# Copyright 2010-2018 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
# limitations under the License.

# Fill a 72x37 rectangle by a minimum number of non-overlapping squares.

from __future__ import print_function
from __future__ import division

from ortools.sat.python import cp_model


def CoverRectangle(num_squares):
    size_x = 72
    size_y = 37

    model = cp_model.CpModel()

    areas = []
    sizes = []
    x_intervals = []
    y_intervals = []
    sxs = []
    sys = []

    for i in range(num_squares):
        size = model.NewIntVar(1, size_y, 'size_%i' % i)
        sx = model.NewIntVar(0, size_x, 'sx_%i' % i)
        ex = model.NewIntVar(0, size_x, 'ex_%i' % i)
        sy = model.NewIntVar(0, size_y, 'sy_%i' % i)
        ey = model.NewIntVar(0, size_y, 'ey_%i' % i)

        i_x = model.NewIntervalVar(sx, size, ex, 'x_interval_%i' % i)
        i_y = model.NewIntervalVar(sy, size, ey, 'y_interval_%i' % i)

        area = model.NewIntVar(1, size_y * size_y, 'area_%i' % i)
        model.AddProdEquality(area, [size, size])

        areas.append(area)
        x_intervals.append(i_x)
        y_intervals.append(i_y)
        sizes.append(size)
        sxs.append(sx)
        sys.append(sy)

    model.AddNoOverlap2D(x_intervals, y_intervals)
    model.AddCumulative(x_intervals, sizes, size_y)
    model.AddCumulative(y_intervals, sizes, size_x)

    model.Add(sum(areas) == size_x * size_y)

    for i in range(num_squares - 1):
        model.Add(sizes[i] <= sizes[i + 1])

    # Creates a solver and solves.
    solver = cp_model.CpSolver()
    solver.parameters.num_search_workers = 4
    status = solver.Solve(model)
    print(solver.StatusName(status), solver.WallTime(), 'ms')

    if (status == cp_model.FEASIBLE):
        display = [[' ' for _ in range(size_x)] for _ in range(size_y)]
        for i in range(num_squares):
            x = solver.Value(sxs[i])
            y = solver.Value(sys[i])
            s = solver.Value(sizes[i])
            c = format(i, ' 01x')
            for j in range(s):
                for k in range(s):
                    if display[y + j][x + k] != ' ':
                        print('ERROR between %s and %s' %
                              (display[y + j][x + k], c))
                    display[y + j][x + k] = c

        for line in range(size_y):
            print("".join(display[line]))
    return status == cp_model.FEASIBLE


for i in range(15):
    print('Trying with size =', i)
    if CoverRectangle(i):
        break


@@ -1879,24 +1879,69 @@
  * size_y)%0A%0A
+    # Symmetry breaking 1: size are ordered.%0A
     for i in
@@ -2006,24 +2006,136 @@
 es%5Bi + 1%5D)%0A%0A
+    # Symmetry breaking 2: first square in one quadrant.%0A    model.Add(sxs%5B0%5D %3C 36)%0A    model.Add(sys%5B0%5D %3C 19)%0A%0A
     # Create
@@ -3040,16 +3040,19 @@
 n range(
+1, 
 15):%0A   

add symmetry breaking