119 lines
3.5 KiB
C++
119 lines
3.5 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 <cstdint>
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#include <cstdlib>
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#include <sstream>
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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 "ortools/base/init_google.h"
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#include "ortools/base/logging.h"
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#include "ortools/constraint_solver/constraint_solver.h"
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// [END import]
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namespace operations_research {
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void NQueensCp(const int board_size) {
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// Instantiate the solver.
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// [START solver]
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Solver solver("N-Queens");
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// [END solver]
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// [START variables]
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std::vector<IntVar*> queens;
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queens.reserve(board_size);
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for (int i = 0; i < board_size; ++i) {
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queens.push_back(
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solver.MakeIntVar(0, board_size - 1, absl::StrCat("x", 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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solver.AddConstraint(solver.MakeAllDifferent(queens));
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// All columns must be different because the indices of queens are all
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// different. No two queens can be on the same diagonal.
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std::vector<IntVar*> diag_1;
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diag_1.reserve(board_size);
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std::vector<IntVar*> 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(solver.MakeSum(queens[i], i)->Var());
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diag_2.push_back(solver.MakeSum(queens[i], -i)->Var());
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}
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solver.AddConstraint(solver.MakeAllDifferent(diag_1));
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solver.AddConstraint(solver.MakeAllDifferent(diag_2));
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// [END constraints]
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// [START db]
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DecisionBuilder* const db = solver.MakePhase(
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queens, Solver::CHOOSE_FIRST_UNBOUND, Solver::ASSIGN_MIN_VALUE);
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// [END db]
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// [START solve]
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// Iterates through the solutions, displaying each.
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int num_solutions = 0;
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solver.NewSearch(db);
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while (solver.NextSolution()) {
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// Displays the solution just computed.
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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 (queens[j]->Value() == 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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solver.EndSearch();
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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) << " failures: " << solver.failures();
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LOG(INFO) << " branches: " << solver.branches();
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LOG(INFO) << " wall time: " << solver.wall_time() << " ms";
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LOG(INFO) << " Solutions found: " << num_solutions;
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// [END statistics]
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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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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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board_size = std::atoi(argv[1]);
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}
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operations_research::NQueensCp(board_size);
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return EXIT_SUCCESS;
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}
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// [END program]
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