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namespace Gecode { namespace Int { namespace GCC {
/** * \defgroup GCCBndSup Support for GCC bounds propagation * * \ingroup FuncIntProp */
/** * \brief Class for computing unreachable values in the value %GCC propagator * * \ingroup GCCBndSup */ class UnReachable { public: /// Number of variables with lower bound int minb; /// Number of variables with upper bound int maxb; /// Number of equal variables int eq; /// Number of smaller variables int le; /// Number of greater variables int gr; };
/** * \brief Bounds consistency check for cardinality variables. * \ingroup GCCBndSup */
template<class Card> ExecStatus prop_card(Space& home, ViewArray<IntView>& x, ViewArray<Card>& k) { int n = x.size(); int m = k.size(); Region r; UnReachable* rv = r.alloc<UnReachable>(m); for(int i = m; i--; ) rv[i].minb=rv[i].maxb=rv[i].le=rv[i].gr=rv[i].eq=0;
for (int i = n; i--; ) { int min_idx; if (!lookupValue(k,x[i].min(),min_idx)) return ES_FAILED; if (x[i].assigned()) { rv[min_idx].minb++; rv[min_idx].maxb++; rv[min_idx].eq++; } else { // count the number of variables // with lower bound k[min_idx].card() rv[min_idx].minb++; int max_idx; if (!lookupValue(k,x[i].max(),max_idx)) return ES_FAILED; // count the number of variables // with upper bound k[max_idx].card() rv[max_idx].maxb++; } }
rv[0].le = 0; int c_min = 0; for (int i = 1; i < m; i++) { rv[i].le = c_min + rv[i - 1].maxb; c_min += rv[i - 1].maxb; }
rv[m-1].gr = 0; int c_max = 0; for (int i = m-1; i--; ) { rv[i].gr = c_max + rv[i + 1].minb; c_max += rv[i + 1].minb; }
for (int i = m; i--; ) { int reachable = x.size() - rv[i].le - rv[i].gr; if (!k[i].assigned()) { GECODE_ME_CHECK(k[i].lq(home, reachable)); GECODE_ME_CHECK(k[i].gq(home, rv[i].eq)); } else { // check validity of the cardinality value if ((rv[i].eq > k[i].max()) || (k[i].max() > reachable)) return ES_FAILED; } }
return ES_OK; }
/** \brief Consistency check, whether the cardinality values are feasible. * \ingroup GCCBndSup */ template<class Card> forceinline bool card_consistent(ViewArray<IntView>& x, ViewArray<Card>& k) { int smin = 0; int smax = 0; for (int i = k.size(); i--; ) { smax += k[i].max(); smin += k[i].min(); } // Consistent if number of variables within cardinality bounds return (smin <= x.size()) && (x.size() <= smax); }
/** * \brief Maps domain bounds to their position in hall[].bounds. * \ingroup GCCBndSup */ class Rank { public: /** * \brief \f$ rank[i].min = z * \Leftrightarrow min(x_i) = hall[z].bounds \f$ */ int min; /** * \brief \f$ rank[i].max = z * \Leftrightarrow max(x_i) = hall[z].bounds \f$ */ int max; };
/** * \brief Compares two indices \a i, \a j of two views * \a \f$ x_i \f$ \f$ x_j\f$ according to the * ascending order of the views upper bounds * * \ingroup GCCBndSup */ template<class View> class MaxInc { protected: /// View array for comparison ViewArray<View> x; public: /// Constructor MaxInc(const ViewArray<View>& x0) : x(x0) {} /// Order forceinline bool operator ()(const int i, const int j) { return x[i].max() < x[j].max(); } };
/** * \brief Compares two indices \a i, \a j of two views * \a \f$ x_i \f$ \f$ x_j\f$ according to the * ascending order of the views lower bounds * * \ingroup GCCBndSup */ template<class View> class MinInc { protected: /// View array for comparison ViewArray<View> x; public: /// Constructor MinInc(const ViewArray<View>& x0) : x(x0) {} /// Comparison forceinline bool operator ()(const int i, const int j) { return x[i].min() < x[j].min(); } };
/** * \brief Compares two cardinality views * \a \f$ x_i \f$ \f$ x_j\f$ according to the index * * \ingroup GCCBndSup */ template<class Card> class MinIdx { public: /// Comparison forceinline bool operator ()(const Card& x, const Card& y) { return x.card() < y.card(); } };
/** * \brief Partial sum structure for constant * time computation of the maximal capacity of an interval. * * \ingroup GCCBndSup */ template<class Card> class PartialSum { private: /// sum[i] contains the partial sum from 0 to i int* sum; /// the size of the sum int size; public: /// Sentinels indicating whether an end of sum is reached int firstValue, lastValue; /// \name Initialization //@{ /// Constructor PartialSum(void); /// Initialization void init(Space& home, ViewArray<Card>& k, bool up); /// Mark datstructure as requiring reinitialization void reinit(void); /// Test whether already initialized operator bool(void) const; //@} /// \name Access //@{ /// Compute the maximum capacity of an interval int sumup(int from, int to) const; /// Return smallest bound of variables int minValue(void) const; /// Return largest bound of variables int maxValue(void) const; /// Skip neigbouring array entries if their values do not differ int skipNonNullElementsRight(int v) const; /// Skip neigbouring array entries if their values do not differ int skipNonNullElementsLeft(int v) const; //@} /// \name Update //@{ /** * \brief Check whether the values in the * partial sum structure containting * the lower cardinality bounds differ * from the actual lower bounds of the * cardinalities. */ bool check_update_min(ViewArray<Card>& k); /** * \brief Check whether the values in the * partial sum structure containting * the upper cardinality bounds differ * from the actual upper bounds of the * cardinalities. */ bool check_update_max(ViewArray<Card>& k); //@} };
template<class Card> forceinline PartialSum<Card>::PartialSum(void) : sum(nullptr), size(-1) {}
template<class Card> forceinline PartialSum<Card>::operator bool(void) const { return size != -1; } template<class Card> inline void PartialSum<Card>::init(Space& home, ViewArray<Card>& elements, bool up) { int i = 0; int j = 0;
// Determine number of holes in the index set int holes = 0; for (i = 1; i < elements.size(); i++) { if (elements[i].card() != elements[i-1].card() + 1) holes += elements[i].card()-elements[i-1].card()-1; }
// we add three elements at the beginning and two at the end size = elements.size() + holes + 5;
// memory allocation if (sum == nullptr) { sum = home.alloc<int>(2*size); } int* ds = &sum[size];
int first = elements[0].card();
firstValue = first - 3; lastValue = first + elements.size() + holes + 1;
// the first three elements for (i = 3; i--; ) sum[i] = i;
/* * copy the bounds into sum, filling up holes with zeroes */ int prevCard = elements[0].card()-1; i = 0; for (j = 2; j < elements.size() + holes + 2; j++) { if (elements[i].card() != prevCard + 1) { sum[j + 1] = sum[j]; } else if (up) { sum[j + 1] = sum[j] + elements[i].max(); i++; } else { sum[j + 1] = sum[j] + elements[i].min(); i++; } prevCard++; } sum[j + 1] = sum[j] + 1; sum[j + 2] = sum[j + 1] + 1;
// Compute distances, eliminating zeroes i = elements.size() + holes + 3; j = i + 1; for ( ; i > 0; ) { while(sum[i] == sum[i - 1]) { ds[i] = j; i--; } ds[j] = i; i--; j = ds[j]; } ds[j] = 0; ds[0] = 0; }
template<class Card> forceinline void PartialSum<Card>::reinit(void) { size = -1; }
template<class Card> forceinline int PartialSum<Card>::sumup(int from, int to) const { if (from <= to) { return sum[to - firstValue] - sum[from - firstValue - 1]; } else { assert(to - firstValue - 1 >= 0); assert(to - firstValue - 1 < size); assert(from - firstValue >= 0); assert(from - firstValue < size); return sum[to - firstValue - 1] - sum[from - firstValue]; } }
template<class Card> forceinline int PartialSum<Card>::minValue(void) const { return firstValue + 3; } template<class Card> forceinline int PartialSum<Card>::maxValue(void) const { return lastValue - 2; }
template<class Card> forceinline int PartialSum<Card>::skipNonNullElementsRight(int value) const { value -= firstValue; int* ds = &sum[size]; return (ds[value] < value ? value : ds[value]) + firstValue; } template<class Card> forceinline int PartialSum<Card>::skipNonNullElementsLeft(int value) const { value -= firstValue; int* ds = &sum[size]; return (ds[value] > value ? ds[ds[value]] : value) + firstValue; }
template<class Card> inline bool PartialSum<Card>::check_update_max(ViewArray<Card>& k) { int j = 0; for (int i = 3; i < size - 2; i++) { int max = 0; if (k[j].card() == i+firstValue) max = k[j++].max(); if ((sum[i] - sum[i - 1]) != max) return true; } return false; }
template<class Card> inline bool PartialSum<Card>::check_update_min(ViewArray<Card>& k) { int j = 0; for (int i = 3; i < size - 2; i++) { int min = 0; if (k[j].card() == i+firstValue) min = k[j++].min(); if ((sum[i] - sum[i - 1]) != min) return true; } return false; }
/** * \brief Container class provding information about the Hall * structure of the problem variables. * * This class is used to * keep the number of different arrays small, that is * an array of type %HallInfo replaces integer arrays for each * of the class members. * * \ingroup GCCBndSup */ class HallInfo { public: /// Represents the union of all lower and upper domain bounds int bounds; /** * \brief Critical capacity pointer * \a t represents a predecessor function where \f$ t_i \f$ denotes the * predecessor of i in bounds */ int t; /** * \brief Difference between critical capacities * * \a d_i is the difference between the capacities of hall[i].bounds * and its predecessor in bounds hall[t[i]].bounds * */ int d; /** * \brief Hall set pointer * * If hall[i].h < i then the half-open interval * [hall[h[i]].bounds,hall[i].bounds) is containd in a Hall * set. * Otherwise holds a pointer to the Hall intervall it belongs to. */ int h; /// Stable Set pointer int s; /// Potentially Stable Set pointer int ps; /** * \brief Bound update * * \a newBound contains either a narrowed domain bound * or is stores the old domain bound of a variable. */ int newBound; };
/** * \name Path compression * * Each of the nodes on the path from \a start to \a end * becomes a direct child of \a to. * \ingroup GCCBndSup */ //@{ /// Path compression for potentially stable set structure forceinline void pathset_ps(HallInfo hall[], int start, int end, int to) { int k, l; for (l=start; (k=l) != end; hall[k].ps=to) { l = hall[k].ps; } } /// Path compression for stable set structure forceinline void pathset_s(HallInfo hall[], int start, int end, int to) { int k, l; for (l=start; (k=l) != end; hall[k].s=to) { l = hall[k].s; } } /// Path compression for capacity pointer structure forceinline void pathset_t(HallInfo hall[], int start, int end, int to) { int k, l; for (l=start; (k=l) != end; hall[k].t=to) { l = hall[k].t; } } /// Path compression for hall pointer structure forceinline void pathset_h(HallInfo hall[], int start, int end, int to) { int k, l; for (l=start; (k=l) != end; hall[k].h=to) { l = hall[k].h; assert(l != k); } } //@}
/** * \name Path minimum * * Returns the smalles reachable index starting from \a i. * \ingroup GCCBndSup */ //@{ /// Path minimum for hall pointer structure forceinline int pathmin_h(const HallInfo hall[], int i) { while (hall[i].h < i) i = hall[i].h; return i; } /// Path minimum for capacity pointer structure forceinline int pathmin_t(const HallInfo hall[], int i) { while (hall[i].t < i) i = hall[i].t; return i; } //@}
/** * \name Path maximum * * Returns the greatest reachable index starting from \a i. * \ingroup GCCBndSup */ //@{ /// Path maximum for hall pointer structure forceinline int pathmax_h(const HallInfo hall[], int i) { while (hall[i].h > i) i = hall[i].h; return i; } /// Path maximum for capacity pointer structure forceinline int pathmax_t(const HallInfo hall[], int i) { while (hall[i].t > i) { i = hall[i].t; } return i; } /// Path maximum for stable set pointer structure forceinline int pathmax_s(const HallInfo hall[], int i) { while (hall[i].s > i) i = hall[i].s; return i; } /// Path maximum for potentially stable set pointer structure forceinline int pathmax_ps(const HallInfo hall[], int i) { while (hall[i].ps > i) i = hall[i].ps; return i; } //@}
}}}
// STATISTICS: int-prop