125 lines
4.3 KiB
Python
125 lines
4.3 KiB
Python
#!/usr/bin/env python3
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# Copyright 2010-2022 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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"""Fill a 60x50 rectangle by a minimum number of non-overlapping squares."""
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from typing import Sequence
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from absl import app
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from ortools.sat.python import cp_model
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def cover_rectangle(num_squares):
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"""Try to fill the rectangle with a given number of squares."""
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size_x = 60
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size_y = 50
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model = cp_model.CpModel()
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areas = []
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sizes = []
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x_intervals = []
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y_intervals = []
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x_starts = []
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y_starts = []
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# Creates intervals for the NoOverlap2D and size variables.
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for i in range(num_squares):
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size = model.NewIntVar(1, size_y, "size_%i" % i)
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start_x = model.NewIntVar(0, size_x, "sx_%i" % i)
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end_x = model.NewIntVar(0, size_x, "ex_%i" % i)
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start_y = model.NewIntVar(0, size_y, "sy_%i" % i)
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end_y = model.NewIntVar(0, size_y, "ey_%i" % i)
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interval_x = model.NewIntervalVar(start_x, size, end_x, "ix_%i" % i)
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interval_y = model.NewIntervalVar(start_y, size, end_y, "iy_%i" % i)
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area = model.NewIntVar(1, size_y * size_y, "area_%i" % i)
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model.AddMultiplicationEquality(area, [size, size])
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areas.append(area)
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x_intervals.append(interval_x)
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y_intervals.append(interval_y)
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sizes.append(size)
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x_starts.append(start_x)
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y_starts.append(start_y)
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# Main constraint.
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model.AddNoOverlap2D(x_intervals, y_intervals)
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# Redundant constraints.
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model.AddCumulative(x_intervals, sizes, size_y)
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model.AddCumulative(y_intervals, sizes, size_x)
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# Forces the rectangle to be exactly covered.
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model.Add(sum(areas) == size_x * size_y)
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# Symmetry breaking 1: sizes are ordered.
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for i in range(num_squares - 1):
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model.Add(sizes[i] <= sizes[i + 1])
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# Define same to be true iff sizes[i] == sizes[i + 1]
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same = model.NewBoolVar("")
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model.Add(sizes[i] == sizes[i + 1]).OnlyEnforceIf(same)
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model.Add(sizes[i] < sizes[i + 1]).OnlyEnforceIf(same.Not())
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# Tie break with starts.
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model.Add(x_starts[i] <= x_starts[i + 1]).OnlyEnforceIf(same)
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# Symmetry breaking 2: first square in one quadrant.
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model.Add(x_starts[0] < (size_x + 1) // 2)
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model.Add(y_starts[0] < (size_y + 1) // 2)
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# Creates a solver and solves.
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solver = cp_model.CpSolver()
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solver.parameters.num_workers = 16
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# solver.parameters.log_search_progress = True
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solver.parameters.max_time_in_seconds = 10.0
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status = solver.Solve(model)
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print("%s found in %0.2fs" % (solver.StatusName(status), solver.WallTime()))
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# Prints solution.
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solution_found = status == cp_model.OPTIMAL or status == cp_model.FEASIBLE
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if solution_found:
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display = [[" " for _ in range(size_x)] for _ in range(size_y)]
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for i in range(num_squares):
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sol_x = solver.Value(x_starts[i])
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sol_y = solver.Value(y_starts[i])
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sol_s = solver.Value(sizes[i])
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char = format(i, "01x")
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for j in range(sol_s):
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for k in range(sol_s):
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if display[sol_y + j][sol_x + k] != " ":
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print(
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"ERROR between %s and %s"
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% (display[sol_y + j][sol_x + k], char)
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)
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display[sol_y + j][sol_x + k] = char
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for line in range(size_y):
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print(" ".join(display[line]))
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return solution_found
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def main(argv: Sequence[str]) -> None:
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if len(argv) > 1:
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raise app.UsageError("Too many command-line arguments.")
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for num_squares in range(1, 15):
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print("Trying with size =", num_squares)
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if cover_rectangle(num_squares):
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break
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if __name__ == "__main__":
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app.run(main)
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