129 lines
3.9 KiB
C++
129 lines
3.9 KiB
C++
// Copyright 2010-2018 Google LLC
|
|
// Licensed under the Apache License, Version 2.0 (the "License");
|
|
// you may not use this file except in compliance with the License.
|
|
// You may obtain a copy of the License at
|
|
//
|
|
// http://www.apache.org/licenses/LICENSE-2.0
|
|
//
|
|
// Unless required by applicable law or agreed to in writing, software
|
|
// distributed under the License is distributed on an "AS IS" BASIS,
|
|
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
// See the License for the specific language governing permissions and
|
|
// limitations under the License.
|
|
|
|
//
|
|
// Golomb ruler problem
|
|
//
|
|
// find minimal ruler so that the differences between ticks are unique.
|
|
//
|
|
// First solutions:
|
|
// 0, 1
|
|
// 0, 1, 3
|
|
// 0, 1, 4, 6
|
|
// 0, 1, 4, 9, 11
|
|
// 0, 1, 4, 10, 12, 17
|
|
// 0, 1, 4, 10, 18, 23, 25
|
|
|
|
#include <cstdio>
|
|
|
|
#include "google/protobuf/text_format.h"
|
|
#include "ortools/base/commandlineflags.h"
|
|
#include "ortools/base/integral_types.h"
|
|
#include "ortools/base/logging.h"
|
|
#include "ortools/sat/cp_model.h"
|
|
#include "ortools/sat/model.h"
|
|
|
|
ABSL_FLAG(bool, print, false, "If true, print the minimal solution.");
|
|
ABSL_FLAG(
|
|
int, size, 0,
|
|
"Size of the problem. If equal to 0, will test several increasing sizes.");
|
|
ABSL_FLAG(std::string, params, "", "Sat parameters.");
|
|
|
|
static const int kBestSolutions[] = {0, 1, 3, 6, 11, 17, 25, 34, 44, 55, 72, 85,
|
|
// just for the optimistics ones, the rest:
|
|
106, 127, 151, 177, 199, 216, 246};
|
|
|
|
static const int kKnownSolutions = 19;
|
|
|
|
namespace operations_research {
|
|
namespace sat {
|
|
|
|
void GolombRuler(int size) {
|
|
CHECK_GE(size, 1);
|
|
CpModelBuilder cp_model;
|
|
|
|
std::vector<IntVar> ticks(size);
|
|
ticks[0] = cp_model.NewConstant(0);
|
|
const int64 max = size * size;
|
|
Domain domain(1, max);
|
|
for (int i = 1; i < size; ++i) {
|
|
ticks[i] = cp_model.NewIntVar(domain);
|
|
}
|
|
std::vector<IntVar> diffs;
|
|
for (int i = 0; i < size; ++i) {
|
|
for (int j = i + 1; j < size; ++j) {
|
|
const IntVar diff = cp_model.NewIntVar(domain);
|
|
cp_model.AddEquality(LinearExpr::Sum({diff, ticks[i]}), ticks[j]);
|
|
diffs.push_back(diff);
|
|
}
|
|
}
|
|
|
|
cp_model.AddAllDifferent(diffs);
|
|
|
|
// Symmetry breaking.
|
|
if (size > 2) {
|
|
cp_model.AddLessThan(diffs.front(), diffs.back());
|
|
}
|
|
|
|
// Objective.
|
|
cp_model.Minimize(ticks.back());
|
|
|
|
// Search strategy.
|
|
cp_model.AddDecisionStrategy(ticks, DecisionStrategyProto::CHOOSE_FIRST,
|
|
DecisionStrategyProto::SELECT_MIN_VALUE);
|
|
|
|
Model model;
|
|
SatParameters parameters;
|
|
parameters.set_search_branching(SatParameters::FIXED_SEARCH);
|
|
// Parse the --params flag.
|
|
if (!absl::GetFlag(FLAGS_params).empty()) {
|
|
CHECK(google::protobuf::TextFormat::MergeFromString(
|
|
absl::GetFlag(FLAGS_params), ¶meters))
|
|
<< absl::GetFlag(FLAGS_params);
|
|
}
|
|
model.Add(NewSatParameters(parameters));
|
|
const CpSolverResponse response = SolveCpModel(cp_model.Build(), &model);
|
|
|
|
if (response.status() == CpSolverStatus::OPTIMAL) {
|
|
const int64 result = SolutionIntegerValue(response, ticks.back());
|
|
const int64 num_failures = response.num_conflicts();
|
|
printf("N = %d, optimal length = %lld (conflicts:%lld, time=%f s)\n", size,
|
|
result, num_failures, response.wall_time());
|
|
if (size - 1 < kKnownSolutions) {
|
|
CHECK_EQ(result, kBestSolutions[size - 1]);
|
|
}
|
|
if (absl::GetFlag(FLAGS_print)) {
|
|
for (int i = 0; i < size; ++i) {
|
|
const int64 tick = SolutionIntegerValue(response, ticks[i]);
|
|
printf("%d ", static_cast<int>(tick));
|
|
}
|
|
printf("\n");
|
|
}
|
|
}
|
|
}
|
|
|
|
} // namespace sat
|
|
} // namespace operations_research
|
|
|
|
int main(int argc, char** argv) {
|
|
absl::ParseCommandLine(argc, argv);
|
|
if (absl::GetFlag(FLAGS_size) != 0) {
|
|
operations_research::sat::GolombRuler(absl::GetFlag(FLAGS_size));
|
|
} else {
|
|
for (int n = 1; n < 11; ++n) {
|
|
operations_research::sat::GolombRuler(n);
|
|
}
|
|
}
|
|
return EXIT_SUCCESS;
|
|
}
|