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#include <gecode/driver.hh>#include <gecode/int.hh>
#include <vector>#include <algorithm>#include <sstream>
using namespace Gecode;
namespace {
using std::vector;
/// Layout of the cards vector<vector<int> > layout; /// information for locating particular cards in the layout vector<int> layer, pile;
/** \brief Generates\ref layout. * * This function generates the layeout and intializes \ref layer and * \ref pile from it. The layout is randomly generated from the * supplied seed. */ void generate(int seed) { // The layout consists of 17 piles of 3 cards each layout = vector<vector<int> >(17, vector<int>(3)); // Deck without the Ace of Spades vector<int> deck(51); for (int i = 51; i--; ) deck[i] = i+1; Support::RandomGenerator rnd(seed+1); std::random_shuffle(deck.begin(), deck.end(), rnd);
// Place cards from deck int pos = 0; for (int i = 17; i--; ) for (int j = 3; j--; ) layout[i][j] = deck[pos++];
// Location-information for each card layer = vector<int>(52); pile = vector<int>(52); for (int i = 17; i--; ) { for (int j = 3; j--; ) { layer[layout[i][j]] = j; pile[ layout[i][j]] = i; } } }}
/** * \brief %Example: Black hole patience * * This example solves instances of the black-hole patience game. * * The model of the problem is mostly taken from "Search in the * Patience Game 'Black Hole'", by Ian P. Gent, Chris Jefferson, Tom * Kelsey, Inês Lynce, Ian Miguel, Peter Nightingale, Barbara * M. Smith, and S. Armagan Tarim. * * The conditional symmetry identified in the above paper can be * eliminated (enabled by default). * * \ingroup Example * */class BlackHole : public Script {protected: IntVarArray x, ///< Card at position y; ///< Position of card
/// Return a string representing the card of value val std::string card(int val) const { const char* suit = "SCHD"; std::ostringstream o; o << std::setw(2) << (1 + (val%13)) << suit[val/13]; return o.str(); }
public: /// Symmetry variants enum { SYMMETRY_NONE, ///< No symmetry breaking SYMMETRY_CONDITIONAL ///< Breaking conditional symmetries }; /// Propagation of placement-rules enum { PROPAGATION_REIFIED, ///< Reified propagation PROPAGATION_DFA, ///< Extensional propagation using automatons PROPAGATION_TUPLE_SET ///< Extensional propagation using tables }; /// Actual model BlackHole(const SizeOptions& opt) : Script(opt), x(*this, 52, 0,51), y(*this, 52, 0,51) { // Black ace at bottom rel(*this, x[0], IRT_EQ, 0);
// x is order and y is placement channel(*this, x, y, opt.ipl());
// The placement rules: the absolute value of the difference // between two consecutive cards is 1 or 12. if (opt.propagation() == PROPAGATION_REIFIED) { // Build table for accessing the rank of a card IntArgs modtable(52); for (int i = 0; i < 52; ++i) { modtable[i] = i%13; } for (int i = 0; i < 51; ++i) { IntVar x1(*this, 0, 12), x2(*this, 0, 12); element(*this, modtable, x[i], x1); element(*this, modtable, x[i+1], x2); const int dr[2] = {1, 12}; IntVar diff(*this, IntSet(dr, 2)); rel(*this, abs(x1-x2) == diff, IPL_DOM); } } else if (opt.propagation() == PROPAGATION_DFA) { // Build table for allowed tuples REG expression; for (int r = 13; r--; ) { for (int s1 = 4; s1--; ) { for (int s2 = 4; s2--; ) { for (int i = -1; i <= 1; i+=2) { REG r1 = REG(r+13*s1); REG r2 = REG((r+i+52+13*s2)%52); REG r = r1 + r2; expression |= r; } } } } DFA table(expression);
for (int i = 51; i--; ) extensional(*this, IntVarArgs({x[i],x[i+1]}), table);
} else { // opt.propagation() == PROPAGATION_TUPLE_SET) // Build table for allowed tuples TupleSet ts(2); for (int r = 13; r--; ) for (int s1 = 4; s1--; ) for (int s2 = 4; s2--; ) for (int i = -1; i <= 1; i+=2) ts.add({r+13*s1, (r+i+52+13*s2)%52}); ts.finalize();
for (int i = 51; i--; ) extensional(*this, IntVarArgs({x[i],x[i+1]}), ts); }
// A card must be played before the one under it. for (int i = 17; i--; ) for (int j = 2; j--; ) rel(*this, y[layout[i][j]] < y[layout[i][j+1]]);
// Compute and break the conditional symmetries that are dependent // on the current layout. // Two cards with the same rank but different suits are symmetric // with respect to their placement in the black hole if changing // their order does not affect any other card. if (opt.symmetry() == SYMMETRY_CONDITIONAL) { // For all ranks for (int r = 13; r--; ) { // For all pairs of suits for (int s1 = 4; s1--; ) { for (int s2 = s1; s2--; ) { int c1 = 13*s1 + r, c2 = 13*s2 + r; // The ace of spades is already placed if (c1 == 0 || c2 == 0) continue; // Piles are handled by the rules of the game if (pile[c1] == pile[c2]) continue; // Fix the right order of the cards int o1 = c1, o2 = c2; if (pile[c1] > pile[c2] && layer[c2] >= layer[c1]) std::swap(o1, o2); // cond is the condition for the symmetry BoolVarArgs ba; // Both cards played after the ones on top of them for (int i = 0; i < layer[o1]; ++i) ba << expr(*this, (y[layout[pile[o1]][i]] < y[o2])); for (int i = 0; i < layer[o2]; ++i) ba << expr(*this, (y[layout[pile[o2]][i]] < y[o1])); // Both cards played before the ones under them for (int i = layer[o1]+1; i < 3; ++i) ba << expr(*this, (y[o2] < y[layout[pile[o1]][i]])); for (int i = layer[o2]+1; i < 3; ++i) ba << expr(*this, (y[o1] < y[layout[pile[o2]][i]])); // Cond holds when all the above holds BoolVar cond(*this, 0, 1); rel(*this, BOT_AND, ba, cond);
// If cond is fulfilled, then we can order the cards // cond -> (y[o1] < y[o2]) rel(*this, !cond || (y[o1] < y[o2])); } } } }
// Install custom brancher branch(*this, x, INT_VAR_NONE(), INT_VAL(&val)); } /// Value selection function for branching static int val(const Space&, IntVar x, int) { int v = -1; int w = 4; for (IntVarValues vals(x); vals(); ++vals) if (layer[vals.val()] < w) { v = vals.val(); if ((w = layer[vals.val()]) == 0) break; } assert(v >= 1 && v < 52); return v; } /// Print instance and solution virtual void print(std::ostream& os) const { os << "Layout:" << std::endl; for (int i = 0; i < 17; i++) { for (int j = 0; j < 3; j++) os << card(layout[i][j]) << " "; if ((i+1) % 3 == 0) os << std::endl; else os << " \t"; } os << std::endl << std::endl;
os << "Solution:" << std::endl; for (int i = 0; i < 52; ++i) { if (x[i].assigned()) os << card(x[i].val()) << " "; else os << " "; if ((i + 1) % 13 == 0) os << std::endl; } os << std::endl; os << std::endl; }
/// Constructor for cloning \a s BlackHole(BlackHole& s) : Script(s) { x.update(*this, s.x); y.update(*this, s.y); } /// Copy during cloning virtual Space* copy(void) { return new BlackHole(*this); }};
/** \brief Main-function * \relates BlackHole */intmain(int argc, char* argv[]) { SizeOptions opt("Black Hole patience"); opt.symmetry(BlackHole::SYMMETRY_CONDITIONAL); opt.symmetry(BlackHole::SYMMETRY_NONE,"none", "no symmetry breaking"); opt.symmetry(BlackHole::SYMMETRY_CONDITIONAL,"conditional", "break conditional symmetries"); opt.propagation(BlackHole::PROPAGATION_TUPLE_SET); opt.propagation(BlackHole::PROPAGATION_REIFIED, "reified", "use reified propagation"); opt.propagation(BlackHole::PROPAGATION_DFA, "dfa", "use DFA-based extensional propagation"); opt.propagation(BlackHole::PROPAGATION_TUPLE_SET, "tuple-set", "use TupleSet-based extensional propagation"); opt.ipl(IPL_DOM); opt.parse(argc,argv); // Generates the new board generate(opt.size()); Script::run<BlackHole,DFS,SizeOptions>(opt); return 0;}
// STATISTICS: example-any