94 lines
2.9 KiB
Python
Executable File
94 lines
2.9 KiB
Python
Executable File
#!/usr/bin/env python3
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# 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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"""This is the Golomb ruler problem.
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This model aims at maximizing radar interferences in a minimum space.
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It is known as the Golomb Ruler problem.
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The idea is to put marks on a rule such that all differences
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between all marks are all different. The objective is to minimize the length
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of the rule.
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see: https://en.wikipedia.org/wiki/Golomb_ruler
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"""
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from absl import app
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from absl import flags
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from google.protobuf import text_format
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from ortools.sat.python import cp_model
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FLAGS = flags.FLAGS
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flags.DEFINE_integer('order', 8, 'Order of the ruler.')
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flags.DEFINE_string('params', 'max_time_in_seconds:10.0',
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'Sat solver parameters.')
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def solve_golomb_ruler(order, params):
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# Create the model.
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model = cp_model.CpModel()
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var_max = order * order
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all_vars = list(range(0, order))
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marks = [model.NewIntVar(0, var_max, f'marks_{i}') for i in all_vars]
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model.Add(marks[0] == 0)
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for i in range(order - 2):
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model.Add(marks[i + 1] > marks[i])
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diffs = []
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for i in range(order - 1):
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for j in range(i + 1, order):
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diff = model.NewIntVar(0, var_max, f'diff [{j},{i}]')
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model.Add(diff == marks[j] - marks[i])
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diffs.append(diff)
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model.AddAllDifferent(diffs)
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# symmetry breaking
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if order > 2:
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model.Add(marks[order - 1] - marks[order - 2] > marks[1] - marks[0])
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# Objective
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model.Minimize(marks[order - 1])
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# Solve the model.
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solver = cp_model.CpSolver()
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if params:
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text_format.Parse(params, solver.parameters)
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solution_printer = cp_model.ObjectiveSolutionPrinter()
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print(f'Golomb ruler(order={order})')
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status = solver.Solve(model, solution_printer)
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# Print solution.
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print(f'status: {solver.StatusName(status)}')
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if status in (cp_model.OPTIMAL, cp_model.FEASIBLE):
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for idx, var in enumerate(marks):
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print(f'mark[{idx}]: {solver.Value(var)}')
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intervals = [solver.Value(diff) for diff in diffs]
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intervals.sort()
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print(f'intervals: {intervals}')
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print('Statistics:')
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print(f'- conflicts: {solver.NumConflicts()}')
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print(f'- branches : {solver.NumBranches()}')
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print(f'- wall time: {solver.WallTime()}s\n')
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def main(_=None):
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solve_golomb_ruler(FLAGS.order, FLAGS.params)
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if __name__ == '__main__':
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app.run(main)
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