276 lines
8.8 KiB
C++
276 lines
8.8 KiB
C++
// Copyright 2010-2011 Google
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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//
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// N-queens problem
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//
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// unique solutions: http://www.research.att.com/~njas/sequences/A000170
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// distinct solutions: http://www.research.att.com/~njas/sequences/A002562
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#include <cstdio>
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#include <map>
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#include "base/commandlineflags.h"
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#include "base/commandlineflags.h"
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#include "base/integral_types.h"
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#include "base/logging.h"
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#include "base/scoped_ptr.h"
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#include "base/stringprintf.h"
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#include "base/map-util.h"
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#include "constraint_solver/constraint_solveri.h"
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DEFINE_bool(use_range, false, "If true, use AllDifferenceRange.");
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DEFINE_bool(print, false, "If true, print one of the solution.");
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DEFINE_bool(print_all, false, "If true, print all the solutions.");
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DEFINE_int32(nb_loops, 1,
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"Number of solving loops to perform, for performance timing.");
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DEFINE_int32(size, 0,
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"Size of the problem. If equal to 0, will test several increasing sizes.");
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DEFINE_bool(use_symmetry, false, "Use Symmetry Breaking methods");
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static const int kNumSolutions[] = {
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1, 0, 0, 2, 10, 4, 40, 92, 352, 724,
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2680, 14200, 73712, 365596, 2279184
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};
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static const int kKnownSolutions = 15;
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static const int kNumUniqueSolutions[] = {
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1, 0, 0, 1, 2, 1, 6, 12, 46, 92, 341, 1787, 9233, 45752,
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285053, 1846955, 11977939, 83263591, 621012754
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};
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static const int kKnownUniqueSolutions = 19;
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namespace operations_research {
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class NQueenSymmetry : public SymmetryBreaker {
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public:
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NQueenSymmetry(Solver* const s, const std::vector<IntVar*>& vars)
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: solver_(s), vars_(vars), size_(vars.size()) {
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for (int i = 0; i < size_; ++i) {
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indices_[vars[i]] = i;
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}
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}
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virtual ~NQueenSymmetry() {}
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protected:
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int Index(IntVar* const var) const {
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return FindWithDefault(indices_, var, -1);
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}
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IntVar* Var(int index) const {
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DCHECK_GE(index, 0);
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DCHECK_LT(index, size_);
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return vars_[index];
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}
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int size() const { return size_; }
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int symmetric(int index) const { return size_ - 1 - index; }
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Solver* const solver() const { return solver_; }
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private:
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Solver* const solver_;
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const std::vector<IntVar*> vars_;
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std::map<IntVar*, int> indices_;
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const int size_;
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};
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// Symmetry vertical axis.
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class SX : public NQueenSymmetry {
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public:
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SX(Solver* const s, const std::vector<IntVar*>& vars) : NQueenSymmetry(s, vars) {}
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virtual ~SX() {}
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virtual void VisitSetVariableValue(IntVar* const var, int64 value) {
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const int index = Index(var);
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IntVar* const other_var = Var(symmetric(index));
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AddIntegerVariableEqualValueClause(other_var, value);
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}
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};
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// Symmetry horizontal axis.
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class SY : public NQueenSymmetry {
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public:
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SY(Solver* const s, const std::vector<IntVar*>& vars) : NQueenSymmetry(s, vars) {}
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virtual ~SY() {}
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virtual void VisitSetVariableValue(IntVar* const var, int64 value) {
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AddIntegerVariableEqualValueClause(var, symmetric(value));
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}
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};
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// Symmetry first diagonal axis.
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class SD1 : public NQueenSymmetry {
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public:
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SD1(Solver* const s, const std::vector<IntVar*>& vars) : NQueenSymmetry(s, vars) {}
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virtual ~SD1() {}
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virtual void VisitSetVariableValue(IntVar* const var, int64 value) {
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const int index = Index(var);
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IntVar* const other_var = Var(value);
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AddIntegerVariableEqualValueClause(other_var, index);
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}
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};
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// Symmetry second diagonal axis.
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class SD2 : public NQueenSymmetry {
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public:
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SD2(Solver* const s, const std::vector<IntVar*>& vars) : NQueenSymmetry(s, vars) {}
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virtual ~SD2() {}
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virtual void VisitSetVariableValue(IntVar* const var, int64 value) {
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const int index = Index(var);
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IntVar* const other_var = Var(symmetric(value));
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AddIntegerVariableEqualValueClause(other_var, symmetric(index));
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}
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};
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// Rotate 1/4 turn.
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class R90 : public NQueenSymmetry {
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public:
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R90(Solver* const s, const std::vector<IntVar*>& vars) : NQueenSymmetry(s, vars) {}
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virtual ~R90() {}
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virtual void VisitSetVariableValue(IntVar* const var, int64 value) {
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const int index = Index(var);
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IntVar* const other_var = Var(value);
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AddIntegerVariableEqualValueClause(other_var, symmetric(index));
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}
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};
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// Rotate 1/2 turn.
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class R180 : public NQueenSymmetry {
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public:
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R180(Solver* const s, const std::vector<IntVar*>& vars)
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: NQueenSymmetry(s, vars) {}
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virtual ~R180() {}
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virtual void VisitSetVariableValue(IntVar* const var, int64 value) {
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const int index = Index(var);
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IntVar* const other_var = Var(symmetric(index));
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AddIntegerVariableEqualValueClause(other_var, symmetric(value));
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}
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};
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// Rotate 3/4 turn.
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class R270 : public NQueenSymmetry {
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public:
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R270(Solver* const s, const std::vector<IntVar*>& vars)
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: NQueenSymmetry(s, vars) {}
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virtual ~R270() {}
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virtual void VisitSetVariableValue(IntVar* const var, int64 value) {
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const int index = Index(var);
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IntVar* const other_var = Var(symmetric(value));
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AddIntegerVariableEqualValueClause(other_var, index);
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}
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};
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void CheckNumberOfSolutions(int size, int num_solutions) {
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if (FLAGS_use_symmetry) {
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if (size - 1 < kKnownUniqueSolutions) {
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CHECK_EQ(num_solutions, kNumUniqueSolutions[size - 1]);
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} else {
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CHECK_GT(num_solutions, 0);
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}
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} else {
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if (size - 1 < kKnownSolutions) {
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CHECK_EQ(num_solutions, kNumSolutions[size - 1]);
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} else {
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CHECK_GT(num_solutions, 0);
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}
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}
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}
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void NQueens(int size) {
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CHECK_GE(size, 1);
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Solver s("nqueens");
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// model
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std::vector<IntVar*> queens;
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for (int i = 0; i < size; ++i) {
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queens.push_back(s.MakeIntVar(0, size - 1, StringPrintf("queen%04d", i)));
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}
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s.AddConstraint(s.MakeAllDifferent(queens, FLAGS_use_range));
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std::vector<IntVar*> vars(size);
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for (int i = 0; i < size; ++i) {
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vars[i] = s.MakeSum(queens[i], i)->Var();
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}
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s.AddConstraint(s.MakeAllDifferent(vars, FLAGS_use_range));
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for (int i = 0; i < size; ++i) {
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vars[i] = s.MakeSum(queens[i], -i)->Var();
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}
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s.AddConstraint(s.MakeAllDifferent(vars, FLAGS_use_range));
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SolutionCollector* const solution_counter = s.MakeAllSolutionCollector(NULL);
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SolutionCollector* const collector = s.MakeFirstSolutionCollector();
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collector->Add(queens);
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std::vector<SearchMonitor*> monitors;
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monitors.push_back(solution_counter);
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monitors.push_back(collector);
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DecisionBuilder* const db = s.MakePhase(queens,
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Solver::CHOOSE_FIRST_UNBOUND,
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Solver::ASSIGN_MIN_VALUE);
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if (FLAGS_use_symmetry) {
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std::vector<SymmetryBreaker*> breakers;
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NQueenSymmetry* const sx = s.RevAlloc(new SX(&s, queens));
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breakers.push_back(sx);
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NQueenSymmetry* const sy = s.RevAlloc(new SY(&s, queens));
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breakers.push_back(sy);
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NQueenSymmetry* const sd1 = s.RevAlloc(new SD1(&s, queens));
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breakers.push_back(sd1);
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NQueenSymmetry* const sd2 = s.RevAlloc(new SD2(&s, queens));
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breakers.push_back(sd2);
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NQueenSymmetry* const r90 = s.RevAlloc(new R90(&s, queens));
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breakers.push_back(r90);
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NQueenSymmetry* const r180 = s.RevAlloc(new R180(&s, queens));
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breakers.push_back(r180);
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NQueenSymmetry* const r270 = s.RevAlloc(new R270(&s, queens));
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breakers.push_back(r270);
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SearchMonitor* const symmetry_manager = s.MakeSymmetryManager(breakers);
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monitors.push_back(symmetry_manager);
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}
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for (int loop = 0; loop < FLAGS_nb_loops; ++loop) {
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s.Solve(db, monitors); // go!
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CheckNumberOfSolutions(size, solution_counter->solution_count());
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}
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const int num_solutions = solution_counter->solution_count();
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if (num_solutions > 0 && size < kKnownSolutions) {
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int print_max = FLAGS_print_all ? num_solutions : FLAGS_print ? 1 : 0;
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for (int n = 0; n < print_max; ++n) {
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printf("--- solution #%d\n", n);
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for (int i = 0; i < size; ++i) {
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const int pos = static_cast<int>(collector->Value(n, queens[i]));
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for (int k = 0; k < pos; ++k) printf(" . ");
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printf("%2d ", i);
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for (int k = pos + 1; k < size; ++k) printf(" . ");
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printf("\n");
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}
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}
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}
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printf("========= number of solutions:%d\n", num_solutions);
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printf(" number of failures: %lld\n", s.failures());
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}
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} // namespace operations_research
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int main(int argc, char **argv) {
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google::ParseCommandLineFlags(&argc, &argv, true);
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if (FLAGS_size != 0) {
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operations_research::NQueens(FLAGS_size);
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} else {
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for (int n = 1; n < 12; ++n) {
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operations_research::NQueens(n);
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}
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}
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return 0;
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}
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