132 lines
3.9 KiB
C++
132 lines
3.9 KiB
C++
// Copyright 2010-2025 Google LLC
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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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// [START program]
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// OR-Tools solution to the N-queens problem.
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// [START import]
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#include <stdlib.h>
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#include <sstream>
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#include <string>
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#include <vector>
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#include "absl/base/log_severity.h"
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#include "absl/log/globals.h"
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#include "absl/strings/numbers.h"
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#include "ortools/base/init_google.h"
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#include "ortools/base/logging.h"
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#include "ortools/sat/cp_model.h"
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#include "ortools/sat/cp_model.pb.h"
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#include "ortools/sat/cp_model_solver.h"
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#include "ortools/sat/model.h"
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#include "ortools/sat/sat_parameters.pb.h"
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#include "ortools/util/sorted_interval_list.h"
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// [END import]
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namespace operations_research {
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namespace sat {
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void NQueensSat(const int board_size) {
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// Instantiate the solver.
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// [START model]
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CpModelBuilder cp_model;
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// [END model]
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// [START variables]
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// There are `board_size` number of variables, one for a queen in each column
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// of the board. The value of each variable is the row that the queen is in.
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std::vector<IntVar> queens;
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queens.reserve(board_size);
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Domain range(0, board_size - 1);
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for (int i = 0; i < board_size; ++i) {
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queens.push_back(
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cp_model.NewIntVar(range).WithName("x" + std::to_string(i)));
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}
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// [END variables]
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// Define constraints.
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// [START constraints]
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// The following sets the constraint that all queens are in different rows.
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cp_model.AddAllDifferent(queens);
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// No two queens can be on the same diagonal.
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std::vector<LinearExpr> diag_1;
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diag_1.reserve(board_size);
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std::vector<LinearExpr> diag_2;
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diag_2.reserve(board_size);
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for (int i = 0; i < board_size; ++i) {
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diag_1.push_back(queens[i] + i);
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diag_2.push_back(queens[i] - i);
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}
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cp_model.AddAllDifferent(diag_1);
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cp_model.AddAllDifferent(diag_2);
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// [END constraints]
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// [START solution_printer]
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int num_solutions = 0;
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Model model;
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model.Add(NewFeasibleSolutionObserver([&](const CpSolverResponse& response) {
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LOG(INFO) << "Solution " << num_solutions;
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for (int i = 0; i < board_size; ++i) {
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std::stringstream ss;
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for (int j = 0; j < board_size; ++j) {
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if (SolutionIntegerValue(response, queens[j]) == i) {
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// There is a queen in column j, row i.
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ss << "Q";
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} else {
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ss << "_";
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}
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if (j != board_size - 1) ss << " ";
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}
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LOG(INFO) << ss.str();
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}
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num_solutions++;
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}));
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// [END solution_printer]
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// [START solve]
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// Tell the solver to enumerate all solutions.
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SatParameters parameters;
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parameters.set_enumerate_all_solutions(true);
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model.Add(NewSatParameters(parameters));
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const CpSolverResponse response = SolveCpModel(cp_model.Build(), &model);
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LOG(INFO) << "Number of solutions found: " << num_solutions;
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// [END solve]
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// Statistics.
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// [START statistics]
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LOG(INFO) << "Statistics";
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LOG(INFO) << CpSolverResponseStats(response);
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// [END statistics]
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}
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} // namespace sat
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} // namespace operations_research
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int main(int argc, char* argv[]) {
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InitGoogle(argv[0], &argc, &argv, true);
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absl::SetStderrThreshold(absl::LogSeverityAtLeast::kInfo);
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int board_size = 8;
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if (argc > 1) {
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if (!absl::SimpleAtoi(argv[1], &board_size)) {
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LOG(INFO) << "Cannot parse '" << argv[1]
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<< "', using the default value of 8.";
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board_size = 8;
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}
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}
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operations_research::sat::NQueensSat(board_size);
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return EXIT_SUCCESS;
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}
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// [END program]
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