94 lines
2.9 KiB
Python
94 lines
2.9 KiB
Python
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# 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 CoverRectangle(num_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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sxs = []
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sys = []
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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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sx = model.NewIntVar(0, size_x, 'sx_%i' % i)
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ex = model.NewIntVar(0, size_x, 'ex_%i' % i)
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sy = model.NewIntVar(0, size_y, 'sy_%i' % i)
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ey = model.NewIntVar(0, size_y, 'ey_%i' % i)
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i_x = model.NewIntervalVar(sx, size, ex, 'x_interval_%i' % i)
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i_y = model.NewIntervalVar(sy, size, ey, 'y_interval_%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(i_x)
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y_intervals.append(i_y)
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sizes.append(size)
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sxs.append(sx)
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sys.append(sy)
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model.AddNoOverlap2D(x_intervals, y_intervals)
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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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model.Add(sum(areas) == size_x * size_y)
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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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# Creates a solver and solves.
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solver = cp_model.CpSolver()
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solver.parameters.num_search_workers = 4
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status = solver.Solve(model)
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print(solver.StatusName(status), solver.WallTime(), 'ms')
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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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x = solver.Value(sxs[i])
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y = solver.Value(sys[i])
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s = solver.Value(sizes[i])
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c = format(i, ' 01x')
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for j in range(s):
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for k in range(s):
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if display[y + j][x + k] != ' ':
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print('ERROR between %s and %s' %
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(display[y + j][x + k], c))
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display[y + j][x + k] = c
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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 i in range(15):
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print('Trying with size =', i)
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if CoverRectangle(i):
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break
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