98 lines
3.0 KiB
C++
98 lines
3.0 KiB
C++
// Copyright 2010-2021 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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// Magic sequence problem
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//
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// Compute a sequence of numbers such that the number of occurrences of i
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// in the sequence is equal to the value of the ith number.
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#include <cstdint>
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#include <cstdlib>
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#include "absl/flags/flag.h"
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#include "absl/strings/str_format.h"
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#include "ortools/base/init_google.h"
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#include "ortools/base/integral_types.h"
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#include "ortools/base/logging.h"
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#include "ortools/sat/cp_model.h"
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ABSL_FLAG(int, size, 50, "Size of the problem.");
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ABSL_FLAG(std::string, params, "log_search_progress:true,num_search_workers:8",
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"Sat parameters.");
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namespace operations_research {
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namespace sat {
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void MagicSequence(int size) {
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CHECK_GE(size, 1);
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CpModelBuilder cp_model;
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std::vector<std::vector<BoolVar>> var_domains(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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var_domains[i].push_back(cp_model.NewBoolVar());
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}
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}
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// Domain constraint on each position.
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for (int i = 0; i < size; ++i) {
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cp_model.AddEquality(LinearExpr::Sum(var_domains[i]), 1);
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}
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// The number of variables equal to j shall be the value of vars[j].
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std::vector<int64_t> values(size);
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std::iota(values.begin(), values.end(), 0); // [0, 1, 2, .., size - 1]
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std::vector<BoolVar> vars_equal_to_j;
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for (int j = 0; j < size; ++j) {
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vars_equal_to_j.clear();
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for (int i = 0; i < size; ++i) {
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vars_equal_to_j.push_back(var_domains[i][j]);
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}
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cp_model.AddEquality(LinearExpr::WeightedSum(var_domains[j], values),
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LinearExpr::Sum(vars_equal_to_j));
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}
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const CpSolverResponse response =
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SolveWithParameters(cp_model.Build(), absl::GetFlag(FLAGS_params));
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if (response.status() == CpSolverStatus::OPTIMAL ||
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response.status() == CpSolverStatus::FEASIBLE) {
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std::string output = "[";
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for (int i = 0; i < size; ++i) {
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if (i != 0) {
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output.append(", ");
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}
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for (int j = 0; j < size; ++j) {
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if (SolutionBooleanValue(response, var_domains[i][j])) {
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absl::StrAppendFormat(&output, "%d", j);
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break;
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}
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}
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}
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output.append("]");
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LOG(INFO) << "Solution = " << output;
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}
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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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absl::SetFlag(&FLAGS_logtostderr, true);
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InitGoogle(argv[0], &argc, &argv, true);
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operations_research::sat::MagicSequence(absl::GetFlag(FLAGS_size));
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return EXIT_SUCCESS;
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}
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