101 lines
2.8 KiB
C++
101 lines
2.8 KiB
C++
// Copyright 2010-2018 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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#include <string>
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#include <vector>
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#include "ortools/base/commandlineflags.h"
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#include "ortools/base/stringprintf.h"
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#include "ortools/sat/cp_model.h"
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#include "ortools/sat/model.h"
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DEFINE_int32(size, 7, "Size of the magic square");
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DEFINE_string(params, "", "Sat paramters");
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namespace operations_research {
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namespace sat {
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void MagicSquare(int size) {
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CpModelBuilder builder;
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std::vector<std::vector<IntVar>> square(size);
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std::vector<std::vector<IntVar>> transposed(size);
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std::vector<IntVar> diag1;
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std::vector<IntVar> diag2;
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std::vector<IntVar> all_variables;
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Domain domain(1, size * size);
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for (int i = 0; i < size; ++i) {
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for (int j = 0; j < size; ++j) {
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const IntVar var = builder.NewIntVar(domain);
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square[i].push_back(var);
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transposed[j].push_back(var);
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all_variables.push_back(var);
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if (i == j) {
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diag1.push_back(var);
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}
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if (i + j == size) {
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diag2.push_back(var);
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}
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}
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}
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// All Diff.
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for (int i = 0; i < size; ++i) {
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builder.AddAllDifferent(all_variables);
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}
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const int sum = size * (size * size + 1) / 2;
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// Sum on rows.
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for (int i = 0; i < size; ++i) {
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builder.AddEquality(LinearExpr::Sum(square[i]), sum);
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}
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// Sum on columns.
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for (int i = 0; i < size; ++i) {
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builder.AddEquality(LinearExpr::Sum(transposed[i]), sum);
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}
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// Sum on diagonals.
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builder.AddEquality(LinearExpr::Sum(diag1), sum);
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builder.AddEquality(LinearExpr::Sum(diag2), sum);
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Model model;
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model.Add(NewSatParameters(FLAGS_params));
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const CpSolverResponse response = SolveWithModel(builder, &model);
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if (response.status() == CpSolverStatus::FEASIBLE) {
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for (int n = 0; n < size; ++n) {
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std::string output;
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for (int m = 0; m < size; ++m) {
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StringAppendF(&output, "%3lld ",
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SolutionIntegerValue(response, square[n][m]));
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}
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LOG(INFO) << output;
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}
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} else {
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LOG(INFO) << "No solution found!";
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}
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LOG(INFO) << CpSolverResponseStats(response);
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}
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} // namespace sat
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} // namespace sat
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int main(int argc, char **argv) {
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base::SetFlag(&FLAGS_logtostderr, true);
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gflags::ParseCommandLineFlags(&argc, &argv, true);
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operations_research::sat::MagicSquare(FLAGS_size);
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return EXIT_SUCCESS;
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}
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