * (wPeriods[max(begin, est_2[task])] - wPeriods[min(end, ect_2[task])]));

	// Calculating the explanation lower bound on the start time
	int expl_wdays_in;
	int expl_lb;
	switch (ttef_expl_deg) {
	case ED_NORMAL:
	case ED_LIFT:
		expl_lb = ttef_analyse_tasks_left_shift(begin, end, min_wdays_in, task, 0, expl_wdays_in);
	case ED_NAIVE:
	default:
		expl_lb = est_2[task];
		const int expl_begin = max(begin, expl_lb);
		const int expl_end   = min(end, ect_2[task]);
		expl_wdays_in = (rho == 1 ? expl_end - expl_begin : wPeriods[expl_begin] - wPeriods[expl_end]);
	}

	// Calculating the lifting energy for the remainder
	int en_lift = min_usage(task) - 1 - (en_avail % min_usage(task));
	en_lift += min_usage(task) * (expl_wdays_in - wdays_avail - 1);

	// More consistency checks
	assert(expl_lb <= est_2[task]);
	assert(expl_wdays_in >= wdays_avail + 1);
	assert(en_lift >= 0);

	// Explaining the update for task 'task'
	if (expl_lb > min_start0(task)) {
		// start[task] >= expl_lb
		expl.push(getNegGeqLit(start[task], expl_lb));
	}
    // Get the negated literal for [[dur[task] >= min_dur(task)]]
    if (min_dur0(task) < min_dur(task)) 
        expl.push(getNegGeqLit(dur[task], min_dur(task)));
    // Get the negated literal for [[usage[task] >= min_usage(task)]]
    if (min_usage0(task) < min_usage(task)) 
        expl.push(getNegGeqLit(usage[task], min_usage(task)));
	
	// Retrieve explanation for the remaining tasks
	ttef_analyse_limit_and_tasks(begin, end, breaks, tasks_tw, tasks_cp, en_lift, expl);

	// Assigning new lower bound
	bound = new_lb;
}

void
CumulativeCalProp::ttef_explanation_for_update_ub(
	int shift_in, const int begin, const int end, const int task, int & bound, vec<Lit> & expl
) {
	// Some constants
	const int maxLimit = max_limit();
	const int * rPeriods = workingPeriods[resCalendar - 1];
	const int * wPeriods = workingPeriods[taskCalendar[task] - 1];

	// Some variables
	list<TaskDur> tasks_tw;
	list<TaskDur> tasks_cp;

	// Retrieving tasks involved in the time interval [begin, end) excluding task 'task'
	const int en_req = ttef_retrieve_tasks(shift_in, begin, end, task, tasks_tw, tasks_cp);

	// Calculating the available energy in the time interval [begin, end)
	const int wdays = (rho == 1 ? end - begin : rPeriods[begin] - rPeriods[end]);
	const int en_avail = maxLimit * wdays - en_req;
	const int breaks = end - begin - wdays;
	
	// Calculating the working days available for the task 'task' in the considered time interval
	const int wdays_avail = en_avail / min_usage(task);
	const int min_wdays_in = wdays_avail + 1;

	// Determining the new upper bound on the latest completion time
	const int new_lct = ttef_get_new_end_time(begin, end, task, wdays_avail);

	// Some consistency checks
	assert(new_lct <= bound);
	assert(rho == 0 || en_avail < min_usage(task) * (min(end, lct_2[task]) - max(begin, lst_2[task])));
	assert(rho == 1 || en_avail < min_usage(task) * (wPeriods[max(begin, lst_2[task])] - wPeriods[min(end, lct_2[task])]));

	// Calculating the explanation lower bound on the start time
	int expl_wdays_in;
	int expl_ub;
	switch (ttef_expl_deg) {
	case ED_NORMAL:
	case ED_LIFT:
		expl_ub = ttef_analyse_tasks_right_shift(begin, end, min_wdays_in, task, 0, expl_wdays_in);
	case ED_NAIVE:
	default:
		expl_ub = lst_2[task];
		const int expl_begin = max(begin, expl_ub);
		const int expl_end   = min(end, lct_2[task]);
		expl_wdays_in = (rho == 1 ? expl_end - expl_begin : wPeriods[expl_begin] - wPeriods[expl_end]);
	}

	// Calculating the lifting energy for the remainder
	int en_lift = min_usage(task) - 1 - (en_avail % min_usage(task));
	en_lift += min_usage(task) * (expl_wdays_in - wdays_avail - 1);

	// More consistency checks
	assert(expl_ub >= lst_2[task]);
	assert(expl_wdays_in >= wdays_avail + 1);
	assert(en_lift >= 0);

	// Explaining the update for task 'task'
	if (expl_ub < max_start0(task)) {
		// start[task] <= expl_ub
		expl.push(getNegLeqLit(start[task], expl_ub));
	}
    // Get the negated literal for [[dur[task] >= min_dur(task)]]
    if (min_dur0(task) < min_dur(task)) 
        expl.push(getNegGeqLit(dur[task], min_dur(task)));
    // Get the negated literal for [[usage[task] >= min_usage(task)]]
    if (min_usage0(task) < min_usage(task)) 
        expl.push(getNegGeqLit(usage[task], min_usage(task)));
	
	// Retrieve explanation for the remaining tasks
	ttef_analyse_limit_and_tasks(begin, end, breaks, tasks_tw, tasks_cp, en_lift, expl);

	// Assigning new lower bound
	bound = new_lct;
}

bool
CumulativeCalProp::ttef_update_bounds(
	int shift_in, 
	std::queue<TTEFUpdate> & queue_update
) {
	while (!queue_update.empty()) {
		const int task  = queue_update.front().task;
			  int bound = queue_update.front().bound_new;
		const int begin = queue_update.front().tw_begin;
		const int end   = queue_update.front().tw_end;
		Clause * reason = NULL;
		if (queue_update.front().is_lb_update) {
			// Lower bound update
			if (new_est[task] == bound) {
				if (so.lazy) {
					vec<Lit> expl;
					ttef_explanation_for_update_lb(shift_in, begin, end, task, bound, expl);
					reason = get_reason_for_update(expl);
				}
                nb_ttef_filt++;
				// Update the lower bound
				if (!start[task]->setMin(bound, reason)) {
					// Conflict occurred
					return false;
				}
				// Set bound_update to true
				bound_update = true;
#if CUMUVERB > 0
		fprintf(stderr, "Bounds Update LB\n");
#endif
			}
		} else {
			// Upper bound update
			if (new_lct[task] == bound) {
				if (so.lazy) {
					vec<Lit> expl;
					ttef_explanation_for_update_ub(shift_in, begin, end, task, bound, expl);
					reason = get_reason_for_update(expl);
				}
				// Update the lower bound
				const int new_ub = getStartTimeForEndTime(task, bound, min_dur(task));
#if CUMUVERB > 0
				fprintf(stderr, "Bounds Update UB: task = %d, old = %d, new = %d \n",task, lst_2[task], new_ub);
#endif
                nb_ttef_filt++;
				if (!start[task]->setMax(new_ub, reason)) {
					// Conflict occurred
					return false;
				}
				// Set bound_update to true
				bound_update = true;
			}
		}
		queue_update.pop();
	}

	return true;
}

int
CumulativeCalProp::ttef_retrieve_tasks(
	const int shift_in, 
	const int begin, const int end, const int fb_id, list<TaskDur> & tasks_tw, list<TaskDur> & tasks_cp) 
{
	int en_req = 0;
	int dur_comp, dur_shift, dur_in;
	// Getting fixed tasks
	for (int ii = 0; ii < task_id.size(); ii++) {
		const int i = task_id[ii];
		if (i == fb_id || lct_2[i] <= begin || end <= est_2[i]) 
			continue;
		if (begin <= est_2[i] && lct_2[i] <= end) {
			// Task lies in the time interval [begin, end)
			en_req += min_energy2[i];
			const int usedDays = min_energy2[i] / min_usage(i);
			tasks_tw.push_back(TaskDur(i, usedDays));
			continue;
		} 
		if (lst_2[i] < ect_2[i] && is_intersecting(begin, end, lst_2[i], ect_2[i])) {
			// Compulsory part partially or fully lies in [begin, end)
			const int begin_comp = max(begin, lst_2[i]);
			const int end_comp = min(end, ect_2[i]);
			dur_comp = end_comp - begin_comp;
			if (rho == 0) {
				const int cal_idx = taskCalendar[i] - 1;
				dur_comp = workingPeriods[cal_idx][begin_comp] - workingPeriods[cal_idx][end_comp];
			}
			dur_shift = 0;
			if (shift_in == 1) {
				dur_shift = get_free_dur_right_shift2(begin, end, i);
				assert(begin <= est_2[i] || dur_shift == 0);
				// Adjusting dur_shift if the resource stays engaged
				if (rho == 1) {
					const int dur_fixed = max(0, ect_2[i] - lst_2[i]);
					dur_shift = min(min_energy2[i] / min_usage(i) - dur_fixed, dur_shift);
				}
			} else {
				assert(shift_in == 2);
				dur_shift = get_free_dur_left_shift2(begin, end, i);
				// Adjusting dur_shift if the resource stays engaged
				if (rho == 1) {
					const int dur_fixed = max(0, ect_2[i] - lst_2[i]);
					dur_shift = min(min_energy2[i] / min_usage(i) - dur_fixed, dur_shift);
				}
			}
			dur_in = dur_comp + dur_shift;
			en_req += min_usage(i) * dur_in;
			tasks_cp.push_back(TaskDur(i, dur_in));
			continue;
		}
		// Task 'i' should not have a compulsory part overlapping the time window [begin, end)
		dur_in = 0;
		if (shift_in == 1) {
			dur_in = get_free_dur_right_shift2(begin, end, i);
			assert(begin <= est_2[i] || dur_in == 0);
			// Adjusting dur_shift if the resource stays engaged
			if (rho == 1) {
				const int dur_fixed = max(0, ect_2[i] - lst_2[i]);
				dur_in = min(min_energy2[i] / min_usage(i) - dur_fixed, dur_in);
			}
		} else {
			assert(shift_in == 2);
			dur_in = get_free_dur_left_shift2(begin, end, i);
			assert(lct_2[i] <= end || dur_in == 0);
			// Adjusting dur_shift if the resource stays engaged
			if (rho == 1) {
				const int dur_fixed = max(0, ect_2[i] - lst_2[i]);
				dur_in = min(min_energy2[i] / min_usage(i) - dur_fixed, dur_in);
			}
		}
		if (0 < dur_in) {
			// Task partially lies in [begin, end)
			en_req += min_usage(i) * dur_in;
			tasks_tw.push_back(TaskDur(i, dur_in));
		}
	}
	return en_req;
}

void
CumulativeCalProp::ttef_analyse_limit_and_tasks(const int begin, const int end, const int breaks, list<TaskDur> & tasks_tw,
	list<TaskDur> & tasks_cp, int & en_lift, vec<Lit> & expl) 
{
	// Getting	explanation for tasks in the time window
	ttef_analyse_tasks(begin, end, tasks_tw, en_lift, expl);
	// Getting explanation for tasks with compulsory parts
	ttef_analyse_tasks(begin, end, tasks_cp, en_lift, expl);
	// Getting explanation for the resource capacity
	int diff_limit = max_limit0() - max_limit();
	if (diff_limit > 0) {
		// Calculate possible lifting
		int lift_limit = min(en_lift / (end - begin - breaks), diff_limit);
		en_lift -= lift_limit * (end - begin - breaks);
		assert(en_lift >= 0);
		if (lift_limit < diff_limit) {
			// limit[%d] <= max_limit() + lift_limit
			expl.push(getNegLeqLit(limit, max_limit() + lift_limit));
		}
	}
}

int
CumulativeCalProp::ttef_analyse_tasks_right_shift(const int begin, const int end, const int dur_in, const int task, const int max_dur_lift, int & last_dur)
{
	// Some assumptions
	assert(est_2[task] < end && begin < lct_2[task]);

	// Defining some constants
	const int lst0 = max_start0(task);
	if (dur_in <= max_dur_lift) {
		last_dur = 0;
		return lst0;
	}
	// Defining more constants
	const int cal_idx    = taskCalendar[task] - 1;
	const int * wPeriods = workingPeriods[cal_idx];
	const int * tCal     = calendar[cal_idx];
	const int min_dur_in = dur_in - max_dur_lift;
	const int begin_in   = max(begin, min(lst_2[task], end));
	const int end_in     = min(lct_2[task], end);
	// Defining some variables
	int workDays = (rho == 1 ? end_in - begin_in : wPeriods[begin_in] - wPeriods[end_in]);
	int last_lst = lst_2[task];
	last_dur = workDays;
	int lst = lst_2[task] + 1;
	int lct = lct_2[task] + 1;

	assert(workDays >= dur_in);

	// Determining the latest possible start time and the number of workDays in the time window [begin, end)
	for (; lst <= lst0; lst++, lct++) {
		if (last_lst >= begin)
			workDays--;
		// Determining the new start time
		assert(tCal[lst - 1] == 1);
		while (tCal[lst] == 0 && lst <= lst0) {
			if (rho == 1 && lst >= begin)
				workDays--;
			lst++;
		}
		if (lst > lst0) {
			return last_lst;
		}
		// Determining the new end time
		assert(tCal[lct - 2] == 1);
		while (tCal[lct - 1] == 0) {
			if (rho == 1 && lct <= end)
				workDays++;
			lct++;
		}
		if (lct <= end)
			workDays++;
		// Check the number of working days in the time window [begin, end)
		if (workDays < min_dur_in) {
			return last_lst;
		}
		// Saving valid shift
		last_lst = lst;
		last_dur = workDays;

		// Some cross checks
		assert(min_dur(task) == wPeriods[last_lst] - wPeriods[lct]);
		assert(rho == 0 || workDays == min(end, lct) - max(begin, last_lst));
		assert(rho == 1 || workDays == wPeriods[max(begin, last_lst)] - wPeriods[min(end, lct)]);
		assert(ttef_analyse_tasks_check_expl_ub(begin, end, task, min_dur_in, last_lst));
	}
	return last_lst;
}

int
CumulativeCalProp::ttef_analyse_tasks_left_shift(const int begin, const int end, const int dur_in, const int task, const int max_dur_lift, int & last_dur)
{
	// Determining the earliest start time so that a certain number of work days are within the time window [begin, end)
	assert(est_2[task] < end && begin < lct_2[task]);
	const int est0 = min_start0(task);
	if (dur_in <= max_dur_lift) {
		last_dur = 0;
		return est0;
	}
	// Some useful constants
	const int cal_idx    = taskCalendar[task] - 1;
	const int * wPeriods = workingPeriods[cal_idx];
	const int * tCal     = calendar[cal_idx];
	const int min_dur_in = dur_in - max_dur_lift;
	const int end_in = min(ect_2[task], end);
	const int begin_in = max(est_2[task], begin);
	int wdays = (rho == 1 ? end_in - begin_in : wPeriods[begin_in] - wPeriods[end_in]);
	int last_est = est_2[task];
	last_dur = wdays;
	int ect = ect_2[task] - 1;
	int est = est_2[task] - 1;
	for (; est >= est0; est--, ect--) {
		assert(tCal[last_est] == 1);
		// Determining the new start time and updating the number of working days
		while (tCal[est] == 0 && est >= est0) {
			if (rho == 1 && est >= begin)
				wdays++;
			est--;
		}
		if (est < est0) {
			return last_est;
		}
		if (est >= begin)
			wdays++;
		// Determining the new end time and updating the number of working days
		assert(tCal[ect] == 1);
		if (ect < end)
			wdays--;
		while (tCal[ect - 1] == 0) {
			if (rho == 1 && ect <= end)
				wdays--;
			ect--;
		}
		// Check the number of working days in the time window [begin, end)
		if (wdays < min_dur_in) {
			return last_est;
		}
		// Saving last valid shift
		last_est = est;
		last_dur = wdays;
		// Some consistency checks
		assert(min_dur(task) == wPeriods[last_est] - wPeriods[ect]);
		assert(rho == 1 || wdays == wPeriods[max(last_est, begin)] - wPeriods[min(ect, end)]);
		assert(rho == 0 || wdays == min(ect, end) - max(last_est, begin));
		assert(ttef_analyse_tasks_check_expl_lb(begin, end, task, min_dur_in, last_est));
	}
	return last_est;
}

bool
CumulativeCalProp::ttef_analyse_tasks_check_expl_lb(const int begin, const int end, const int task, const int dur_in, const int expl_lb) {
	const int cal_idx = taskCalendar[task] - 1;
	const int ect = getEndTimeForStartTime(task, expl_lb, min_dur(task));
	const int begin_expl = max(begin, expl_lb);
	const int end_expl = max(begin, min(end, ect));
	const int dur_expl_in = (rho == 1 ? end_expl - begin_expl : workingPeriods[cal_idx][begin_expl] - workingPeriods[cal_idx][end_expl]);
	if (dur_in > dur_expl_in) {
#if CUMUVERB > 2
		printf("xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\n");
		printf("EXPL LB\n");
		printf(" tw [%d, %d); expl_lb %d\n", begin, end, expl_lb);
		printf(" task %d: start [%d, %d]; end [%d, %d];\n", task, est_2[task], lst_2[task], ect_2[task], lct_2[task]);
		printf(" start0 [%d, %d]\n", min_start0(task), max_start0(task));
		printf(" min_dur %d; dur_in %d;\n", min_dur(task), dur_in);
		printf(" min_energy2 %d; min_usage %d;\n", min_energy2[task], min_usage(task));
		printf(" tw_expl [%d, %d]; dur_expl_in %d, rho %d\n", begin_expl, end_expl, dur_expl_in, rho);
		for (int i = max(minTime, begin - 5); i < min(maxTime, end + 5); i++) {
			printf("%d ", calendar[cal_idx][i]);
		}
		printf("\n");
#endif
		return false;
	}
	return true;
}

bool
CumulativeCalProp::ttef_analyse_tasks_check_expl_ub(const int begin, const int end, const int task, const int dur_in, const int expl_ub) {
	const int cal_idx = taskCalendar[task] - 1;
	const int lct = getEndTimeForStartTime(task, expl_ub, min_dur(task));
	const int end_expl = min(lct, end);
	const int lst = max(begin, min(end, expl_ub));
	const int dur_expl_in = (rho == 1 ? end_expl - lst : workingPeriods[cal_idx][lst] - workingPeriods[cal_idx][end_expl]);
	if (dur_in > dur_expl_in) {
#if CUMUVERB > 2
		printf("xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\n");
		printf("EXPL UB\n");
		printf(" tw [%d, %d); expl_ub %d\n", begin, end, expl_ub);
		printf(" task %d: start [%d, %d]; end [%d, %d];\n", task, est_2[task], lst_2[task], ect_2[task], lct_2[task]);
		printf(" start0 [%d, %d]\n", min_start0(task), max_start0(task));
		printf(" min_dur %d; dur_in %d;\n", min_dur(task), dur_in);
		printf(" min_energy2 %d; min_usage %d;\n", min_energy2[task], min_usage(task));
		printf(" lst [%d, %d]; dur_expl_in %d, rho %d\n", lst, end_expl, dur_expl_in, rho);
		for (int i = max(minTime, begin - 5); i < min(maxTime, end + 5); i++) {
			printf("%d ", calendar[cal_idx][i]);
		}
		printf("\n");
#endif
		return false;
	}
	return true;
}

void
CumulativeCalProp::ttef_analyse_tasks(const int begin, const int end, list<TaskDur> & tasks, int & en_lift, vec<Lit> & expl) {
	while (!tasks.empty()) {
		const int i = tasks.front().task;
		int dur_in = tasks.front().dur_in;
		int expl_lb, expl_ub;
		int est0 = min_start0(i);
		int lst0 = max_start0(i);
		// TTEF_cal: running variable for loops t, storages for execution times sto1 and sto2
		int t, sto1, sto2;
		// Calculate possible lifting
		// TTEF_cal: several changes were necessary
		switch (ttef_expl_deg) {
		case ED_NORMAL:
                // XXX Is min_dur correct
			if (rho == 1) {
				// Resource stays engaged
				sto1 = workingPeriods[taskCalendar[i]-1][begin] - workingPeriods[taskCalendar[i]-1][begin + dur_in];
				sto2 = min_dur(i) - sto1;
				sto1 = 0;
				t = begin;
				while(sto1 < sto2 && t > 0){
					if (calendar[taskCalendar[i]-1][t-1] == 1) sto1++;
					t--;
				}
				expl_lb = min(est_2[i], t);
				expl_ub = lst_2[i];//max(lst_2[i], end - dur_in);
			} else {
				// Resource is released
				sto1 = 0;
				sto2 = min_dur(i) - dur_in;
				t = begin;
				while(sto1 < sto2 && t > 0){
					if(calendar[taskCalendar[i]-1][t-1]==1) sto1++;
					t--;
				}
				expl_lb = min(est_2[i], t);
				sto1 = 0;
				sto2 = dur_in;
				t = end;
				while(sto1 < sto2 && t > 0){
					if(calendar[taskCalendar[i]-1][t-1]==1) sto1++;
					t--;
				}
				expl_ub = max(lst_2[i], t);
			}
			//expl_lb = begin + dur_in - min_dur(i); expl_ub = end - dur_in;
			break;
		//-----------------------------------------------------------
		case ED_LIFT: 
			{
				int dur_in_lb = 0;
				int dur_in_ub = 0;
				// Computing maximal lift for the work days inside the time window [begin, end)
				const int max_lift = en_lift / min_usage(i);
				// Computing the lifted lower and upper bound on the start time
				expl_lb = ttef_analyse_tasks_left_shift( begin, end, dur_in, i, max_lift, dur_in_lb);
				expl_ub = ttef_analyse_tasks_right_shift(begin, end, dur_in, i, max_lift, dur_in_ub);
				// Some consistency checks
				assert(dur_in - dur_in_lb <= max_lift);
				assert(dur_in - dur_in_ub <= max_lift);
				assert(ttef_analyse_tasks_check_expl_lb(begin, end, i, min(dur_in_lb, dur_in_ub), expl_lb));
				assert(ttef_analyse_tasks_check_expl_ub(begin, end, i, min(dur_in_lb, dur_in_ub), expl_ub));
				// Computing the used lift
				const int dur_lift = dur_in - min(dur_in_lb, dur_in_ub);
				// Updating the remaining energy for lifting
				en_lift -= min_usage(i) * dur_lift;
			}
			break;
		//-----------------------------------------------------------
		case ED_NAIVE:
		default:
			expl_lb = est_2[i]; expl_ub = lst_2[i];
		}
		//printf("%d: dur_in %d/%d; en_in %d; est0 %d; lst0 %d\t", i, dur_in, dur[i], dur_in * min_usage(i), est0, lst0);
		if (est0 < expl_lb) {
			//printf("s[%d] >= %d; ", i, expl_lb);
			expl.push(getNegGeqLit(start[i], expl_lb));
		}
		if (expl_ub < lst0) {
			//printf("s[%d] <= %d; ", i, expl_ub);
			expl.push(getNegLeqLit(start[i], expl_ub));
		}
        // Get the negated literal for [[dur[i] >= min_dur(i)]]
        if (min_dur0(i) < min_dur(i)) 
            expl.push(getNegGeqLit(dur[i], min_dur(i)));
        // Get the negated literal for [[usage[i] >= min_usage(i)]]
        if (min_usage0(i) < min_usage(i)) 
            expl.push(getNegGeqLit(usage[i], min_usage(i)));
		//printf("\n");
		tasks.pop_front();
	}
}

inline bool
CumulativeCalProp::is_intersecting(const int begin1, const int end1, const int begin2, const int end2) {
	return ((begin1 <= begin2 && begin2 < end1) || (begin2 <= begin1 && begin1 < end2));
}

/*** EOF ***/