golomb8.py

#!/usr/bin/env python3
# Copyright 2010-2021 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
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"""This is the Golomb ruler problem.

This model aims at maximizing radar interferences in a minimum space.
It is known as the Golomb Ruler problem.

The idea is to put marks on a rule such that all differences
between all marks are all different. The objective is to minimize the length
of the rule.
"""

from absl import app
from absl import flags
from ortools.constraint_solver import pywrapcp

FLAGS = flags.FLAGS

# We disable the following warning because it is a false positive on constraints
# like: solver.Add(x == 0)
# pylint: disable=g-explicit-bool-comparison


def main(_):
    # Create the solver.
    solver = pywrapcp.Solver('golomb ruler')

    size = 8
    var_max = size * size
    all_vars = list(range(0, size))

    marks = [solver.IntVar(0, var_max, 'marks_%d' % i) for i in all_vars]

    objective = solver.Minimize(marks[size - 1], 1)

    solver.Add(marks[0] == 0)

    # We expand the creation of the diff array to avoid a pylint warning.
    diffs = []
    for i in range(size - 1):
        for j in range(i + 1, size):
            diffs.append(marks[j] - marks[i])
    solver.Add(solver.AllDifferent(diffs))

    solver.Add(marks[size - 1] - marks[size - 2] > marks[1] - marks[0])
    for i in range(size - 2):
        solver.Add(marks[i + 1] > marks[i])

    solution = solver.Assignment()
    solution.Add(marks[size - 1])
    collector = solver.AllSolutionCollector(solution)

    solver.Solve(
        solver.Phase(marks, solver.CHOOSE_FIRST_UNBOUND,
                     solver.ASSIGN_MIN_VALUE), [objective, collector])
    for i in range(0, collector.SolutionCount()):
        obj_value = collector.Value(i, marks[size - 1])
        time = collector.WallTime(i)
        branches = collector.Branches(i)
        failures = collector.Failures(i)
        print(('Solution #%i: value = %i, failures = %i, branches = %i,'
               'time = %i ms') % (i, obj_value, failures, branches, time))
    time = solver.WallTime()
    branches = solver.Branches()
    failures = solver.Failures()
    print(('Total run : failures = %i, branches = %i, time = %i ms' %
           (failures, branches, time)))


if __name__ == '__main__':
    app.run(main)