107 lines
3.3 KiB
C++
107 lines
3.3 KiB
C++
// Copyright 2010-2014 Google
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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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//
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// Golomb ruler problem
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//
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// find minimal ruler so that the differences between ticks are unique.
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//
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// First solutions:
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// 0, 1
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// 0, 1, 3
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// 0, 1, 4, 6
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// 0, 1, 4, 9, 11
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// 0, 1, 4, 10, 12, 17
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// 0, 1, 4, 10, 18, 23, 25
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#include <cstdio>
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#include "base/commandlineflags.h"
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#include "base/commandlineflags.h"
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#include "base/integral_types.h"
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#include "base/logging.h"
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#include "base/stringprintf.h"
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#include "constraint_solver/constraint_solver.h"
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DEFINE_bool(print, false, "If true, print the minimal solution.");
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DEFINE_int32(
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size, 0,
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"Size of the problem. If equal to 0, will test several increasing sizes.");
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static const int kBestSolutions[] = {0, 1, 3, 6, 11, 17, 25,
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34, 44, 55, 72, 85,
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// just for the optimistics ones, the rest:
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106, 127, 151, 177, 199, 216, 246};
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static const int kKnownSolutions = 19;
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namespace operations_research {
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void GolombRuler(int size) {
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CHECK_GE(size, 1);
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Solver s("golomb");
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// model
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std::vector<IntVar*> ticks(size);
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ticks[0] = s.MakeIntConst(0); // X(0) = 0
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const int64 max = 1 + size * size * size;
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for (int i = 1; i < size; ++i) {
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ticks[i] = s.MakeIntVar(1, max, StringPrintf("X%02d", i));
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}
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std::vector<IntVar*> diffs;
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for (int i = 0; i < size; ++i) {
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for (int j = i + 1; j < size; ++j) {
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IntVar* const diff = s.MakeDifference(ticks[j], ticks[i])->Var();
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diffs.push_back(diff);
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diff->SetMin(1);
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}
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}
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s.AddConstraint(s.MakeAllDifferent(diffs));
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OptimizeVar* const length = s.MakeMinimize(ticks[size - 1], 1);
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SolutionCollector* const collector = s.MakeLastSolutionCollector();
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collector->Add(ticks);
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DecisionBuilder* const db = s.MakePhase(ticks, Solver::CHOOSE_FIRST_UNBOUND,
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Solver::ASSIGN_MIN_VALUE);
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s.Solve(db, collector, length); // go!
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CHECK_EQ(collector->solution_count(), 1);
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const int64 result = collector->Value(0, ticks[size - 1]);
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const int num_failures = collector->failures(0);
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printf("N = %d, optimal length = %d (fails:%d)\n", size,
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static_cast<int>(result), num_failures);
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if (size - 1 < kKnownSolutions) {
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CHECK_EQ(result, kBestSolutions[size - 1]);
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}
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if (FLAGS_print) {
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for (int i = 0; i < size; ++i) {
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const int64 tick = collector->Value(0, ticks[i]);
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printf("%d ", static_cast<int>(tick));
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}
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printf("\n");
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}
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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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gflags::ParseCommandLineFlags( &argc, &argv, true);
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if (FLAGS_size != 0) {
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operations_research::GolombRuler(FLAGS_size);
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} else {
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for (int n = 1; n < 11; ++n) {
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operations_research::GolombRuler(n);
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}
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}
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return 0;
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}
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