103 lines
3.4 KiB
Python
103 lines
3.4 KiB
Python
# Copyright 2010-2018 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 72x37 rectangle by a minimum number of non-overlapping squares."""
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from __future__ import print_function
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from __future__ import division
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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 = 72
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size_y = 37
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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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startx = model.NewIntVar(0, size_x, 'sx_%i' % i)
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endx = model.NewIntVar(0, size_x, 'ex_%i' % i)
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starty = model.NewIntVar(0, size_y, 'sy_%i' % i)
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endy = model.NewIntVar(0, size_y, 'ey_%i' % i)
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interval_x = model.NewIntervalVar(startx, size, endx, 'ix_%i' % i)
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interval_y = model.NewIntervalVar(starty, size, endy, 'iy_%i' % i)
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area = model.NewIntVar(1, size_y * size_y, 'area_%i' % i)
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model.AddProdEquality(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(startx)
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y_starts.append(starty)
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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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# Symmetry breaking 2: first square in one quadrant.
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model.Add(x_starts[0] < 36)
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model.Add(y_starts[0] < 19)
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# Creates a solver and solves.
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solver = cp_model.CpSolver()
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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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if status == cp_model.FEASIBLE:
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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('ERROR between %s and %s' %
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(display[sol_y + j][sol_x + k], char))
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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 status == cp_model.FEASIBLE
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for num in range(1, 15):
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print('Trying with size =', num)
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if cover_rectangle(num):
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break
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